Ethnobotany has been, for too long, a descriptive discipline. However, ethnobotanists are increasingly calling for a paradigm shift towards the formulation of unifying theories and hypothesis-driven research in ethnobotany. Here, we formulated a theory, termed time-since-introduction theory, to explain the integration of alien plants into local pharmacopoeias in their recipient environment. This theory suggests that the factor time is paramount in determining which alien plants are more likely to be included in the medicinal flora of the areas they are introduced in. The theory relies on three hypotheses, the availability and versatility hypotheses alongside the residence time hypothesis newly proposed in the present study. We tested this theory by fitting a structural equation model to ethnobotanical data collected on South Africa’s alien woody flora. Although residence time is a direct predictor of medicinal status of alien plants, it is a better predictor when mediated through plant versatility. These findings are in support of the theory, and we consequently proposed a framework with which to understand different paths linking all three hypotheses. Collectively, our study shows the value of time in the development of ethnobotanical knowledge and fully responds to the pressing call for paradigm shift in ethnobotany.

This work discusses the relationship between foreign direct investment (FDI) and pollution in Spain using an autoregressive distributed lag regression model (ARDL) from 1961 to 2018. The authors apply the theoretical context of pollution haven/halo and conclude that FDI in Spain does not contribute to the transfer of green technologies for cleaner production, despite being included within the European environmental regulatory framework. The authors also verify the adequacy of the environmental Kuznets curve (EKC) and the Load Capacity Curve hypothesis (LCC) in the Spanish environmental context and find that income per capita has a positive effect on environmental sustainability and quality. In this sense, the further development of an efficient renewable energy infrastructure could efficiently drive to a better standards all pollution indexes in Spain, including nuclear energy production, contributing the emissions neutrality aimed by the EU by 2050.

A wide range of research has been developed in the empirical literature regarding income and price elasticities of health care expenditure (HCE). The results are mixed, as researchers employ different methodologies and data sources. The benefits of the panel data method, such as greater data variation, less collinearity, and more degrees of freedom, made it attractive among economists. However, the pooled mean group (PMG) method provides robust estimates compared to conventional methods, such as the mean group estimator and dynamic fixed-effects estimator. As such, this paper applies the PMG method to scrutinize the effect of income and price on U.S. health care consumption using a panel of 46 states. The income and price elasticities were found to be 0.85 and -0.48, respectively, which partially describes the recessionary decline in health care consumption following the Great Recession. In addition, the model reveals that the short-run income elasticity is smaller than the long-run. This confirms that U.S. health care consumption follows the permanent income hypothesis. Consequently, the short-run efficacy of public policies targeting HCE remains limited. The results of this paper suggest reconsidering and adjusting health care policies during a recession so as to avoid probable long-run adverse effects on HCE.

We find that the overnight returns of Korean exchange-traded index funds (ETFs) are significantly positive, whereas the subsequent intraday returns are negative. These intraday return reversals are caused by relatively higher opening prices than the closing prices. In the Korean ETF market, where institutional investors are dominant participants, the return reversals are not explained by the attention hypothesis as in Berkman et al. [1]. Hence, we investigate whether the disagreement hypothesis can explain return reversals. Under the disagreement situations between positive and negative traders at the open, positive traders can have a positive influence on the ETF prices by increasing their investments. However, negative traders, who give up investments due to limited short selling opportunities in the ETF market, have no effects on the prices. Comparing ETF markets with KOSPI 200 Futures where there are no restrictions on short selling, we find that short selling constraints are significant factors for the return reversals. This implies that disagreement among the investors can cause return reversals even in the markets without noise traders. Using unique Korean market data, we conclude that return reversals cannot be completely explained by the attention hypothesis, and that disagreement among investors is also a significant factor for the return reversals. This study contributes to the existing literature by showing that the attention hypothesis does not explain return reversals in the ETF market completely, and suggesting the disagreement hypothesis as an alternative.

The origin of life has not been solved as yet, in spit of the time passage more than thirty years from publication of RNA world hypothesis by W. Gilbert (1986), which is based on the “gene/replicator--first” theory. On the contrary, I have proposed [GADV]-protein world hypothesis (GADV hypothesis), assuming that life emerged from [GADV]-protein world, which is grounded on the “protein/metabolism-first” theory. However, two weak points of protein world hypothesis, (i) protein cannot be produced without gene, and (ii) protein cannot be self-replicated, have been frequently pointed out by supporters of RNA world hypothesis. Then, I examined whether the two weak points could be overcome by GADV hypothesis or not. From the results, it was confirmed that (i) [GADV]-protein could be pseudo-replicated in the absence of gene owing to protein 0^th-order structure or [GADV]-amino acids, and (ii) the replication ability is not always required from the beginning but it is sufficient to acquire it at some time point until the emergence of life. Thus, it was concluded that life emerged as [GADV]-protein world hypothesis, which is grounded on the “protein/metabolism-first” theory, expects.

Introduction: The environmentally acquired aerobic spore-forming (EAS-Fs) bacteria that are ubiquitous in nature (e.g. soil) are transient colonisers of the mammalian gastro-intestinal tract. Without regular exposure, their numbers quickly diminish. These species of bacteria have been suggested to be essential to the normal functioning of metabolic and immunogenic health. The modern Western lifestyle restricts exposure to these EAS-Fs, possibly explaining part of the pathogenesis of many Western diseases. To date, the only animal studies that address specific microbiome modelling are based around germ-free animals. We have designed a new animal model that specifically restricts exposure to environmental sources of bacteria. Methodology: A new protocol, termed Super Clean, that involves housing mice in autoclaved individually ventilated cages (IVCs), with autoclaved food / water, and strict ascetic handling practice was first experimentally validated. The quantification of EAS-Fs was assessed by heat-treating faecal samples and measuring colony forming units (CFUs). This was then compared to mice in standard-conditions. Mice were housed in their respective groups from birth until 18 months. Stool samples were taken throughout the experiment to assess for abundance in transiently acquired environmental bacteria. Clinical, biochemical, histological, and gene expression markers were analysed for diabetes, hypercholesterolaemia, obesity, inflammatory bowel disease, and non-alcoholic fatty liver disease (the “diseases of the West”). Results: Our results show that stringent adherence to the Super Clean protocol produces a significantly decreased abundance of aerobic spore-forming Bacillota after 21 days. This microbiomic shift was correlated with significantly increased levels of obesity and impaired glucose metabolism. There was no evidence of colitis, liver disease or hypercholesterolaemia. Conclusion: This new murine model successfully isolates EAS-Fs, and has the potential utility for future research allowing for the investigation into the clinical impact living in relative hygienic conditions.

Ayurveda as a healthcare system has survived for thousands of years but continues to be dogged by reported lack of efficacy of the treatments in clinical trials. The reported lack of efficacy could be due to a real lack of efficacy (which then contradicts the survival of Ayurveda as a functional medical system enjoying considerable public patronage) or could be attributed to inadequacies in the efforts towards evidence generation or in a larger context the overall scientific conduct of research in Ayurveda. In an effort towards better evidence generation, there is an immediate need for standardizing the design, conduct and reporting of clinical trials of Ayurveda but it is a daunting task. For this effort to benefit the scientific endeavors of Ayurveda researchers, it should allow the researchers to be able to apply Ayurveda’s multi-component, individualized and inherently holistic approach. Statistical principles can benefit this effort. Statistical hypothesis testing (SHT) is central to these statistical principles and also aligns well with conventional scientific principles of evidence generation. Although there are challenges with SHT, good practitioners engaged in it do much more than just apply the mathematical theory behind it. As a particular example, lot of time in clinical trial designing is spent in addressing biases and designing trials prudently by minimizing the effect of such biases. SHT can benefit such an effort objectively. There is a need for Ayurveda researchers to engage deeply and mindfully about biases in study design in order to gain scientific validity and acceptability. The article highlights issues that arise in Ayurveda research, and discusses few ways of dealing with these issues using statistical principles.

Theoretical physics addresses the fundamental principles of nature and the mysteries of the universe. In the last century, the theory of relativity challenged people's understanding of time and space, while quantum mechanics revealed various forms of energy. However, the concept of gravity remains elusive. All matter in the universe is composed of energy that can be converted into other forms, yet it is always conserved. However, achieving a state of equilibrium, represented by the equal sign, can be challenging to achieve on both macro and quantum scales. A phenomenon that can transition from one state to infinity is called collision and is essential for understanding natural phenomena and physical processes throughout the universe. In the study of general relativity cannot be three-dimensional problems to gain mathematical inspiration, understand the application of new dimensions. Here, we elucidate the nature of gravity, which inspires the solution of the Riemann hypothesis. Our results show that the conduction mode of dimensional energy is defined by Euler's formula. And a special mode of collision is derived which translates into vibration.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

1. Darwin’s naturalization hypothesis predicts that alien species closely related to native species are less likely to naturalize because of strong competition due to niche overlap. Closely related species are likely to attract similar herbivores and to release similar plant volatiles following herbivore attack, thus could attract the same predators. However, the importance of phylogenetic relatedness on the interaction between alien and native plants has never been tested in a multitrophic context. 2. In a mesocosm experiment we grew six alien target plant species alone and in competition with nine native plant species of varying phylogenetic relatedness. To test the effects of multitrophic interactions on the performance of alien target species, we used enclosure cages to expose plants to the presence and absence of herbivorous arthropods, predatory arthropods and nematodes. 3. Surprisingly, biomass and number of flowering structures increased with presence of competitors for some of the alien species, but overall there was no consistent competition effect. Similarly, we found that none of the multitrophic-interaction treatments affected survival, biomass or number of flowering structures of the alien species. 4. We conclude there was no significant relationship between performance measures of the alien species and their phylogenetic relatedness to the native competitors.

In this article, it is demonstrated that if the zeta function does not have a sequence of zeros whose real part converges to 1, then it cannot have any zeros in the critical strip, showing that the Riemann Hypothesis is false.

Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and therefore all free energies, do obey scaling. Although we limit ourselves to such a system, we elaborate about the possibilities of finding universality, as well as the precise values of the critical exponents using thermodynamics only.

In this paper, the elemental construct of an I-shaped fin cooling a heat generating volume is studied through the entropy production perspective. Using the constructal design method framework with entropy production minimization as an objective leads to different optimal shape ratio, different from the ones obtained using the excess of temperature. Moreover, the optimal shape ratio evolution is not necessary the same for local entropy production minimization (excess of entropy production) and global entropy production (entropy produced in the whole area). Finally, an analysis on a possible dimensionless number is introduced for the study of constructal plates.

Conventional models do not fully explain composition of the solar system – for example, the presence of p-nuclei and post-post-Fe-nuclei remains not yet understood (and is one of the great unresolved puzzles of nuclear astrophysics in general); other puzzles exist. We offer a hypothesis which can explain the appearance of non-native elements in the solar system, and a feasible scenario for its implementation. The hypothesis suggests that a nuclear-fission "event" occurred in the inner part of the solar system at the time currently defined as the birth of the system. Conventional models have never considered fission as a contributing nuclei-production mechanism. Upon examination of the existing models and factual data (presented in volumes of publications but never combined into an aggregate), we identified one plausible scenario by which a fission event (not demolishing the entire solar system) could occur: an encounter with a compact super-dense stellar "fragment" (with specific properties) and its "explosion" in fission-cascades. Such scenario also helps resolve other long-standing puzzles of the solar system. For example, it provides that the fission-produced nuclei subsequently transformed into the material that (eventually) accreted into the "rocky" objects in the system (terrestrial planets, asteroids, etc.) and enriched the pre-existed hydrogen-helium objects (the Sun and the gaseous giants) – this offers an explanation for the planets’ inner position and compositional differences within the predominantly hydrogen-helium rest of the solar system. Other implications also follow.

Cahuachi (Nazca River Valley, South Peru) was the major ceremonial center of the Nasca civilization. According to previous studies, it was struck and destroyed by three El Niño-Southern Oscillation events, which would have occurred around 100 BCE, 600 CE and 1000 CE, respectively. At the end of the series of events, the ceremonial center would have been buried by a cap of conglomerates. Despite this hypothesis raised well-founded doubts regarding its geochronological and paleoenvironmental implications, it is uncritically used as a reference in geoarchaeological research. In the present study, optically stimulated luminescence (OSL) dating results of some samples taken from alluvial deposits at Cahuachi are reported, with the aim to evaluate the literature’s hypothesis. Since the obtained ages are older than the Holocene epoch, such a hypothesis must be rejected. A number of field evidences corroborate this result. Finally, the advancement in fluvial geomorphology knowledge of the Nazca River Valley is briefly discussed.

In this note we prove that the Riemann hypothesis is false. The proof is by contradiction based on a criterion of Hu.

The Riemann zeta function plays a crucial role in number theory and its applications. The Riemann Hypothesis (RH) posits that zeros of other than the trivial ones are located on the line defined by the equation Re(s) =1/2. This paper introduces a novel and straightforward proof of the Riemann Hypothesis. The proof employs a standard method, utilizing the eta function in place of the zeta function, under the assumption that the real part is greater than zero. The equation for the real and imaginary parts of the Riemann zeta function (eta function) is completely separated. Initially, let with s= . The value of the real part is determined by solving the equation, and the process is repeated for identifying the potential roots shared by the two functions, a common value is obtained, leading to a =1/2, which represents the real part of the main root of the function ζ(s). By plotting the zeta function for the obtained a, it is determined that the function has a root only at a =1/2. In another analysis, by identifying the roots of the common potential between the two functions ζ(s) and ζ(1-s), a common value is obtained, which leads to a =1/2. This value represents the real part of the main root of the function ζ(s). Additionally, using a standard method and with the help of two functions ζ(s) and ζ(1-s), the real part of the root of the zeta function is obtained. To create a generator function for prime numbers in terms of b, one can solve the root of the zeta function where it equals one (i.e., and obtain a relationship between b’ and prime numbers. Giving the value of zeta equal to one and s' = a' + ib’, similar to zeta equal to zero, the roots are again placed on the line. Then, by using the zeta function defined by multiplying prime numbers, we arrive at a new meaningful relation between b’ and its corresponding prime number is obtained.

The basic idea is to expand the completed zeta function $\xi(s)$ in MacLaurin series (infinite polynomial), which can be further expressed as infinite product (Hadamard product) by conjugate complex roots. Finally, the functional equation $\xi(s)=\xi(1-s)$ leads to $(s-\alpha_i)^2 = (1-s-\alpha_i)^2, i \in \mathbb{N}$ with solution $\alpha_i= \frac{1}{2}, i \in \mathbb{N}$, where $\alpha_i$ are the real parts of the zeros of $\xi(s)$, i.e., $s_i =\alpha_i\pm j\beta_i, i\in \mathbb{N}$. Therefore, a proof of the Riemann Hypothesis is achieved.

Aim: This study aimed to carrying out a prospective survey on socio-demographics and lifestyle factors among a population of Caribbean immigrants living in the US. Materials and Methods: The data were processed and analysed using the SPSS software and Excel. Crosstabulations were done. The Chi-square test was use to evaluate different hypotheses in this study. Statistical significance was defined as p<0.05.Results: Gender was found statistically significant difference with the country of birth of the Caribbean immigrants (p=0.038), and in the cleanness of their neighbourhoods (p=0.045). There were differences in occupations between males and females (p=0.001). Males were less unemployed than females (p=0.011). Gender also showed statistically significant difference in how easy the immigrants balanced their work and personal life (p=0.044). Age groups depicted differences in the physical health of the immigrants (p=0.001). The use of alcohol and tobacco was not an important risk factor among participants (p=0.529).Conclusions: These facts suggest that socio-demographics among a population of Caribbean immigrants were significantly different among genders. However the use of tobacco and alcohol showed not significant differences among the immigrants.

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

Serendipity favors the prepared mind, but how does the brain make that lucky find? Analyzing the cerebral mechanisms behind an exceptional (albeit trivial) discovery, the author suggests that a combination of ‘concept cells’ and the Global Neuronal Workspace Hypothesis could explain how we make great discoveries.

This two-part series describes how to test hypotheses on molecular mechanisms that underlie biological phenomena, using preclinical drug testing as a simplified example. While pursuing drug testing in preclinical research, it is important for students to understand the limitations of descriptive as well as mechanistic studies. The former does not identify any causal links between two or more variables; it identifies the presence or absence of correlations. The latter has caveats presented in Parts I and II of this series. Part II also describes how to test for a causal link between drug-induced activation of biological targets and therapeutic outcomes. Here, the mechanism of action of the drug is identified with pharmacological or genetic approaches that modify the expression/activity of the drug targets. Without interference with the proposed mechanism of action, a causal link between activation (or inhibition) of the target P and the therapeutic outcomes of drug D cannot be established. Using pharmacological agonists and antagonists, gene knockout and overexpression, or protein knockdown tools, designing a full-factorial three-way ANOVA forces the investigator to include the appropriate control groups, mitigating the risk of false positive or false negative conclusions. Upon completion of this series, the educator and student will have some of the tools in hand to design mechanistic studies and interpret various experimental outcomes, with knowledge of strengths and limitations of preclinical research.

Many discoveries in the biological sciences have emerged from observational studies, but student researchers also need to learn how to design experiments that distinguish correlation from causation. For example, identifying the physiological mechanism of action of drugs with therapeutic potential requires the establishment of causal links. Only by specifically interfering with the purported mechanisms of action of a drug can the researcher determine how the drug “causes” its physiological effects. Typically, pharmacological or genetic approaches are employed to modify the expression and/or activity of the biological drug target or downstream pathways, to test if the salutary properties of the drug are thereby abolished. However, experimental techniques have caveats that tend to be underappreciated, particularly for the newer methods. In this two-part series, the caveats and strengths of mechanistic preclinical research are described, using the intuitive example of pharmaceutical drug testing in experimental models of human diseases. This series is not intended to tackle the perpetual clash between the frequentist approach to statistics and other schools of thought. Rather, Part I focuses on technical practicalities and common pitfalls of cellular and animal models designed for drug testing, and Part II describes in simple terms how to leverage a full-factorial three-way ANOVA, to test for causality in the link between drug-induced activation (or inhibition) of a biological target and therapeutic outcomes. Upon completion of this series, the student is expected to appreciate the strengths as well as limitations of mechanistic research and to avoid some of its pitfalls.

This paper presents proof of Riemann's hypothesis by utilizing the golden ratio and the ellipse's eccentricity in six dimensions. This proof extends across all scientific fields. this research introduces logical and mathematical principles for distributing, recognizing, and categorizing prime numbers. It also explores the relationship between prime numbers and the complex conjugate of five prime numbers in various dimensions. Accordingly, it delves into the classification of even numbers based on prime numbers. This study examines the proof of Riemann's hypothesis from a geometric dimension perspective. Based on this, the mathematical structure of an integrated theory is defined. properties and principles associated with prime numbers reveal connections between quantum mechanics and general relativity.

The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis. Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$, $\gamma \approx 0.57721$ is the Euler-Mascheroni constant and $\log$ is the natural logarithm. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's criterion on superabundant numbers, we prove that the Riemann hypothesis is true.

Mental Disorders are an important public health problem. The main of this study was to analyze the prevalence of Mental Disorders and Environmental Quality. Data on the Prevalence of Mental Disorders, Gross Domestic Product, and Median Years of Schooling from 178 countries were used. A positive association was observed and was independent of Gross Domestic Product and Median Years of Schooling.

This paper presents a statistical approach to identify the underlying roughness characteristics in synthetic aperture radar (SAR) intensity data. The physical modeling of this kind of data allows the use of the Gamma distribution in the presence of fully-developed speckle, i.e., when there are infinitely many independent backscatterers per resolution cell, and none dominates the return. Such areas are often called ``homogeneous'' or ``textureless'' regions. The GI0 distribution is also a widely accepted law for heterogeneous and extremely heterogeneous regions, i.e., areas where the fully-developed speckle hypotheses do not hold. We propose three test statistics to distinguish between homogeneous and inhomogeneous regions, i.e., between gamma and GI0 distributed data, both with a known number of looks. The first test statistic uses a bootstrapped non-parametric estimator of Shannon entropy, providing a robust assessment in uncertain distributional assumptions. The second test uses the classical coefficient of variation (CV). The third test uses an alternative form of estimating the CV based on the ratio of the mean absolute deviation from the median to the median. We apply our test statistic to create maps of \(p\)-values for the homogeneity hypothesis. Finally, we show that our proposal, the entropy-based test, outperforms existing methods, such as the classical CV and its alternative variant, in identifying heterogeneity when applied to both simulated and actual data.

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

The association between mental illness and violent crimes such as homicide is complex. In 1939, Lionel Penrose hypothesized that the availability of psychiatric hospital beds was inversely related to the prison population, presumably due to the hospitalization of potential offenders with a mental illness. Subsequent studies have found evidence for this association, but questions remain about the contributions of confounding factors. Moreover, there has been a move towards deinstitutionalization and community care of the mentally ill over the past six decades. In this study, the association between national homicide rates and three measures of the availability of psychiatric care – the numbers of psychiatrists, general hospital psychiatric beds, and psychiatric hospital beds per 100,000 population – was examined using a time-lagged correlation analysis. Associations between homicide rates and socioeconomic factors associated with crime were also examined. It was found that the availability of psychiatrists and of general hospital psychiatric beds were both negatively correlated with homicide rates, and that the association with general hospital psychiatric beds remained significant even after correction for confounding factors. These results suggest the need for a more nuanced interpretation of Penrose’s original formulation, involving the interplay of social, economic factors and psychological factors rather than linear causality.

The provenance of the aminoacyl-tRNA synthetases (aaRS) poses challenging questions because of their role in the emergence and evolution of genetic coding. We investigate evidence about their ancestry from curated structure-based multiple sequence alignments of a structurally invariant “scaffold” shared by all 10 canonical Class I aaRS. Three uncorrelated phylogenetic metrics—residue-by-residue conservation, its variance, and row-by-row cladistic congruence—imply that the Class I scaffold is a mosaic assembled from distinct, successive genetic sources. These data are especially significant in light of: (i) experimental fragmentations of the Class I scaffold into three partitions that retain catalytic activities in proportion to their length; and (ii) evidence that two of these partitions arose from an ancestral Class I aaRS gene encoding a Class II ancestor in frame on the opposite strand. Phylogenetic metrics of different modules vary in accordance with their presumed functionality. A 46-residue Class I “protozyme” roots the Class I molecular tree prior to the adaptive radiation of the Rossmann dinucleotide binding fold that refined substrate discrimination. Such rooting is consistent with near simultaneous emergence of genetic coding and the origin of the proteome, resolving a conundrum posed by previous inferences that Class I aaRS evolved long after the genetic code had been implemented in an RNA world. Further, pinpointing discontinuous enhancements of aaRS fidelity establishes a timeline for the growth of coding from a binary amino acid alphabet.

Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x) = \left(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x) \leq 0$ is satisfied for some number $x \geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x) \leq 0$ and $S(x)\geq 0$ are satisfied for some number $x \geq 3$ or when $\frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log \theta(x)} \leq 1$ is satisfied for some number $x \geq 13.1$.

Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. Let $q_{1} = 2, q_{2} = 3, \ldots, q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m} q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann Hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n > 5040$ such that Robin inequality does not hold and $n < (4.48311)^{m} \times N_{m}$, where $N_{m} = \prod_{i = 1}^{m} q_{i}$ is the primorial number of order $m$.

The origin of cancer remains one of the most important enigmas in modern biology. The prevailing paradigm has failed to grasp a comprehensive view of the disease. Naturally, therapies developed under the current assumptions are inadequate and cancer is practically an incurable disease. Meanwhile, descriptive studies continuously extend the molecular complexity of cancer without an equivalent advancement in its understanding. Furthermore, they tend to accumulate inconsistencies inexplicable under the classical view. This paper presents a compelling theory of the origin of carcinomas. By hypothesis, a series of generic events in epithelial tissues promoted by cellular aging and inflammation enables the reactivation of developmental programs. The origin of carcinomas in vivo is described as the time-ordered cell state transitions undergone by epithelial cells in the hyperplasia due to replicative senescence and inflammation towards a mesenchymal undifferentiated endogenous cell state with cancerous behavior. In support of the theory, the molecular, cellular, and histopathological evidence is critically reviewed. A plausible model for the origin of carcinomas is presented to explain the mechanism underlying carcinogenesis from an evolutive and developmental perspective. The implications of the hypothesis in the current strategies for cancer prevention and treatment are discussed along with rational alternatives and some predictions for possible experimental validation.

The primary purpose of this article is to provide a brief overview about the notion of the \textit{Mertens Function} $M(n)$ and \textit{Redheffer Matrices} $\mathbb{A}_{n}$ and, to derive specific order estimates for $M(n)$, in order to analyze the location of the non-trivial zeros of the \textit{Riemann Zeta function} $\zeta(s)$. A priori using the above concepts, the article aims at establishing a necessary and sufficient condition for the \textit{Riemann Hypothesis} to hold true.

Human language and social cognition are two key disciplines that have traditionally been studied as separate domains. However, emerging research from detailed studies of comparative animal behavior, human social behavior, language acquisition in children, social cognitive neuroscience, and the cognitive neuroscience of language suggest that language and social cognition are two deeply interrelated capacities of the human species. For instance, recent developmental studies on the acquisition of language in infants and young children, draw attention to the important crucial benefits associated with several different aspects of social stimulation for youngsters, including the quantity and quality of linguistic input, dyadic infant/child-to-parent verbal and non-verbal social interactions, and other important social cues integral for facilitating language learning and social bonding. Studies of the adult human brain further suggest a high degree of specialization for sociolinguistic information processing, memory retrieval, and comprehension, suggesting the function of these regions may link language with social cognition and social bonding. In effect, the social brain and social complexity hypotheses may jointly help to explain how neurotypical children and adults learn language, why autistic adults and children exhibit simultaneous deficits in language and social cognition, and why nonhuman primates and other animals with significant computational abilities do not acquire the capacity for language. But perhaps most critically, the following article argues that this and related research will allow scientists to generate a holistic profile and deeper understanding of the healthy adult social brain, while developing more innovative and effective diagnoses, prognoses, and treatments for maladies and deficits also associated with the social brain.

By the strong relation between ξ function and the Riemann ζ function, we will prove the Riemann hypothesis which states that ”All non-trivial zeros z = x+y i of ζ must lie on the critical line x = 1/2". ”.

This paper provides the straight proof for the Riemann Hypothesis.The proof has been formulated with the modified version of Riemann Xi function ξ(s) , that shows the relationship with upper incomplete gamma function.

In this paper, the distribution of prime numbers is expressed based on proving the Riemann hypothesis. The relationship between three numbers, three, six, and nine, and the modality to the distribution of prime numbers, is one of the results of Riemann's zeta function. Prime numbers are classified into six groups of single-digit numbers. There are no prime numbers in groups of three, six, and nine. The groups are made based on the sum of the internal digits. And for each set, there is an angle in the complex plane. The distance between the prime numbers in each group has a regular pattern. This pattern is a multiple of the numbers three, six, and nine. According to Euler's number, for an angle of 60 degrees, the real part of the cosine is 1/2. Accordingly, all prime numbers are related to angles greater than 60 degrees to 90 degrees. As a result, based on the relationship between the golden spiral and the complex conjugate of the zeta function, the function in The 1/2 point becomes zero based on the prime numbers.

The power of movement in plants” by Charles Darwin details many examples of oscillatory growth exemplified more recently at the single cell level by pollen tube tip oscillations and associated ion fluxes, particularly Ca²⁺and H⁺. That implies an underlying growth oscillator based on the recent discovery that classical AGPs bind Ca²⁺ at the cell surface. The juxtaposition of AGPs with three other components embedded in the plasma membrane is evidence of a Ca²⁺ cycle that generates cytosolic Ca²⁺. It involves Ca²⁺ channels, auxin efflux “PIN” proteins and an auxin-activated proton pump that dissociates AGP-Ca²⁺ on demand. While the apparent simplicity of this system satisfies Occam’s Razor its hypothetical role as a global growth oscillator demands rigorous experimental appraisal. The wide ramifications extend from pollen tubes to stomatal guard cells. Stomata act as crucial components of a water hypercycle that contributes to homeostasis of a warming planet by regulating evaporative cooling, reflective cloud cover generated by vast forests and the high albedo of snow-capped mountains including polar ice-caps . The Gaia hypothesis of James Lovelock and Lynn Margulis is a brilliant metaphor.

In this paper we investigate some properties of square-free numbers. In particular, we study a function that counts the number of square-free numbers no larger than the given number n. We show that this function has asymptotics consistent with the predictions of the Riemann hypothesis and use this to obtain new and better estimates of the density of square-free numbers. Finally, we present a well-known generalization of the concept of a square-free number to monoids and research on square-free factorizations.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

In this study, a simple approach to solving the Riemann Hypothesis, one of the most prominent unsolved problems in the field of Number Theory in mathematics and one of the “Millenium Prize Problems”, is presented. The Riemann Hypothesis, a conjecture about distribution of prime numbers, has remained unsolved since it was first proposed by German mathematician, Bernhard Riemann in 1859. This paper introduces an analytic continuation of the Zeta Function as well as symmetric approach through integration by parts to address this hypothesis. The proposed solution is obtained through analytical continuation in the critical strip 0<Re(s)<1 to establish that Re(s)=1/2.

World Health Organization (WHO) provides the guideline for managing the Particulate Matter (PM) level because when the PM level is higher, it threats the human health. For managing PM level, the procedure for measuring PM value is needed firstly. We use Tapered Element Oscillating Microbalance (TEOM)-based PM measuring sensors because it shows higher cost-effectiveness than Beta Attenuation Monitor (BAM)-based sensor. However, TEOM-based sensor has higher probability of malfunctioning than BAM-based sensor. In this paper, we call the overall malfunction as an anomaly, and we aim to detect anomalies for the maintenance of PM measuring sensors. We propose a novel architecture for solving the above aim that named as Hypothesis Pruning Generative Adversarial Network (HP-GAN). We experimentally compare the several anomaly detection architectures to certify ours performing better.

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

Aim: The aim in this study was to conduct a prospective survey regarding the socio-demographics and lifestyle risk factors for cancer of a population of Caribbean immigrants living in the U.S. Materials and Methods: The data were processed and analysed using SPSS software 27 and Excel. Crosstabulations were performed. The chi-square test was used to evaluate differ-ent hypotheses. Statistical significance was defined as p < 0.05. Results: Statistically significant differences in the country of birth of the Caribbean immigrants were found for sex (p = 0.038) and the cleanness of their neighbourhoods (p = 0.045). We found differences in occupations between men and women (p = 0.001). Men were less unemployed than women (p = 0.011). Sex also showed statistically significant differences in how easily the immigrants balanced their work and per-sonal life (p = 0.044). Age groups depicted differences in the physical health of the immigrants (p = 0.001). The use of alcohol and tobacco was not an important risk factor among participants (p = 0.529). Conclusions: These findings suggest that the sociodemographics risk factors for cancer among a population of Caribbean immigrants were significantly different between the sexes. However, the use of tobacco and alcohol showed insignificant differences among the immigrants.

This work uses a new approach to investigate the Riemann hypothesis, drawing conclusions about its trueness. It is based on the more general method presented in a very recent publication, by the same author, showing in detail how to approach that very well-known and interesting problem. This is achieved by means of the theory of dynamical systems (Poincaré index associated to equilibria of 2-dimensional systems) and the study of the zeros of the Dirichlet eta function, defined by a Dirichlet series. By using the well-known fact that the zeros of the eta function include all zeros of the Riemann zeta function in the (open) critical strip, excluded the critical line, ((0,1/2) ∪ (1/2,1)) × (−∞,∞), the development proceeds using only the eta function. In addition, the open and simply connected region (1/2,1) × (0,∞) is used along the text, taking into account the symmetries of zeros of the functions under analysis in the critical strip. The basic line of proof is to find the mathematical expression for the Poincaré index of the vector field associated to the eta function, assuming the existence of a zero of the eta function outside the critical line (in (1/2,1) × (0,∞)), and investigating the resulting unfoldings. Eventually, an inconsistency occurs and the proof ends by contradiction.

: Aim: The aim in this study was to conduct a prospective survey regarding the sociodemographics and lifestyle risk factors for cancer of a population of Caribbean immigrants living in the U.S. Materials and Methods: The data were processed and analysed using SPSS software 27 and Excel. Crosstabulations were performed. The chi-square test was used to evaluate different hypotheses. Statistical significance was defined as p &lt; 0.05. Results: Statistically significant differences in the country of birth of the Caribbean immigrants were found for sex (p = 0.038) and the cleanness of their neighbourhoods (p = 0.045). We found differences in occupations between men and women (p = 0.001). Men were less unemployed than women (p = 0.011). Sex also showed statistically significant differences in how easily the immigrants balanced their work and personal life (p = 0.044). Age groups depicted differences in the physical health of the immigrants (p = 0.001). The use of alcohol and tobacco was not an important risk factor among participants (p = 0.529). Conclusions: These findings suggest that the sociodemographics risk factors for cancer among a population of Caribbean immigrants were significantly different between the sexes. However, the use of tobacco and alcohol showed insignificant differences among the immigrants.

The etiological agent of various viral diseases has been identified, and clinical characteristics and complications of each disease are well known. In general, a viral disease appears as acute systemic inflammatory disease, but after acute infection, some patients remain asymptomatic carriers or suffer chronic viral diseases, suggesting that the phenomena are unavoidable processes for viruses’ coexistence with their hosts as virome in microbiota of human species. Although each viral disease has been described as having different pathophysiology, the host's control systems, including immune systems, against the insults from any viral infections, have the same components in previously healthy hosts. Therefore, considering the characteristics of the life cycle of viruses being dependent on the host cell and the same immune components of the host, it is reasonable assumption that there is a common immune mechanism to respond to the insults from all viral diseases. The authors discuss on the characteristics of virus infection and unresolved issues in viral diseases and propose a rationale of early immune modulators for acute insults from viral diseases based on our clinical experiences and the protein-homeostasis-system hypothesis.

Hashimoto’s thyroiditis (HT) is a gender autoimmune disease that is manifested by chronic inflammation of thyroid. Clinical trial studies (CTSs) use molecular biotechnologies (MB) to approach HT appearance. Aims of this study was to analyze the applications of MB in CTSs carried out in HT populations (HT-CTSs). Further, to evaluate the role of MB in the context of hygiene hypothesis (HH). From 75 HT-CTSs found at https://beta.clinicaltrials.gov/ web place, forty-five were considered for this investigation. Finally, six HT-CTSs were reported as molecular HT-CTSs (mHT-CTSs) because of these were planning to utilize MB. Two of mHT-CTSs were settled on French population to isolate DNA viral sequences. Blood, urine, and thyroid tissues biospecimens were analyzed to pick out parvo and polyoma viruses. Two mHT-CTSs carried out in China, were aimed to identify oral and fecal microbiotas by measuring PCR sequencing of 16S rRNA gene. Two mHT-CTSs were programmed in USA and Greece, respectively, for interception of DNA polymorphisms to associate with genetic susceptibility to HT. In conclusion, MB are mainly employed in HT-CTSs for infective pathogenesis and genetic fingerprinting of HT. Besides, MB don't prove the evidence of HH; however, they are useful for direct evidence of the presence of viruses.

A paradigm shift away from null hypothesis significance testing seems in progress. Based on simulations, we illustrate some of the underlying motivations. First, P-values vary strongly from study to study, hence dichotomous inference using significance thresholds is usually unjustified. Second, statistically significant results have overestimated effect sizes, a bias declining with increasing statistical power. Third, statistically non-significant results have underestimated effect sizes, and this bias gets stronger with higher statistical power. Fourth, the tested statistical hypotheses usually lack biological justification and are often uninformative. Despite these problems, a screen of 48 papers from the 2020 volume of the Journal of Evolutionary Biology exemplifies that significance testing is still used almost universally in evolutionary biology. All screened studies tested default null hypotheses of zero effect with the default significance threshold of p = 0.05, none presented a pre-specified alternative hypothesis, pre-study power calculation, and the probability of ‘false negatives’(beta error). The results sections of the papers presented 49 significance tests on average (median 23, range 0–390). Of 41 studies that contained verbal descriptions of a ‘statistically non-significant’ result, 26 (63%) falsely claimed the absence of an effect. We conclude that studies in ecology and evolutionary biology are mostly exploratory and descriptive. We should thus shift from claiming to ‘test’ specific hypotheses statistically to describing and discussing many hypotheses (possible true effect sizes) that are most compatible with our data, given our statistical model. We already have the means for doing so, because we routinely present compatibility (‘confidence’) intervals covering these hypotheses.

While immutability is Blockchain's* much celebrated covenant, change is the rule of life. The paradox has seriously limited real-world deployability of Smart Contracts (SC), faltering its mainstream adoption and sustainability. Once implemented, SC remains unstoppable even if its execution makes losses, as evident in the recently exploded $50+B DeFi industry. How do we reconcile the two and make DeFI/Blockchain profitable and sustainable? A DISC (Dynamic Immutable Smart Contract) hypothesis was proposed to resolve the paradox. Using an existing decentralized IoT device framework we test the DISC hypothesis, by designing/implementing a DISC protocol that delivers an algorithmically controlled dynamic off-chain data feed into a self-executing SC. The experiment successfully introduced limited dynamism into SC without compromising its immutability or undermining user control over their SC terms. If consistently reproduced in diverse settings, the DISC protocol could earn an important milestone in the evolution of Blockchain's decentralized economy of the future.

During the current COVID-19 pandemic caused by SARS-CoV-2, clinicians and scientists are working assiduously to unravel its pathophysiology and find effective treatments. An impressive number of papers has been published on SARS-CoV-2, exposing the complexity of the disease, the tendency of scientists to form hypotheses within their area of expertise, and the lack of orchestration of research. Hypotheses and research findings mainly complement each other, though sometimes controversies can be discerned among various theories and study results. Our overview aims to portray the ‘big picture’ of COVID-19, visualising the interwovenness of different pathophysiological pathways, with a focus on cytokine-induced pathology, the sequelae of ACE2 downregulation, and thrombosis associated with microvascular injury. It aids in overseeing the effects of repurposed drugs on intended targets, but also alerts to the (adverse) effects on interacting pathways. The overview shows how comorbidities probably increase susceptibility to (severe) COVID-19 and provides the possible pathophysiological origin of signs, symptoms, and biochemical abnormalities.

The reliability analysis allows to estimate the system's probability of detecting and identifying outlier. Failure to identify an outlier can jeopardise the reliability level of a system. Due to its importance, outliers must be appropriately treated to ensure the normal operation of a system. The system models are usually developed from certain constraints. Constraints play a central role in model precision and validity. In this work, we present a detailed optical investigation of the effects of the hard and soft constraints on the reliability of a measurement system model. Hard constraints represent a case in which there exist known functional relations between the unknown model parameters, whereas the soft constraints are employed for the case where such functional relations can slightly be violated depending on their uncertainty. The results highlighted that the success rate of identifying an outlier for the case of hard constraints is larger than soft constraints. This suggested that hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. After identifying and removing possible outliers, one should set up the soft constraints to propagate the uncertainties of the constraints during the data processing. This recommendation is valid for outlier detection and identification purpose.

In this paper we evaluate the effects of hard and soft constraints on the Iterative Data Snooping (IDS), an iterative outlier elimination procedure. Here, the measurements of a levelling geodetic network were classified according to the local redundancy and maximum absolute correlation between the outlier test statistics, referred to as clusters. We highlight that the larger the relaxation of the constraints, the higher the sensitivity indicators MDB (Minimal Detectable Bias) and MIB (Minimal Identifiable Bias) for both the clustering of measurements and the clustering of constraints. There are circumstances that increase the family-wise error rate (FWE) of the test statistics, increase the performance of the IDS. Under a scenario of soft constraints, one should set out at least three soft constraints in order to identify an outlier in the constraints. In general, hard constraints should be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. In that process, one should opt to set out the redundant hard constraints. After identifying and removing possible outliers, the soft constraints should be employed to propagate their uncertainties to the model parameters during the process of least-squares estimation.

Studies on the structure of economic systems are, most frequently, carried out by the methods of informational statistics. These methods, often accompanied by a wide range of indicators (Shannon entropy, Balassa coefficient, Herfindahl specialty index, Gini coefficient, Theil index etc.) around which a wide literature has been created over time, have a major disadvantage. Such weakness is related to the imposition of the system condition, therefore the need to know all the components of the system (as absolute values or as weights). This restriction is difficult to accomplish in some situations, and in others, this knowledge may be irrelevant, especially when there is an interest in structural changes only in some of the components of the economic system (either we refer to the typology of economic activities - NACE or of territorial units – NUTS). This article presents a procedure for characterizing the structure of a system and for comparing its evolution over time, in the case of incomplete information, thus eliminating the restriction existent in the classical methods. The proposed methodological alternative uses a parametric distribution, with subunit values for the variable. The application refers to Gross Domestic Product values for five of the 28 European Union countries, with annual values of over 1,000 billion Euros (Germany, Spain, France, Italy and United Kingdom) for the years 2003 and 2015. A form of the Wald sequential test is applied to measure changes in the structure of this group of countries, between the years compared. The results of this application validate the proposed method.

Understanding the mechanism, how entirely new (EntNew) gene/protein or the first ancestral gene/protein of a family was created, should be one of the most important issues in the biological sciences. However, the mechanism is totally unknown still now. On the other hand, it is well known that mature protein is generally rigid and one catalytic center exists on the protein. Creation of such a mature EntNew gene/protein should be, of course, carried out through random process, because it cannot be designed in advance. However, the EntNew gene/protein never be created by random polymerization of the respective monomeric units, because of the extraordinary large sequence diversities of ~10¹⁸⁰ and ~10¹³⁰, respectively. Protein 0^th-order structure or a specific amino acid composition, in which immature but water-soluble protein can be produced even through random process, holds the key for solving the difficult problem. As it was fragmentally described in the previous papers how and where EntNew gene/protein was created, I describe in detail in this review three processes generating EntNew gene/protein with some flexibility under three genetic codes, the universal genetic code, SNS primitive code and GNC primeval code, and discuss why the mature gene/protein could be created through the processes.

The Riemann hypothesis, renowned for its deep connection to the distribution of prime numbers, remains a central problem in mathematics. Understanding the distribution of primes is crucial for developing efficient algorithms and advancing our knowledge of number theory. The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. Several equivalent formulations of the Riemann hypothesis exist. Robin's criterion for the Riemann hypothesis is based on an inequality that divisor sum function $\sigma$ must satisfy at natural numbers greater than 5040. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. By using Robin's criterion on superabundant numbers, we present a novel approach that culminates in a complete proof of the Riemann hypothesis. This work is an expansion and refinement of the article "Robin's criterion on divisibility", published in The Ramanujan Journal.

This article describes a new application of the global optimization method HQF ASA to the investigation of the Riemann hypothesis, in the sense of searching for zeros of the Riemann zeta function ζ outside the critical line but inside the (open) subset of the critical strip ((0,1/2)∪(1/2,1))×(−∞,∞). The underlying idea is very simple: a complex root r of a given complex function f : C → C must satisfy the condition ||f(r)|| = 0, that is, f(r) must have 2-dimensional Eu- clidean norm equal to 0, considering r as a point of R2. In the opposite direction, for any r ∈ C, ||f(r)|| = 0 implies f(r) = 0 and r is a root of f. Focusing again on the Riemann zeta function ζ, the open and simply connected region Rc = (1/2,1)×(0,∞) is used along the text, taking into account the symmetries of zeros of ζ in the critical strip. In this fashion, finding a global optimizer for ||ζ|| is equivalent to finding a root of ζ. Therefore, and taking into account the well-known efficacy of HQF ASA, a good sign of the trueness of RH would be not finding global minima in several optimization sessions with expanding subsets of Rc. In practical terms, several optimization sessions are executed using QMF ASA with increasing subsets of Rc, searching for global minima of ||ζ||. After presenting numerical results and figures, the adequacy of the proposed approach as a tool for preliminary empirical analysis for this type of problem is discussed.

Conditional Independence (CI) testing is fundamental in statistical analysis. For example, CI testing helps validate causal graphs or longitudinal data analysis with repeated measures in causal inference. CI testing is difficult, especially when testing involves categorical variables conditioned on a mixture of continuous and categorical variables. Current parametric and non-parametric testing methods designed for continuous variables and can quickly fall short in the categorical case. This paper presents a computational approach for CI testing for categorical data types, which we call computational conditional independence (CCI) testing. The test procedure is based on permutation and combines machine learning prediction algorithms and Monte Carlo Cross-Validation. We evaluated the approach through simulation studies and assessed the performance against alternative methods; the generalized covariance measure (GCM) test, the kernel conditional independence (KCI) test, and testing with multinomial regression. We find that the computational approach to testing has utility over the alternative methods, and we can achieve better control over type-I-error rates. We hope this work can expand the toolkit for CI testing for practitioners and researchers.

The physiological mechanism of membrane potential generation relies on the passage of mobile ions across the plasma membrane, which is selectively permeable to mobile ions. The existence of a membrane and the transport of ions across it are essential for the generation of membrane potential. However, a long-forgotten theory, Association-Induction hypothesis, asserts that the heterogeneous distribution of charges in space, due to ion adsorption, is the true cause of membrane potential generation. Using an artificial living cell model consisting of a viscous aqueous solution, the mechanism of membrane potential generation is restudied in this work. The results indicate that membrane potential can be generated even in the absence of a plasma membrane and that ion adsorption leading to a heterogeneous spatial charge distribution is an essential factor for membrane potential generation. Consequently, the authors invites people to reconsider the Association-Induction hypothesis as a genuine mechanism for generating membrane potential.

Modern gastroenterology, which occupies the pages of scientific journals without alternative, began as an initiative of manufacturers of diagnostic equipment. For widespread advertising, they selected practical doctors who were not familiar with the methodology of science and superficial knowledge of physiology. This is how a group led by DeMeester arose, which in 1976 published the DeMeester score, i.e., the normal limit for esophageal pH monitoring. pH <4, less than 4% of the time per day was considered normal, i.e., it was unreasonably claimed that such reflux is physiological. This article proves that this study was carried out with numerous methodological errors, which led to an erroneous conclusion. For a long time, pH monitoring was considered the gold standard and with its help hypotheses were proposed that form the basis of modern gastroenterology. The article proves the fallacy of 13 hypotheses, which are presented as theories. Numerous articles using pH monitoring have publicized this method. Practitioners became "great scientists", equipment manufacturers became successful businessmen. Over time, they found other groups of practitioners to promote devices for impedance ph monitoring, high-resolution manometry, and many others. At the same time, a network of reviewers who believe in the infallibility of the luminaries do not allow studies that contradict their faith to be published. Thus, fundamental science was destroyed, which alone could assess the harm of false research both for science and for patients. Conclusion This study provides a list of hypotheses, that were previously considered theories, but since scientific evidence has proven these assumptions to be false, they should be excluded from subsequent use and citation.

In the first part of this article, we discuss and generalize the complete convergence introduced by Hsu and Robbins (1947) to the r-complete convergence introduced by Tartakovsky (1998). We also establish its relation to the r-quick convergence first introduced by Strassen (1967) and extensively studied by Lai (1976). Our work is motivated by various statistical problems, mostly in sequential analysis. As we show in the second part, generalizing and studying these convergence modes is important not only in probability theory but also to solve challenging statistical problems in hypothesis testing and changepoint detection for general stochastic non-i.i.d. models.

This essay is a personal insight based on my own experience in the Iberian Pyrenees, which addresses three situations common in paleoecological research, such as the verification of previously devised hypotheses (anticipation), the finding on unknown events in unstudied sites (discovery) and the finding of unexpected outputs in already known areas (serendipity). The account is concentrated on the value of the coring sites by themselves as generators of paleoecological knowledge, rather than on the actual findings, which are presented and discussed in the corresponding data papers. The main aim is to show that there is still much room for new findings, even in areas that have been surveyed for long time and are supposed to be well known, from a paleoecological perspective. Finally, some general lessons are derived and conceptualized.

A generalization of the sum of divisors function involves a recursive definition. This leads to variants of superabundant numbers, colossally abundant numbers, and Gronwall's theorem (relevant to the Riemann hypothesis).

Accurate prediction of the membrane potential by membrane theory is possible on the basis that the plasma membrane is selectively permeable to ions and that permeability determines the characteristics of the membrane potential. However, an experimental and artificial cell system with an impermeable membrane serving as a model plasma membrane has a non-zero membrane potential, and this potential generated across the membrane is somehow consistent with the potential characteristics predicted by the membrane theory, despite the impermeability of the membrane to ions. A long-forgotten theory, called the association-induction hypothesis (AIH), has emerged as a more plausible mechanism for generating the membrane potential than the membrane theory to explain this unexpected behavior. The AIH asserts that ion-selective membrane permeability is not necessary for the generation of the membrane potential, which is contrary to the membrane theory. Although such an idea is not easy to accept, the experimental results clearly suggest the correctness of the AIH.

This paper investigates whether optimisation methods with the population made up of one solution can suffer from structural bias just like their multisolution variants. Following recent results highlighting the importance of choice of strategy for handling solutions generated outside the domain, a selection of single solution methods are considered in conjunction with several such strategies. Obtained results are tested for the presence of structural bias by means of a traditional approach from literature and a newly proposed here statistical approach. These two tests are demonstrated to be not fully consistent. All tested methods are found to be structurally biased with at least one of the tested strategies. Confirming results for multisolution methods, it is such strategy that is shown to control the emergence of structural bias in single solution methods. Some of the tested methods exhibit a kind of structural bias that has not been observed before.

Relationships between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem are discussed. Whether a function similar to Chebyshev’s second function is square-root close to a line having a slope different from 1 is discussed. The nontrivial zeros of the Riemann zeta function can be used to approximate many functions in analytic number theory. For example, it could be said that the nontrival zeta function zeros and the Möbius function generate in essence the same function - the Mertens function. A different approach is to start with a sequence that is analogous to the nontrivial zeros of the zeta function and follow the same procedure with both this sequence and the nontrivial zeros of the zeta function to generate in essence the same function. A procedure for generating such a function is given.

Objetives/Background: Vitamin D Binding Protein (VDBP) and free vitamin D are new markers that are being studied as a possible markers of vitamin D status. The main aim of our study was to analyse the VDBP genotype and quantify the levels of VDBP and free vitamin D in a sample of cystic fibrosis (CF) patients. Methods: Multicentre, cross-sectional and prospective study including patients with CF, exocrine pancreatic insufficiency who were clinically stable. We investigated vitamin D levels (total and free) and the different VDBP haplotypes. Free vitamin D levels were measured using an electro-chemiluminescence assay. Results: A sample of 48 patients was obtained (52% male; median age 13.8 years). The most common allele of VDBP was Gc1s (72%)>Gc2 (52%)>Gc1f (27%). Median calcidiol was 21.2 ng/ml (IR 15.3 - 26.9), 81% had levels in the insufficiency range: 23 patients (48%) below 20 ng/ml, and 16 (33%) between 20 and 30 ng/ml. The median free vitamin D level was 4.2 pg/ml (IR 3.9 – 5.6). A positive correlation was observed between calcidiol and free vitamin D levels (r=0.871; p<0.0001). After adjustment for season, vitamin D supplementation, sex and CFrelated diabetes, patients with Gc1f polymorphism had a lower risk of vitamin D deficiency, OR 0.22 (95% CI 0.05 – 0.99), p=0.027. A negative linear trend was observed between the polymorphisms grouped into 3 categories (Gc1/Gc1, Gc1/Gc2, and Gc2/Gc2, in that order) and vitamin D and free vitamin D levels (p=0.025 and p=0.033, respectively). Conclusion: In CF, as in the general population, the most common VDBP haplotype in Caucasian race is Gc1s. VDBP polymorphisms influence serum vitamin D and free vitamin D levels in CF patients. There is a good correlation between free vitamin D and calcidiol levels, suggesting that measuring the latter in CF does not seem to provide any additional benefit.

The growing energy consumption in the cryptocurrency and artificial intelligence (AI) industries is becoming an increasingly critical issue. This paper discusses methods for addressing this problem using data compression algorithms and the optimization of computational processes. Specifically, we examine research results that demonstrate the potential for significantly reducing energy consumption through mathematical solutions, such as the Riemann Hypothesis. We also present the notarized test results of an image compression program developed by the author. The work was presented at a UN panel session and an ECO webinar, receiving recommendations for implementation in ECO member countries. Additionally, modern technologies for accelerating cryptographic methods and algorithms are considered.The growing energy consumption in the cryptocurrency and artificial intelligence (AI) industries is becoming an increasingly critical issue. This paper discusses methods for addressing this problem using data compression algorithms and the optimization of computational processes. Specifically, we examine research results that demonstrate the potential for significantly reducing energy consumption through mathematical solutions, such as the Riemann Hypothesis. We also present the notarized test results of an image compression program developed by the author. The work was presented at a UN panel session and an ECO webinar, receiving recommendations for implementation in ECO member countries. Additionally, modern technologies for accelerating cryptographic methods and algorithms are considered.

The fundamental divergence in foundation of modern physics lies in the incompatibility between quantum theory and relativity. This study created a relative continuum, found a mathematical tool for the cosmic continuum; proposed dark particle hypothesis, filled gap on minimum existence quantity particle; discovered new equivalence principle, bridged differences in foundation of physics; and established an ideal model, revealed deep essence of cosmic and material structure. In this model, any cosmic system is a continuum composed of existence continuum relative to the wavelength of bosons energy waves and its dimension continuum. This model provides new perspectives on the fundamental problems of physics and cosmology. Firstly, it elucidated the physical mechanism of bosons in fundamental interactions. Secondly, it reconstructed the understanding of the basic unit of the cosmic and material structure. Thirdly, it updated the inherent concepts about the existence form and existence dimension. Fourthly, it restored the causality truth of wave function collapse in quantum mechanics.

Although the dopamine hypothesis of schizophrenia explains the effects of all the available antipsychotics in clinical use, there is an increasing need for developing new drugs for the treatment of positive, negative, and cognitive symptoms of chronic psychoses. Xanomeline-trospium (KarXT) is a drug combination that is based on the essential role played by acetylcholine in the regulation of cognitive processes and the interactions between this neurotransmitter and other signaling pathways in the central nervous system, with a potential role in the onset of schizophrenia, Alzheimer’s disease, and substance use disorders. A systematic literature review that included four electronic databases (PubMed, Cochrane, Clarivate/Web of Science, and Google Scholar) and the US National Library of Medicine database for clinical trials detected 21 sources referring to 14 studies focused on KarXT, out of which only four have published results. Based on the results of these trials, the short-term efficacy and tolerability of xanomeline-trospium are good, but more data is needed before this drug combination may be recommended for clinical use. However, on a theoretical level, the exploration of KarXT is useful for increasing the interest of researchers in finding new, non-dopaminergic, antipsychotics that could be used either as monotherapy or as add-on drugs.

High-dimensional measurement error data are becoming more prevalent across various fields. Research on measurement error regression models has gained increasing attention due to the risk of drawing inaccurate conclusions if measurement errors are ignored. When the dimension p is larger than the sample size n, it is challenging to develop statistical inference methods for high-dimensional measurement error regression models due to the existence of bias, nonconvexity of objective function, high computational cost and many other difficulties. Over the past few years, some works have overcome the aforementioned difficulties and proposed several statistical inference methods. This paper mainly reviews the current development on estimation, hypothesis testing and variable screening methods for high-dimensional measurement error regression models and shows the theoretical results of these methods with some directions worthy of exploring for future research.

This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate. An argument is put forward, based on the efficient market hypothesis, why a proper risk-adjusted discount rate should enter into the Black-Scholes model instead of the risk-free rate. The resulting pricing equation for derivatives and in particular the formula for European call options is then shown to depend explicitly on the drift of the underlying asset, which is following a geometric Brownian motion. It is conjectured that with the generalized model, the predicted results by the model could be closer to real data. The adjusted pricing model could partly also explain the mystery of volatility smile. The present model also provides answers to many finance professionals and academics who have been intrigued by the risk-neutral features of the original Black-Scholes pricing framework. The model provides generally different fair values for financial derivatives compared to the Black-Scholes model. In particular, the present model predicts that the original Black-Scholes model tends to undervalue for example European call options.

A concise proof of the Riemann Hypothesis is presented by clarifying the Hadamard product expansion over the zeta zeros, demonstrating that the Riemann Hypothesis is true.

Different cohort studies documented a lower glomerular filtration rate (GFR) in former extremely low birth weight (ELBW, <1000 g) neonates throughout childhood when compared to term controls. The current aim is to pool these studies to describe the GFR pattern over the pediatric age range. To do so, we conducted a systematic review on studies reporting on GFR measurements in former ELBW cases while GFR data of healthy age-matched controls included in these studies were co-collected. Based on 248 hits, 6 case-control and 3 cohort studies were identified, with 444 GFR measurements in 380 former ELBW cases (median age 5.3-20.7 years). The majority were small (17-78 cases) single center studies, with heterogeneity in GFR measurement (inulin, Cystatin C or creatinine estimated GFR formulae) tools. Despite this, the median GFR (ml/kg/1.73m²) within case-control studies was consistently lower (-13, range -8 to -25%) in cases, so that a relevant minority (15-30%) has a eGFR<90 mgl/kg/1.73m²). Consequently, this pooled analysis describes a consistent pattern of reduced eGFR in former ELBW cases throughout childhood. Research should focus on perinatal risk factors for impaired GFR and long-term outcome, but is hampered by single center cohorts, study size, and heterogeneity of GFR assessment tools.

Human cytomegalovirus (HCMV) is a β-herpes virus that is a significant pathogen within immune compromised populations. HCMV morbidity is induced through viral dissemination and inflammation. Typically, viral dissemination is thought to follow Fenner’s hypothesis where virus replicates at the site of infection, followed by replication in the draining lymph nodes, and eventually replicating within blood filtering organs. Although CMVs somewhat follow Fenner’s hypothesis, they deviate from it by spreading primarily through innate immune cells as opposed to cell free virus. Also, in vivo CMVs infect new cells via cell to cell spread and disseminate directly to secondary organs through novel mechanisms. We review the historic and recent literature pointing to CMV’s direct dissemination to secondary organs and the genes that it has evolved for increasing its ability to disseminate. We also highlight aspects of CMV infection for studying viral dissemination when using in vivo animal models.

This literature review aims to gain a deeper understanding of Spinosaurus aegyptiacus’s dorsal sail regarding its function as thermoregulation, display, or hydrodynamic. The function of S. aegyptiacus’s dorsal sail has been widely debated for many years. The three most popular hypotheses are that it was used as a biological mechanism of thermoregulation, display, or hydrodynamic. The display hypothesis includes attracting mates, intimidating rivals, and social communication with other members. This literature review delves into each of the three hypotheses using past studies and excavation sites to analyze their validity. For the hydrodynamic aspect, the lifestyle of S. aegyptiacus must first be established. Based on existing research, we cannot conclude that there is a definitive primary function of Spinosaurus aegyptiacus’s dorsal sail. However, it is likely that its sail served the crucial function of display, since it would have a large surface area and could thus be a distinguishable characteristic of S. aegyptiacus that could determine mating success. Additionally, it is probable that the sail had supplementary roles in thermoregulation and hydrodynamics.

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces new hypotheses through simple experiments with empirical evidence and theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches. Boldly contemplating the probability of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. In other words, if we do not accept the hypothesis of an afterlife, we may not be able to discuss the experimental results in the context of any alternative theories. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. This article sheds light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it seeks to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements including psychological well-being and intelligence.

Hsp70.1 has dual functions as chaperone protein and lysosomal stabilizer. Previously, we reported that calpain-mediated cleavage of carbonylated Hsp70.1 causes ischemic neuronal death by inducing lysosomal rupture. Recently, we found that the consecutive injections of vegetable oil-peroxidation product ‘hydroxynonenal’ induces hepatocyte death via the similar cascade. As Hsp70.1 is related also to fatty acid β-oxidation in the liver, its deficiency is known to cause accumulation of fat. Genetic deletion of betaine-homocysteine S-methyltransferase (BHMT) was reported to perturb choline metabolism, inducing decrease of phosphatidylcholine with the resultant hepatic steatosis. Here, focusing on disorders of Hsp70.1 and BHMT, we studied the mechanism of hepatocyte degeneration and steatosis, using monkeys after the consecutive injections of synthetic hydroxynonenal. As these monkeys showed a significant impairment of liver functions, the liver tissues without and with hydroxynonenal injections were compared by proteomics, immunoblotting, immunohisto-chemical and electron microscopic analyses. Western blotting showed upregulation of neither Hsp70.1 nor BHMT, but an increased cleavage of both proteins. Proteomics showed downregulation of Hsp70.1, while 2-fold increments of carbonylated BHMT. Hsp70.1 carbonylation was negligible, showing a marked contrast to ischemic neurons which were associated with ~10-fold increments. The control liver histologically showed lipid droplets in Ito cells, but lipid depositions within hepatocytes were very little. In contrast, after hydroxynonenal injections, widespread fatty degeneration and focal coagulation necrosis were observed with accumulation of numerous tiny lipid droplets within and around the degenerating/dying hepatocytes. Electron microscopy showed lysosomal membrane permeabilization/rupture, remarkable dissolution of mitochondria and rough ER membrane, and proliferation of abnormal peroxisomes. It is probable that disruptions of rough ER caused impaired synthesis of Hsp70.1 and BHMT proteins, while impairments of mitochondria and peroxisomes presumably contributed to the sustained generation of reactive oxygen species. Since both Hsp70.1 and BHMT are vulnerable to the long-standing oxidative stressor, hydroxynonenal-induced disorders facilitated degeneration and steatosis of hepatocytes, respectively.

Severe COVID-19 is associated with viraemia and multiple organ disease. Similar clinicopathological features have been previously seen in SARS and MERS. Clinically, the severity of SARS, MERS and COVID-19 has been associated with the presence of SARS-CoV, MERS-CoV or SARS-CoV2 viraemia in affected patients. In vitro work has looked at the pattern of viral entry and release from polarised epithelial cells infected by coronaviruses. This work has demonstrated a correlation between the severity of a coronavirus infection and the ability of the virus to reach and infect the basal surface of host cells. It has been postulated that this ability helps the virus invade the bloodstream of the host, resulting in a systemic infection with multiple organ involvement. Here we propose that basal surface release and entry of COVID-19 into and out of cells at epithelial-endothelial interface plays a key pathogenic role in severe COVID-19 disease.

Cancer cells are believed to be recognized and controlled by the immune system of the host, especially the adaptive immune system. Cancers may be initiated by a single gene defect in stem cells or regenerating cells during the replacement of old or injured tissue cells, and additional gene defect(s) then occur. To compensate for missing proteins intracellular homeostasis systems, such as proteostasis, may work with activation of new genes. The risk or predisposing factors in cancers may be related to the number of tissue cell renewals (the turnover time) and the probability of gene defect(s). Oncological symptoms may be associated with substances that are derived from antigens expressed on cancer cells and those derived from damaged cancer cells with corresponding immune reactions. In patients with cancers or other conditions, inadequate immune components to control these substances may result in chronic inflammatory or autoimmune diseases. Cancer cells communicate with host cells, including the immune cells such as T cells, for survival and proliferation and may need assistance from immune cells against intracellular infections or physicochemical insults. T cell-based immune therapeutics have been developed and clinically used in some cancers, especially in advanced cancers. We further discuss the oncogenesis, pathophysiology of cancers, and unresolved issues in tumor immunology and reinterpret the effectiveness of T cell-based therapies under the protein-homeostasis-system hypothesis.

Whether and how P2X7 receptor knockout (KO) modulates central post-stroke pain (CPSP) induced by lesions of the ventrobasal complex (VBC) of the thalamus regarding behavioral, molecular, and electrical recording parameters remains unclear. Following the experimental protocols of a rat hemorrhage CPSP model, the VBC of the thalamus of wild-type and P2X7 receptor KO mice was injected with 10 mU/0.2 μl type IV collagenase to produce an animal model of stroke-like thalamic hemorrhage. Behavioral data showed that the CPSP group induced thermal and mechanical pain, while the P2X7 receptor KO group showed reduced thermal and mechanical pain behaviors. Molecular assessments revealed that the CPSP group had lower expression of NeuN and KCC2 and higher expression of GFAP, IBA1, and BDNF. The P2X7 KO group showed lower expression of GFAP, IBA1, and BDNF and higher expression of KCC2 than the CPSP group. The expression of NKCC1, GABAa receptor, and TrkB did not differ significantly between the control, CPSP, and P2X7 receptor KO groups. Muscimol application increased multiunit numbers and [Cl-] influx in the membrane in the CPSP group, while P2X7 receptor KO reduced multiunit activity and [Cl-] outflux. P2X4 receptor expression was significantly decreased in the 100 kb but not the 50 kb site in the P2X7 receptor KO group. Altogether, the P2X7 hypothesis of CPSP was proposed, wherein P2X7 receptor KO changed the CPSP pain behavior, numbers of astrocytes and microglia, CSD amplitude of the anterior cingulate cortex and the medial dorsal thalamus, BDNF and KCC2 expression, [Cl-], and P2X4 activation in 100 kb with P2X7 receptors. The present findings have implications for the clinical treatment of CPSP symptoms.

This review delves into the significance of chemical communication in mammals, with an emphasis on the role of the vomeronasal system in sensing pheromone-mediated interactions. The vomeronasal system shapes a variety of social and sexual behaviors, including reproduction, hierarchy formation, maternal bonding, and species recognition. Intriguingly, this system presents a vast degree of evolutionary variability, more so than variations observed in the olfactory system. This adaptive diversity underscores the challenges in studying the vomeronasal system, emphasizing the need for detailed research into its neuroanatomy and functional morphology. This review traverses an array of topics central to our understanding of chemical communication in mammals. We begin with the foundational role and basic concepts of chemocommunication. This is followed by an in-depth exploration of the olfactory systems. Subsequently, the neuroanatomical underpinnings of the vomeronasal system are juxtaposed against those of the olfactory system. Our focus then shifts to an exhaustive study of the sensory element of the vomeronasal system, the vomeronasal organ, and the integrating center of this information, the accessory olfactory bulb. The discussion extends to secondary projections of both the olfactory and vomeronasal systems in the light of the dual olfactory hypothesis. The review culminates with a detailed look at four specific models of vomeronasal system organization belonging to four evolutionarily distinct mammalian families: rodents, marsupials, herpestids, and bovids. These have been meticulously analyzed by the authors, aiming to spotlight the significant morphofunctional differences stemming from the adaptive changes imprinted on the system.

Climate change has become a major concern for developing countries given the risk that it posses on energy and food independence, and on general productivity. Despite having an energy system with low carbon intensity when compared to other Latin American countries, Colombia is already facing climate change impacts and requires urgent efforts to mitigate them. As a developing country, the challenge is bigger as policies for economic growth should be in line with the global commitment of reducing greenhouse gas emissions. With the aim of contributing to the design of climate policies, this study assesses the impact of economic development on the environment by examining the validity of the Environmental Kuznets Curve hypothesis for Colombia. Statistically validated and stable autoregressive distributed lag models are estimated for three different environmental indicators: carbon dioxide emissions, methane emissions, and ecological footprint. Moreover, the effects of other variables such as urbanization, foreign direct investment, value added of agricultural and industrial sectors, and energy use are analyzed with dynamic simulations. Empirical evidence supports a long-run equilibrium relationship among investigated variables and the existence of an inverted U-shaped EKC relationship between Gross Domestic Product (GDP) and methane emissions, and GDP and ecological footprint. Shifting to renewable energy sources and leveraging the use of cleaner technologies in agricultural and industrial sectors are found to be key for economic growth without harming the environment.

This study estimates the effects of double long memory and structural breaks on the persistence level of six major cryptocurrency markets. We apply the Bai and Perron’s structural break test, Inclán and Tiao’s iterated cumulative sum of squares (ICSS) algorithm, and the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model with different distributions. The results show that long memory and structural breaks characterize the conditional volatility of cryptocurrency markets and confirm our hypothesis that ignoring structural breaks leads to an underestimation of the persistence of volatility modelling. The ARFIMA-FIGARCH model with structural breaks and a skewed Student–t distribution fits the cryptocurrency market’s price dynamics well.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

Nitrogen and phosphorous support the ecosystem by supplying nutrients to algae and aquatic plants. Having them in excess results in the eutrophication of waters creating quality problems. In the past, nitrogen has been widely investigated for wells in the context of groundwater flow. However, a national-scale nitrogen assessment in rivers and streams has not received enough attention. In this research, the Wilcoxon rank sum test, as a non-parametric hypothesis testing method, has been applied to nitrogen concentration in the form of nitrate-nitrogen and nitrite-nitrogen in rivers and streams of the Contiguous United States. This approach was particularly selected because of the non-normal and positively skewed nitrogen levels occurring in the surface flow. This method was able to identify the impaired body of waters as well as quantify the confidence, significance, and errors involved. The Northern Appalachians (NAP), Northern Plains (NPL), and Xeric (XER) ecoregions were worsening in the nitrogen-nitrate condition with NAP, and XER needed immediate actions. The nitrite-nitrogen condition did not pose an immediate threat, so mitigation plans should focus more on nitrate-nitrogen remediation. It was shown that the method was superior to the two-sample t-test by yielding lower type II errors.

Evolutionary medicine argues that disease can arise because modern conditions do not match those in which we evolved. For example, a decline in exposure to commensal microbes and gastrointestinal helminths in developed countries has been linked to increased prevalence of allergic and autoimmune inflammatory disorders (the hygiene hypothesis). Accordingly, microbial and helminthic probiotic therapies have been explored as Darwinian treatments for these disorders. A further possibility is that loss of old friend commensals also increases the sterile, aging-associated inflammation known as inflammaging, that contributes to a range of age-related diseases, including cardiovascular disease, dementia and cancer. Interestingly, Crowe et al. (2020) recently reported that treatment with a secreted glycoprotein from a parasitic nematode can protect against murine aging by induction of anti-inflammatory mechanisms. Here, we explore the hypothesis that restorative helminth therapy would have anti-inflammaging effects. Could worm infections provide broad-spectrum protection against age-related disease?

A plenty of theories on the origin of genetic codes have been proposed so far, yet all ignored the energetic driving force, its relation to the biochemical system, and most importantly, the missing “matchmaker” between proteins and nucleic acids. Here, a new hypothesis is proposed, according to which ATP is at the origin of the primordial genetic code by driving the coevolution of the genetic code with the pristine biochemical system. This hypothesis aims to show how the genetic code was produced e.g. by photochemical reactions in a protocell that derived from a lipid vesicle enclosing various life’s building blocks (e.g. nucleotides and peptides). At extant cell, ATP is the only energetic product of photosynthesis, and is at the energetic heart of the biochemical systems. ATP could energetically form and elongate chains of both polynucleotides and polypeptides, thus acting a “matchmaker” between these two bio-polymers and eventually mediating precellular biochemical innovation from energy transformation to informatization. ATP was not the only one that could drive the formation of polynucleotides and polypeptides, but favored by precellular selection. The protocell innovated a photosynthesis system to produce ATP efficiently and regularly with the aids of proteins and RNA/DNA. The completion of permanently recording the genetic information by DNA marked the dawn of cellular life operated by Darwinian evolution. The ATP hypothesis assumes or supports the photochemical origin of life, shedding light on the origins of both photosynthetic and biochemical systems, which remains largely unknown thus far. Based on ATP hypothesis, virus (like the new coronavirus) could not be the earliest life on Earth, as it has neither biochemical systems nor lipid bilayer membrane that provided relatively isolated environment for the development of protobiochemical reactions, although it owns the genetic code of a cellular life. Virus could not be a bridge between life and non-life, but is an anti-life substance, as it depletes cellular material for its own replication, and then spreads by destroying the host cells. It can be imagined that if cellular life are completely wiped out by the virus, the complete destruction of life on Earth would be inevitable.

Recent observations of the dark energy density have demonstrated the fine-tuning problem, and the challenges faced by theoretical modeling. In this study, we apply the self-similar symmetry (SSS) model, describing the hierarchical structure of the universe based on the Dirac large numbers hypothesis, to Einstein's cosmological term. We introduce a new similarity dimension, D_B, in the SSS model. Using the D_B SSS model, the cosmological constant Λ is simply expressed as a function of the cosmic microwave background (CMB) temperature. The result shows that both the gravitational constant G and Λ are coupled with the CMB temperature, which simplifies the solution of Einstein's field equations for the variable Λ-G model.

Age is an influential factor in the Second Language Acquisition (SLA). The debate on whether young learners are more successful than older learners has been going on for more than half of a century, starting from the Critical Period Hypothesis, which is based on brain structure. This study examines a range of studies revolving around the Critical Period Hypothesis in the past several decades to analyze the common SLA belief ‘Younger learners are more skillful than older learners in acquiring second language.’ The study disagrees that all younger learners are more advantageous than older learners in all areas of SLA. In fact, learners from different age categories have unique advantages and disadvantages in SLA. Moreover, the study approves a more holistic perspective on a wider range of non-biological factors that impact the success of SLA. At the end, the study puts forward a diversity of instructional methods that suit children and adolescents specifically in Vietnamese English Education context.

This paper intoduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the his- torical evolution of understaning an empirical medical process faciltated by the fractal calculus perspective. Herein we trace the analysis of the time series for heart rate varability (HRV) developed for diagnosing the cardiovascular health of a patient. This is done herein by introducing four (one empirical which en- tails three theoretical fractal models) distinct but related fractal models each one introduced to solve a particular problem arising from a fundamental defect in the previous model but in generalizing a model at one stage to resolve the problem associated with the defect another is invariably introduced by the re- placement model. It is through the utilization of the fractional calculus that the necessity for rethinking how to systematically incorporate additonal layers of complexity are revealed ultimately resulting in a 'complete' description of its empirical dynamics in fractal terms.

Alzheimer’s Disease (AD), a progressive and debilitating condition, is reported to be the most common type of dementia, with at least 55 million people believed to be currently affected. Many causation hypotheses of AD exist, yet the intriguing link between viral infection and its possible contribution to the known etiology of AD has become an attractive focal point of research for the field and a challenging study task. In this review, we will explore the historical perspective and milestones that led the field to investigate the viral connection to AD. Specifically, several viruses such as Herpes Simplex Virus 1 (HSV-1), Zika virus (ZIKV), and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), along with several others mentioned, include the various viruses presently considered within the field. We delve into the strong evidence implicating these viruses in the development of AD. We will also extend beyond these mere associations by carefully analyzing the potential mechanisms by which viruses may contribute to AD pathology. This includes but is not limited to direct neuronal infections, dysregulation of immune responses, and the impact on protein processing. Controversies and challenges of the viral-AD relationship emerge as we tease out these potential mechanisms considered. Looking forward, we emphasize the future directions the field should take to tackle the remaining unanswered questions and the glaring research gaps that persist. Overall, this review aims to provide a comprehensive survey of the past, present, and future of the potential link between viral infections and their association with AD development.

It has not been reasonably explained still now, how the “chicken and egg relationship” between gene and protein was formed, although RNA world hypothesis was proposed to aim at explaining formation process of the relationship about 40 years ago. On the other hand, GADV hypothesis advocates that life emerged after five members of the fundamental life system; cell structure, metabolism, tRNA, genetic code and gene, were piled up one by one onto immature [GADV]-proteins, which were produced by random joining of [GADV]-amino acids on the primitive Earth. Furthermore, formation process of the first (GNC)n RNA gene encoding a mature [GADV]-protein can be also reasonably explained according to the hypothesis as follows. Double-stranded (ds)-(GNC)n RNA could be produced by complementary strand synthesis of a single-stranded (ss)-(GNC)n RNA, which was formed by random joining of GNC anticodons carried by four types of AntiC-SL tRNAs. Successively, the first (GNC)n RNA gene was generated upon maturation of an immature [GADV]-protein, which was produced through expression of codon sequence on one strand of ds-(GNC)n RNA, as accumulating necessary base substitutions and raising a weak catalytic activity of the immature protein to a more active state. It is considered that, consequently, a gene encoding a mature protein, which has the “chicken and egg relationship”, was generated for the first time. Therefore, it can be concluded that the “chicken and egg relationship” was built not by formation of either one, gene or protein, but by maturation of an immature gene, which was lead by improvement of catalytic activity of an immature protein. That is, it can be concluded that the reason, why it was unable to give an answer to the question on the formation process of the “chicken-egg relationship” thus far, is because it was an unanswered question.

This paper shows that by applying the Nyquist-Shannon sampling theorem, the spatial and temporal resolution of a simulation can be no more than half the resolution of the simulating reality. This has significant implications for not only the values of the observables in the simulation but also its physical laws. This progressive halving of nested simulations coupled with the minimum resolution compatible with the production of a simulation also sets a limit to the nestedness of a lineage of simulations (it is by no means infinite). The limit of nestedness is then used to calculate the probability that we are living in a simulation assuming a single base reality. This will be shown to be significantly lower than popular expectation. A Kardashev-like scale, with three variants, is also developed to gauge the technological advancement of a civilization in relation to the extent to which it can extract information from space and time.

In light of the self-simulation hypothesis, a simple form implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in context of geometric state sum models.

In the case of vascular plants the process of water loss by leafs and water absorption by the root is well known. There is agreement on the passive nature of long-distance moisture movement in the dead cells of the xylem; however, controversy exists focusing on the long-distance water transport principle. Hales (1726) founded a view of bulk flow based on water suction after experiments with cut twigs. The previous doctrine of long-distance water transport within vessel elements and tracheid of the xylem of intact plants – the relevant cohesion theory in text books – was developed mainly by Boehm (1893), Renner (1911) and Dixon (1914) with plant artefacts. Water movement according to this theory is based on an assumed hydrodynamic bulk fluid flow in xylem in continuous water columns (free of water vapour space), under tension, according to the law of Poiseuille (see e.g. Dixon 1914). Physically hydrodynamics is part of fluid mechanics, as a result Poiseuille’s law is usually valid only for hydrodynamic bulk flow in ideal capillaries (Sutera & Skalak, 1993). Besides the basic requirement for transport, according to cohesion theory, the existence of ideal capillaries is not compatible with either: “Because vessel elements and tracheid do not stand as ideal capillaries. …” (Bresinsky et al. 2008, translated from German). Unlike ideal capillaries, the walls of vessel elements and tracheid interact with the transported water. These walls are able to function as a source or as a sink for the transported water because of interaction with the cell walls. With the interaction, vessel elements and tracheid, part of the xylem, can shrink and swell, unlike ideal capillaries. Because the xylem (in woody plants part of the wood) is inconsistent with the basic law of fluid flow, the equation of mass balance (Zimmermann et al. 2004) and cohesion theory are not strictly followed.Many plant physiologists view the cohesion theory as appropriate, however, this theory remains controver­sial, i.e. by Eisenhut (1988), Laschimke (1990) and Hahn (1993). Nultsch (1996) gives doubts referring to the present doctrine of plant water transport. Zimmermann et al. (2004) reject the cohesion theory and conclude: “... that the arguments of the proponents of the Cohesion Theory are completely misleading” (Zimmermann et al. 2004). Hence cohesion theory can be treated as inapplicable and the question arises: how does water transport in fact function? In the following, it is gone into in more detail. A sorption hypothesis of actual water transport, based on empirical fact, shall be addressed in this paper.

The SI unit of length, the Metre, is presently defined by taking the fixed numerical value of the fundamental constant `c', the invariant speed of light in vacuum. This definition has the same physical basis as the previous definition, as the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. With the atomic standard second defined in terms of the ground state hyperfine transition in Caesium-133, this definition is supposed to provide a universally reproducible standard of length. However, this relies on Einstein's singular postulate that the relative velocity of light in vacuum is an invariant constant that is independent of any inertial motion of the reference laboratory. I argue that the basis of the definition of the standard metre should be changed to the specific form, "the length of the path equal to the two-way propagation of light in vacuum during a time interval of 1/299 792 458 of a second", to be compatible and consistent with the fact that it is only the two-way relative velocity that is consistent with being an invariant. The null result in the Michelson-Morley two-way experiment, and in all such experiments to date, is consistent with a Galilean one-way propagation of light (relative velocity $c'=c\pm v$) as well as an invariant relative velocity of light. All practical methods and protocols related to the implementation of length standard involve also a two-way propagation, not conforming to the present definition. Besides, this redefinition is absolutely necessary because the relative velocity of light in one-way propagation is indeed Galilean, and not an invariant, as proved here in multiple ways including a direct experiment.

The precise mathematical description of gaze patterns is still an unsettled matter of debate. This can, consequently, affect the analysis of this type of data in its practical applications. In this scope, we show evidence that a Lévy-flight description of eye-gaze trajectories is not only appropriate but its scale invariant properties are remarkably useful to assist in diagnosing children with Attention Deficit and Hyperactivity Disorder (ADHD), alongside with the usual cognitive tests. Using this picture, we find that the distribution of the characteristic exponent of Lévy-flights statistically is different in children with ADHD. Furthermore, we observe that these children deviate from a strategy that is considered optimal for searching processes, in contrast to non-ADHD children. We focus on the case where both eye-tracking data and data from a cognitive test are present and show that the study of gaze patterns in children with ADHD can help in identifying this condition. Since eye-tracking data can be gathered during cognitive tests without needing extra time-consuming specific tasks, we argue that it is in prime position to provide assistance in the arduous task of ADHD diagnosing.

Ad- and desorption forces move water in living xylem/wood from the root to the leaf thermodynamically. The doctrine of plant water transport, the so-called cohesion- or cohesion-tension theory, postulates however that the process is physically based on a hydraulic fluid flow with negative pressure in water conducting tubes originating from the leaves. Lower pressure (suction) driven volume flow is physically a branch of mechanics. Moisture absorbed from the soil via the root is thought to be pulled up the stem by the leaves in continuous and tensioned threads of water. It is assumed that the hydraulic Hagen/Poiseuille flow law, derived for tubes, applies in the xylem. In a textbook of botany you can find the opinion: "Just as the pipes of a water pipe supply necessary water to each household, leaf nerves supply water and nutrient salts to each individual cell.” (Translated from German). Many plant physiologists consider this hydraulic principle to be correct, but it does not remain unchallenged. Doubts are repeatedly expressed. The question arises: How does water transport actually take place? It is shown how the diffusive/adsorption transport principle works. The partial dehydration (desorption) of the plant, driven by the diffusive process of transpiration, forms a combined concentration and adsorption-site gradient for water in the xylem matrix. Especially with open stomata the lowest moisture concentration and the highest number of adsorption-sites for water (sites with free van der Waals forces), can be found in the mesophyll cell walls at the liquid/vapor boundary in the leaf. The water taken up by the root moves spontaneously in the direction of this boundary and can thus partially or completely compensate for the existing concentration- and adsorption-site- differences for water. Thus, a thermodynamic overlapping diffusive/adsorptive movement of moisture along the stationary xylem/wood takes place. After the introduction and a review of some controversies with cohesion theory, the physiology of the processes associated with long-distance water displacement is mentioned below. A thermodynamic adsorption hypothesis of the natural water transport in plants, based on known facts, is presented.