Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte-Carlo stochastic integration, approximated, or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy and the Kullback-Leibler divergence of mixtures. We illustrate the versatile method by reporting on our experiments for approximating the Kullback-Leibler divergence between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures, and Gamma mixtures.

In this research paper, we implement the theory of the primorial function, to develop the Supremum and Infimum bounds for the sum of (log(p))². There are, however, considerable computational difficulties related to these bounds. Therefore, from a pragmatic point of view, a set of Upper and Lower bounds had been developed to bypass this issue. Despite the increased estimation error, the Upper and Lower bounds are still considered sufficiently accurate, while facilitating an easy and fast computation of the estimate of the sum.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

In actuarial practice, the modeling of total losses tied to a certain policy is a non-trivial task. Traditional parametric models to predict total losses have limitations due to complex distributional features such as extreme skewness, zero inflation, multi-modality, etc., and the lack of explicit solutions for log-normal convolution. In the recent literature, the application of the Dirichlet process mixture for insurance loss has been proposed to eliminate the risk of model misspecification biases; however, the effect of covariates as well as missing covariates in the modeling framework is rarely studied. In this article, we propose novel connections among covariate-dependent Dirichlet process mixture, log-normal convolution, and missing covariate imputation. Assuming an individual loss is log-normally distributed, we develop a log skew-normal Dirichlet process to approximate the log-normal sum. As a generative approach, our framework models the joint of outcome and covariates, which allows to impute missing covariates under the assumption of missingness at random. The performance is assessed by applying our model to several insurance datasets, and the empirical results demonstrate the benefit of our model compared to the existing actuarial models such as the Tweedie-based generalized linear model, generalized additive model, or multivariate adaptive regression spline.

Background: Cloud-native software systems often have a much more decentralized structure and many independently deployable and (horizontally) scalable components, making it more complicated to create a shared and consolidated picture of the overall decentralized system state. Today, observability is often understood as a triad of collecting and processing metrics, distributed tracing data, and logging. The result is often a complex observability system composed of three stovepipes whose data is difficult to correlate. Objective: This study analyzes whether these three historically emerged observability stovepipes of logs, metrics and distributed traces could be handled more integrated and with a more straightforward instrumentation approach. Method: This study applied an action research methodology used mainly in industry-academia collaboration and common in software engineering. The research design utilized iterative action research cycles, including one long-term use case. Results: This study presents a unified logging library for Python and a unified logging architecture that uses the structured logging approach. The evaluation shows that several thousand events per minute are easily processable. Conclusion: The results indicate that a unification of the current observability triad is possible without the necessity to develop utterly new toolchains.

We evaluate the nested sum $\sum_{a_{n - 1} = c}^{a_n } {\sum_{a_{n - 2} = c}^{a_{n - 1} } { \cdots \sum_{a_0 = c}^{a_1 } {x^{a_0 } } } }$ where $a_n$ and $c$ are any integers and $x$ is a real or complex variable. Consequently, we evaluate multiple sums involving the terms of a general second order sequence, the Horadam sequence (W_j (a, b; p, q)), defined for all non-negative integers j by the recurrence relation W₀ = a, W₁ = b; W_j = pW_j−1 − qW_j−2 (j≥2); where a, b, p and q are arbitrary complex numbers, with p ≠ 0, q ≠ 0.

In this paper, we present sums and partial sums of Horadam sequences via generating functions which extends a recent result of Prodinger.

This study provides a comprehensive comparison of the Peter Chew Sum method and Newton's Sum in Quadratic Root Function Computations. Both methods offer significant advancements by alleviating the need for memorization of multiple formulas. However, when confronted with higher-order quadratic root functions such as the calculation of power 33. Newton's Sum method proves cumbersome due to its requirement of all previous answers for final computation, leading to increased steps and error risks. In contrast, the Peter Chew Sum method simplifies the computational process by requiring only a few previous answers, resulting in a more straightforward series of operations. We contextualize our analysis within the historical progression of mathematical techniques, highlighting the transformative leap represented by the Peter Chew Sum method in quadratic root function computations. Peter Chew Sum addressing the limitations of Newton's Sum , especially concerning higher-order functions such as the calculation of power 256. Furthermore, study demonstrates that the innovative approach of the Peter Chew Sum method not only simplifies complex computations but also fosters enhanced conceptual understanding among students. In conclusion, study findings underscore the profound impact of the Peter Chew Sum method on quadratic root function computations.

The log data generated during the operation of a software system contains information about the system, and using logs for anomaly detection can detect system failures in a timely manner. Most of the existing log anomaly detection methods are specific to a particular system, have cold start problems, and are sensitive to updates in log format. In this paper, we propose a log anomaly detection method LogBD based on pre-training model and domain adaptation, which uses the pre-training model BERT to learn the semantic information of logs, and can solve the problems caused by multiple meaning words and log statement updates. An anomaly detection method LogBD based on distance to determine anomalies is constructed based on domain adaptation, using TCN networks to extract common features of different system logs and map them to the same hypersphere space. Finally, experiments are conducted on two publicly available datasets to evaluate the method, and the experimental results show that the method can better solve the log instability problem and has some improvement in the cross-system log anomaly detection effect.

The lattice reduction aided(LRA) algorithm has attracted widely attention of researchers in MIMO systems because of its low complexity to achieve full diversity. However, most lattice reduction auxiliary algorithms do not directly improve system performance. In this paper, a modified lattice reduction successive interference cancellation (SIC) algorithm is proposed for MIMO OFDM system mild changing the complexity of LRA algorithm. At present, the MMSE SQRD algorithm has the problem of regarding too much useful signals as the residual interference which cannot be cancelled by successive interference cancellation. Since the diagonal elements of useful signals are non-zero, the components of the symbols to be detected still present in the interference term, treating all the signals as interference will be resulted in performance loss. To solve this problem, the modified matrix is proposed.by moving this symbol component into the signal term, the proposed algorithm can provide the better performance than MMSE SQRD algorithm. The analysis shows that the LRA-MMSE-SIC algorithm of proposed in this paper significantly improves the system performance with mild increasing the complexity. The simulation results show that the performance of the proposed algorithm is improved by 1dB and 8dB compared with the comparison algorithm when the bit error rate is 10−3.

This study analyzed the technical efficiency of barley production by smallholder farmers in Meket district, Amhara National Regional State, Ethiopia. A cross sectional data from a sample of 123 barley producers during the 2016/17 production season was collected by applying two stage random sampling. To address the objective of the study, both descriptive statistics and econometric models were used to analyze the data. The trans-log functional form of the production function simultaneously with single stage estimation approach was used to estimate the production of barley output and technical inefficiency factors. The estimated stochastic production frontier model indicated that input variables such as fertilizer, human labor and oxen power were the significant variables to increase the quantity of barley output while, barley seed had a negative effect. The estimated mean levels of technical efficiency of the sample farmers were about 70.9% which revealed that, presence of a room to increase their technical efficiency level on average by 29.1% with the existing resources. The discrepancy ratio gamma indicated that 63% of the total variation from the frontier comes due to technical inefficiency while, the remaining 37% comes due to factors outside the control of farmers. Among the hypothesized factors that affect technical inefficiency; education level, extension contact and number of barley plots significantly and negatively affected technical inefficiency score. Besides, practice of crop rotation, distance of residence from the nearest main market, total expenditure and soil fertility was found to have a positive and significant effect. Hence, emphasis should be given to decrease the inefficiency level of those more inefficient farm households via experience sharing among the farmers and usage of improved or certified barley seed. Besides to this, policies and strategies of the government should be directed towards increasing farmers’ education, improve the system of input distributions and institutional facilities.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

The orthogonal matrix with cube be symmetric is a common class of matrices with important properties. We pay attention to this kind of matrices. By using the close relationship between the eigenvalues of a matrix and the trace of its power, we obtain the algorithm for its all possible different eigenvalues and multiplicities. The calculation formula is expressed only by the trace of a matrix and its power, avoiding solving the characteristic polynomial. The method is simple and practical. Furthermore, a new essential characterization for the sum of orthogonal matrix pairs being orthogonal is given as well.

Continuous discovery and update of applications or their boundaries running in cloud environments in an automatic way is a highly required function of modern data center ops solutions. Prior attempts to address this problem within various products or projects were/are applying rule-driven approaches or machine learning techniques on specific types of data − network traffic as well as property/configuration data of infrastructure objects, which all have their drawbacks in effectively identifying roles of those resources. The current proposal (ADLog) leverages log data of sources, which contain incomparably richer contextual information, and native constructs of VMware Aria Operations for Logs in terms of Event Types and their distributions to group those entities, potentially automatically enrich with indicative tags, and recommend for further management tasks and policies. Our methods discriminate not only diverse kinds of applications, but also their specific deployments thus providing hierarchical representation of the applications in time and topology. For several applications under Aria Ops management in our experimental test bed, we discover those in terms of similarity behavior of their components with a high accuracy. The validation of the proposal paves the path for an AI-driven solution in the cloud management scenarios.

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

This work presents the design and analysis of a novel metal-insulator-insulator-metal (MIIM) rectenna with an added meta lens on top of it for efficient and robust infrared (IR) energy harvesting at 28.3 THz. To ensure maximum transfer of the captured IR radiations by an antenna with better impedance matching, the log-spiral antenna terminals are used as rectenna electrodes while two different insulators are placed between its feeding terminals to form the MIIM rectenna. A split ring-based resonating metasurface is designed and placed on the top of the MIIM rectenna to focus the incoming electromagnetic radiations. The characterization of the MIIM rectenna with added meta lens, in terms of absorbed E-field, is performed for the four different work function metals (gold aluminum, silver, and copper) as well as four combinations of aluminum oxide, titanium oxide, zinc oxide, and copper oxide as insulators. The focusing of illuminating IR radiations by the integrated meta lens to the rectenna structure enhances its field-capturing characteristic by more than 400% as compared to conventional structures. In addition, the proposed design shows improved rectification properties in terms of better impedance matching and rectification efficiency, particularly for the best configuration of Au-Al2O3-Cu2O-Cu rectenna with added metasurface. Future applications of this study include the development of efficient IR energy harvesting systems for remote sensing, wireless communication, and other IoT devices.

Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.

In the literature, estimation of weighted extropy are least considered. In this paper some non parametric estimators of weighted extropy are given. The validation and comparison of the estimators are implemented with the help of simulation study and data illustration. The usefulness of the estimators are demonstrated using real data sets.

Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.

We show broadband sum-frequency generation (SFG) in the Green-Yellow-Orange-Red spectral range using bismuth triborate, BiB3O6 crystal (BIBO) as nonlinear material. We perform a noncollinear phase-matching configuration within BIBO crystal using the remaining light behind the second harmonic generation stage and the infrared idler of an optical parametric amplifier (OPA). The obtained mixing radiation of ultrafast light sources to generate femtosecond pulses across 520.5 to 742.5 nm region is observed. SFG spectrum from single-pass cross-correlation intensity over such visible range is showed. The SFG wavelengths as a function of tunable wavelength idler OPA agrees with the expectations of parametric conversion condition and open the door to practical multi-beam or multi-color sum-frequency generators.

We present an ontology log-OLOG- representation of the classical Miller-Urey experiment, usually considered as a paradigm for spontaneous generation of biomolecules on the prebiotic Earth and also, as a key in understanding the chemical evolution phenomena linked to the origins of life. Ologging The Miler-Urey experiment enables us, through the categorical notion of fibre product or pullback, to define the concept of Biogenic Space, as a space containing low complexity biogenic units subjected to appropriate physical and chemical conditions, facilitating the synthesis of highly complex organic molecules. Also, we characterize the Biogenic Space as a concrete universal object that could be associated with the preconditions for life inside various structures in the universe such as exoplanets and exomoons located in habitable zones, but also in interstellar and intergalactic organic clouds.

Numerous fractured hydrocarbon reservoirs exist in the metamorphic basement of the Pannonian Basin in Hungary. Many decades of experience in production have proven that these reservoirs are highly compartmentalised, resulting in a complex mosaic of permeable and impermeable domains situated next to each other. Consequently, in most fields, only a small amount of the total hydrocarbon reserve can be extracted. This paper aims to locate the potential migration pathways inside the most productive basement reservoir of the Pannonian Basin, using a multiscale approach. To achieve this, evaluation well-log data, DFN modelling and a composition analysis of fluid trapped in a vein-filling zeolite phase are combined. Data on a single well are presented as an example. The results of the three approaches indicate the presence of two highly fractured intervals separated by a barely fractured amphibolite. The two zones are probably part of the communicating fracture system inside the single metamorphic mass. The gas analysis further specifies the migrated fluids and indicates hydrocarbons of a composition similar to that of the recently produced oil. Consequently, we conclude that the two zones do not only form an ancient migration pathway but are also members of a more recent hydrocarbon system.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

Soil-borne beneficial microbes establish symbioses with plant hosts, and play key roles during growth and development therein. In this study, two fungal strains, FLP7 and B9, were isolated from the rhizosphere microbiome associated with Choy Sum (Brassica rapa var. parachinensis) and barley (Hordeum vulgare), respectively. Sequence analyses of the internal transcribed spacer and 18S ribosomal RNA genes combined with colony and conidial morphology identified FLP7 and B9 to be Penicillium citrinum strains/isolates. Plant-fungus interaction assays revealed that isolate B9 showed significant growth promotion effects in Choy Sum plants cultivated in normal soil, as well as under phosphate-limiting conditions. In comparison to the mock control, B9-inoculated plants showed a 34% increase in growth in aerial parts, and an 85% upsurge in the fresh weight of roots when cultivated in sterilized soil. The dry biomass of such fungus-inoculated Choy Sum increased by 39% and 74% for the shoots and roots, respectively. Root colonization assays showed that P. citrinum associates directly with the root surface but does not enter or invade the root cortex of the inoculated Choy Sum plants. Preliminary results also indicated that P. citrinum can promote growth in Choy Sum via volatile metabolites too. Interestingly, we detected relatively higher amounts of gibberellins and cytokinins in axenic P. citrinum culture filtrates through liquid-chromatography mass-spectrometry analyses. This could plausibly explain the overall growth induction in P. citrinum-inoculated Choy Sum plants. Furthermore, the phenotypic growth defects associated with the Arabidopsis ga1 mutant could be chemically complemented by the exogenous application of P. citrinum culture filtrate, which also showed accumulation of fungus-derived active gibberellins. Our study underscores the importance of transkingdom beneficial effects of such mycobiome-assisted nutrient assimilation, and beneficial fungus-derived phytohormone-like metabolites in induction of robust growth in urban farmed crops.

Hypertension stands as the foremost modifiable risk factor for cardiovascular disorders in South Asia. This research demonstrates the superiority of statistical models over traditional approaches in identifying clinical risks related to hypertension. Leveraging individual-level data from the Bangladesh Demographic and Health Survey (2017-18), a unified dataset was created. Adhering to JNC7 and ACC/AHA guidelines for hypertension classification, two prominent regression models were employed to estimate the prevalence of undiagnosed hypertension. A substantial 16% of hypertension cases in Bangladesh remain undetected. The study identifies undiagnosed hypertension as a heightened risk, particularly among the youth and residents of Sylhet and Rangpur divisions. Statistical models exhibit efficacy in discerning undiagnosed hypertension and associated factors in South Asia. Subsequent investigations should incorporate biological markers to enhance statistical models and ascertain their practicality.

Digital music is one of the most important things in market due to the music royalties’ distribution in Korea. As the music market is transformed to the digital music market such as download the music and streaming, the distribution of music royalties starting from online service provider (OSP) has come to be a highly important part for music rights holders. One of the most important issues in current music royalties’ distribution in Korea is the unfair way of music royalties due to indiscriminative repeat streaming of digital music. To prevent this, music log usage data from several OSPs was collected in day-based system, however, there was a limit to identify detailed information on the use of music in current state. This paper analyzed the structural problems and limitations of settlement of music royalties, and provides a structure in which there can be transparent settlement and distribution between users and rights holders as one of the institutional measures. We’ll also propose various AI-based applications using music log usage data. The proposed system will hopefully be used for public purposes.

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

Given a fuzzy normed space $ \left( X,N \right) $‎, ‎we will introduce the notion of fuzzy near best approximation within a relative distance $ \rho \geq 0 $‎. ‎Some basic properties are characterized and also many examples for illustration are presented‎.

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 $m$.

Factorization reduces computational complexity and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize global joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for trees and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is their common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development in factorization algorithms for physical modeling of complex molecular systems.

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

In this paper, we give all non splitting bi-unitary superperfect polynomials divisible by one or two irreducible polynomials over the prime field of two elements. We prove the nonexistence of odd bi-unitary superperfect polynomials over F2.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

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).

In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.

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.

The fast and reliable processing of medical images is of paramount importance to adequately generate data to feed machine learning algorithms that can prevent and diagnose health issues. Here we benchmark different compressed sensing techniques applied to magnetic resonance imaging as a means to reduce the acquisition time spent in the collection of data and signals that form the image. We show that by using these techniques, it is possible to reduce the number of signals needed and, therefore, substantially decrease the time to acquire the measurements. To this end, we have considered and compared different algorithms: the Iterative Re-Weighted Least Squares, the Iterative Soft Thresholding Algorithm, the Iterative Hard Thresholding Algorithm, the Primal Dual Algorithm and the Log-Barrier Algorithm. We have implemented such algorithms in different analysis programs that have been used to perform the reconstruction of the images and found that the Iterative Soft Thresholding Algorithm gives the optimal results. We found that the images obtained with this algorithm have less quality than the original ones, but the quality is good enough to distinguish each body structure and detect any health problems.

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

We study various properties of the polygonal numbers; such as their recurrence relations; fundamental identities; weighted binomial and ordinary sums; partial sums and generating functions of their powers; and a continued fraction representation for them. A feature of our results is that they are presented naturally in terms of the polygonal numbers themselves and not in terms of arbitrary integers; unlike what obtains in most literature.

The aim of this article is to summarize recent bioinformatic and statistical developments applicable to NMR-based metabolomics. Extracting relevant information from large multivariate datasets by statistical data analysis strategies may be of considerable complexity. Typical tasks comprise for example classification of specimens, identification of differentially produced metabolites, and estimation of fold changes. In this context it is of prime importance to minimize contributions from unwanted biases and experimental variance prior to these analyses. This is the goal of data normalization. Therefore, special emphasize is given to different data normalization strategies. In the first part, we will discuss the requirements and the pros and cons for a variety of commonly applied strategies. In the second part, we will concentrate on possible solutions in case that the requirements for the standard strategies are not fulfilled. In the last part, very recent developments will be discussed that allow reliable estimation of metabolic signatures for sample classification without prior data normalization. In this contribution special emphasis will be given to techniques that have worked well in our hands.

Balanced and coordinated economic development across regions is a critical goal of regional economic development and new-type urbanization in China. However, few studies have examined economic growth convergence clubs at the county level. To extend the research on convergence clubs, this research applies a log t convergence test and a dynamic spatial ordered Probit model (DSOP) to endogenously identify economic growth convergence clubs in counties and to examine the influence of initial states and structures on club convergence probability. The study sample covers 2286 counties of China from 1992 to 2010. The results show significant convergence club patterns at the county levels, resulting in the gradual formation of six convergence clubs. The DSOP estimation results show that per capita fixed assets, population density and industrialization have promoted convergence club formation to varying degrees.

Introduction: This empirical study investigates the impact of two distinct mathematical problem-solving methods – the Algebraic Formula Method and the Newton Sum Method – on enhancing ChatGPT's competence in effectively solving quadratic root functions. The integration of Artificial Intelligence (AI) into mathematical problem-solving has paved the way for innovative approaches. In this study, we delve into the Algebraic Formula Method and the Newton Sum Method, essential techniques for solving quadratic root functions. We aim to showcase the profound influence of these methods on ChatGPT's capacity to excel in solving quadratic equations. Evidence Through concrete evidence, we demonstrate ChatGPT's adept utilization of the Newton Sum Method for quadratic root function calculations. While ChatGPT can compute quadratic root functions of the form α^15 + β^15 using this method, its proficiency in using algebraic formula methods typically extends only up to α^4 + β^4. This marked discrepancy underscores the pivotal role that different methods play in amplifying the AI system's mathematical capabilities Result The results of this study provide concrete evidence of ChatGPT's superior utilization of the Newton Sum Method for calculating quadratic root functions. The model adeptly computes expressions of the form α^15 + β^15 using this method, while its proficiency using algebraic formula methods is generally limited to α^4 + β^4. This striking discrepancy underscores the transformative impact that different methods can have on elevating the AI system's mathematical prowess. Conclusion :Pushing Boundaries: Pioneering Novel Maths Approaches for Overcoming Limitations in AIThis study serves as an illuminating testament to the significance of pioneering innovative methodologies, rules, theorems, or formulas to surmount the current limitations in AI systems like ChatGPT. These innovative pursuits hold the key to unlocking the untapped potential that lies within, propelling AI systems to greater heights of proficiency. In essence, they offer a strategic pathway towards expanding the capabilities of AI and pushing the boundaries of what can be achieved. Discussion The outcomes derived from this study underscore the significant influence wielded by the method selection in augmenting the mathematical competencies of ChatGPT. Particularly noteworthy is the application of the Newton Sum Method, which surfaces as a compelling exemplar. This method serves as a pivotal conduit through which the model surpasses its prior constraints, allowing it to venture into the realm of calculations entailing higher exponents. Implications and Future Research: These findings not only contribute to AI's mathematical competencies but also emphasize the need for pioneering new methods, rules, theorems, or formulas to further enhance AI systems like ChatGPT. Future research could explore the development of novel mathematical techniques tailored to AI systems, thus expanding their capabilities across diverse problem-solving domains.

Finding the ideal statistical method for grouping phenological data is always an important step for breeders to draw correct conclusions from it possibly. In this paper, K-cluster analysis is presented as a perfect tool for grouping phenological data. The present research was performed based on the phenological data of 61 strawberries (Fragaria × ananassa) cultivars of different geo-graphical origins grown in Estonian conditions. Groups of strawberry cultivars were deter-mined according to flowering and ripening time: early, middle and late, based on the sum of ef-fective temperatures above +5°C. The result of the K-cluster analysis carried out in this way makes it possible to precisely plan the ripening time of berries of different strawberry cultivars. Using such analysis data, it is possible to combine with different early, mid or late strawberry cultivars to extend the picking period. Also, this technique can be used to study the effect of cli-matic changes occurring over the years on the phenology of strawberry cultivars grown in the region.

The current work aims to develop an approximation of the slice of Minkowski sum of finite number of ellipsoids, sliced up by an arbitrarily oriented plane in Euclidean space $\mathbb{R}^3$ that, to the best of the author's knowledge, has not been addressed yet. This approximation of the actual slice is in a closed form of an explicit parametric equation in the case that the slice is not passing through those zones of the Minkowski surface with high curvatures, namely the "corners". At corners with high curvatures an alternative computational algorithm is introduced in which a family of ellipsoidal inner and outer bounds of the Minkowski's sum are used to construct a "narrow strip" for the actual slice of Minkowski sum. This strip can narrow persistently for a few more number of constructing bounds to precisely coincide on the actual slice of Minkowski sum. This algorithm is also applicable to the cases of slice of Minkowski sum of ellipsoids with high aspect ratio. In line with the main goal, some ellipsoidal inner and outer bounds of the Minkowski sum are reviewed, including the so called "Kurzhanski's" bounds. Also some ellipsoidal approximations are suggested for the Minkowski sum, which they can be used, as well as the inner and outer bounds, in calculation of the suggested parametric approximation of the slice of Minkowski sum.

In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

We construct a real square system related to a given over-determined real system. We prove that the simple real zeros of the over-determined system are the simple real zeros of the related square system and the real zeros of the two systems are one-to-one correspondence with the constraint that the value of the sum of squares of the polynomials in the over-determined system at the real zeros is identically zero. After certifying the simple real zeros of the related square system with the interval methods, we assert that the certified zero is a local minimum of the sum of squares of the input polynomials. If the value of the sum of the squares of the input polynomials at the certified zero is equal to zero, it is a zero of the input system. As an application, we also consider the heuristic verification of the isolated zeros of polynomial systems and their multiplicity structures. Notice that a complex system with complex zeros can be transformed into a real system with real zeros.

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. It has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7. Any polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7, we give an explicit construction of a Pogorelov and a non-Pogorelov polytopes. Any Pogorelov polytope different from Löbel polytopes can be constructed from the 5- or the 6-barrel by cuttings off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes there is a stronger result. Any fullerene different from the 5-barrel and the (5, 0)-nanotubes can be constructed by only cuttings off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result can not be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cuttings off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons.

The Gulf of Suez is a sedimentary rift-basin with thick evaporites and complex structural settings that presents challenges to achieving quality imaging based on seismic reflection data. Such subsurface settings and the lack of 3D seismic data poses challenges in building reservoir models to guide hydrocarbon exploration and development, especially in southern parts the Gulf of Suez. This study attempts to overcome the challenges of both 2D seismic interpretation and building a static reservoir model of two Miocene reservoir formations, Ras Ghara Field, Southern Gulf of Suez. Integration of well log data analysis of nine wells and regional-tectonics cognizant 2D seismic interpretation of nineteen 2D seismic lines enabled a reliable 3D static reservoir model. The Miocene reservoir characterization reveals heterogeneity in lithofacies distribution, with thick evaporite sequences causing seismic reflection distortions. Significant hydrocarbon accumulations are associated with horst fault blocks. The Miocene reservoirs demonstrate effective porosity of 14-33%, water saturation of 16-65%, and hydrocarbon saturation of 35-84%. Two new prospects are identified based on structure, facies distribution, and petrophysical results, with estimated original oil in place (OOIP) of 2,002,404 stock tank barrels (STB) and 1,175,580 STB for the Kareem Formation, and 6,302,916 STB and 2,841,894 STB for the Rudeis Formation.

Context: Anomaly detection in a data center is a challenging task, having to consider different services on various resources. Current literature shows the application of artificial intelligence techniques to either log files or monitoring data: the former created by services at run time, while the latter produced by specific sensors directly on the physical or virtual machine. Objectives: We propose a model that exploits information both in log files and monitoring data to identify patterns and detect anomalies over time. Methods: The key idea is to use on one side natural language processing solutions to detect problems at service level, extracting words that represent anomalies. Clustering and topic modeling techniques have been used to identify patterns and group them with respect to topics. On the other side time series anomaly detection technique has been applied to sensors data in order to combine problems found in the log files with problems stored in the monitoring data. Results: We have tested our approach on a real data center equipped with log files and monitoring data that can characterize the behaviour of physical and virtual resources in production. We have observed a correspondence between anomalies in log files and monitoring data, e.g. an increase in memory usage or machine load. The results are extremely promising. Conclusion: Our model requires to integrate site administrators' expertise in order to consider all critical scenario in the data center and understand results properly.

The circuitry of the summarized "floating" differential stages (FDS) based on complementary field-effect transistors with a control p-n junction (CJFET), intended for use in low-noise analog microcircuits, for example, operational amplifiers. The results of modeling the flow characteristics of one of the CJFET FDSs in the LTSpice XVII environment at low temperatures (down to -197 ⁰С) and exposure to a neutron flux in the range of 1e13 ÷ 1e15 n / cm² are presented.

A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the c.d.f. of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.

Log collection and storage is a crucial process for enterprises around the globe. Log analysis helps identify potential security breaches and, in some cases, is required by law for compliance. However, enterprises often delegate these responsibilities to third-party Cloud Service Providers (CSPs), where the logs are collected and processed for anomaly detection and stored in a data warehouse for archiving. Prevalent schemes rely on plain (unencrypted) data for anomaly detection. More often, these logs can reveal sensitive information about an organization or the customers of that organization. Hence, it is best to keep it encrypted at all times. This paper presents "SigML++," an extension of work done in "SigML." We utilize Fully Homomorphic Encryption (FHE) with the Cheon-Kim-Kim-Song (CKKS) scheme for supervised log anomaly detection on encrypted data. We use an Artificial Neural Network (ANN) based probabilistic polynomial approximations using a Perceptron with linear activation. We probabilistically approximate the Sigmoid activation function (σ(x)) in the encrypted domain for the intervals [−10,10] and [−50,50]. Experiments show better approximations for Logistic Regression (LR) and Support Vector Machine (SVM) for low-order polynomials.

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.

Utilizing unmanned aerial vehicles (UAVs) to facilitate wireless communication has emerged as a viable and promising strategy aimed at enhancing both current and prospective wireless systems. This approach offers many advantages by establishing line-of-sight connections, optimizing operational efficiency, and enabling flexible deployment capabilities in various terrains. Thus, in this paper, we investigate UAV communication in a relaying network in which a UAV helps communication between a source and two destination users while flying to a location. To have a complete view of our proposed system, we consider both orthogonal multiple access as OFDM and non-orthogonal multiple access (NOMA) scenarios. Moreover, we apply successive convex optimization (SCO) and the Block-coordinate gradient descent (BCGD) for the sum-rate optimization problems to improve the system performance under constraints of total bandwidth and total power at the ground base station and UAV. The experimental results validate that the achievable secrecy rates are notably enhanced by using our proposed algorithms and show optimal trends for critical parameters, such as transmit powers, the flight trajectory and speed of UAV, and resource allocation of OFDM and NOMA.

The European pear is a climacteric fruit species characterized by high storability. 'Conference', a pear cultivar very popular on the market, can be stored in a CA room without major losses for half a year. However, for ‘Conference’ storage to be successful, the fruit must be harvested fully developed even before it enters the climatic maturation phase. Harvested too early or too late, pears will taste bad, have physiological disorders and will be poorly storable. Among the various methods used to determine the optimal harvest date, the degree-days method, which relies of the sum of active temperatures, seems to be relatively accurate and easy to apply. During 11 years of study, ‘Conference’ pears were harvested on 4 dates (every 4-5 days) chosen based on measurements and observations, and then, after a six-month storage period, the optimum harvest date was determined. During the growing season, temperature was measured using an automatic weather station to calculate the sum of active temperatures from full bloom to the optimal harvest date. Measurements made after storage were analysed and the sum of active temperatures needed for the proper development of ‘Conference’ pear was calculated to be 2469 degree days. The calculations are very accurate because the dispersion calculated using the standard deviation was only 20 °. The base temperature with the smallest error was 0 °. On the basis of the study results, this method can be recommended as useful for determining the optimal harvest date.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

The issue of workplace toxicity constitutes a major problem for employers, employees and society at large. Toxicity in a workplace context relates to damaging behaviours perpetrated by individuals and organisations that netatively impact on the health and wellbeing of others. Workplace toxicty is habitually associated with activities such as bullying, harrassment, unethical and even illegal acts. In this article, today’s workplace is likenened to a cage where ambition and greed drive people to engage in toxic behaviour to fight for whatever scarce rewards are on offer. Set against a backdrop of continuous demands on employees in a era of constant change and challenge, leadership practice in the 21st century is understandably seeped in complexity. Whilst conditions of scarcity are in fact constructed by employers in today’s lean environments, workplace toxicity has significant implications for organisational leaders in terms of work place disputes, absenteeism and litigation etc. Twentieth century hierarchial and autocratic leadership models are now deemed to be both obsolete and wholly inadedgate to inform leadership practice in the knowledge era. This conceptual article looks at the efficacy of complexity leadership theory (CLT) in empowering today’s leader to better understand and address 21st century workplace toxicity.

In the present work, we provide an electronic structure based method for the “on-the-fly” deter- mination of vibrational sum frequency generation (v-SFG) spectra. The predictive power of this scheme is demonstrated at the air-water interface. While the instantaneous fluctuations in dipole moment are obtained using the maximally localized Wannier functions, the fluctuations in polar- izability are approximated to be proportional to the second moment of Wannier functions. The spectrum henceforth obtained captures the signatures of hydrogen bond stretching, bending, as well as low-frequency librational modes.

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

In this study, we consider a Lambert series whose coefficients are the sum of divisors function. Utilizing the Lambert series in the sequel we introduce a normalized linear operator JR_(α,β) (z) by applying the convolution with Rabotnov function. We then, acquire sufficient conditions for JR_(α,β) (z) to be Univalent, Starlike and Convex respectively. In each component of this study, we expand the derived results by applying two Robin's inequalities, one of which is equivalent to the Riemann hypothesis.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

The Stochastic Optimisation Software (SOS) is a Java platform facilitating the algorithmic design process and the evaluation of metaheuristic optimisation algorithms. It reduces the burden of coding miscellaneous methods for dealing with several bothersome and time-demanding tasks such as parameter tuning, implementation of comparison algorithms and testbed problems, collecting and processing data to display results, measuring algorithmic overhead, etc. SOS provides numerous off-the-shelf methods including 1) customised implementations of statistical tests, such as the Wilcoxon Rank-Sum test and the Holm-Bonferroni procedure, for comparing performances of optimisation algorithms and automatically generate result tables in PDF and LaTeX formats; 2) the implementation of an original advanced statistical routine for accurately comparing couples of stochastic optimisation algorithms; 3) the implementation of a novel testbed suite for continuous optimisation, derived from the IEEE CEC 2014 benchmark, allowing for controlled activation of the rotation operator. each testbed function. Moreover, this article comments on the current state of the literature in stochastic optimisation and highlights similarities shared by modern metaheuristics inspired by nature. It is argued that the vast majority of these algorithms are simply a reformulation of the same methods and that metaheuristics for optimisation should be simply treated as stochastic processes with less emphasis on the inspiring metaphor behind them.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials D_m(n,k) and U_m(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n^2m+1.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Kinetic parameters of SO2 adsorption on unburned carbons from lignite fly ash and activated carbons based on hard coal dust were determined. The model studies were performed using the linear and non-linear regression method for the following models: pseudo first and second-order, intraparticle diffusion, and chemisorption on a heterogeneous surface. The quality of the fitting of a given model to empirical data was assessed based on: R2, R, Δq, SSE, ARE, χ2, HYBRID, MPSD, EABS, and SNE. It was clearly shown that it is the linear regression that more accurately reflects the behaviour of the adsorption system, which is consistent with the first-order kinetic reaction – for activated carbons (SO2+Ar) or chemisorption on a heterogeneous surface – for unburned carbons (SO2+Ar and SO2+Ar+H2O(g)+O2) and activated carbons (SO2+Ar+H2O(g)+O2). Importantly, usually, each of the approaches (linear/non-linear) indicated a different mechanism of the studied phenomenon. A certain universality of the χ2 and HYBRID functions has been proved, the minimization of which repeatedly led to the lowest SNE values for the indicated models. Fitting data by any of the non-linear equations based on the R or R2 functions only, cannot be treated as evidence/prerequisite of the existence of a given adsorption mechanism.