Road networks are monitored to evaluate their decay level and the performances regarding ride comfort, vehicle rolling noise, fuel consumption, etc. In this study, an Inertial Measurement Unit is proposed by using a low-cost three-axis Micro-Electro-Mechanical Systems accelerometer and a GPS instrument, which are connected to a Raspberry Pi Zero W board and embedded inside a vehicle to monitor indirectly the road condition. To assess the level of pavement decay, the comfort index awz defined by the ISO 2631 standard was considered. Considering 21 km of roads, with different levels of pavement decay, validation measures made using the proposed IMU, another pre-assembled IMU, and a Road Surface Profiler were performed. Therefore, comparisons between awz determined with accelerations measured on the two different IMU are made; in addition, also correlations between awz, International Roughness Index (IRI), and Ride Number (RN) were performed. The results were shown very good correlations between the awz calculated with the proposed IMU and ones in the other IMU. In addition, the correlations between awz and IRI and RN were showed promising results, considering the use and the costs of the proposed IMU as a reliable method to assess the pavements decay in road networks where the use of traditional systems is difficult and/or not cheap.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

The Soil Conservation Service - Curve Number (SCS-CN) method is extensively used to calculate the runoff from rainfall over a large catchment over the world. Slope is an important criterion for runoff but a very few attempts have been made to evaluate the effect of slope on the CN with runoff potential. The objective of this paper is to summarise the historical review on the effects of slope on CN and runoff potential in various regions by the hydrologists. This paper also depicts that how the various researchers proved the importance of consideration of slope for CN and runoff estimation. In addition, paper highlights the key features of research in future like to classify the watersheds on slope based CN, accurate Antecedent Moisture Condition (AMC) and proper initial abstraction in the various regions etc. Considering these parameters an accurate runoff estimation can be predicted and managed properly in the urban watersheds.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

Micro-technology has played a substantial role in bioscience, biomedical and biotechnological research due to its core advantages in modern science and engineering. It has created unique development in various sectors of bio-research and upsurges the efficacy of research at the molecular level in recent years. Microfluidic technology makes it possible to manipulate sample volumes at the micro- and nano-level (called nanofluidics) with terrific control outside in vivo cellular microenvironment, enabling the reduction of discrepancies between in vivo and in vitro environments as well as reducing reaction time and cost. In this review, we discuss various effective integrations of microfluidic technologies into biotechnology and its paradigmatic significance in bio-research, supporting mechanical and chemical in vitro cellular micro-environment. Specific innovations relating to the application of microfluidics to advance microbial life, solitary and co-cultures along with a multiple-type cell culturing, cellular communications, cellular interactions and population dynamics are discussed.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

Human number understanding is thought to rely on the analogue number system (ANS), working according to Weber’s law. We propose an alternative account, suggesting that symbolic mathematical knowledge is based on a discrete semantic system (DSS), a representation that stores values in a semantic network, similar to the mental lexicon or to a conceptual network. Here, focusing on the phenomena of numerical distance and size effects in comparison tasks, first we discuss how a DSS model could explain these numerical effects. Second, we demonstrate that DSS model can give quantitatively as appropriate a description of the effects as the ANS model. Finally, we show that symbolic numerical size effect is mainly influenced by the frequency of the symbols, and not by the ratios of their values. This last result suggests that numerical distance and size effects cannot be caused by the ANS, while the DSS model might be the alternative approach that can explain the frequency-based size effect.

The existence of multiple copies of genes is a well-known phenomenon. A gene family is a set of sufficiently similar genes, formed by gene duplication. In earlier works conducted on limited number of completely sequenced and annotated genomes it was found that size of gene family and size of genome are positively correlated. Additionally, it was found that several atypical microbes deviated from the observed general trend. In this study, we reexamined these associations on a larger dataset consisting of 1484 prokaryotic genomes and using several ranking approaches. We applied ranking methods in such a way that genomes with lower number of paralogs would have lower rank. Until now only simple ranking methods were used; we applied the Kemeny optimal aggregation approach as well. Regression and correlation analysis were utilized in order to accurately quantify and characterize the relationships between measures of paralog indices and genome size. In addition, boxplot analysis was employed as a method for outlier detection. We found that, in general, all paralog indexes positively correlate with an increase of genome size. As expected, different groups of atypical prokaryotic genomes were found for different types of paralog quantities.

A ~3-kb deletion-type DNA copy-number variation (CNV, esv3587290) located at intron 7 of the VANGL1 gene (1p13.1, MIM*610132) has been proposed as a genetic factor for developing lupus nephritis (LN) in adult systemic lupus erythematosus (SLE) patients across European-descent populations, but its replication in other ethnicities has been inconsistent and its association with LN in childhood-onset SLE (cSLE) remains unknown. Here, we performed an exploratory association study in a sample of 66 unrelated cSLE Mexican patients (11 males, 55 females; ages 7.8 to 18.6 years). Two stratified groups were compared: cSLE patients with (N=37) or without (N=29) LN, as diagnosed by renal biopsy (N=15), proteinuria (N=33), urinary protein:creatinine ratio >0.2 (N=34), and erythrocyturia and/or granular casts in urinary sediment (N=16). For esv3587290 CNV genotyping, we performed an end-point PCR assay with breakpoint confirmation by Sanger sequencing. We also determined the allelic frequencies of the esv3587290 CNV in 181 deidentified ethnically-matched individuals (reference group). The obtained genotypes were tested for Hardy-Weinberg equilibrium (HWE) by 2 test. Associations between LN and esv3587290 CNV were tested by calculating the Odds Ratio (OR) and using Pearson's 2 tests with a 95% confidence interval and p≤0.05. Contrary to the results described in European-descent populations, the esv3587290 CNV showed a significant protective effect against LN development (OR 0.14, 95% CI 0.066-0.31, p≤0.05), whereas the wild-type homozygous VANGL1 genotype showed a risk trend for LN development (OR 2.15, 95% CI 0.7711-6.18, p≤0.05). Finally, we characterized the precise breakpoint of the esv3587290 CNV as NG_016548.1(NM_138959.3):c.1314+1339_1315-897del (https://databases.lovd.nl/shared/variants/0000918418#00025811) in our population. This report supports the notion that a broad genetic heterogeneity underlies the susceptibility for developing LN.

Keywords: pelvic ultrasound, follicle number per ovary, FNPO, ovarian volume, PCOM, upper normal limits, referral population

This study describes the seasonal course of denitrifying and nitrate reducing bacteria in a dimictic mesotrophic lake (Lake Scharmützelsee, Brandenburg, Germany) within a three-year period from 2011 to 2013. The bacterial cell numbers were quantified by fluorescence microscopy, most probable number (MPN) and PCR dependent quantification of the chromosomal 16S rDNA and of the nirS and nirK gene copy number. The highest seasonal differences (up to three orders of magnitudes) has been measured by MPN in the epilimnion. This variation was not reflected by PCR dependent approaches or direct microscopical enumeration. At adverse conditions (low temperature and/or low nitrate concentrations), the differences between MPN and gene copy numbers increased up to five orders of magnitudes and decreased to one magnitude at favorable environmental conditions. These results can be explained best by an increasing ratio of viable but not cultivable (VBNC) cells or dead cells at impairing conditions. In the hypolimnion, the courses of MPN and nir gene copy numbers were similar. This can be explained by higher feeding pressure and therefore smaller amounts of dormant cells. In the pelagial in general, the total cell numbers enumerated by either microscopical or molecular approaches were similar. In the sediment, more than 99 % of the DNA was obviously not related to viable bacteria but was rather “dead DNA” in dead cells or adsorbed to particle surfaces.

This study considers the values of the credit payments that are made at random values for both payment size and number. The simultaneous existence of the two random variables increases the total value of the volatility of the payment process. The dependence for the simultaneous influence of the two random variables is derived by applying conditional probabilistic formulations. Formal relations apply to animal husbandry credit payments. The credit policy was analyzed for the cases of regular payments and with a stochastic number of payments. A recommendation for the upper level of credit payments is proposed based on a model predictive approach using historical payment data. A credit management algorithm is derived, in which decision-making for credit payments is formally derived and numerically discussed. The application of derived quantitative relations is empirically applied to real data on animal husbandry. The recommendations from the dependencies obtained allow a reduction in the mean values of credit payments, which correspond to a reduction in the credits used for business management, without a change in business policy.

We show that the compound samarium hexaboride is a strong topological insulator using the eigenvalues of the space inversion operator in the low-energy limit of the periodic Anderson model. Additionally, we assume the presence of the ferromagnetic exchange interaction (M). A Dirac cone like feature in the surface state energy spectra is observed for M equals zero in a certain parameter range. For M not equal to zero, there is no Kramers degeneracy. We have been able to show that this phase corresponds to the quantum anomalous Hall state by calculating Berry curvature and the Chern number. Using Floquet theory, we further show that the access to a novel state with broken time reversal symmetry is possible due to the normal incidence of circularly polarized optical field on the surface of the compound despite M being absent.

(1)Background:The purpose of the study was conducted to investigate the recovery of heart rate according to the performance level and rest interval conditions during 65%1RM bench press exercise;(2)Methods:The subjects of this study were eight healthy male college studentsin their 20 (years) attending University C. 1RM was measured before theexperiment, and the exercise sequence of six rest intervals (30sec, 1, 2, 3, 4,5min) was randomly selected and cross-distribution experiment. The experimental measurement was conducted a total of six times according to the rest interval condition (six conditions) once every 3 days to minimize the learning effect. The data was verified with repeated measures Two-way ANOVA and Contrast's repeated method was applied for post-comparison;(3)Results: First, the amount of exercise and the number of repetitions statistically substantially dropped (p<.001) as the number of sets rose, and a greater decline was shown when the rest periods got shorter. Second, the heart rate after exercise was increased significantly (p<.01) as the set progressed in the long rest interval conditions (4, 5min), and the heart rate after rest was increased statistically significantly (p<,05) as the set progressed in the short rest interval conditions (30sec, 1min). Third, the heart rate recovery rate (%) was able to perform more repetitions than in the short rest interval condition due to the relatively high physiological recovery of the neuromuscular and circulatory system under the long rest interval condition;(4)Conclusions: Therefore, according to the rest conditionduring the 65%1RM bench press exercise conducted in this study, the restinterval condition of 2~3min may be effective in improving muscular endurance,and the rest interval condition of 4~5min may be effective in improving muscular hypertrophy. As a result of this study, there was a significant difference in exercise performance (repetition) and physiological recovery depending on the rest interval condition according to the set progress during the same intensity resistance exercise. Through this, it is judged that it is possible to adjust the amount of exercise appropriate for the purpose of training by adjusting not only the intensity during resistance exercise but also the rest interval between sets.

This work presents a design and model of the thermo-hydrodynamic behavior applying CFD for pin-fin heat sink with square shape (rectangular fin profile), through a novel pin arrangement that improves heat removal in the system. The novelty consist in the insertion of a deflector row that will help to direct the flow, so it hits the rectangular cross-sectional fins the presents in the system. The heat sink model is placed in channel designed in which air flows as suitable medium, and its overall performance is investigated. In addition, a constant heat flux is applied to the bottom wall of the heat sink model, equal values and amounts that​ correspond to the heat fluxes generated by current electronic equipment and devices. The numerical results of the global thermal resistance, the pressure drop and the Nusselt number are reported. The results allow determining best arrangement or geometry configuration, location and functionality of the fin-deflectors were collocated for evaluate thermal-hydraulic efficiency of system.

Next Generation Sequencing (NGS), now widely used in the clinical setting, offers an efficient and comprehensive molecular approach for patients with Familial hypercholesterolemia (FH). Although the dominant form of disease is mostly due to low-density lipoprotein receptor (LDLR) small-scale pathogenic variants, approximately 10% of molecularly defined FH cases are due to Copy Number Variations (CNVs). Here, we report a novel large deletion of the LDLR gene involving exons 4–18, identified by bioinformatic analysis of NGS data in an Italian family. A long PCR strategy was employed for breakpoint region analysis where an insertion of 6 nucleotides (TTCACT) was found. Two Alu sequences, identified within intron 3 and exon 18, could underlie the identified rearrangement by a Nonallelic Homologous Recombination (NAHR) mechanism. NGS proves to be a powerful tool used to precisely identify CNVs, in addition to small-scale variants in FH-related genes. At this purpose, the use and implementation of this cost-effective, efficient molecular approach meets the clinical need for personalized diagnosis in FH cases.

: Polymer single screw extrusion is a major industrial processing technique used to obtain plastics products. To assure high outputs, tight dimensional tolerances, and excellent product performance, extruder screws may show different design characteristics. Barrier screws, which contain a second flight in the compression zone, have become quite popular as they promote and stabilize polymer melting. Therefore, it is important to design efficiently extruder screws and decide whether a conventional screw will do the job efficiently, or a barrier-screw should be considered instead. This work uses multi-objective evolutionary algorithms to design conventional and barrier screws (Maillefer screws will be studied) with optimized geometry. Processing of two polymers, Low Density Polyethylene and Polypropylene, is analyzed. A methodology based on the use of Artificial Intelligence (AI) techniques, namely data mining, decision making and evolutionary algorithms, is presented and utilized to obtain results with practical significance, based on relevant performance measures (objectives) used in the optimization. For the various case studies selected, Maillefer screws were generally advantageous for processing LDPE, while for PP the use of both types of screws would be feasible.

The proliferation of devices for the Internet of Things (IoT) and their implication in many activities of our lives have led to a considerable increase in concern about the security of these devices, posing a double challenge for designers and developers of products. On the one hand, the design of new security primitives, suitable for resource-limited devices, that can facilitate the inclusion of mechanisms and protocols to ensure the integrity and privacy of the data exchanged over the Internet. On the other hand, the development of techniques and tools to evaluate the quality of the proposed solutions as a step prior to their deployment, as well as to monitor their behavior once in operation against possible changes in operating conditions arising naturally or as a consequence of a stress situation forced by an attacker. To address these challenges, this paper first describes the design of a security primitive that plays an important role as a component of a hardware-based root of trust, as it can act as a source of entropy for true random number generation (TRNG) or as a physical unclonable function (PUF) to facilitate the generation of identifiers linked to the device on which it is implemented. The work also illustrates different software components that allow carrying out a self-assessment strategy to characterize and validate the performance of this primitive in its dual functionality, as well as to monitor possible changes in security levels that may occur during operation as a result of device aging and variations in power supply or operating temperature. The designed PUF/TRNG is provided as a configurable IP module, which takes advantage of the internal architecture of the Xilinx Series-7 and Zynq-7000 programmable devices and incorporates an AXI4-based standard interface to facilitate its interaction with soft- and hard-core processing systems. Several test systems that contain different instances of the IP have been implemented and subjected to an exhaustive set of on-line tests to obtain the metrics that determine its quality in terms of uniqueness, reliability, and entropy characteristics. The results obtained prove that the proposed module is a suitable candidate for various security applications. As an example, an implementation that uses less than 5% of the resources of a low-cost programmable device is capable of obfuscating and recovering 512-bit cryptographic keys with virtually zero error rate.

The exact similarity solutions (also called as special exact solutions) of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, no similarity solutions for two dimensional turbulent boundary layers have been reported in the literature. With the help of dimensional analysis and invariance principle, Prandtl mixing length $\ell=\kappa y$ for one dimensional turbulent boundary layer is extended to $\ell(x,y)=\kappa y (1-\frac{y}{\delta})\sqrt{\frac{\nu}{U\delta}} $ for the two dimensional turbulent boundary layers, furthermore, with a similarity transformation, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation $f'''+ ff''+\beta(1-f'^2)+\kappa^2[\eta^2(1-\eta)^2f''|f''|]'=0$. As an application, similarity solutions of the two dimensional turbulent boundary layer on a flat plate at zero incidence have been studied in detail. To solve the ordinary differential equation numerically, a complete Maple code is provided.

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no similarity solutions (special exact solutions) have ever been found. In the light of Blasius' pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. By author's Maple code, we numerically solve the ordinary differential equation and produce some useful quantities.

Fibroepithelial lesions (FL) of the breast, in particular Phyllodes tumors (PT) and fibroadenomas, pose a significant diagnostic challenge. There are no generally accepted criteria that distinguish benign, borderline, malignant PT, and FA. Combined genome-wide DNA methylation and copy number variant (CNV) profiling is an emerging strategy to classify tumors. We compiled a series of patient-derived archival biopsy specimens reflecting the FL spectrum and histological mimickers including clinical follow-up data. DNA methylation and CNVs were determined by well-established microarrays. Comparison of the patterns with a pan-cancer dataset assembled from public resources including "The Cancer Genome Atlas" (TCGA) and "Gene Expression Omnibus" (GEO) suggests that FLs form a methylation class distinct from both control breast tissue as well as common breast cancers. Complex CNVs were enriched in clinically aggressive FLs. Subsequent fluorescence in situ hybridization (FISH) analysis detected respective aberrations in the neoplastic mesenchymal component of FLs only, confirming that the epithelial component is non-neoplastic. Of note, our approach could lead to the elimination of the diagnostically problematic category of borderline PT and allow for optimized prognostic patient stratification. Furthermore, the identified recurrent genomic aberrations such as 1q gains (including MDM4), CDKN2a/b deletions and EGFR amplifications may inform therapeutic decision-making.

The most common index for representing structural condition of the pavement is the structural number. The current procedure for determining structural numbers involves utilizing falling weight deflectometer and ground-penetrating radar tests, recording pavement surface deflections, and analyzing recorded deflections by back-calculation manners. This procedure has two drawbacks: 1. falling weight deflectometer and ground-penetrating radar are expensive tests, 2. back-calculation ways has some inherent shortcomings compared to exact methods as they adopt a trial and error approach. In this study, three machine learning methods entitled Gaussian process regression, m5p model tree, and random forest used for the prediction of structural numbers in flexible pavements. Dataset of this paper is related to 759 flexible pavement sections at Semnan and Khuzestan provinces in Iran and includes “structural number” as output and “surface deflections and surface temperature” as inputs. The accuracy of results was examined based on three criteria of R, MAE, and RMSE. Among the methods employed in this paper, random forest is the most accurate as it yields the best values for above criteria (R=0.841, MAE=0.592, and RMSE=0.760). The proposed method does not require to use ground penetrating radar test, which in turn reduce costs and work difficulty. Using machine learning methods instead of back-calculation improves the calculation process quality and accuracy.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

We review and assess the classic SIR and SEIR epidemiological models regarding possible applications to the COVID-19 pandemic. In spite of numerous more complicated models, we show how the qualitative features of the solution to the SIR and SEIR models continue to provide valuable public health insights in some scenarios. Using estimated COVID-19 data as of this date, the SEIR model shows that if it were possible to reduce R₀ from 2.5 to 1.25 through social distancing and other measures, the maximum fraction of the population that would become infected at any particular time would drop from 17% to 4%, provided that all of the model assumptions are satisfied. Finally, we compare the classic SIR model with a recent stochastic model with favorable results. Since this comparison underscores the importance of underlying connectivity assumptions, we conclude with Monte-Carlo simulations with specific connectivity that reproduce the classical SIR model with standard incidence.

Reliability assessment in traditional power distribution systems has played a key role in power system planning, design, and operation. Recently, new information and communication technologies have been introduced in power systems automation and asset management, making the distribution network even more complex. In order to achieve efficient energy management, the distribution grid has to adopt a new configuration and operational conditions that are changing the paradigm of the actual electrical system. Therefore, the emergence of the cyber-physical systems concept to face future energetic needs requires alternative approaches for evaluating the reliability of modern distribution systems, especially in the smart grids environment. In this paper, a reliability approach that makes use of failure modes of power and cyber network main components is proposed to evaluate risk analysis in smart electrical distribution systems. We introduce the application of Failure Modes and Effects Analysis (FMEA) method in future smart grid systems in order to establish the impact of different failure modes on their performance. A smart grid test system is defined and failure modes and their effects for both power and the cyber components are presented. Preventive maintenance tasks are proposed and systematized to minimize the impact of high-risk failures and increase reliability.

A novel plasma source of pulsed electrolyte cathode atmospheric pressure discharge (pulsed-ECAD) driven by an alternating current (AC) power supply coupled with a high voltage diode was generated, and the discharge was generated in the open-to-air atmosphere between a metal electrode and a small-sized flowing liquid cathode. The spatial distribution of plasma temperatures (excitation, vibrational and rotational) of the pulsed-ECAD were investigated. The electron excitation temperature of H T_exc(H), vibrational temperature of N₂ T_vib(N₂), and rotational temperature of OH T_rot(OH) were measured as 4900±36-6800±108 K, 4600±86-5800±100 K and 1050±20-1140±10 K, respectively. Meanwhile, the temperature characteristics of dc solution cathode glow discharge (dc-SCGD) were also studied for comparison with pulsed-ECAD. The effects of operating parameters, including discharge voltage and discharge frequency, on the plasma temperatures were investigated. The electron number density determined in the discharge system and dc-SCGD were within the range (3.8–18.9) ×10¹⁴ cm^-3 and 2.6×10¹⁴-17.2×10¹⁴ cm^-3, respectively.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

This paper proposes the optimization method for the minimum mass of permanent magnet (PM) excited homopolar inductor alternator (HIA) with air-gap winding used for high-speed driving system. The calculation results show that there is an optimal value for shell diameter and unit number of HIA to make the mass to be smallest. A 1 MW at 22000 rpm PM excited HIA is designed. The analytical results are verified by the FEM simulations. The losses, temperature rise, rotor stress and modal of the PM excited HIA are also analyzed. The calculation results show that the solid rotor eddy-current losses and the temperature rise of PM excited HIA are acceptable. Also the rotor strength is adequate, and the rotor system is a stiffness rotor, and it can safely operate. Finally, the comparison between PM excited HIA and permanent magnet rotor machine is discussed.

The mathematical modelling of reverse logistics inventory systems ignores that returned items may arrive out of sequence, i.e. with different number of remanufacturing times. Moreover, such modelling assumes that the retuned items may retain the same quality upon recovery regardless of how many times they have been previously remanufactured. This paper develops a new mathematical expression of the percentage of retuned items that can be remanufactured a finite number of times. The proposed expression is modelled as a function of the expected number of times an item can be remanufactured on its life cycle and the number of times an item can be technologically (or optimally) remanufactured based on its quality upon recovery. The model developed in this paper considers joint production and remanufacturing options. The return rate is a varying demand dependent rate, which is a decision variable with demand, product deterioration, manufacturing and remanufacturing rates being arbitrary functions of time. The model considers the initial inventory of returned items in the mathematical formulation, which enables decision makers to adjust all functions and input parameters for subsequent cycles. Illustrative examples indicate that dependent purchasing price of recovery items and the incorporation of remanufacturing investment cost significantly impact on the optimal remanufacturing policy.

Classical enzyme kinetics are summarized and linked with modern discoveries here. The time course of sequential catalytic events by biological macromolecular enzyme is analyzed at the molecular level; the relationships between catalytic efficiency (turnover number), catalytic rate/velocity, the amount of time taken and physical/biochemical conditions of the system are discussed. This writing tries to connect the microscopic molecular behavior of enzyme to kinetic data obtained in experiment, and the hypothesis proposed here provide an interpretation to previous experimental observations and can be testified by future experiments.

An iterative outlier elimination procedure based on hypothesis testing, commonly known as Iterative Data Snooping (IDS) among geodesists, is often used for the quality control of the modern measurement systems in geodesy and surveying. The test statistic associated with IDS is the extreme normalised least-squares residual. It is well-known in the literature that critical values (quantile values) of such a test statistic cannot be derived from well-known test distributions, but must be computed numerically by means of Monte Carlo. This paper provides the first results about Monte Carlo-based critical value inserted to different scenarios of correlation between the outlier statistics. From the Monte Carlo evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, overidentifications and statistical overlap associated with IDS in the presence of a single outlier. Based on such probability levels we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for the case where IDS is in play. MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances that the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection, but the lower the rates of outlier identification. For that case, the larger the Type I Error, the larger the ratio between MIB and MDB. We also highlight that an outlier becomes identifiable when the contribution of the measures to the wrong exclusion rate decline simultaneously. In that case, we verify that the effect of the correlation between the outlier statistics on the wrong exclusion rates becomes insignificant from a certain outlier magnitude, which increases the probability of identification.

The main purpose of this paper is to introduce and investigate degenerate Poisson distrib- ution which is a new extension of the Poisson distribution including the degenerate expo- nential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and di¤erence operator property. Moreover, we acquired the skewness and the kurtosis for the degenerate Poisson distribution. We also derive its moment generating function by which we define the degenerate Bell polynomials and give a connection for these polynomials related to the unsigned Stirling numbers of the …rst kind.

By imposing the condition of non-vanishing expectation values for the amplitude and phase of field operators, pure quantum states are identified composed of two consecutive number states. These pure states also deliver noise-free radiation modes restricting the “half-photon noise” to the expectation value of the lowest level of dynamic and coherent number states. As a result, instantaneous phase-sensitive amplification of photons is easily controlled and direct evaluation of time or distance - varying wavefront distributions of photons and phases can be carried out for sub-Poissonian distributions of photons without the need for quasi-probabilities.

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faa di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal inequalities, product inequalities, logarithmic convexity for multi-order logarithmic numbers and polynomials by virtue of some properties of completely monotonic functions.

Traditional gene set enrichment analysis falters when applied to large genomic domains, where neighboring genes often share functions. This spatial dependency creates misleading enrichments, mistaking mere physical proximity for genuine biological connections. Here we present Spatial Adjusted Gene Ontology (SAGO), a novel cyclic permutation-based approach, to tackle this challenge. SAGO separates enrichments due to spatial proximity from genuine biological links by incorporating the genes' spatial arrangement into the analysis. We applied SAGO to various datasets in which the identified genomic intervals are large, including replication timing domains, H3K9me3 and H3K27me3 large domains, HiC compartments and lamina associated domains (LADs). Intriguingly, applying SAGO to prostate cancer samples with large copy number alteration (CNAs) domains eliminated most of the enriched GO terms, thus helping to accurately identify biologically relevant gene sets linked to oncogenic processes, free from spatial bias.

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl's mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data

In the framework of mean field approximation, we consider a spin system consisting of two interacting sub-ensembles: spins interactions with in each sub-ensemble are ferromagnetic, while the inter-ensemble interactions are antiferromagnetic. We define the effective number of the nearest neighbors, and show that if the two sub-ensembles have the same effective number of the nearest neighbors, the classical form of critical exponents (, , , ) gives way to the non-classical form (, , , ), and the scaling function changes simultaneously. We demonstrate that this system allows for two second-order phase transitions and two first-order phase transitions. We observe that an external magnetic field does not destroy the phase transitions, but only shifts their critical points, allowing for control of the system’s parameters. We discuss the regime when the magnetization as a function of the magnetic field develops a low-magnetization plateau, and show that the height of this plateau abruptly rises to the value of one when the magnetic field reaches a critical value. Our analytical results are supported by a Monte Carlo simulation of a three-dimensional layered model.

Investment management is a common process and practice used for achieving a desirable investment goal or outcome. Investment assessment should be carried out at various stages of project realization in accordance with capital investment volume. Investment risk management implies the effective control of all procedures and monitoring of risks in all phases of the investment project. Because of the reason that a single indicator in probability calculation of achieving optimal return from the investment does not exist, performing sufficiently reliable estimates of the quality of investments becomes a tedious task. There are many indicators, factors, and criteria required for consideration to reach the effective solution of the investment problem. Unfortunately, the systematic variation of economic situations in the marketplace stipulates the continuous and frequent changes of investment conditions and environment in which the investor should act and operate. Hence, the rules required for providing a reasonable quality of investment projects can be based only on investor’s management strategy and rely on investor’s intuition and practice. The importance of classification in investment management and decision making process is undeniable. The objects to be classified are described using assessments in accordance with various criteria which can be both quantitative and qualitative. With a competent formulation of the investment process, both methods are used in parallel. There exist various decision making approaches for the investment management, and simple additive weighting (SAW) is one of the well-known multi-criteria decision making (MCDM) methods aiming to provide an optimal decision for decision maker when solving various real-life problems, and particularly, investment problem. In this paper, fuzzy simple additive weighting (FSAW) method in group decision making is applied to undertake the capital investment expenditure for purchasing cars with the purpose of renting them to the public. The development of existing FSAW method is accomplished and this process involves the sensibility of outcomes to changes in the rate of fuzziness represented with decisions taken. Eventually, the degree of fuzziness involved in an analysis that directly attempts to model the immanent vagueness and imperfectness in particular precedency judgments made, is determined. A numerical example illustrates the importance and effectiveness of the suggested approach with the aim of ranking alternatives and hence, determining the most preferred alternative in MCDM problem.

Firstly, we present a more explicit formulation of the complete system $D(N)$ of representatives of Manin's symbols over $\mathbb{Q}$, which was initially given by Shimura. Then we establish a bijection between $D(M)\times D(N)$ and $D(MN)$ for $(M,N)=1$, which reveals a recursive structure between Manin's symbols of different levels. Based on Manin's complete system $\Pi (N)$ of representatives of cusps on $X_0(N)$ and Cremona's characterization of the equivalence between cusps, we establish a bijection between a subset $C(N)$ of $D(N)$ and $\Pi (N)$, and then establish a bijection between $C(M)\times C(N)$ and $C(MN)$ for $(M,N)=1$. We also provide a recursive structure for elliptical points on $X_0(N)$. Based on these recursive structures, we obtain recursive algorithms for constructing Manin symbols over $\mathbb{Q}$, cusps and elliptical points on $X_0(N)$. This gives rise to a more efficient algorithms for modular elliptic curve. As direct corollaries of these recursive structures, we present a recursive version of the genus formula and an elementary proof of formulas of the numbers of $D(N)$, cusps and elliptical points on $X_0(N)$.

The APOE locus has garnered significant clinical interest because of its association with Alzheimer's disease (AD) and longevity. This genetic association appears across multiple genes in the APOE locus. Despite the apparent differences between AD and longevity, both conditions share a commonality of aging-related changes in mitochondrial function. This commonality is likely due to accumulative biological effects, partly exerted by the APOE locus. In this study, we investigated changes in mitochondrial structure/function-related markers using oxidative stress-induced human cellular models and postmortem brains (PMBs) from individuals with AD and normal controls. Our results reveal a range of expressional alterations, either up- or down-regulated, in these genes in response to oxidative stress. In contrast, we consistently observed an upregulation of multiple APOE locus genes in all cellular models and AD PMBs. Additionally, the effects of AD status on mitochondrial DNA copy number (mtDNA CN) varied depending on APOE genotype. Our findings imply a potential coregulation of APOE locus genes, possibly occurring within the same topologically associating domain (TAD) of the 3D chromosome conformation. The coordinated expression of APOE locus genes could impact mitochondrial function, contributing to the development of AD or longevity. Our study underscores the significant role of the APOE locus in modulating mitochondrial function and provides valuable insights into the underlying mechanisms of AD and aging, emphasizing the importance of this locus in clinical research.

Single-layer core corrugated sandwich panels generally consist of a corrugated core and two layers of panels, while multi-layer core corrugated sandwich panels are formed by stacking multiple layers of panels with multiple layers of core layers. In this study, integrated multilayer core corrugated sandwich panels with different shapes of corrugated cores (triangular, trapezoidal, and rectangular) and the different number of core layers were fabricated using 3D printing technology, and the mechanical behavior of such multilayer core corrugated sandwich panels under quasi-static three-point bending was investigated using experiments and numerical simulations. The effects of core shape and number of core layers on the bending deformation process, damage mode, load carrying capacity, and bending energy dissipation capacity of multilayer core sandwich panels are discussed. Parametric design of multilayer triangular core corrugated sandwich panels was also carried out by finite element software ABAQUS. It was found that a new multilayer corrugated sandwich panel with a multi-layer core is better than the single core shape multilayer corrugated sandwich panel in terms of bending load capacity, energy dissipation capacity and deformation capacity can be obtained through the combination design of different core shapes.

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

Ostreococcus tauri is a simple unicellular green alga representing an ecologically important group of phytoplankton in oceans worldwide. Modern molecular techniques must be developed in order to understand the mechanisms that permit adaptation of microalgae to their environment. We present for the first time in O. tauri a detailed characterization of individual genomic integration events of foreign DNA of plasmid origin after PEG-mediated transformation. Vector integration appears to be random, occurring mainly at a single locus, and thus confirming the utility of this technique for insertional mutagenesis. While the mechanism of double-stranded DNA repair in the O. tauri model remains to be elucidated, we clearly demonstrate by genome resequencing that the integration of the vector leads to frequent structural variations (deletions/insertions and duplications) and some chromosomal rearrangements in the genome at the insertion loci, and often within the vector sequence itself. From these observations, we speculate that a non-homologous end joining-like mechanism is required during random insertion events, as described in plants and other freshwater algal models. PEG-mediated transformation is therefore a promising molecular biology tool, not only for functional genomic studies, but also for biotechnological research in ecologically important marine algae.

Fluid mechanics of flow in hydrophobic, rectangular microchannels with finite aspect ratios is of paramount importance. In such microchannels, not only the effect of the side walls should be taken into account, but also the classical assumption of no-slip boundary condition (BC) is no longer valid at the solid-liquid interface. Accordingly, slip flow can occur in microchannels fabricated from surfaces with low wetting conditions, hydrophobic surfaces. Determining the interactions of liquid molecules adjacent to solid surface is still a challenging issue, and it is especially important in small scale domains. Herein, the fluid mechanics of flow through rectangular hydrophobic microchannels has been reconsidered by taking into account the general Navier-slip BCs at the solid-liquid interface. For fully developed incompressible flow in microchannels at low Reynolds number, partial differential equation (PDE) of the momentum equation simplifies to the classical Poisson equation. Accordingly, by analytically solving the Poisson equations with general Navier-slip BCs, the most general forms of velocity distributions, flow rate, friction factor and Poiseuille number have been obtained.

In this study, the field measurement-based validation of a novel sediment transport calculation method is presented. River sections with complex bed topography and inhomogeneous bed material composition highlight the need for an improved sediment transport calculation method. The complexity of the morphodynamic features can result in the simultaneous appearance of the gravel and finer sand dominated sediment transport (e.g. parallel bed armoring and siltation) at different regions within a shorter river reach. For the improvement purpose of sediment transport calculation in such complex river beds, a novel sediment transport method was elaborated. The base concept of it is the combined use of two already existing empirical sediment transport models. The method was already validated against laboratory measurements. The major goal of this study is the verification of the novel method with a real river case study. The combining of the two sediment transport models is based on the implementation of a recently presented classification method of the locally dominant sediment transport nature (gravel or sand transport dominates). The results are compared with measured bed change maps. The verification clearly refers to the meaningful improvement in the sediment transport calculation by the novel manner in case of spatially varying bed content.

The heavy demand of water resources from the Zarqa River Basin (ZRB) has resulted in a base-flow reduction of the River from 5m³/s to less than 1m³/s. This paper aims at predicting Curve Numbers (CN) as a baseline scenario and proposing restoration scenarios for ZRB. The method includes classifying the soil type and land use, predicting CNs, and proposing CN restoration scenarios. Prediction of existing CNs will be in parallel with the runoff prediction using the US Army Corps of Engineers HEC-1 Model, and Rainfall-Runoff Model (RRM). The models have been set up at the land use distribution of 0.3% water body, 9.3% forest and orchard, 71% mixture of grass, weeds, and desert shrubs, 7.0% crops, 4.0% urban areas, and 8.4% bare soil. The results show that CN under dry condition are 59, 78 under a normal condition and 89 under a wet condition. During vegetation period, CN are 52, 72 and 86 for the dry, normal and wet condition respectively. The restoration scenarios; CN decreases runoff, and increases soil moisture when using the contours, terraces and crop residues. Analyzing results of CN scenarios will be a fundamental tool to support end-users related to their targets to achieve watershed restoration.

The water cushion depth of stilling basin with shallow-water cushion is a key factor that affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the water cushion is considered as “shallow” has not be stated clearly for now, and only conceptual description is provided. This paper attempts to specify the best water cushion depth based on the flow regime of hydraulic jump and underflow speed; namely, in case of critical hydraulic jump in the basin, the best water cushion depth is located where the minimum distance to the bottom plate of the stilling basin is 1/5~1/4 of the water cushion depth. The theoretical analysis indicates, at different inclinations of discharge chute (θ) and depth ratios of inlet (m), instead of monotonic change, the Froude number (Fr) at inlet of the stilling basin with shallow-water cushion firstly reduces and then increases as the flow velocity at discharge chute inlet (V) increases; the parameters of inflection point (critical flow velocity and critical Fr) increase as the inclinations of discharge chute (θ) and depth ratios of inlet (m) increase. Such regularity is the theoretical basis for selecting representative study cases. The reliability of the large eddy simulation calculation results are verified by a model test; in the paper, 30 cases including five different Froude numbers and six shallow-water cushion depths are selected, for calculating the hydraulic factors such as flow profile, flow regime and flow velocity in the stilling basin with shallow-water cushion; and the varying pattern between the best depth of stilling basin with shallow-water cushion (depth-to-length ratio) and the inflow Froude number is obtained which indicates that the best depth of stilling basin with shallow-water cushion varies little as the change of the Froude number before reaching the critical Froude number; however, the best depth-to-length ratio of stilling basin with shallow-water cushion increases as the Froude number increases after the critical Froude number is reached. The study results in this paper are of reference significance to design and calculation of the stilling basin with shallow-water cushion.

Euler’s product formula over the primes and Euler’s zeta function equate to enshrine the Fundamental Theorem of Arithmetic that every integer > 1 is the product of a unique set of primes. The product formula has no zero, and with a domain ≤1 Euler’s zeta diverges. Dirichlet’s eta function η(s), negates alternate terms of zeta, permitting convergence when s∈C and Re(s) < 1, and its non-trivial zeros {ρ}, have a deep relationship with the distribution of the primes. The Riemann Hypothesis is that all the non-trivial zeros have Re(ρ) = 1/2. This work examines the symmetries in a partial Euler’s zeta series with a complex domain equating it to the difference between two finite vector series whose matched terms have mirror-image arguments, but whose magnitudes differ when Re(s) ≠ 1/2. Analytical continuation generates a modified eta series η_l(s), in which every l^th term is multiplied by (1-l). If the integer l is appropriately determined by the Im(s), similar paired finite vector series have a difference that closely follows η_l (s) and their terminal vectors intersect in a unique way permitting zeros only when Re(s) = 1/2. Furthermore, those vectors tracking the derivatives of the series, have a special relationship permitting zeros of the differential only when Re(s) > 1/2.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

We presented a fractional order model to capture the transmission dynamics of Anthrax infection with a nonlinear force of infection and its long-term impacts. Analysis by the standard Fabrizio Caputo approach established the model is well-posed and investigation on the stability of the model, Anthrax-free equilibrium as connected to the basic reproduction number R0

Abstract: In this study, a computational fluid dynamics (CFD) simulation was conducted to validate the CFD model with experimental data from Zimparov et.al (2012), which investigates the heat transfer performance in a spirally corrugated tube that has a twisted tape inserted. The heat transfer was then compared to a simple corrugated tube without the twisted tape and to a smooth tube with no corrugations and no twisted tape. This simulation is compared with a previous experimental study conducted by (Zimparov et al. 2012), which focuses on tubes with a height-to-diameter ratio e/Di > 0.04 and small relative pitches of the twisted tape, H/Di. The largest improvement was noticed in the tube with e/Di= 0.057 and ridge pitch-to-height ratio p/e=6.77 with a twisted tape of H/Di= 4.7. This tube is labeled 5035. Tube 5035 was found to have the most significant enhancement, hence the focus of the CFD simulation will be on this tube, and the simulation will range for Reynolds numbers, 3.5 x 103 < Re < 5.0 x 104. The focus of this simulation is the evaluation of heat transfer and friction factors; a metric was used to obtain an empirical representation of the tube’s performance. Keywords: Spirally corrugated tube; Twisted tape; Heat transfer enhancement; Friction factor; Nusselt number; Computational fluid dynamics (CFD); Star CCM+

The divination function of China's Yijing has led to its circulation for thousands of years. In our exploration of Yijing's characteristics using big data, we have discovered variations in results between the coin toss method and the ancient yarrow-stalk method of divination, known as "the number for the great expansion method of divination(大衍之数)". The yarrow-stalk method serves as the fundamental method of divination in Yijing and continues to hold significance in studying the essential characteristics of Yijing. Despite the complexity of yarrow calculations, advancements in computer technology and big data have simplified its application. By employing the yarrow-stalk method, we simulated changes in the 64 hexagrams, calculated probabilities and proportions of hexagram alterations, and derived fundamental characteristics and patterns of hexagrams. Additionally, we constructed the spatial representation of lines and hexagrams. Through a binary system rearrangement, we created a 64x64 matrix illustrating hexagram transformations. Subsequently, we generated 100 million random hexagrams and analyzed line and hexagram changes accordingly. Our findings indicate the following:(1) Big data analysis reveals evident asymmetry in the hexagrams obtained through the yarrow-stalk method, with a triangular fractal characteristic forming the background.(2) Each of the 64 hexagrams exhibits a distinct probability distribution when transforming into other hexagrams, which can be categorized into five types.(3)The occurrence probabilities of Laoyang, Laoyin, Shaoyang, and Shaoyin are 18.61%, 6.387%, 31.38%, and 43.62% respectively. The probabilities of Yin and Yang occurrences are nearly equal, each close to 50%. However, the probability of Laoyang is approximately three times higher than that of Laoyin.(4) Visualized and analyzed the characteristics of hexagram changes greater than 100000 times using 3D statistical maps and Sankey diagram.These results demonstrate that the yarrow-stalk method effectively unveils the characteristics and underlying patterns of the 64 hexagrams. This study provides a novel approach for scientifically exploring the internal laws governing the 64 hexagrams in Yijing.

This study presents the numerical investigation of bioconvective nanofluid (NF) flow compris-ing gyrotactic microorganisms through convective boundary conditions (CBC) enclosing heat and mass transmission analysis above an inclined extending cylinder. Via appropriate transfor-mation, the set of Partial Differential Equations is transformed into a scheme of nonlinear ODEs. A new set of variables are presented in the directive to get the first-order convectional equations and, then solved numerically by using bvp4c. The influence of several factors on velocity, ener-gy, concentration, and the density of motile microorganisms (DMM) is investigated and exam-ined. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number (SN), DMM, and Nusselt number (NN). The present conse-quences display a validation with published. For confirmation of bvp4c, the ND-solve approach is also applied. Error analysis is also examined for the confirmation of the mathematical model.

Prostate cancer (PC) is the most frequently diagnosed non-skin cancer in the world. Previous studies showed that genomic alterations represent the most common mechanism for molecular alterations that cause the development and progression of PC. Great efforts have been done to identify common protein-coding genetic variations; however, the impact of non-coding variations including regulatory genetic variants is not still well understood. To gain an understanding of the functional impact of genetic variants, particularly, regulatory variants in PC, we developed an integrative pipeline (AGV) that used whole genome/exome sequences, GWAS SNPs, chromosome conformation capture data, and ChIP-Seq signals to investigate the potential impact of genomic variants on the underlying target genes in PC. We identified 646 putative regulatory variants, of which 30 of them significantly altered the expression of at least one protein-coding gene. Our analysis of chromatin interactions data (Hi-C) revealed that the 30 putative regulatory variants may affect 131 coding and non-coding genes. Interestingly, our study showed the 131 protein-coding genes are involved in disease-related pathways including Reactome and MSigDB in which for most of them targeted treatment options are currently available. Together, our results provide a comprehensive map of genomic variants in PC and revealed their potential contribution to prostate cancer progression and development.

IL1RA intron 2 86-bp repeat and IL4 intron 3 70-bp repeat are VNTRs that have been associated with various diseases, but their role in obesity is elusive. The objective of this study was to investigate the association of IL1RA and IL4 VNTRs with obesity and adiposity in 315 Malaysian subjects (128 M/187 F; 23 Malays/251 ethnic Chinese/41 ethnic Indians). The allelic distributions of IL1RA and IL4 were significantly different among ethnicities, and the alleles were associated with total body fat (TBF) classes. Individuals with IL1RA I/II genotype or allele II had greater risk of having higher adiposity - even after controlling for ethnicity [Odds Ratio (OR) of I/II genotype = 12.21 (CI = 2.54, 58.79; p = 0.002); II allele = 5.78 (CI = 1.73, 19.29; p = 0.004)]. However, IL4 VNTR B2 allele was only significantly associated with overall adiposity status before adjusting for ethnicity [OR = 1.53 (CI = 1.04, 2.23; p = 0.03)]. TBF was also significantly higher in those with IL1RA II allele compared with I allele (31.79 ± 2.52 vs. 23.51 ± 0.40; p = 0.005). Taken together, IL1RA intron 3 VNTR seems to be a genetic marker for overall adiposity status in Malaysian subjects.

In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. %The tight upper bounds for the energies of a graph and its line graph are given. More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$.

In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

Mitochondrial malfunction is supposed to be involved in the etiology and pathology of major depressive disorder (MDD). Here, we aimed to identify and characterize the molecular pathomechanisms related to mitochondrial disfunction in adult human skin fibroblasts which were derived from MDD patients or non-depressive control subjects. We found that MDD fibroblasts showed significantly impaired mitochondrial functioning: basal and maximal respiration, spare respiratory capacity, non-mitochondrial respiration and ATP-related oxygen consumption was lower. Moreover, MDD fibroblasts harbor lower ATP levels and showed hyperpolarized mitochondrial membrane potential. To investigate cellular resilience, we challenged both groups of fibroblasts with hormonal (dexamethasone) or metabolic (galactose) stress for one week, and found that both stressors increased oxygen consumption but lowered ATP content in MDD as well as in non-depressive control fibroblasts. Interestingly, the bioenergetic differences between fibroblasts from MDD or non-depressed subjects, which were observed under non-treated conditions, could not be detected after stress. Our findings support the hypothesis that altered mitochondrial function causes a bioenergetic imbalance which is associated with the molecular pathophysiology of MDD. The observed alterations in OXPHOS and other mitochondria-related properties represent a basis for further investigations of pathophysiological mechanisms and might open new ways to gain insight into antidepressant signaling pathways.

Chromosome analysis (CA) and chromosomal microarray analysis (CMA) have been successfully used to diagnose genetic disorders. However, many conditions remain undiagnosed due to limitations in resolution (CA) and detection of only unbalanced events (CMA). Optical genome mapping (OGM) has the potential to address these limitations by capturing both structural variants (SVs) resulting in copy number changes and balanced rearrangements with high resolution. In this study, we investigated OGM’s concordance using 87 SVs previously identified by CA, CMA, or Southern blot. Overall, OGM was 98% concordant with only three discordant cases: (1) uncalled translocation with one breakpoint in a centromere; (2) uncalled duplication with breakpoints in the pseudoautosomal region 1; and (3) uncalled mosaic triplication originating from a marker chromosome. OGM provided diagnosis for three previously unsolved cases: (1) disruption of the SON gene due to a balanced reciprocal translocation; (2) disruption of NBEA gene due to an inverted insertion; (3) disruption of the TSC2 gene due to a mosaic deletion. We show that OGM is a valid method for detection of many types of SVs in a single assay and is highly concordant with legacy cytogenomic methods; however, it has limited SV detection capabilities in centromeric and pseudoautosomal regions.

Climate change-induced temperature fluctuations pose a significant threat to crop production, particularly in the Southern Hemisphere. This study investigates the transcriptome and physiological responses of rapeseed to post-flowering temperature increases, providing valuable insights into the molecular mechanisms underlying rapeseed tolerance to heat stress. Two rapeseed genotypes, Lumen and Solar, were assessed under control and heat stress conditions in field experiments conducted in Valdivia, Chile. Results showed that seed yield and seed number were negatively affected by heat stress, with genotype-specific responses. Lumen exhibited a 9.3% average seed yield reduction, while Solar showed a 28.7% reduction. RNA-seq analysis of siliques and seeds revealed tissue-specific responses to heat stress, with siliques being more sensitive to temperature stress. Hierarchical clustering analysis identified distinct gene clusters reflecting different aspects of heat stress adaptation in siliques, with a role for protein folding in maintaining silique development and seed quality under high temperature conditions. In seeds, three distinct patterns of heat-responsive gene expression were observed, with genes involved in protein folding and response to heat showing genotype-specific expression. Gene coexpression network analysis revealed major modules for rapeseed yield and quality, as well as the trade-off between seed number and seed weight. Overall, this study contributes to understanding the molecular mechanisms underlying rapeseed tolerance to heat stress and can inform crop improvement strategies targeting yield optimization under changing environmental conditions.

The DNS of film boiling requires strong computational resources that are difficult to obtain for a daily CFD use by the practitioners of the industrial R&amp;D experts. On the other hand, the film boiling experiments are associated with the usage of the expensive and highly sophisticated apparatus, and the research to this end is found to be relatively difficult due to high heat flow rates that are present in the process itself. When combined with a transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid has been proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, the turbulent flow has been found as an important parameter in obtaining the accurate solution of the temperature field evolution in a solid specimen, via the proper modeling of turbulent kinetic energy (TKE) value, that has been imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin-Helmholtz instability theory in conjunction with the boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10 % of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient has matched the error bands prescribed by the authors of the paper that has presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30 % higher. The further inspection has revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method has shown full capability for further pursuing the industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate continuous non-Archimedean and p-adic functional Zauner conjectures.

We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results. \begin{enumerate}[\upshape(i)] \item Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying $\left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2$ for all $ \lambda_j \in \mathbb{K}, 1\leq j \leq n$, for all $n \in \mathbb{N}.$ Let $\mathcal{X}$ be a $d$-dimensional non-Archimedean Banach space over $\mathbb{K}$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and the operator $S_{f, \tau} : \text{Sym}^m(\mathcal{X})\ni x \mapsto \sum_{j=1}^nf_j^{\otimes m}(x)\tau_j^{\otimes m} \in \text{Sym}^m(\mathcal{X})$, is diagonalizable, then \begin{align}\label{NONFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds. \item For a prime $p$, let $\mathbb{Q}_p$ be the p-adic number field. Let $\mathcal{X}$ be a $d$-dimensional p-adic Banach space over $\mathbb{Q}_p$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and there exists $b \in \mathbb{Q}_p$ such that $ \sum_{j=1}^{n}f_j^{\otimes m}(x) \tau_j^{\otimes m} =bx$ for all $ x \in \text{Sym}^m(\mathcal{X}),$ then \begin{align}\label{PADICFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds. \end{enumerate} We formulate non-Archimedean functional and p-adic functional Zauner conjectures.

In this paper, we present the extension of the pressure-based solver designed for the simulation of compressible and/or incompressible two-phase flows of viscous fluids. The core of the numerical scheme is based on the hybrid Kurganov— Noele — Petrova/PIMPLE algorithm. The governing equations are discretized in the conservative form and solved for velocity and pressure, with the density evaluated by an equation of state. The acoustic-conservative interface discretization technique helps to prevent the unphysical instabilities on the interface. The solver was validated on various cases in wide range of Mach number, both for single-phase and two-phase flows. The numerical algorithm was implemented on the basis of the well-known open-source Computational Fluid Dynamics library OpenFOAM in the solver called interTwoPhaseCentralFoam. The source code and the pack of test cases are available on GitHub: https://github.com/unicfdlab/hybridCentralSolvers

The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lema\^itre-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations.

This article introduces a new way of using a Fibre Bragg Grating (FBG) sensor for detecting the presence and number of occupants in the monitored space in a Smart Home (SH). CO₂ sensors are used to determine the CO₂ concentration of the monitored rooms in an SH. CO₂ sensors can also be used for occupancy recognition of the monitored spaces in SH. To determine the presence of occupants in the monitored rooms of the SH, the newly devised method of CO₂ prediction, by means of an Artificial Neural Network (ANN) with a Scaled Conjugate Gradient (SCG) algorithm using measurements of typical operational technical quantities (indoor temperature, relative humidity indoor and CO₂ concentration in the SH) is used. The goal of the experiments is to verify the possibility of using the FBG sensor in order to unambiguously detect the number of occupants in the selected room (R104) and, at the same time, to harness the newly proposed method of CO₂ prediction with ANN SCG for recognition of the SH occupancy status and the SH spatial location (rooms R104, R203, and R204) of an occupant. The designed experiments will verify the possibility of using a minimum number of sensors for measuring the non-electric quantities of indoor temperature and indoor relative humidity and the possibility of monitoring the presence of occupants in the SH using CO₂ prediction by means of the ANN SCG method with ANN learning for the data obtained from only one room (R203). The prediction accuracy exceeded 90% in certain experiments. The uniqueness and innovativeness of the described solution lie in the integrated multidisciplinary application of technological procedures (the BACnet technology control SH, FBG sensors) and mathematical methods (ANN prediction with SCG algorithm, the Adaptive Filtration with of LMS algorithm) employed for the recognition of number persons and occupancy recognition of selected monitored rooms of SH.

This paper briefly reviews the state of the art in artificial intelligence including inductive and deductive methods. Deep learning and ensemble machine learning lie in inductive methods while automated reasoning implemented in deductive computer languages (Prolog, Otter, and Z3) is based on deductive methods. In the inductive methods, intelligence is inferred by pseudorandom number for creating the sophisticated decision trees in Go (game), Shogi (game), and quiz bowl questions. This paper demonstrates how to wisely use the pseudorandom number for solving coin-weighing puzzles with the deductive method. Monte Carlo approach is a general purpose problem-solving method using random number. The proposed method using pseudorandom number lies in one of Monte Carlo methods. In the proposed method, pseudorandom number plays a key role in generating constrained solution candidates for coin-weighing puzzles. This may be the first attempt that every solution candidate is solely generated by pseudorandom number while deductive rules are used for verifying solution candidates. In this paper, the performance of the proposed method was measured by comparing with the existing open source codes by solving 12-coin and 24-coin puzzles respectively.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

The traditional sequent peak algorithm (SPA) was used to assess the reservoir volume (VR) for comparison with deficit volume, DT, (subscript T representing the return period) obtained from the drought magnitude (DM) based method with draft level set at the mean annual flow on 15 rivers across Canada. At an annual scale, the SPA based estimates were found to be larger with an average of nearly 70% compared to DM based estimates. To ramp up DM based estimates to be in parity with SPA based values, the analysis was carried out through the counting and the analytical procedures involving only the annual SHI (standardized hydrological index, i.e. standardized values of annual flows) sequences. It was found that MA2 or MA3 (moving average of 2 or 3 consecutive values) of SHI sequences were required to match the counted values of DT to VR. Further, the inclusion of mean, as well as the variance of the drought intensity in the analytical procedure, with aforesaid smoothing led DT comparable to VR. The distinctive point in the DM based method is that no assumption is necessary such as the reservoir being full at the beginning of the analysis - as is the case with SPA.

Multi-stakeholder based construction projects are subject to various risk factors due to dynamic business environments. These risks affect project activities which indirectly impact construction costs, resulting in delays and poor building quality. So, managing these project risks requires suitable risk mitigation strategies to evaluate and analyse their severity. Hence, risk evaluation and assessment of construction projects is a multi-criteria decision making (MCDM) problem. In present real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D number domain to handle three types of ambiguous evaluations, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D number based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster-Shafer (D-S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D number extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D number is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches (D-COPRAS, D-ARAS, D-MABAC, and D-TOPSIS). Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed for verify the robustness of the proposed method.

In the paper, the authors establish two identities to express the generating function of the Chebyshev polynomials of the second kind and its higher order derivatives in terms of the generating function and its derivatives each other, deduce an explicit formula and an identities for the Chebyshev polynomials of the second kind, derive the inverse of an integer, unit, and lower triangular matrix, present several identities of the Catalan numbers, and give some remarks on the closely related results including connections of the Catalan numbers respectively with the Chebyshev polynomials, the central Delannoy numbers, and the Fibonacci polynomials.

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

This review is a first attempt at bringing together various concepts from research on wall- and magnetically-bounded turbulent flows. Brief reviews of both fields are provided: The main similarities identified are coherent (turbulent) structures, flow generation and transport barriers. Examples are provided and discussed.

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

This paper identifies a criterion for choosing the largest set of rejected hypotheses in high-dimensional data analysis where Multiple Hypothesis testing is used in exploratory research to identify significant associations among many variables. The method neither requires predetermined thresholds for level of significance, nor uses presumed thresholds for false discovery rate. The upper limit for number of rejected hypotheses is determined by finding maximum difference between expected true hypotheses and false hypotheses among all possible sets of rejected hypotheses. Methods of choosing a reasonable number of rejected hypotheses and application to non-parametric analysis of ordinal survey data are presented.

This paper investigates the search for an exact analytic solution to a temporal first-order differential equation that represents the number of customers in a non-stationary or time-varying

Variational Auto-Encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the Simplicial Auto-Encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a data set better than a standard VAE.

Liquid biopsies are an integral part of the diagnosis of cancer. Here, we have extended previous validation studies of a new targeted NGS panel to include the detection of copy number amplifications (CNAs), fusions, and exon skipping variants. Detection of these gene classes included specimens from clinical and healthy donors and cell lines (fusions: ROS1, EML4-ALK, NTRK1), (exon skipping: MET exon 14), and (CNAs: HER2, CDK6, EGFR, MYC and MET). The limit of detection (LOD) for fusion/skipping was 42 copies (QC threshold = 3 copies) and was verified using 3 additional fusion/skipping variants. LOD for CNAs was 1.40-fold-change (QC threshold = 1.15-fold change) and was verified with 3 additional CNAs. In precision studies, all fusion/skipping variants were detected in all runs and all days of testing (n=18/18; 100%); average CV for repeatability was 20.5% (range 8.7% - 34.8%), and for reproducibility was 20.8% (range 15.7% - 30.5%). For CNAs, 28/29 (96.6%) copy gains were detected. For CNAs, average CV of 1.85% (range 0% to 5.49%) for repeatability and 6.59% (range 1.65% to 9.22%) for reproducibility. The test panel meets the criteria for being highly sensitive and specific and extends its utility for the detection of clinically relevant variants in cancer.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

The influence of linear and nonlinear modes of ADC driver on the operational amplifier (Op-Amp), which has different values of maximum output voltage slew rate, on the effective number of bits of ADC is considered. It is shown that the effective number of bits of ADC when op-amps on bipolar transistors with input signal amplitudes exceeding 50-100 mV is determined by the nonlinear modes of its input differential stage.

The object of this work is to determine the correlation on the Nusselt number on the individual rows of a four-row tubular finned heat exchanger with continuous fins with a staggered tube arrangement using CFD modelling. Correlations for calculating Darcy-Weisbach friction factors on individual tube rows were also determined. Relationships for the Nusselt number and friction factor derived for the entire exchanger based on CFD modelling were compared with those available in the literature determined using experimental data. The maximum relative differences between the Nusselt number for a four-row exchanger determined experimentally and by CFD modelling are in the range from 22% for a Reynolds number based on a tube's outside diameter of 1,000 to 30% for a Reynolds number of 13,000. The maximum relative differences between the friction factor for a four-row exchanger determined experimentally and by CFD modelling are in the range of 50% for a Reynolds number based on a tube outer diameter of 1,000 to 10% for a Reynolds number of 13,000. The CFD modeling performed shows that in the range of Reynolds numbers based on hydraulic diameters from 150 to 1,400, the Nusselt number for the first row in a four-row finned heat exchanger is about 22% to 15% higher than the average Nusselt number for the entire exchanger. In the range of Reynolds number changes based on hydraulic diameter from 2,800 to 6,000, the Nusselt numbers on the first and second rows of tubes are close to each other. Correlations on Nusselt numbers and friction factors derived for individual tube rows can be used in the design of plate-fin and tube heat exchangers used in equipment such as air-source heat pumps, automotive radiators, air-conditioning systems and in air hot-liquid coolers. In particular, the correlations can be used to select the optimum number of tube rows in the exchanger.

Finding out how cells with the same genome change fates in differentiation commitment is a challenge of biology. We used MCF-7 breast cancer cells treated with the ErbB2 ligand heregulin (HRG), which induces differentiation, to address if and how the constitutive pericentromere-associated domains (PADs) may be involved in this process. PAD-specific repressive heterochromatin (H3K9me3) and active euchromatin (H3K4me3) marking, centromere (CENPA) labelling, qPCR, acridine-orange-DNA structural test, and microscopic image analysis were applied. We found a two-step DNA unfolding, at 15-20 min and 60 min after HRG treatment, coinciding with bi-phasic activation of the early response genes (c-FOS family) and two steps of critical phase transition which were revealed in transcriptome studies. In control, the distribution of PAD number and size displays a power-law scaling with a boundary at the nucleolus. PADs’ clustering correlates with centromere numbers. 15 min after HRG treatment, the unravelling of PADs occurs, coinciding with the first step of euchromatin unfolding. The second step is associated with transcription of long-non-coding-RNA from satellite III DNA. We hypothesize that splitting of the PAD clusters under the critical size threshold of the silencing domain abrupts position effect variegation. It allows the first genome transcription avalanche to occur, starting differentiation commitment.

New insights into the causes and mechanisms of congenital heart disease (CHD) have been gained through the use of next-generation sequencing. Examination of the whole exome sequence detects detrimental gene variations modifying single or contiguous nucleotides, that are characterised as pathogenicity based on statistical assessments of families. and correlates with congenital heart disease, elevated expression during heart development, and reduction of harmful protein-coding mutations in the general population. Patients with CHD and extracardiac abnormalities enriched for gene classes meeting these criteria. CHDs and extracardiac defects, supporting a common set of pathways in the organogenesis of CHDs. Single-cell transcriptomics data reveal the expression of genes associated with CHD in specific cell lineages, and emerging evidence suggests that genetic variants disrupt multicellular genes essential for cardiogenesis. Metrics and units are being tracked in whole genome sequence studies.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

Background: Cervical cancer prevention in regions with limited access to screening and HPV vaccination necessitates innovative approaches. This study explored the potential of a test-and-treat strategy using mRNA HPV tests to impact cervical cancer prevention in a high-prevalence HIV population. Methods: A cervical screening study was conducted at three South African hospitals involving 710 under-screened, non-pregnant women (25 to 65 years) without known cervical diseases. Cytology, HPV testing, colposcopy, and biopsies were performed concurrently. Histopathologists determined final histological diagnoses based on biopsy and LLETZ histology. mRNA-HPV-genotyping for 3 (16, 18, 45) to 8 (16, 18, 31, 33, 35, 45, 52, 58) high-risk types was performed on leftover liquid-based cytology material. The preventive potential of the test-and-treat approach was estimated based on published data, reporting the causative HPV types in cervical cancer tissue from South African women. Treatment was provided as needed. Results: HPV positivity rate more than doubled from 3-type (15.2%; 95% CI: 12.6-17.8) to 8-type mRNA (31.5%; 95% CI: 28.8-34.9) combinations, significantly higher among HIV-positive women. CIN3+ prevalence among HIV-positive women (26.4%) was double that of HIV-negative women (12.9%) (p&lt;0.01). The 6-type combination showed the best balance of sensitivity, specificity and treatment group size, and effectiveness to prevent cervical cancer. A 4-type combination (16, 18, 35, 45) could potentially prevent 77.6% (95% CI: 71.2-84.0) of cervical cancer burden by treating 20% and detecting 41.1% of CIN3 cases in the study group. Similarly, a 6-type combination (16, 18, 31, 33, 35, 45), treating 25% and including 62% of CIN3 cases, might prevent 85% of cervical cancer cases (95% CI: 79.6-90.6) among HIV-positive and negative women. Conclusion: Employing mRNA HPV tests within a test-and-treat approach holds huge promise for targeted cervical cancer prevention in under-screened populations. Testing for mRNA of the 6 highest-risk HPV types in this population and treating them all is projected to effectively prevent progression from CIN3 to invasive cervical cancer while reducing overtreatment in resource-constrained settings.

This paper attempts to develop a Dynamic Mode Decomposition (DMD) based Reduced Order Model (ROMs) which can quickly but accurately predict the forces and moments experienced by a road vehicle such that they be used by an on-board controller to determine the vehicle's trajectory. DMD can linearize a large dataset of high-dimensional measurements by decomposing them into low-dimensional coherent structures and associated time-dynamics. This ROM then also can be applied to predict the future state of the fluid flow. Existing literature on DMD is limited to low Reynolds number applications. This paper presents DMD analyses of the flow around an idealized road vehicle, called the Ahmed body, at a Reynolds number of 2.7E6. The high dimensional dataset used in this paper was collected from a computational fluid dynamics (CFD) simulation performed using Menter's shear stress transport (SST) turbulence model within the context of Improved Delayed Detached Eddy Simulations (IDDES). The DMD algorithm, as available in literature, was found to suffer nonphysical dampening of the medium-to-high frequency modes. Enhancements to the existing algorithm were explored, and a modified DMD approach is presented in this paper which includes: (a) a requirement of higher sampling rate to obtain higher resolution of data, and (b) a custom filtration process to remove spurious modes. The modified DMD algorithm thus developed was applied to the high Reynolds number, separation dominated flow past the idealized ground vehicle. The effectiveness of the modified algorithm was tested by comparing future predictions of force and moment coefficients as predicted by the DMD-based ROM to the reference CFD simulation data, and found to offer significant improvement.

Recent wastewater testing suggests the poliovirus is reemerging, raising questions about the efficacy of the current inactivated polio vaccine and mass vaccination to eradicate poliomyelitis. The present study reassessed reported outcomes from the placebo-control study of the 1954 Salk inactivated poliomyelitis vaccine field trial, which studied a population of 1,829,916 U.S. school children from the first three grades. The placebo-control study of the trial reported that the polio vaccine was 80% to 90% effective in reducing cases of laboratory confirmed paralytic poliomyelitis, 60% to 70% effective against type 1 of the virus, and greater than 90% effective against types 2 and 3 of the poliovirus. However, these outcomes are reported as relative risk reductions, and the absolute risk reductions of the 1954 polio vaccine field trial were never reported to the public. The present paper’s analysis reveals to the public for the first time that the inactivated poliomyelitis vaccine's absolute risk reduction of laboratory confirmed paralytic poliomyelitis in the placebo-control study is 0.01% to 0.02%, an extraordinarily low clinical effect that impugns the Salk polio vaccine’s reported effectiveness. Furthermore, absolute risk reductions for the three poliovirus types are 0.01%, 0.00%, and 0.01%, respectively. Outcome reporting bias in the 1954 inactivated poliomyelitis vaccine field trial casts doubt on eradication of the poliovirus through mass vaccination.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

On February 24, 2022 Russia started the full-scale invasion of Ukraine, which created an unprecedented number of refugees. To estimate the influence of this humanitarian disaster on the COVID-19 pandemic dynamics, the averaged daily numbers of cases and reproduction numbers in Ukraine, the UK, Poland, Germany, the Republic of Moldova, and in the whole world were calculated for the period February-April 2022. The registered numbers of cases were compared with ones calculated with the use of the generalized SIR-model and corresponding parameter identification procedure for the previous epidemic waves in Ukraine, Poland, Germany, and the world. Since before February 24, 2022 the estimation of the number of infectious persons per capita in Ukraine 3.6 times exceeded the global figure, the increase of the number the new cases and the pandemic duration was expected. In March 2022 the increase of the averaged number of new cases in the UK, Germany, and worldwide was visible. A simple formula to estimate the effective reproduction number based on the smoothed accumulated numbers of cases is proposed. The results of calculations agree with the figures presented by John Hopkins University and demonstrate a short-term growth of the reproduction number in the UK, Poland, Germany, Moldova, and worldwide in March 2022.

Extensive genome structure variation, such as copy number variations (CNVs) and presence/absence variations, is the basis for the remarkable maize genetic diversity; however, the effect of CNVs on maize herbivory defense remains largely underexplored. Here, we report that the naturally occurring duplication of the maize 9-lipoxygenase gene, ZmLOX5, leads to increased resistance of maize to herbivory by fall armyworms (FAW). Previously, we showed that ZmLOX5-derived oxylipins are required for defense against chewing insect herbivores and identified several inbred lines, including Yu796, that contained duplicated CNVs of ZmLOX5, referred to as Yu796-2×LOX5. To test whether introgression of the Yu796-2×LOX5 locus into the herbivore-susceptible B73 background that contains a single ZmLOX5 gene is a feasible approach to increase resistance, we generated a series of near-isogenic lines that contained either 2, 1 or 0 copies of the Yu796-2×LOX5 locus in the B73 background by six back crosses (BC6). Droplet digital PCR (ddPCR) confirmed the successful introgression of the Yu796-2×LOX5 locus in B73. The resulting B73-2×LOX5 inbred line displayed increased resistance against FAW associated with increased expression of ZmLOX5, increased wound-induced production of its primary oxylipin product, the α-ketol, 9-hydroxy-10-oxo-12(Z),15(Z)-octadecadienoic acid (9,10-KODA), and the downstream defense hormones regulated by this molecule, 12-oxo-phytodienoic acid (12-OPDA) and abscisic acid (ABA). Surprisingly, wound-induced JA-Ile production was not increased in B73-2×LOX5, resulting from the increased JA catabolism. Furthermore, B73-2×LOX5 displayed enhanced drought tolerance likely due to increased ABA and 12-OPDA content. Taken together, this study revealed that the duplicated CNV of ZmLOX5 quantitively contributes to maize antiherbivore defense and presents proof-of-concept evidence that the introgression of naturally occurring duplicated CNVs of a defensive gene into the productive, but susceptible, crop varieties is a feasible breeding approach for enhancing plant resistance to herbivory and tolerance to abiotic stress.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

Current prenatal genetic evaluation showed a significantly increase in non-invasive screening and the reduction of invasive diagnostic procedures. To evaluate the diagnostic efficacy on detecting common aneuploidies, structural chromosomal rearrangements and pathogenic copy number variants (pCNV), we performed a retrospective analysis on a case series initially analyzed by aneuvysion fluorescence in situ hybridization (FISH) and karyotyping then followed by array comparative genomic hybridization (aCGH). Of the 386 cases retrieved from the past decade, common aneuploidies were detected in 137 cases (35.5%), other chromosomal structural rearrangements were detected in four cases (1%), and pCNV were detected in five cases (1.3%). The relative frequencies for common aneuploidies suggested a under detection of sex chromosome aneuploidies. Approximately 9.5% of cases with common aneuploidies showed a mosaic pattern. Inconsistent results between FISH and karyotyping were noted in cases with pseudo-mosaicism introduced by culture artifact or variable cellular proliferation from cells with mosaic karyotypic complements under in vitro cell culture. Based on findings from this case series, cell-based FISH and karyotyping should be performed to detect common aneuploidies, structural chromosomal abnormalities, and mosaic pattern. DNA-based aCGH and reflex FISH should be performed to detect and confirm genomic imbalances and pCNV. Practice points to ensure the diagnostic accuracy and efficacy were summarized.

During the conceptual and preliminary design stage of a ship, designers need to ensure that the selected principal dimensions and parameters are good enough to deliver a stable ship (statically and dynamically) besides deadweight and speed. To support this, the initial intact stability of the proposed ship is required to be calculated, and in doing so, the lightship weight and its detailed breakdown are necessary to be known. After hull steel weight, machinery weight, mainly, marine propulsion and power generation machinery, play a vital role in the lightship weight estimate of a ship due to its robustness. The correct estimation of respective weights improves the accuracy of calculating a ship's initial stability typically to be designed and built. Hence, it would be advantageous for the designer to convince the ship owner. A total of 3006 marine propulsion (main marine diesel) engines and 348 power generation (auxiliary marine diesel) engines/generators of various power output (generators output for auxiliary engines), engine RPM and cylinder number of different engine makers are collected. These are analyzed and presented in both tabular and graphical forms to demonstrate the possible relationship between marine propulsion engine weight and power generation engine weight, and their respective power output, RPM, cylinder number, power-RPM ratio and power-RPM ratio per cylinder.In this article, the authors have attempted to investigate the behavior of marine propulsion engine weight and power generation engine/generator weight regarding engine power output, generator power output, engine RPM and cylinder number (independent variables). Further attempts have been made to identify those independent variables that influence the weight of the marine propulsion engine and power generation engine/generator (dependent variables), and their interrelationships. A mathematical model has thus been developed and proposed, as a guiding tool, for the designer to estimate the weight of main and auxiliary engines more accurately during the conceptual and preliminary design stage.