Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

Count data are used in many fields of practice, especially Poisson distribution as a popular choice for the marginal process distribution. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of process. In this paper, the explicit formulas are proposed to evaluate performance characteristics of Double Moving Average control chart (DMA) for Integer valued autoregressive of serial dependence Poisson process. The characteristics of the control chart are frequently measured as Average Run Length (ARL) which means that the average of observations are taken before a system is signaled to be out-of-control. These proposed explicit formulas of ARL are simple and easy to implement for practitioner. The numerical results show that the DMA chart performs better than others when the magnitudes of shift are moderate and large.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

S5 0716+714 is a well known BL-Lac object, one of the brightest and most active blazars. The discovery in the Very High Energy band (VHE, E > 100 GeV) by MAGIC happened in 2008. In January 2015 the source went through the brightest optical state ever observed, triggering MAGIC follow-up and a VHE detection with ~ sigma significance (ATel #6999). Rich multi-wavelength coverage of the flare allowed us to construct the broad-band spectral energy distribution of S5 0716+714 during its brightest outburst. In this work we will present the preliminary analysis of MAGIC and Fermi-LAT data of the flaring activity in January and February 2015 for the HE and VHE band, together with radio (Metsahovi, OVRO, VLBA, Effelsberg), sub-millimeter (SMA), optical (Tuorla, Perkins, Steward, AZT-8+ST7, LX-200, Kanata), X-ray and UV (Swift-XRT and UVOT), in the same time-window and discuss the time variability of the MWL light curves during this impressive outburst.

To estimate the recreational value provided by the Foy’s Lake annually using the most applicable model for on-site data is the main objective of this study. Adhere to the objective of this study; Individual Travel Cost Method (ITCM) has been applied and Zero Truncated Poisson Regression Model has been found plausible among other models to estimate consumer surplus. Based on the findings of the study, an estimate of the consumer surplus or recreational benefits per trip per visitor can be recommended as BDT 5,875 or US $ 73.44 and counting the consumer surplus per trip per visitor, the annual recreational value (total consumer surplus) provided by the lake is found to be BDT 321 million or US $ 40.2 million.

High redshift blazars are among the most powerful objects in the Universe. Although they represent a significant fraction of the extragalactic hard X-ray sky, they are not commonly detected in gamma-rays. High redshift (z>2) objects represent <10 per cent of the AGN population observed by Fermi so far, and gamma-ray flaring activity from these sources is even more uncommon. The characterization of the radio-to-gamma-ray properties of high redshift blazars represents a powerful tool for the study of the energetics of such extreme objects and the Extragalactic Background Light. This contribution will present results of multi-band campaigns, from radio to gamma-rays, on PKS 0836+710, PKS 2149-306, and TXS 0536+145. The latter is the highest redshift detection of a flaring gamma-ray blazar so far. At the peaks of their respective flares these sources reached an apparent isotropic gamma-ray luminosity of about 10^50 erg/s, which is comparable with the luminosity observed from the most powerful blazars. The physical properties derived from the multi-wavelength observations of these sources are then compared with those shown by the high redshift population.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

QSO B0218+357 is a blazar located at a cosmological redshift of 0.944. The source is gravitationally lensed by a spiral galaxy located at the redshift of 0.68. Strong gravitational lensing splits the signals emitted by the source into two components separated by 10-12 days, as observed in radio and gamma-ray bands. In July 2014 a GeV flare was observed by Fermi-LAT, triggering follow-up observations with the MAGIC telescopes at energies above 100 GeV. The expected time delay between the components allowed us to plan broad band MWL observations before, during and after the trailing component of the emission. The MAGIC observations at the expected time of arrival of the trailing component resulted in the first detection of QSO B0218+357 in Very-High-Energy (VHE, >100 GeV) gamma rays. It is both the farthest known VHE object and one of only a few Flat Spectrum Radio Quasars detected in this energy range. We report here the observed multiwavelength spectral and temporal properties of the emission during the 2014 flare.

The discovery by the Large Area Telescope on board Fermi of variable gamma-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of AGN with relativistic jets in addition to blazars and radio galaxies. Considering that NLSy1 are usually hosted in spiral galaxies, this finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. We report on a systematic investigation of the gamma-ray properties of a sample of radio-loud NLSy1, including the detection of new objects, using 7 years of Fermi-LAT data with the new Pass 8 event-level analysis. In addition we discuss the radio-to-very-high-energy properties of the gamma-ray emitting NLSy1, their host galaxy, and black hole mass in the context of the blazar scenario and the unification of relativistic jets at different scales.

In this paper, we establish some inequalities bounding the ratio Г_p,k(x)/Г_p,k(y), where Г_p,k(.) is the (p,k)-analogue of the Gamma function. Consequently, some previous results are recovered from the obtained results.

Land degradation is a serious impediment to improving rural livelihoods in Eastern Africa. This paper identifies major land degradation patterns and causes, and analyzes the determinants of sustainable land management (SLM) in three countries (Ethiopia, Malawi and Tanzania). The results show that land degradation hotspots cover about 51%, 41%, 23% and 23% of the terrestrial areas in Tanzania, Malawi and Ethiopia respectively. The analysis of nationally representative household surveys shows that the key drivers of SLM in these countries are biophysical, demographic, regional and socio-economic determinants. Secure land tenure, access to extension services and market access are some of the determinants incentivizing SLM adoption. The implications of this study are that policies and strategies that facilities secure land tenure and access to SLM information are likely to incentivize investments in SLM. Local institutions providing credit services, inputs such as seed and fertilizers, and extension services must also not be ignored in the development policies.

The present review paper aims at collecting and discussing the research work, numerical and experimental, carried out in the field of Fluid-Structure Interaction (FSI) in one-dimensional (1D) pressurized transient flow in the time-domain approach. Background theory and basic definitions are provided for the proper understanding of the assessed literature. A novel frame of reference is proposed for the classification of FSI models based on pipe degrees-of-freedom. Numerical research is organized according to this classification, while an extensive review on experimental research is presented by institution. Engineering applications of FSI models are described and historical accidents and post-accident analyses documented.

Radio loud active galactic nuclei are composed of different spatial features, each one characterized by different spectral properties in the radio band. Among them, blazars are the most common class of sources detected at gamma-rays by \fermi, and their radio emission is dominated by the flat spectrum compact core. In this contribution, we explore the connection between emission at high energy revealed by \fermi\ and at radio frequency. Taking as a reference the strong and very highly significant correlation found between gamma rays and cm-$\lambda$ radio emission, we explore different behaviours found as we change the energy range in gamma rays and in radio, therefore changing the physical parameters of the zones involved in the radiation emission. We find that the correlation weakens when we consider (1) gamma rays of energy above 10 GeV (except for high synchrotron peaked blazars) or (2) low frequency radio data taken by the Murchison Widefield Array; on the other hand, the correlation strengthens when we consider mm-$\lambda$ data taken by ALMA.

Metal, primarily Fe and Zn, deficiencies affect over half of the world's population. Human diets with prevalent cereal products cause micronutrient malnutrition. Biofortification is one of the most effective approaches to alleviate malnutrition. Spring wheat genetically stable (M7) mutant lines developed with 100 and 200 Gy gamma treatments to broaden genetic variation and search for new resources were analyzed for nutritionally important minerals (Ca, Mg, K, Fe, and Zn), their bioavailability, and grain protein content (GPC). The variation was 172.3–883.0 mg/kg for Ca, 472.9–1088 mg/kg for Mg, 3128.6–5487.5 mg/kg for K, 40.9–89.0 mg/kg for Fe, and 22.2–89.6 mg/kg for Zn. In mutant lines, among the investigated minerals, the highest increases in concentrations were observed in Fe, Zn, and Ca when compared to the parent. Some mutant lines, mostly in the 100 Gy-derived germplasm, had two to three times higher Fe, Zn, and Ca concentrations, lower phytic acid concentration (1.4–2.1 times), and 6.5–7% higher GPC compare to the parent. Variation was detected for the Ca:Phy, Mg :Phy, Phy:K, Phy:Fe, and Phy:Zn molar ratios, (1.27–10.41, 5.05–18.68, 1.66–4.87, 1.40–5.32 and 1.78–11.78, respectively). The results showed how the genetic variation could be generated through radiation and be useful to develop biofortification by micronutrient varieties with their appropriate bioavailability to overcome malnutrition.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

In this paper, we introduce two discrete degenerate random variables, namely the degenerate binomial and degenerate Poisson random variables. We deduce the expectations of the degenerate binomial random variables. We compute the generating function of the moments of the degenerate Poisson random variables, which leads us to define the new type degenerate Bell polynomials, and hence obtain explicit expressions for the moments of those random variables in terms of such polynomials. We also get the variances of the degenerate Poisson random variables. Finally, we illustrate two examples of the degenerate Poisson random variables.

The main focus when developing software is to improve the reliability and stability of a software system. When software systems are introduced, these systems are used in field environments that are the same as or close to those used in the development-testing environment; however, they may also be used in many different locations that may differ from the environment in which they were developed and tested. In this paper, we propose a new software reliability model that takes into account the uncertainty of operating environments. The explicit mean value function solution for the proposed model is presented. Examples are presented to illustrate the goodness-of-fit of the proposed model and several existing non-homogeneous Poisson process (NHPP) models and confidence intervals of all models based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

Nanopores with irregularities are promising tools for distinguishing nano-size objects by their shape, but the forces on the object that critically influence its axial and rotational movement are unclear. The physics of the situation was described using the Poisson-Nernst-Planck and Navier-Stokes equations. With uniformly charged object the axial Coulomb and dielectric pressure (which opposes it and is surprisingly important), control the object's axial movement and rotation. Even without external pressure the hydrodynamic pressure is significant (negative at its upper and positive at its lower surface), but its total value is almost zero. If the object is charged only on the upper surface the axial upper Coulomb pressure is near zero close to the center, but negative near its end (the pressure is zero at the lower surface). The total axial dielectric pressure, which is largely dominated by the pressure at the upper surface, is positive along the length of the object becoming pronounced near its end. The axial hydrodynamic pressure is negative and significant at the upper surface (zero at the lower surface), diminishes in value near the object's end, critically influencing its axial movement, which becomes much faster. At its end the axial dielectric pressure prevails, and controls its rotation.

Mind-body interaction and its manifestations at the brain level has been studied extensively in the field of consciousness research. Fara-darmani Consciousness Field, as claimed by Mohammad Ali Taheri (the founder), is a method of connecting with the Cosmic Consciousness Network through human mind and his brain has a detective role in this process. As a result of this connection, the scanning process of the state of a being, e.g., the health status of the cells and consequently organs is performed. This study was conducted to evaluate the effects of the Fara-darmani Consciousness Field connection on electroencephalogram (EEG) features as an important biomarker of the brain functioning. The results showed that there was a significant increase in the gamma2 frequency band (35-40 Hz) power in the frontal lobe in medial frontal gyrus (BA6) and paracentral lobule (BA31) of the brain during the task condition compared to the rest condition in a Fara-therapist population. Considering the cortical electrical activity of Fara-therapist’s brain during Fara-darmani Consciousness Field connection, characterizing increase in the power of gamma wave and the activity of the areas affecting on memory, attention, perception and default mode network intrinsic activity. This manifestation distinguishes Fara-darmani Consciousness Field connection from other known methods dealing with the mind-body interaction criterion mainly different types of mediation.

In a recent paper, Sarikaya et al. introduced a new analogue of the classical Gamma function which they called, the conformable Gamma function. Motivated by their results, this paper seeks to establish some inequalities for the conformable Gamma and Polygamma functions. Among other analytical tools, the procedure relies on the generalized forms of some classical inequalities.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

Beginning in 2012, our understanding of human papillomavirus (HPV) subcellular trafficking has undergone a drastic paradigm shift. Work from multiple laboratories has revealed that HPV has evolved a unique means to deliver its viral genome (vDNA) to the cell nucleus, relying on a myriad of host cell proteins and processes. The major breakthrough finding from these recent endeavors was the realization of L2-dependent utilization of cellular sorting factors for the retrograde transport of vDNA away from degradative endo/lysosomal compartments to the Golgi, prior to mitosis-dependent nuclear accumulation of L2/vDNA. An overview of current models of HPV entry, subcellular trafficking, and the role of L2 during initial infection is provided below, highlighting unresolved questions and gaps in knowledge.

This article shortly introduces Gaussian processes as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength light curves of the blazar PKS 1502+106 are discussed.

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

In this paper, modelling designing and simulation of a Ward Leonard layout system is done using robust control theory. In order to increase the performance of the Ward Leonard layout system with H infinity optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers are used. The open loop response of the Ward Leonard layout system shows that the system needs to be improved. Comparison of the Ward Leonard layout system with H∞ optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers to track a desired step speed input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed Ward Leonard layout system with H infinity optimal control synthesis controller in improving the percentage overshoot and the settling time.

The demand of high data rate and ubiquitous coverage in heterogeneous cellular (HetNets) is increasing progressively. In order to meet this demand, sophisticated model having applied interference reduction scheme and cell association technique is needed. The small base station (sBS)are deployed inside the broadcasting area of macro base station (mBS), in heterogeneous cellular networks (HetNets). Since mBS has high transmission power therefore a large number of users get connected with mBS. This causes disproportion of load distribution across the HetNets. For load balancing users from high power mBS are migrated to low power sBS to increase network capacity and to decrease the load from mBS. This results in interference in the communication signal because of strong mBS Interference. Hence, we need interference management technique to mitigate interference and user association and to efficiently use sBSs’ resources. Inter-cell interference (ICI) limit the HetNets’ performance. Additionally, there exist deliberate jamming interference which depends on jammers transmission power and its proximity with the target, which notably degrades the network performance. In this paper, we employ reverse frequency allocation scheme (RFA) to reduce inter cell interference, deliberate jamming interference and to accomplish load balancing. The proposed setup is analyzed inquisitively and with the help of simulations. The result shows reduction in interferences as well as balance of load distribution in the network achieved by employing RFA scheme together with cell association.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

A Wireless Body Area Sensor Network (WBASN) is combination of numerous sense nodes, positioned onto/close or inside a person body. Wireless Body Area Sensor Networks (WBASN) is a developing automation trend that exploits wireless sensor nodes to put instantaneous wearable well-being of ill person to improve individual’s existence. The sensor nodes might be used outwardly to observe abundant health parameters (like heart activity, blood pressure and cholesterol) of an ill person at a vital site within hospital. Hence the goal of WBASN is much crucial, enhancing the lifetime of nodes is compulsory to sustain many issues such as utility and efficiency. It is essential to evaluate time that when the first node will die it we want to refresh or change the battery reason is that loss of crucial information is not tolerable. The lifetime is termed as the time interval when a first node dies out due to battery exhaustion. In our proposed protocol life time of a network is the main concern as well other protocol related issues such as throughput, path loss, and residual energy. Bio-sensors are used for deployment on human body. Poisson distribution and equilibrium model techniques have been used for attaining the required results. Multi-hop network topology and random network node deployment used to achieve minimum energy consumption and longer network lifetime.

In a wireless network, locations of base stations (BSs)/access points (APs)/sensor nodes can be modeled based on stochastic processes, e.g., a Poisson point process (PPP) or a deterministic pattern planned ahead by providers. While deterministic deployment does not provide tractable interference analysis in general, PPP yields tractable analysis for interference. However, PPP allows APs to be deployed very close to each other and gives pessimistic results compared to the field measurements. In this study, in order to address this issue, Lloyd’s algorithm, which functions as a bridge between random and structural APs deployments, is investigated for analyzing coverage probability in a network. The link distance distribution is modeled as a mixture of Weibull distributions and its parameters are obtained by using the expectation-maximization (EM) algorithm for each iteration of Lloyd’s algorithm. The link distance distribution is further utilized for calculating the coverage probability approximately by exploiting the tractability of PPP.

Most existing flexible count regression models allow only approximate inference. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under- and overdispersion). The new method, referred as “balanced discretization”, consists in discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation in terms of the continuous distribution. For illustrative purposes, we have developed the family of balanced discrete gamma distributions which can model equi-, under- and overdispersed count data. This family of count distributions is appropriate for building flexible count regressionmodels because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we have shown that under equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersion, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data is Poisson distributed.

Dispersion tests based on the second order component of smooth test statistics are related to Fisher’s Index of Dispersion test, used for testing for the Poisson distribution when there are no covariates present. Such tests have been recommended in [1] to test for the Poisson distribution when covariates are present. The modified Borel-Tanner (MBT) distribution seems suited to data with extra zeroes, a monotonic decline in counts and longer tails. Here we recommend a dispersion test for the MBT distribution for both when covariates are absent and when they are present.

Tuberculosis cause of death worldwide and the leading cause from a single infectious agent, ranking above Human immunodeficiency virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS). The aim of this study is to ascertain the trend of tuberculosis prevalence and the effect of HIV prevalence onl Tuberculosis case in some West African countries from 2000 to 2016 using count panel data regression models. The data used annual HIV and Tuberculosis cases spanning from 2000 to 2016 extracted from online publication of World health Organization (WHO). Panel Poisson regression model and Negative binomial regression model for fixed and random effects were used to analyzed the count data, the result revealed a positive trend in TB cases while increased in HIV cases leads to increase in TB cases in West African countries. Among the competing models used in this study, Panel Negative Binomial Regression Model with fixed effect emerged the best model with log likelihood value of -1336.554. This study recommended that Government and NGOs need more strategies to fight against HIV menace in West Africa as this will in turn reduced TB cases in West Africa.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

The research work examined the trend of HIV/AIDS, Tuberculosis, and Hepatitis diseases in Plateau state. Annual data from 2003 to 2018 was collected from the department of biostatistics at Plateau State Specialist Hospital (PSSH), Jos. The methods of analysis used are the Poisson Autoregressive Model (PAR(1)) and the Poisson Exponentially Weighted Moving Average Model (PEWMA). The results revealed a significant annual decrease of 23.9% and 4% in Tuberculosis and HIV/AIDS respectively. Furthermore, the results showed a significant annual increase of 46% in Hepatitis. The PEWMA model used revealed that TB increased by 0.02% when there is an increase in HIV but not significant, while Hepatitis significantly aggravates TB by at least 0.24%. Also, there is a significant rise in HIV by 0.85% when TB increases but Hepatitis has no such effect on HIV. Lastly, PEWMA model indicated a rise of 0.5% in Hepatitis cases when there is an increase in TB, but a surge in HIV has no such effect on Hepatitis cases in Jos. The study recommended that fight against TB should be intensified since TB cases significantly affect both HIV and Hepatitis in Jos, Nigeria.

The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the comparison of the maximum likelihood estimates and the Bayes estimates of two-parameter power function distribution. The Bayes estimates are obtained, using conjugate priors, under five loss functions consist of square error, precautionary, weighted, LINEX and DeGroot loss function. The Gibbs sampling algorithm is proposed to generate samples from posterior distributions and in result the Bayes estimates are computed. The comparison of the maximum likelihood estimates and the Bayes estimates are done through the root mean squared errors. One real-life data set is analyzed to illustrate the evaluation of proposed methods of estimation. Finally, results from the simulation are discussed to assess the performance behavior of the maximum likelihood estimates and the Bayes estimates.

Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more sensitive tests of Lorentz symmetry. In the photon sector, astrophysical observations, in particular polarization measurements, are a very powerful tool because tiny deviations from Lorentz invariance will accumulate as photons propagate over cosmological distances. The Standard-Model Extension (SME) provides a theoretical framework in the form of an effective field theory that describes low-energy effects due to a more fundamental quantum gravity theory by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension d of the corresponding operator and lead to a wavelength, polarization, and direction dependent phase velocity of light. In this paper, we analyze optical polarization measurements from 63 Active Galactic Nuclei (AGN) and Gamma-ray Bursts (GRBs) in order to search for Lorentz violating signals. We derive the first set limits on each of the 10 individual birefringent coefficients of the minimal SME with d = 4, with 95% confidence limits on the order of 10⁻³⁴ on the dimensionless coefficients.

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

Different contact materials along with optimization of the deposition techniques expand the possibilities to obtain high performance room temperature CdTe-based X/γ-ray detectors. The heterostructures with ohmic (MoOx) and Schottky (MoOx, TiOx, TiN, and In) contacts, created by DC reactive magnetron sputtering and vacuum thermal evaporation, as well as In/CdTe/Au diodes with a p-n junction, formed by laser-induced doping, were developed and investigated. Depending on the pre-treatment of the surface of semi-insulating p-CdTe crystals, deposition of a MoOx film formed an ohmic or Schottky contact. Based on the calculations and IV characteristics of the fabricated Mo-MoOx/р-CdTe/MoOx-Mo, In/CdTe/MoOx-Mo, Ti-TiOx/р-CdTe/MoOx-Mo, and Ti-TiN/р-CdTe/MoOx-Mo Schottky-diode detectors, the current transport processes were described in the models of the carrier generation-recombination within the space-charge region (SCR) at low bias voltages, and space-charge limited current at higher voltages, respectively. The energies of generation–recombination centers, density of trapping centers, and carrier lifetimes were determined. A sharp increase in the reverse current in the Mo-MoOx/р-CdTe/MoOx-Mo, Ti-TiOx/р-CdTe/MoOx-Mo, and Ti-TiN/р-CdTe/MoOx-Mo heterostructures at high bias was discussed in frames of the Poole–Frenkel emission model. Nanosecond laser irradiation of the In electrode, pre-deposited on the p-CdTe crystals, resulted in an increase in the voltage range, corresponding to the carrier generation-recombination in the SCR, in the IV characteristics of the In/CdTe/Au diodes. Such In/CdTe/Au p-n junction diodes demonstrated high energy resolutions (7%@59.5 keV, 4%@122 keV, and 1.6%@662 keV).

Chikungunya virus (CHIKV) and Zika virus (ZIKV) have recently emerged as global infections with consequential disability adjusted life years (DALYs) and economic burden. This study aimed to explore the spatiotemporal heterogeneity in the occurrence of CHIKV and ZIKV outbreaks throughout Barranquilla, Colombia during 2014 and 2016 and explored the potential for clustering. Incidence data were fitted using multiple Bayesian Poisson models based on a suite of explanatory variables as potential risk factors and multiple options for random effects. A best fit model was used to analyse the case incidence risk for both epidemics to identify any risk factors during their epidemics. Neighbourhoods in the northern region of Barranquilla were hotspots for the outbreaks of both CHIKV and ZIKV. Additional hotspots occurred in the south-western and central regions of the CHIKV and ZIKV outbreaks, respectively. Multivariate conditional autoregressive models strongly identified higher socioeconomic strata (SES) and residing in detached houses as risk factors for ZIKV case incidences. These novel findings challenge the belief that these infections are driven by social vulnerability and merits further study both in Barranquilla and throughout the tropical and subtropical regions of the world.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

Roses are one of the most important floricultural crops, and their essential oils have long been used for cosmetics and aromatherapy. We investigated the volatile compound compositions of 12 flower-color mutant variants and their original cultivars. Twelve rose mutant genotypes were developed by treatment with 70 Gy of 60Co gamma irradiation of six commercial rose cultivars. Essential oils from the flowers of the 18 genotypes were analyzed by gas chromatography–mass spectrometry. Seventy-seven volatile compounds were detected, which were categorized into five classes: hydrocarbons, terpenoids, alcohols, esters, and others. Hydrocarbons, alcohols, and esters were major components in all rose flowers. The mutant genotypes CR-S8 and CR-S9 showed higher contents of hydrocarbons than the original cultivar. In addition, CR-S1, CR-S3, and CR-S4 mutant genotypes showed higher ester contents than their original cultivar. Nonacosane, 2-methylhexacosane, and 2-methyltricosane were major volatile compounds among all genotypes. Hierarchical cluster analysis of the rose genotypes gave four groups according to grouping among the 77 volatile compounds. These findings will be useful for the selection of rose genotypes with improved volatile compounds.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

Different forces play a key-role in the stability of food colloid dispersions. Focus is here on those controlling attraction and/or repulsion, which concur to stabilization, phase separation, coagulation, and are quite evident in water-based systems. Combination of attractive and repulsive forces favors, or hinders, the association of colloid entities; such processes are often met in food technology. The above processes depend on the forces at work, and on colloid concentration in the medium (i.e. on inter-particle distance). Worked examples deals with milk manipulation procedures, ending in cheese formation. The whole milk-working sequence is controlled by the combination of forces leading to aggregation and phase separation of casein and other milk components. Thereafter, one gets either fresh, for prompt consumption, or aged cheeses. The combination of attractive (van der Waals, vdW, and depletion) with repulsive (double layer, DL, but also with steric) forces results in the dominance of aggregation versus dispersion modes in all steps of milk transformation, which depend on the distance among colloid particles, on the amplitude of the mentioned forces, and on their decay length. The combined role of double layer and van der Waals (vdW) forces is at the basis of the DLVO theory on colloid stability, which is properly modified when these forces overlap with steric stabilization and, eventually, with depletion. Steric effects are dispersive, depletion ones favor colloid nucleation in a single phase. The milk manipulation chain is a worked example of the intriguing association features controlled by the mentioned forces (and of ancillary ones, as well), and indicates which forces favor the formation of products such as Parmesan or Mozzarella cheese, but are not alien to the preparation of many other dairy products.

Succinic semialdehyde dehydrogenase deficiency (SSADH-D) is a genetic disorder that results from the aberrant metabolism of the neurotransmitter γ-amino butyric acid (GABA). The disease is caused by the impaired activity of the mitochondrial enzyme succinic semialdehyde dehydrogenase. SSADH-D manifests as varying degree of mental retardation, autism, ataxia and epileptic seizures, but the clinical picture is highly heterogeneous. So far, there is no approved therapy for this disease. In this review, we briefly summarize the molecular genetics of SSADH-D, the past and ongoing clinical trials and the emerging features of the molecular pathogenesis, including redox imbalance and mitochondrial dysfunction. The main aim of this review is to discuss the potential use of further therapy approaches that have so far not been tested in SSADH-D, such as pharmacological chaperones, read-through drugs and gene therapy. Special attention will also be paid to elucidating the role of patient advocacy organizations in facilitating research and in the communication between the researchers and the patients.

With new discoveries and insights in atomic and optical physics, the field of spectroscopy is advancing to a new level with applications ranging from material science to astronomy. We here propose a theoretical description of a potential new phenomenon resulting from the extension of Compton's experiment on the scattering of high energy photons through atomic electrons. How the proposed phenomenon can be tested experimentally is discussed in the paper as well.

Introduction: Tuberculosis (TB) is one of the most prevalent respiratory diseases in the world. In 2020 there were at least 9.9 million new infections, with 1.5 million deaths. Approximately 10% of people infected with Mycobacterium tuberculosis (LTBI) develop the disease during the first 2 to 5 years after infection. Currently in South America, the diagnosis of LTBI continues to be per-formed through the Mantoux tuberculin skin test (TST). Objective: The objective of our study was to compare the sensitivity of a new immunofluorescence IGRA test against a widely available IGRA kit on the market. Material and method: Close contact to infectious patients with TB, or HIV patients or immunocompromised for another cause were recruited. Two interferon gamma release assay (IGRA) diagnostic kits were used and compared with TST. Results: 76 patients were recruited. 93.42% were Chilean nationality, 98.68% of the patients did not have immunosuppres-sion. The sensitivity of the new technique was 88.89% and specificity 92.50% in the study popula-tion compared to the IGRA previously used. In the subgroup older than 36 years, the sensitivity was 95.65% and the specificity 89.47%. Conclusion: IGRA techniques are a new resource in clini-cal laboratories to be able to make an accurate diagnosis in LTBI in the region of the Americas. In our population, the greatest benefit of this new IGRA would be observed in people over 36 years of age, where the sensitivity of the technique was like that of the currently available test.

The purpose of this study is to assess the concentration-response relations between conjunctivitis and exposure to ambient ozone. This retrospective study includes emergency department (ED) visits for conjunctivitis in Edmonton, Canada, for the period April 1992–March 2002. Daily average levels of ozone (range: 1.2–50.9, ppb), of temperature, and of relative humidity were estimated and used for the period of the study. For each of the considered exposure lags, (from 0 to 9 days), six different models were fitted to estimate the concentration-response function. The goodness of fit was assessed using the Akaike information criterion. During the period of the study, 17,211 ED visits for conjunctivitis were recorded and used. For all subjects together, a positive statistically significant association was obtained for the exposure lagged by 5 days. For female subjects, lags 1, 3, and 9 had positive statistically significant associations (lag 2 had negative associations). For male subjects, only lag 5 had a positive statistically significant association. The estimated non-linear concentration-response functions for the considered groups (all, males, females) and lags, revealed the associations along the exposure levels. The fitted shapes are described by algebraic functions and may have various forms. The estimated functions are useful to determine the risk associated with exposure to ground-level ozone.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

Interferon gamma (IFNg) is a pleiotropic cytokine that can potentially reprogramme the tumour microenvironment. However, the antitumour immunomodulatory properties of IFNg still need to be validated due to variable therapeutic outcomes in preclinical and clinical studies. We developed a replication-deficient Semliki Forest virus vector expressing IFNg (SFV/IFNg) and evaluated its immunomodulatory antitumour potential in vitro in a model of 3D spheroids and in vivo in immunocompetent 4T1 mouse breast cancer model. We demonstrated that SFV-derived IFN-g stimulated bone marrow macrophages to acquire the tumoricidal M1 phenotype in 3D nonattached conditions. Coculturing SFV/IFNg-infected 4T1 spheroids with BMDMs inhibited spheroid growth. In the orthotopic 4T1 mouse model, intratumoural administration of SFV/IFNg virus particles alone or in combination with the Pam3CSK4 TLR2/1 ligand led to significant inhibition of tumour growth compared to the administration of the control SFV/Luc virus particles. Analysis of the composition of intra-tumoural lymphoid cells isolated from tumours after SFV/IFNg treatment revealed an increase in CD4+ and CD8+ and a decrease in T-reg (CD4+/CD25+/FoxP3+) cell populations. Furthermore, a significant decrease in the populations of cells bearing myeloid cell markers CD11b, CD38 and CD206 was observed. In conclusion, the SFV/IFNg vector induces a therapeutic antitumour T-cell response and inhibits myeloid cell infiltration in treated tumours.

In Sub-Saharan African Countries such as Nigeria with high prevalence rate, Child HIV/AIDs acquired through Mother-to-Child transmission (MTCT) can be largely prevented by using a well-established prevention programme and scheme. This study examined factors that can enhanced Prevention of Mother-to-Child transmission (PMTCT) in Nasarawa State. To achieve this, structured questionnaire were used to collect data from one hundred and sixteen (116) women attending two (2) primary facilities and two (2) secondary facilities in the State. This study utilized methods of Poisson Regression, Negative Binomial Regression and Logistic Regression Analyses. Results revealed that women with at least a secondary school education, women with husband in military and women with perceived confidentiality of their HIV status significantly enhanced PMTCT of HIV in Nasarawa State while significant proportion of the women attest to the fact that drugs are available in the facilities (p-value=0.0000<0.05) . Other factors include mother income level, willingness to continue with PMTCT programme and women in support group can also enhanced PMTCT though they are not significant. This study recommends that the factors identified should be explored by NGOs, Ministry of Health and, Support groups and other relevant agencies since they have the capacity to enhanced PMTCT of HIV in Nasarawa State, Nigeria.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these popular distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is the upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of a random discrete variable. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

Technology development changes society and society demands new and innovative technology development. We analyze technology to understand society and technology itself. Many researches have been introduced in various fields. Most of them were about patent analysis. This is because detailed and accurate results of research and development are patented. In this paper, we study on new patent analysis method based on count data model and Bayesian regression analysis. Using count data model, we analyze the technological keywords extracted from the collected patent documents. We use the posterior distribution of Bayesian statistics to reflect the experience and knowledge of the relevant technological experts in the analysis model. Moreover, we apply the proposed model to finding sustainable technologies. Finding and developing sustainable technologies is an important activity for companies and research institutes to maintain their technological competitiveness. To illustrate how our modeling could be applied to real domain, we carry out a case study using the patent documents related to artificial intelligence.

The name PNP was introduced by Eisenberg and Chen because it has important physical meaning beyond being the first letters of Poisson-Nernst-Planck. PNP also means Positive-Negative-Positive, the signs of majority current carriers in different regions of a PNP bipolar transistor. PNP transistors are two diodes in series PN + NP that rectify by changing the shape of the electric field. Transistors can function as quite different types of nonlinear devices by changing the shape of the electric field. Those realities motivated Eisenberg and Chen to introduce the name PNP in 1993.The pun “PNP = Poisson-Nernst-Planck = Positive-Negative-Positive” has physical content. It suggests that Poisson-Nernst-Planck systems like open ionic channels cannot be assumed to have constant electric fields. Indeed, the equations of electrodynamics make it more or less impossible that a channel have a constant electric field, if there is permanent charge nearby. The electric field must be studied and computed because its change of shape is unavoidable for charged channels, and the shape of the electric field is likely to be important in the function of biological systems, as it is in semiconductor systems.

For the in-house validation of a droplet digital PCR method, a factorial experimental design was implemented. This design serves different purposes. On the one hand, it is an efficient design in relation to the workload involved in achieving a desirable level of reliability of variance estimates. On the other hand, it allows a partitioning of total variance into different components, thus providing information regarding the dominant sources of random variation. The statistical modelling reflects the actual measurement mechanism, establishing relationships between nominal target DNA copies per well, the range of variation of copy numbers per droplet, probability of detection values, and estimated numbers of copies.

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.

The brain rhythms are essential for information processing in neuronal networks. Oscillations recorded in different brain regions can be synchronized and have a constant phase difference, i.e. be coherent. Coherence between local field potential (LFP) signals from different regions in the brain may be correlated with the performance of cognitive tasks, from which it is concluded that these regions of the brain are involved in the task performance together. In this review, we discuss why coherence occurs and how it is coupled to the information transfer between different regions of the hippocampal formation. Coherence in theta and gamma frequency ranges is described since these rhythms are most pronounced during the hippocampus-dependent attention and memory. We review in vivo studies of interactions between different regions of the hippocampal formation in theta and gamma frequency bands. The kay provisions of the review: 1) coherence emerges from synchronous postsynaptic currents in principal neurons, occurring as a result of synchronization of neuronal spike activity; 2) synchronization of neuronal spike patterns in two regions of the hippocampal formation can be realised through induction or resonance; 3) coherence at a specific time point reflects the transfer of information between regions of the hippocampal formation, in particular, gamma coherence reflects the coupling of active neuronal ensembles. Overall, coherence is not an epiphenomenon, but an important physiological process that has certain generation mechanisms and performs important functions in information processing and transmission across the brain regions.

Chikungunya virus (CHIKV) and Zika virus (ZIKV) have recently emerged as global infections with consequential disability adjusted life years (DALYs) and economic burden. This study aimed to explore the spatiotemporal heterogeneity in the occurrence of CHIKV and ZIKV outbreaks throughout Barranquilla, Colombia during 2014 and 2016 and explored the potential for clustering. Incidence data were fitted using multiple Bayesian Poisson models based on a suite of explanatory variables as potential risk factors and multiple options for random effects. A best fit model was used to analyse the case incidence risk for both epidemics to identify any risk factors during their epidemics. Neighbourhoods in the northern region of Barranquilla were hotspots for the outbreaks of both CHIKV and ZIKV. Additional hotspots occurred in the south-western and central regions of the CHIKV and ZIKV outbreaks, respectively. Multivariate conditional autoregressive models strongly identified higher socioeconomic strata (SES) and residing in detached houses as risk factors for ZIKV case incidences. These novel findings challenge the belief that these infections are driven by social vulnerability and merits further study both in Barranquilla and throughout the tropical and subtropical regions of the world.

The dentate gyrus (DG) is part of the hippocampal formation and is essential for important cognitive processes such as navigation and memory. The oscillatory activity of the DG network is believed to play a critical role in cognition. DG circuits generate three main rhythms: theta, beta, and gamma, which participate in the specific information processing performed by DG neurons. In the temporal lobe epilepsy (TLE), cognitive abilities are impaired, which may be due to drastic alterations in the DG structure and network activity during epileptogenesis. The theta rhythm and theta coherence are especially vulnerable in dentate circuits; disturbances in DG theta oscillations and their coherence may be responsible for general cognitive impairments observed during epileptogenesis. Some researchers suggested that the vulnerability of DG mossy cells is a key factor in the genesis of TLE, but others did not support this hypothesis. The aim of the review is not only to present the current state of the art in this field of research but to help pave the way for future investigations by highlighting the gaps in our knowledge to completely appreciate the role of DG rhythms in brain functions. Disturbances in oscillatory activity of the DG during TLE development are described in detail that may be a diagnostic marker in the treatment of this disease.

The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of the series manipulation method. Furthermore, two correlations including Bernoulli and Euler polynomials for gamma distribution polynomials are provided by utilizing of their generating functions.

We show that the quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems allowing exposing its falsity.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

Gamma titanium aluminides (γ-TiAl) present an excellent behaviour under high temperature conditions, being a feasible alternative to nickel-based superalloy components in aeroengine sector. However, considered as a difficult to cut material, process cutting parameters require special study to guarantee components quality. In this work, developed drilling mechanistic model is a useful tool in order to predict drilling force (F_z) and torque (T_c) for optimal drilling conditions determination. The model is validated for three types of Gamma-TiAl alloys. Integral hard metal end-drilling tools and different cutting parameters (feeds and cutting speeds) are tested in three different sized holes for each alloy.

A critical analysis of the classical definition of outsiders is given. Some examples show that this notion is not universal and has at least two drawbacks. Particularly, the set of outsiders may have the probability arbitrary close to one half. On the other hand, the deleting of the set of outsiders may dramatically change the value of the median.

Understanding the spatially varying effects of demographic factors on the spatio-temporal variation of intestinal parasites infections is important for public health intervention and monitoring. This paper presents a hierarchical Bayesian spatially varying coefficient model to evaluate the effects demographic factors on intestinal parasites morbidities in Ghana. The modeling relied on morbidity data collected by the District Health Information Management Systems. We developed Poisson and Poisson-gamma spatially varying coefficient Models. We used the demographic factors, unsafe drinking water, unsafe toilet and unsafe liquid waste disposal as model covariates. The models were fitted using the Integrated Nested Laplace Approximations (INLA). The overall risk of intestinal parasites infection was estimated to be 10.9 per 100 people with a wide spatial variation in the district-specific posterior risk estimates. Substantial spatial variation of increasing multiplicative effects of unsafe drinking water, unsafe toilet and unsafe liquid waste disposal occurs on the variation of intestinal parasites risk. The structured residual spatial variation widely dominates the unstructured component, suggesting that the unaccounted-for risk factors are spatially continuous in nature. The study concludes that both the spatial distribution of the posterior risk and the associated exceedance probability maps are essential for monitoring and control of intestinal parasites.

Analyses of the Hubble diagrams are presented for SN1a supernovae and gamma ray bursts in the redshift ranges z = 0.01–1.3 and 0.034–8.1, respectively. Data are presented on the typical z/μ scale and also on the less common yet increasingly sensitive photon flight time t/(z+1) scale. The primary conclusion is that on the basis of the presently accessible data in the redshift range z = 0.01–8.1, the slope of the Hubble diagram is, or is extremely close to, exponential.

With the development of nuclear technology application, radiation safety has been widely concerned, and there is an urgent need for novel shielding materials. Among the various options available, non-lead organic composite shielding material has emerged as a promising solution in the field of radiation shielding due to its high strength, easy processing, and light weight. In this study, tungsten/epoxy resin (W/EP) composite samples with tungsten weight fraction from 0% to 60% were prepared. The shielding and mechanical properties of W/EP composites were investigated. The results show that the results showed that the higher the tungsten content, the greater the shielding capacity of W/EP composites, particularly for low-energy gamma ray (γ) shielding. However, the addition of tungsten reduces the impact strength and tensile properties of the material. Overall, for 300 keV γ-ray, W/EP with 30% tungsten content has comparable shielding capacity to ordinary concrete. W/EP composite materials can serve as shielding materials for low-energy γ-rays.

The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on ℤ_{p}. Also, we acquire two fermionic p-adic integrals of p-adic gamma function in terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.

Over the past decade, our knowledge of the $\gamma$-ray sky has been revolutionized by ground- and space-based observatories by detecting photons up to several hundreds of tera-electron volt (TeV) energies. A major population of the $\gamma$-ray bright objects are active galactic nuclei (AGN) with their relativistic jets pointed along our line-of-sight. Gamma-ray emission is also detected from nearby mis-aligned AGN such as radio galaxies. While the TeV-detected radio galaxies ($TeVRad$) only form a small fraction of the $\gamma$-ray detected AGN, their multi-wavelength study offers a unique opportunity to probe and pinpoint the high-energy emission processes and sites. Even in the absence of substantial Doppler beaming $TeVRad$ are extremely bright objects in the TeV sky (luminosities detected up to $10^{45}~erg~s^{-1}$), and exhibit flux variations on timescales shorter than the event-horizon scales (flux doubling timescale less than 5 minutes). Thanks to the recent advancement in the imaging capabilities of high-resolution radio interferometry (millimeter very long baseline interferometry, mm-VLBI), one can probe the scales down to less than 10 gravitational radii in $TeVRad$, making it possible not only to test jet launching models but also to pinpoint the high-energy emission sites and to unravel the emission mechanisms. This review provides an overview of the high-energy observations of $TeVRad$ with a focus on the emitting sites and radiation processes. Some recent approaches in simulations are also sketched. Observations by the near-future facilities like Cherenkov Telescope Array, short millimeter-VLBI, and high-energy polarimetry instruments will be crucial for discriminating the competing high-energy emission models.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

Recent research has identified the gut-brain axis as a key mechanistic pathway and potential therapeutic target in depression. In this paper, the potential role of gut hormones as potential treatments or predictors of response in depression is examined, with specific reference to the peptide hormone motilin. This possibility is explored through two methods: (a) a conceptual review of the possible links between motilin and depression, including evidence from animal and human research as well as clinical trials, and (b) an analysis of the relationship between a functional polymorphism (rs2281820) of the motilin (MLN) gene and cross-national variations in the prevalence of depression. It was observed that (a) there are several plausible mechanisms, including interactions with diet, monoamine, and neuroendocrine pathways, to suggest that motilin may be relevant to the pathophysiology and treatment of depression, and (b) there was a significant correlation between rs2281820 allele frequencies and the prevalence of depression after correcting for multiple confounding factors. These results suggest that further evaluation of the utility of motilin and related gut peptides as markers of antidepressant response is required, and that these molecular pathways represent potential future mechanisms for antidepressant drug development.

This article examines the impact of some system parameters on an industrial system composed of two dissimilar parallel units with one repairman. The active unit may fail due to essential factors like aging or deteriorating, or exterior phenomena such as Poisson shocks that occur at various time periods. Whenever the value of a shock is larger than the specified threshold of the active unit, the active unit will fail. The article assumes that the repairman has the right to take any of two decisions at the beginning of the system operation: either a takes a vacation if the two units work in a normal way, or stay in the system to monitor the system until the first system failure. In case of having a failure in any of the two units during the absence of the repairman, the failing unit will have to wait until the repairman is called back to work. We suppose that the value of every shock is assumed to be i.i.d. with some known distribution. The length of the repairman’s vacation, repair time, and recall time are arbitrary distributions. Various reliability measures have been calculated by the supplementary variable technique and the Markov’s vector process theory. At last, numerical computation and graphical analysis have been given for a particular case to validate the derived indices.

In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on ℤ_{p}. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gamma function. We acquire a representation for the p-adic Euler constant by means of the q-Boole polynomials. We finally develop a novel, explicit and interesting representation for the p-adic Euler constant including Stirling numbers of the first kind.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

The normal and Poisson distribution assumptions in the normal-Poisson mixed effects regression model are often too restrictive for many real count data. Several works have independently relaxed the Poisson conditional distribution assumption for counts or the normal distribution assumption for random effects. This work couples some recent advances in these two regards to develop a skew t–discrete gamma regression model in which the count outcomes have full dispersion flexibility and random effets can be skewed and heavy tailed. Inference in the model is achieved by maximum likelihood using pseudo-adaptive Gaussian quadature. The use of the proposal is demonstrated on a popular owl sibling negotiation data. It appears that, for this example, the proposed approach outperforms models based on normal random effects and the Poisson or negative binomial count distribution.

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

In humans, finely tuned gamma synchronization (60-90 Hz) rapidly appears at movement onset in a motor control network involving primary motor cortex, the basals ganglia and motor thalamus. Yet the functional consequences of brief movement-related synchronization are still unclear. Distinct synchronization phenomena have also been linked to different forms of motor inhibition, including relaxing antagonist muscles, rapid movement interruption and stabilizing network dynamics for sustained contractions. Here I will introduce detailed hypotheses about how intra- and inter-site synchronization could interact with firing rate changes in different parts of the network to enable flexible action control. The here proposed cause-and-effect relationships shine a spotlight on potential key mechanisms of cortico-basal ganglia-thalamo-cortical communication. Confirming or revising these hypotheses will be critical in understanding the neuronal basis of flexible movement initiation, invigoration and inhibition. Ultimately, the study of more complex cognitive phenomena will also become more tractable once we understand the neuronal mechanisms underlying behavioural readouts.

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

We review a modern differential geometric description of the fluid isotropic motion and featuring it the diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. There is analyzed the adiabatic liquid dynamics, within which, following the general approach, there is explained in detail, the nature of the related Poissonian structure on the fluid motion phase space, as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product. We also present a modification of the Hamiltonian analysis in case of the isotermal liquid dynamics. We study the differential-geometric structure of the adiabatic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and invariant theory. In particular, we construct an infinite hierarchies of different kinds of integral magneto-hydrodynamic invariants, generalizing those before constructed in the literature, and analyze their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, some generalization of the canonical Lie-Poisson type bracket is obtained.

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

We utilized all Spanish marriage records available at the municipality level from 2005-2007 to model spatial variations in intermarriage. We constructed a spatial regime zero inflated Poisson model and grouped-data probit model, with spatially lagged regressors, to predict the absolute and relative presence of intermarriage between Spaniards and migrants based on structural characteristics of the local marriage markets and their neighboring areas (i.e., relative group size, homogeneity of national origins, and sex ratio indicators). Our models do not assume collapsibility of the marriage market. Instead, they incorporate the local dimension of the marriage market and examine the association between intermarriage and structural variables at the spatial local level. The model also investigates intermarriage variation by size of place. The local characteristics of the marriage markets are robust indicators of both the absolute and relative importance of intermarriage, but their impact varies by size of municipality. The relative size of the migrant community positively impacts intermarriage. The homogeneity of the origins of migrants is negatively related to it. The impact of sex ratios in the migrant and native communities on intermarriage is not uniform across all municipalities and is not always related to more intermarriage.

Cystathionine gamma-lyase (CSE) is an essential Hydrogen sulphide (H2S)-producing enzyme that regulates diverse processes related to cardiovascular function. It is crucial to understand how exogenous H2S regulates CSE expression in vascular endothelial cells during hypoxia. We examined the regulatory effect of 100 μM H2S on the transcription and expression of CSE in HUVECs during hypoxia by luciferase assay, Western blotting, and quantitative RT-qPCR. Exogenous H2S influenced the promoter activity of CSE in HUVECs during hypoxia. Compared with 0 μM H2S, 100 μM H2S decreased the mRNA expression of CSE in HUVECs. Compared with 0 μM H2S, 100 μM H2S decreased the protein expression of CSE in HUVECs after 2 h of hypoxia. These findings suggest that vascular endothelial cells can respond to changes in H2S concentration in the blood during hypoxia.

In this paper we re-investigated the relationship between the symmetry of inertial systems and the Lorentz transformation. We found that when we just follow the following three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, then we can totally construct a general coordinate transformation to meet the symmetry of inertial systems, and with a special assumption on the speed of light, we can construct a non-Lorentz transformation between inertial systems to make the particle’s energy have a limited value, which is similar to the rainbow model. Similar to the usual Lorentz violating models, the non-Lorentz transformation in this paper lead to a new modified disperse relation. We applied the obtained disperse relation to analyze the photon’s arrival time lag effect in astronomy and found that the "maximum energy" derived in our model is somewhat related to the "maximum energy" assumed in the rainbow model.

Alcohol use disorder (AUD) is a chronically relapsing disease characterized by loss of control in seeking and consuming alcohol (ethanol) driven by recruitment of brain stress systems. However, AUD differs among the sexes: men are more likely to develop AUD, but women progress from casual to binge drinking and heavy alcohol use more quickly. The central amygdala (CeA) is a hub of stress and anxiety, with corticotropin releasing factor (CRF)-CRF1 receptor and GABAergic signaling dysregulation occurring in alcohol dependent male rodents. However, we recently showed that GABAergic synapses in female rats are less sensitive to the acute effects of ethanol. Here, we used patch clamp electrophysiology to examine the effects of alcohol dependence on the CRF-modulation of rat CeA GABAergic transmission of both sexes. We found that GABAergic synapses of naïve female rats were unresponsive to CRF application compared males, although alcohol dependence induced a similar CRF responsivity in both sexes. In situ hybridization revealed that females had less CeA neurons containing mRNA for the CRF1 receptor (Crhr1) than males, but in dependence, the percentage of Crhr1-expressing neurons in females increased, unlike males. Overall, our data provide evidence for sexually dimorphic CeA CRF system effects on GABAergic synapses in dependence.

Photothrombotic stroke (PTS) stimulates the level of N- and C-terminal fragments of Amyloid precursor protein (APP) growth in the cytoplasm of ischemic penumbra cells not earlier but at 24 hours. Here we have shown that APP fragments are visualized in thin unmyelinated fibers of neurons, in containing mitochondria large fibers and in synapses but absent in the nuclei. At 24 hours after PTS, some elements of the destroyed tissue accumulated a significant amount of APP protein. The level of ADAM10 α-secretase decreased on the first day after PTS in the rat brain cortex and ADAM-10 co-localized with the lipid raft marker caveolin-1. PTS caused no changes in the level of β-secretase BACE1 either on the first day after PTS or in the early recovery period. The expression of proteins of the γ-secretase complex: presenilin-1 and nicastrin increased in astrocytes, but not in penumbra neurons after PTS. The β-secretase inhibitor LY2886721 did not affect the infarct size of the mouse cerebral cortex and the level of apoptosis of cells in the perifocal region after PTS. Whereas the inhibitor of γ-secretase DAPT reduced the expression of glial fibrillary acidic protein (GFAP) in astrocytes, prevented the growth of apoptosis of mouse cerebral cortex cells reducing the infarct volume on the 7th and 14th days after PTS. DAPT may be considered as a drug for stroke therapy.

The dermatological manifestations of Long Covid (LC) have languished in the shadows of chronic fatigue and brain fog. Yet they are all linked by gut dysbiosis and the cytokine triad of TNF-α, IL-1β, and IL-6. The gut microbiome common not only to LC, psoriasis, AA, and vitiligo but also to neurodegenerative disease has been recently described. This gut microbiome induces an altered tryptophan metabolism linked to autoimmune disease. SARS CoV2 invades enterochromaffin cells rich in ACE2 receptors and curtails absorption of the essential amino acid tryptophan and subsequent synthesis of serotonin and melatonin. This review suggests that an etiologic prebiotic (d-mannose)/probiotic (lactobacilli, bifidobacteria)/postbiotic (butyrate) approach to autoimmune skin disease that improves intestinal barrier integrity and that suppresses the triad of TNF-α, IL-6, and IL-1β may enhance or even eliminate the traditional immunotherapy of targeted monoclonal antibodies, Janus kinase inhibitors, and steroids. Health benefits of this approach extend well beyond suppression of autoimmune skin disease.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

Additive manufacturing or 3D printing applying polycaprolactone-(PCL)-based medical devices represents an important branch of tissue engineering, where the sterilization method is a key process for further safe application in vitro and in vivo. In this study, the authors intend to access the most suitable gamma radiation conditions to sterilize PCL-based scaffolds in a preliminary biocompatibility assessment, envisioning future studies for airway obstruction conditions. Three radiation levels were considered, 25 kGy, 35 kGy and 45 kGy and evaluated as to their cyto- and biocompatibility. All three groups presented biocompatible properties, indicating an adequate sterility condition. As for the cytocompatibility analysis, devices sterilized by 35 kGy and 45 kGy showed better results, with the 45 kGy showing overall improved outcomes. This study allowed to select the most suitable sterilization condition for PCL-based scaffolds, aiming at immediate future assays, by applying 3D-customized printing techniques to specific airway obstruction lesions of the trachea.

In this review, we present the latest exclusion limits obtained with astroparticles for Lorentz Invariance Violation (LIV) in the photon sector. We discuss the techniques known as energy-dependent time delay or time lag, subluminal pair production threshold shift, superluminal photon decays and superluminal photon splitting. Perspectives for future results in LIV with the next generation of experiments are also addressed.

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

The article presents the results of the γ-ray and fast neutrons impact on various rice species, in order to obtain mutant forms resistant to salinity (NaCl) and drought factors (sorbite). They are going to be used as initial forms in synthetic selection when creating varieties, adapted to the stressful conditions of, both, soil and climate in the Kazakhstan Aral Sea. The average lethal doses (LD50) of γ-rays and fast neutrons, as well as, the average NaCl and sorbite lethal concentrations were established. A distinct dependence on the effect of ionizing radiation and stress factors on the number of induced resistant mutant forms has been related to the initial rice variety. The largest number of mutant forms was obtained from the local variety Syr Suluy, followed by Leader and Aikerim varieties. Out of all varieties, only 1% of the initially irradiated by γ-rays seeds survived, while after fast neutron irradiation – 4,3%. M1 mutant plants significantly differ from the initial forms in terms of morphological features – plant height, panicle length, and grain size. They are tolerant to lodging, and have short and highly sterile panicles, indicating that they are mutants.

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized 20 x 20 m convex and non-convex environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment and at lower computational complexity per action. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than 95% median completion rate for up to seven obstructions.