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This paper studies finite sample minimax optimal randomization schemes and estimation schemes in estimating parameters including the average treatment effect, when treatment effects are heterogeneous. A randomization scheme is a distribution over a group of permutations of a given treatment assignment vector. An estimation scheme is a joint distribution over assignment vectors, linear estimators, and permutations of assignment vectors. The key element in the minimax problem is that the worst case is over a class of distributions of the data which is invariant to a group of permutations. First, I show that given any assignment vector and any estimator, the uniform distribution over the same group of permutations, namely the complete randomization scheme, is minimax optimal. Second, under further assumptions on the class of distributions and the objective function, I show the minimax optimal estimation scheme involves completely randomizing an assignment vector, while the optimal estimator is the difference-in-means under complete invariance and a weighted average of within-block differences under a block structure, and the number of treated units is determined by the Neyman allocation.

A basic assumption of the classic reinsurance model is that the distribution of the loss is precisely known. In practice, only partial information is available for the loss distribution due to the lack of data and estimation error. We study a distributionally robust reinsurance problem by minimizing the maximum Value-at-Risk (or the worst-case VaR) of the total retained loss of the insurer for all loss distributions with known mean and variance. Our model handles typical stop-loss reinsurance contracts. We show that a three-point distribution achieves the worst-case VaR of the total retained loss of the insurer, from which the closed-form solutions of the worst-case distribution and optimal deductible are obtained. Moreover, we show that the worst-case Conditional Value-at-Risk of the total retained loss of the insurer is equal to the worst-case VaR, and thus the optimal deductible is the same in both cases.

Many lipid membranes of eukaryotic cells are asymmetric, which means the two leaflets differ in at least one physical property, such as lipid composition or lateral stress. Maintaining this asymmetry is helped by the fact that ordinary phospholipids rarely transition between leaflets, but cholesterol is an exception: its flip-flop times are in the microsecond range, so that its distribution between leaflets is determined by a chemical equilibrium. In particular, preferential partitioning can draw cholesterol into a more saturated leaflet, and phospholipid number asymmetry can force it out of a compressed leaflet. Combining highly coarse-grained membrane simulations with theoretical modeling, we investigate how these two driving forces play against each other until cholesterol's chemical potential is equilibrated. The theory includes two coupled elastic sheets and a Flory-Huggins mixing free energy with a χ parameter. We obtain a relationship between χ and the interaction strength between cholesterol and lipids in either of the two leaflets, and we find that it depends, albeit weakly, on lipid number asymmetry. The differential stress measurements under various asymmetry conditions agree with our theoretical predictions. Using the two kinds of asymmetries in combination, we find that it is possible to counteract the phospholipid number bias, and the resultant stress in the membrane, via the control of cholesterol mixing in the leaflets.

Let X k 1 k = 1 ∞ , X k 2 k = 1 ∞ , … , X k d k = 1 ∞ be d independent sequences of Bernoulli random variables with success-parameters p 1 , p 2 , … , p d respectively, where d ≥ 2 is a positive integer, and 0 p j 1 for all j = 1 , 2 , … , d . Let S j ( n ) = ∑ i = 1 n X i j = X 1 j + X 2 j + ⋯ + X n j , n = 1 , 2 , … . We declare a “rencontre” at time n , or, equivalently, say that n is a “rencontre time,” if S 1 ( n ) = S 2 ( n ) = ⋯ = S d ( n ) . We motivate and study the distribution of the first (provided it is finite) rencontre time.

In this paper we obtain explicit estimates and existence results on the number of F q -rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.

Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) f ′ ′ + P ( z ) f = 0 , where P ( z ) is a polynomial. These results have been used by several authors to find interesting properties of solutions of (*). That said, many people have remarked that the proofs and discussion concerning asymptotic integration theory that are, for example, in E. Hille’s 1969 book Lectures on Ordinary Differential Equations are difficult to follow. The main purpose of this paper is to make this theory more understandable and accessible by giving complete explanations of the reasoning used to prove the theory and by writing full and clear statements of the results. A considerable part of the presentation and explanation of the material is different from that in Hille’s book.

We investigate distribution of eigenvalues of growing size Toeplitz matrices [ a n + k − j ] 1 ≤ j , k ≤ n as n → ∞ , when the entries { a j } are “smooth” in the sense, for example, that for some α > 0 , a j − 1 a j + 1 a j 2 = 1 − 1 α j ( 1 + o ( 1 ) ) , j → ∞ . Typically they are Maclaurin series coefficients of an entire function. We establish that when suitably scaled, the eigenvalue counting measures have limiting support on [ 0 , 1 ] , and under mild additional smoothness conditions, the universal scaled and weighted limit distribution is | π log ⁡ t | − 1 / 2 d t on [ 0 , 1 ] .

A fundamental problem in coding theory is to find the values of A ( n , d ) , i.e., the A ( n , d ) is the size of the maximum binary code set of length n and minimum Hamming distance d . And A ( n , d ) can also be viewed as the size of maximum independent set of d − 1 t h -power of the n -dimensional hypercube Q n . In order to further understand and study this problem, we study the distribution of the maximum clique and the structure of the point of Q n d for d ≤ 5 .

The concept of reference change values (RCVs) for diagnosis and monitoring of diseases has become well established. Several models habe been developed, e. g. one assuming a normal distribution and another one for a log-normal distribution. RCV values calculated for some measurands with both models are compared with each other and led to similar results. A few examples led to RCV values which are not plausible for diagnostic purposes. Although statistical concepts of RCV values are well established, their clinical relevance remains questionable at least for some measurands. Studies with clinicians are required whether RCVs are of practical usefulness.

In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.

For a system (or unit) whose lifetime is measured by the number cycles, according to the discrete time age replacement policy, it is replaced preventively after n cycles or correctively at failure, whichever occurs first. In this paper, discrete time age replacement policy is revisited when the lifetime of the system is modeled by a discrete phase-type distribution. In particular, the necessary conditions for the unique and finite replacement cycle which minimizes the expected cost per unit of time are obtained. The necessary conditions are mainly based on the behavior of the hazard rate. The results are illustrated for some special discrete phase-type lifetime distributions. Computational results are also presented for the optimal replacement cycle under specific real life setups.

In this study, the ECT system was used to study the temporal and spatial distribution characteristics of bed density in an ADMFB under the influence of superficial gas velocity and static bed height. The results show that, In the axial distribution, the closer to the top of the bed at low gas velocity( 13 cm/s), the lower the density. In the radial distribution, the closer to the central axis, the lower the density. With the decrease of static bed height, the radial uniformity becomes worse. The optimal gas velocity is 12.5 cm/s, under which the bed spatial distribution is the most uniform, and the ecart probable moyen of spherical particles is 0.06. The separation density is smaller than the bed density and is close to the central axis density.

As a recently arisen framework, Label Distribution Learning (LDL) is one of the most appropriate machine learning paradigms to solve the label ambiguity problems. Due to the high cost, it is intractable to directly collect annotated distribution-level data. Therefore, Label Enhancement (LE) is proposed to obtain the label distribution for training LDL model by mining the information hidden in the logical labels. Accordingly, LE is usually taken as the pre-processing of LDL algorithm to learn with logical labels in previous methods. These two-stage learning methods may reduce the performance of LDL. To this end, we propose a unified framework called L 2 which simultaneously conducts Label Enhancement and Label Distribution Learning on samples and logical labels to fully exploit the implicit information for learning optimal LDL model. Specifically, the recovery of label distribution benefits from not only the optimization of the conventional LE objective function but also the feedback of LDL loss. What is more, the recovered distribution labels can be directly applied to the supervision of LDL training in an end-to-end way. Extensive experiments illustrate that L 2 can correctly recover the distribution-level data from the logical labels, and the trained LDL model can perform favorably against state-of-the-art LDL algorithms with the recovered distribution data. 1

In this paper, we investigate the joint functional distribution of Selberg zeta functions for principal congruence subgroups. We prove that the joint universality theorem for these zeta functions holds in the strip 0.85 σ 1 . As a corollary, we obtain the functional independence for the zeta functions.

LPN (learning parity with noise) problem is a good candidate for post-quantum cryptography which enjoys simplicity and suitability for weak-power devices. Dottling et al. (ASIACRYPT 2012) initiated the first secure public key encryption (PKE) under the low-noise LPN assumption. Kiltz et al. (PKC 2014) proposed a simpler and more efficient scheme using double-trapdoor technique from the same assumption. Both schemes abide the decoding failure rate (DFR) 2 − Θ ( k ) (k is the security parameter) and there exists CPA/CCA2-secure PKE with squared-exponential DFR 2 − Θ ( k 2 ) from constant-noise LPN (Yu and Zhang, CRYPTO 2016). In this work, we give a positive answer with squared-exponential DFR in the low-noise setting. More precisely, we first introduce a variant (VxLPN) of the low-noise Exact LPN (xLPN, proposed by Jain et al. at ASIACRYPT 2012 and used as building block in commitments and zero-knowledge proofs), where the coefficient matrix A follows the uniform distribution over { 0 , 1 } q × n ( n = Θ ( k 2 ) , q = Θ ( n ) ), the secret x is sampled from B μ n ( B μ is the Bernoulli distribution with noise rate μ = Θ ( 1 q ) ), and the noise e follows a column vector distribution uniform over { z ∈ { 0 , 1 } q : | z | = q μ } . A series of reductions show that VxLPN is at least as hard as the standard LPN for the same noise rate μ. We then construct from the VxLPN CPA/CCA2 secure PKE schemes with squared-exponential DFR 2 − Θ ( k 2 ) which share the common structure extrinsically with Kiltz et al. and Yu-Zhang schemes. The secret key(s) in our schemes are simply sampled from the Bernoulli distribution, and comparatively, the secret key(s) in Yu-Zhang schemes must be chosen from a tailored version of Bernoulli distribution (along with the coefficient matrix A that follows a distribution D λ n × n = U n × λ ⋅ U λ × n induced by multiplying two random matrices in the public key, λ = Θ ( log 2 ⁡ n ) ) in order to guarantee the correctness of their schemes. Consider the performance on 128-bit security level, our CCA2-secure scheme only holds 117.79 MB public keys, 67.31 MB secret keys and 10.15 KB ciphertexts, and thus is more efficient than the schemes of Dottling et al. and Kiltz et al. ((14.53 GB, 14.48 GB, 14.06 KB) and (161.78 MB, 92.45 MB, 13.60 KB) respectively).

We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two explicit versions of the inverse function theorem, the first via general distribution and separation inequalities that may be of independent interest, the second via a careful implementation of classical Newton iteration., Comment: 49 pages

We perform a stochastic stability analysis with observation errors. Players recurrently play a symmetric two-player normal form game with one another and respond to the strategy distribution of other players. In each period, a revising player observes the strategy distribution and chooses a best response to it. Her observation is perturbed with positive probability and she may respond to the misperceived strategy distribution. The robustness of Nash equilibria to such observation errors is examined. We find that only transition probabilities within states where no player plays any strictly dominated strategy matter for stochastic stability. A more precise set of stochastically stable states is characterized for several particular observation error models. For the local interaction model, the set of stochastically stable states is robust to addition of strategies that do not survive iterative elimination of strictly dominated strategies regardless of error types (action/observation) under certain conditions.

Motivated by the analysis of range queries in databases, we introduce the computation of the depth distribution of a set B of n d-dimensional boxes (i.e., axis aligned d-dimensional hyperrectangles), which generalizes the computation of the Klee's measure and maximum depth of B . We present an algorithm to compute the depth distribution running in time within O ( n d + 1 2 log ⁡ n ) , using space within O ( n log ⁡ n ) , and refine these upper bound for various measures of difficulty of the input instances. Moreover, we introduce conditional lower bounds for this problem which not only provide insights on how fast the depth distribution can be computed, but also clarify the relation between the Depth Distribution problem and other fundamental problems in computer science.

Imbalanced data problem is a big challenge for judicial data analysis since it often leads to a low accuracy of the data classification . Synthesizing new samples by means of oversampling is a useful method to handle this problem. However, most oversampling algorithms have been obtained regardless of noise samples and the data distribution has not been fully taken into consideration. For this purpose, an improved cluster-based synthetic oversampling algorithm, namely distributed fuzzy-based adaptive synthetic oversampling (DFBASO) algorithm, is proposed by simultaneously considering the distribution of inter-class, the distribution of intra-cluster and the characteristic of noise samples. The proposed DFBASO algorithm is equipped with: 1) fuzzy c-means (FCM) clustering algorithm application for samples of minority and majority classes; 2) weighted distribution based on two factors including the inter-class distance and the cluster capacity; and 3) a mixed synthetic method under different distribution cases of intra-cluster. Finally, the judicial data set and eight public data sets are utilized to show the effectiveness and universal applicability of the proposed DFBASO algorithm for the imbalanced data classification.

The cumulative distribution function of the non-central chi-square distribution χ ν ′ 2 ( λ ) , ν ∈ R + possesses an integral representation in terms of a generalized Marcum Q -function. Regarding some already known-results, here we derive a simpler form of the cumulative distribution function for ν = 2 n ∈ N degrees of freedom. Also, we express these representations in terms of an incomplete Fox–Wright function p Ψ q ( γ ) and the generalized incomplete hypergeometric functions concerning the important special cases such as 1 Γ 1 , 2 Γ 1 and 2 γ 1 . New identities are established between 1 Γ 1 and 2 Γ 1 as well.

The designer's exercise consists of designing a rights structure that formalizes the idea of power distribution in society. A solution is implementable in largest consistent set by a rights structure if there exists a rights structure such that for each preference profile, the largest consistent set of the game played by agents coincides with the set of outcomes that the solution would select for it. In a setting with transfers, every Maskin monotonic solution is implementable. This finding implies that the class of implementable solutions in core equilibria is unaltered by farsighted reasoning. (C) 2021 The Author(s). Published by Elsevier Inc.

We derive conditions on the products of stochastic matrices guaranteeing the existence of a unique limit invariant distribution. Belying our approach is the hereby defined notion of restricted triangulated Laman graphs. The main idea is the following: to each triangle in the graph, we assign a stochastic matrix. Two matrices can be adjacent in a product only if their corresponding triangles share an edge in the graph. We provide an explicit formula for the limit invariant distribution of the product in terms of the individual stochastic matrices.

The subject of this study is three fundamental procedures of contemporary data analysis: outlier detection, clustering and classification. These issues are considered in a conditional approach – the introduction of specific (e.g., current) values to the model allows, in practice, a significantly precise description of the reality under research. The same methodology has been used for all three of the above tasks, and it considerably facilitates the interpretations, potential modifications and practical applications of the material investigated. Using non-parametric methods frees the procedures under investigation from a distribution in the considered dataset. This paper contains a complete set of formulas that allow easy implementation of the presented material in real-world problems.

Three-way approximations of fuzzy sets are an important scheme of granular computing, by abstracting a fuzzy set to its discrete three option-alternatives which adhere to human cognitive behaviors and reduce the computational burden. The key point of such three-way approximations of fuzzy sets is how to choose a suitable design leading to their realization. Undesired three-way approximations might be produced if the selected mechanism is unsuitable to data distribution. In this study, the principles for constructing three-way approximations of fuzzy sets are summarized. The following taxonomy of these principles is provided, namely (i) uncertainty balance-based principle, (ii) prototype-based principle, and (iii) model-based invoking the tradeoff between classification error and the number of data that have to be classified. A number of detailed optimization models are discussed in detail. To evaluate the performance of different construction principles, a general unsupervised learning framework based on three-way approximations of fuzzy sets is exhibited. Some synthetic data sets along with sixteen data sets from UCI repository are involved for experiments. Friedman testing followed by Holm-Bonferroni testing are exploited to test the performance significance of the proposed criteria, which can provide insights and deliver guidance when choosing a principle for constructing three-way approximations of fuzzy sets in the real-world scenarios. The research methods in this paper can also be extended to supervised and semi-supervised learning areas.

We consider an Erlang loss system with state-dependent arrival rates. Given the system is in steady-state and there are j customers being served, the system operator may wish to know about the distribution of arrival states for the j customers in service. Specifically, they may want the steady-state probability that any given customer entered when the system had i servers busy, given j customers are currently being served. We term this metric the conditional entry-state distribution and develop an algorithm to compute it.

In this article, we propose a new probabilistic model for the distribution of ranks of elliptic curves in families of fixed Selmer rank, and compare the predictions of our model with previous results, and with the databases of curves over the rationals that we have at our disposal. In addition, we document a phenomenon we refer to as Selmer bias that seems to play an important role in the data and in our models.

Spiking neural P systems (SNP systems) are a class of distributed and parallel computation models, which are inspired by the way in which neurons process information by means of spikes, where a neuron fires and distributes the spikes to all the neurons linked by synapses with the firing neuron. In this work, a new spike distribution mechanism is introduced, where the produced spikes are distributed to a set of neurons indicated by the target indications. The computation power of SNP systems with this new spike distribution mechanism is investigated. It is demonstrated that SNP systems with such a distribution mechanism are Turing universal as both number generators and function computing devices. Moreover, it is shown that 6 neurons (respectively, 15 neurons) are sufficient for constructing a universal SNP system with the proposed spike distribution mechanism as a number generator (respectively, as a function computing device). By comparing with the classical one, it can be found that the proposed spike distribution mechanism is a powerful feature in terms of the number of neurons used to construct universal SNP systems.

Fuel cell polarisation performance is typically reported under controlled/constant temperature conditions, as a sign of robust metrology. However, in practice, fuel cells self-heat as they generate current; which varies the temperature across the polarisation curve and affects performance. More detail regarding the internal cell operation can be gleaned by current and temperature distribution mapping. For the case of an unheated cell, ‘self-heating’ increases the cell temperature and improves performance, resulting in a ‘voltage recovery’ and a more homogeneous current and water distribution. For actively heated cells, a reduced current is observed in regions of high temperature and low humidity. The positioning of the gas manifolds also has a decisive impact on performance by affecting the reactant concentration, humidity and water distribution. Counter- and cross-flow orientations in a self-heating cell were studied, with a counter-flow orientation with air flowing with gravity producing the most uniform temperature distribution.

This paper aims to effectively solve the problem of the influence maximization in social networks. For this purpose, an influence maximization method that can identify influential nodes via the community structure and the influence distribution difference is proposed. Firstly, the network embedding-based community detection approach is developed, by which the social network is divided into several high-quality communities. Secondly, the solution of influence maximization is composed of the candidate stage and the greedy stage. The candidate stage is to select candidate nodes from the interior and the boundary of each community using a heuristic algorithm, and the greedy stage is to determine seed nodes with the largest marginal influence increment from the candidate set through the sub-modular property-based Greedy algorithm. Finally, experimental results demonstrate the superiority of the proposed method compared with existing methods, from which one can further find that our work can achieve a good tradeoff between the influence spread and the running time.

We study pairs of non-zero algebraic numbers ( α , λ ) such that T r Q ( α , λ ) / Q ( λ α n ) ∈ Z for n lying in suitable subsets I of N . In this short note, we give a satisfactory account to these circle of questions. This theme arises naturally in the study of distribution of exponential sequences modulo one. Finally we indicate that the analogous results do not hold for global fields in positive characteristic.

The significance of electrical load forecasting on the electrical distribution network has become eminent with the entry of energy sector and electrical market. This paper of research comprehends a model for forecasting the electrical load distribution. This paper highlights the forecasting on the electrical distribution system by taking into account the load ambiguities. Support Vector Machine (SVM), which is a machine learning algorithm is the prediction or forecasting model utilized in the proposed paper for forecasting the electrical load distribution. The ambiguities that impact the electrical load distribution are; cooling loads, indoor heat gains and cooling parameters are taken into account during the prediction. The demand for electrical load is impacted by many factors starting from the climatic conditions to the economic-socio influences. The proposed load prediction model is reliable, beneficial and an enhancing model for the conservation of electrical energy in the distribution network.

Strength distribution of advanced ceramics is commonly characterized by two-Parameter (2P) Weibull distribution. However, deviation of strength distribution from 2P-Weibull distribution may occur in ceramics due to various mechanisms. R-curve behavior is one of these mechanisms where increase of fracture resistance with the extension of crack occurs. In such cases, 2P-Weibull distribution may not be the best fitting distribution function based on the goodness-of-fitness tests. This article examines the effectiveness of three-parameter (3P) Weibull distribution function for fitting the strength variation due to R-curve effect by using experimental and virtual strength data. The effect of Weibull parameters, degree of increase in crack resistance and number of samples on effectiveness of fitting via 3P-Weibull distribution is investigated. It is reported that 3P-Weibull distribution function fits the strength distribution better than 2P-Weibull distribution function for materials showing R-curve behavior when the crack resistance curve is steep and Weibull modulus is high. Furthermore, it is shown that at least 100 samples should be used for a reliable estimate when the material exhibits R-curve behavior.

Label Distribution Learning (LDL) is a general learning framework that assigns an instance to a distribution over a set of labels rather than a single label or multiple labels. Current LDL methods have proven their effectiveness in many machine learning applications. As of the first formulation of the LDL problem, numerous studies have been carried out that apply the LDL methodology to various real-life problem solving. Others have focused more specifically on the proposal of new algorithms. The purpose of this article is to start addressing the LDL problem as of the data pre-processing stage. The baseline hypothesis is that, due to the high dimensionality of existing LDL data sets, it is very likely that this data will be incomplete and/or that poor data quality will lead to poor performance once applied to the learning algorithms. In this paper, we propose an oversampling method, which creates a superset of the original dataset by creating new instances from existing ones. Then, we apply already existing algorithms to the pre-processed training set in order to validate the effcacy of our method. The effectiveness of the proposed SSG-LDL is verified on several LDL datasets, showing significant improvements to the state-of-the-art LDL methods.

Live-working is the development trend of smart grid, and the development of high-performance live-working robot system is the inevitable demand of technology development. A dual-arm live-working robot system is developed to overcome the problems existing in the design and application of the current live-working robots. The system is composed of operation module, reference board platform module, insulation cover and control system module. The power-driven cooperative UR10 mechanical manipulators are used, and standardized mechanical interfaces are adopted to make sure that the assembly and testing process is very efficient and convenient. ANSYS Workbench is used to analyze the strength of the whole robot to guarantee the requirements of strength and deformation. The mass of the whole robot is minimized to less than 170kg during the lead wire procedure.

The goal of this research was to optimize the cost of goods distribution to some locations. The problem can be considered as Vehicle Routing Problem (VRP). The main characteristic of this problem is that the solution space expands exponentially. In our case at hand, the goods distribution that have been done, mostly done manually. Therefore, it may not optimize the costs of distribution. Manual optimization cannot be used if the number is locations is more than five because the solution space is too big to solve by hand. Pigeon Inspired Optimization (PIO) is proposed as a heuristic method for optimizing the VRP to optimize the cost and then it will be compared with Particle Swarm Optimization (PSO) method as comparison algorithm. Evaluation was conducted by comparing their performance in optimizing cost for several solution spaces. The achieved result is the shortest distribution path according to the constraints given and has lowest total cost of distribution. It can be concluded that PIO is better for optimizing the goods distribution path so that the distribution cost becomes minimal.

The dynamic behavior of a machine tool is the result of the mass, stiffness and damping distribution, which are highly influenced by local properties. As a result, it can change significantly for different axis positions. Modeling the dynamic behavior accurately and at the same time efficiently is challenging and prevents the holistic optimization of machine tools. Therefore, this publication presents an approach to identify optimization potentials using flexible multibody models with local damping information. The energy distribution as well as the receptance are analyzed for different machine states to determine damping-based optimization capabilities. A comparison to state-of-the-art models shows the improved efficiency of the presented procedure.

It is well known that carrier distribution in InGaN multiple quantum wells (MQWs) can be significantly inhomogeneous. However, the conventional ABC recombination model assumes that carriers are uniformly distributed throughout the MQW. In this paper, a modified ABC model that considers the unequal carrier density in the QWs was developed. From the analysis of the developed ABC model, the effective recombination coefficients and modified internal quantum efficiency (IQE) were obtained for an arbitrary carrier distribution in MQWs. The efficiency droop was found to be aggravated as the carrier distribution was increasingly inhomogeneous. However, it was also found that the effect of inhomogeneous carrier distribution alone was not sufficient to explain the IQE droop with the theoretical Auger recombination coefficient based on indirect Auger processes. The developed ABC model is expected to provide insight into the influence of inhomogeneous carrier distributions in MQWs on the efficiency droop in GaN-based light-emitting diodes.

By using a Korteweg-deVries-Burgers(KdV-Burgers) equation and considering the dust size distribution, we have studied effects of the dust size distribution on the shock wave in dusty plasma. The dependence of characteristics of the shock wave on different dust size distributions has been given. It is found that the speed and amplitude of a shock wave considering the dust size distribution are larger than that of the dusty plasma with the averaged dust size. However, the width of a shock wave considering the dust size distribution is smaller than that of the dusty plasma with the averaged dust size.

A theory is formulated that relates the rates of the three topological events to the evolution of the face distribution function. Implementation of the theory requires introduction of the concept of participation probabilities which reflect the face distribution of those grains that are incident upon the events. The prediction of the evolving face distribution is tested with a 3-D Monte Carlo simulation of the grain growth process that permits evaluation of the topological event rates by face class and the participation probabilities. The theory also develops a relation between the average number of faces per grain and the topological rates as well as the asymptotic distribution function; these results are also tested using the simulation. The transient period prior to normal grain growth is explained in terms of the evolution of the event rates that control the creation of small grains and evolve the face distribution to its final shape.

The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau’s conjecture. We discuss the Bateman–Horn conjecture, its applications, and its origins.

Facial expression recognition task as a crucial step for emotion recognition remains an open challenge that due to individual expression correlation/ambiguity. In this paper, to tackle these challenges, a novel model with the correlation emotion label distribution learning is proposed for near-infrared (NIR) facial expression recognition which associates multiple emotions with each expression depend on the similarity of expressions. Firstly, the similarities of the seven basic expressions are calculated, and then guide the correlation emotion label distribution by predicting the latent label probability distribution of the expression. Furthermore, the proposed model can be learned in an end-to-end manner via a constructed convolutional neural network to classify the six basic facial expressions. Experimental results on Oulu_CASIA database demonstrate that the proposed method has achieved the superior performance on NIR expression recognition.

Recently, Andrews defined a partition function $\mathcal{EO}(n)$ which counts the number of partitions of $n$ in which every even part is less than each odd part. He also defined a partition function $\overline{\mathcal{EO}}(n)$ which counts the number of partitions of $n$ enumerated by $\mathcal{EO}(n)$ in which only the largest even part appears an odd number of times. Andrews proposed to undertake a more extensive investigation of the properties of $\overline{\mathcal{EO}}(n)$. In this article, we prove infinite families of congruences for $\overline{\mathcal{EO}}(n)$. We next study parity properties of $\overline{\mathcal{EO}}(n)$. We prove that there are infinitely many integers $N$ in every arithmetic progression for which $\overline{\mathcal{EO}}(N)$ is even; and that there are infinitely many integers $M$ in every arithmetic progression for which $\overline{\mathcal{EO}}(M)$ is odd so long as there is at least one. Very recently, Uncu has treated a different subset of the partitions enumerated by $\mathcal{EO}(n)$. We prove that Uncu's partition function is divisible by $2^k$ for almost all $k$. We use arithmetic properties of modular forms and Hecke eigenforms to prove our results., Accepted in Journal of Number Theory