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A classical result of K. L. Chung and W. Feller deals with the partial sums S k S_k arising in a fair coin-tossing game. If N n N_n is the number of “positive” terms among S 1 S_1 , S 2 S_2 , …, S n S_n then the quantity P ( N 2 n = 2 r ) P(N_{2n} = 2r) takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for P ( N 2 n + 1 = r ) P(N_{2n+1} = r) , r = 0 r = 0 , 1 1 , 2 2 , …, 2 n + 1 2n+1 . We get to this ansatz by adaptating the Feynman–Kac methodology.

Cooperation among kin is common in animal societies. Kin groups may form by individuals directly discriminating relatives based on kin recognition cues, or form passively through natal philopatry and limited dispersal. We describe the genetic landscape for a primitively eusocial wasp, Polistes dominula, and ask whether individuals choose cooperative partners that are nearby and/or that are genetic relatives. Firstly, we genotyped an entire sub-population of 1361 wasps and found genetic structuring on an extremely fine scale: the probability of finding genetic relatives decreases exponentially within just a few meters of an individual’s nest. At the same time, however, we found a lack of genetic structuring between natural nest aggregations within the population. Secondly, in a separate dataset where ~2000 wasps were genotyped, we show that wasps forced experimentally to make a new nest choice tended to choose new nests near to their original nests, and that these nests tended to contain some full sisters. However, a significant fraction of wasps chose nests that did not contain sisters, despite sisters being present in nearby nests. Although we cannot rule out a role for direct kin recognition or natal nest-mate recognition, our data suggest that kin groups may form via a philopatric rule-of-thumb, whereby wasps simply select groups and nesting sites that are nearby. The result is that most subordinate helpers obtain indirect fitness benefits by breeding cooperatively.

The Rock–scissors–paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players’ payoff when a tie occurs.

This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundacao para a Ciencia e a Tecnologia, Portugal.

The results of analyzing the process of paper manufacture on the paper machine (PM) in terms of automatic control problems are given in the paper. They are presented in the form of parametric schemes of each part of the PM indicating the main input and output variables, as well as control and perturbation effects. Wire, drying and press parts, sections of pulp preparation, wet washing, screening, inlet and calender are considered in the paper. Construction of parametric schemes is the first step in creating an automatic control system. Based on the obtained results, it is concluded that the most attention from the point of view of control should be given to the PM drying section and calender. The conclusion is associated with a large number of perturbations, acting on these processes and negatively affecting the quality of the finished products but also lead to increasing production costs. With the set parameters of the PM processes, it is possible to formulate an optimal control problem that is the next step in creating an automatic control system.

In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.

Sunaga considered all computational procedures, which had beenВ traditionally defined on real numbers, as being too ideal andВ proposed to replace them by the procedures on real intervals inВ order to make everything "more realistic". Sunaga studied manyВ different kinds of numerical procedures including the Taylor-seriesВ interval solution of the initial-value problem of ordinaryВ differential equations.The purpose of the present note is to mark the 60-th anniversary of the publication of the seminal work by the Japan mathematician Teruo Sunaga. The paper summarizes the results of his Master Thesis. Sunaga's work sets the foundation of the contemporary interval analysis and reliable computing. This is an interdisciplinary field, combining abstract mathematical theories and practical applications related to computer science, numerical analysis and mathematical modeling in the natural, engineering and social-economic sciences.

In this paper, we consider precoder designs for multiuser multiple-input-single-output (MISO) broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data-transmissions, namely, the GZF-DP precoder, where the suffix \lq{}DP\rq{} stands for \lq{}dirty-paper\rq{}. The GZF-DP precoder is designed to generate a band-shaped and lower-triangular effective channel $\vec{F}$ such that only the entries along the main diagonal and the $\nu$ first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) $\nu$ users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sum-rate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water-filling, but with modified water-levels depending on the parameter $\nu$. While for the minimum user-rate maximization that measures the quality of the service (QoS), the optimal power allocation is directly solved in closed-form which also depends on $\nu$. Moreover, we propose two low-complexity user-ordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show through numerical results that, the proposed GZF-DP precoder with a small $\nu$ ($\leq\!3$) renders significant rate increments compared to the previous precoder designs such as the linear ZF and user-grouping based DPC (UG-DP) precoders., Comment: 31 pages, 13 figures, submitted to IEEE Transactions on Wireless Communications in Aug. 2016

We correct a mistake in a lemma in the paper cited in the title and show that it did not affect any of the other results of the paper. To this end, we prove results on linearly disjoint field extensions that do not seem to be commonly known. We give an example to show that a separability assumption in one of these results cannot be dropped (doing so had led to the mistake). Further, we discuss recent generalizations of the original classification of defect extensions.

Ebaid et al. (2020) proposed the following new extended FGM copula (1) C ( u , v ) = u v [ 1 + a ( 1 − u ) ( 1 − v ) ( 1 − b u ) ( 1 − b v ) ] , 0 ≤ b < 1. Ebaid et al. (2020) claimed that, the adm...

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

We correct an error in the paper of Z. Shen, S. Li, and J. Zhang published in [4]. In addition, we give an answer to a question posed by the authors.

Transitive inference (TI) is a form of logical reasoning that involves using known relationships to infer unknown relationships (A > B; B > C; then A > C). TI has been found in a wide range of vertebrates but not in insects. Here, we test whether Polistes dominula and Polistes metricus paper wasps can solve a TI problem. Wasps were trained to discriminate between five elements in series (A 0 B−, B 0 C−, C 0 D−, D 0 E−), then tested on novel, untrained pairs (B versus D). Consistent with TI, wasps chose B more frequently than D. Wasps organized the trained stimuli into an implicit hierarchy and used TI to choose between untrained pairs. Species that form social hierarchies like Polistes may be predisposed to spontaneously organize information along a common underlying dimension. This work contributes to a growing body of evidence that the miniature nervous system of insects does not limit sophisticated behaviours.

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas that are g-satisfiable (i.e. some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if $\frac{g}{k} < \frac{1}{2}$ and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus we give a dichotomy for a natural fragment of promise constraint satisfaction problems (PCSPs) on arbitrary finite domains. The hardness side is proved using the algebraic approach, via a new general NP-hardness criterion on polymorphisms of the problem, based on a gap version of the Layered Label Cover problem. We show that previously used criteria are insufficient -- the problem hence gives an interesting benchmark of algebraic techniques for proving hardness of approximation problems such as PCSPs., Comment: Full version of an ICALP 2020 paper

I am grateful to Jiandong Ren for providing readers with a unified treatment of compound sums with frequency component in the (a,b,0) class of counting distributions, which is central to insurance ...

Paperfolding sequences are represented by 0’s and 1’s. In this paper, we introduce paper-oor sequences which are represented by nonnegative integers. We investigate the structure of paper-oor sequences which represent the oors obtained by paperfoldings. Mathematics Subject Classication: 97A20, 68R99

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC)-a system of higher-order logic modulo theories-and prove its soundness and refutational completeness w.r.t. both standard and Henkin semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in both semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schonflukel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

In their celebrated paper (Furst et al., Math. Syst. Theory 17(1), 13---27 (12)), Furst, Saxe, and Sipser used random restrictions to reveal the weakness of Boolean circuits of bounded depth, establishing that constant-depth and polynomial-size circuits cannot compute the parity function. Such local restrictions have played important roles and have found many applications in complexity analysis and algorithm design over the past three decades. In this article, we give a brief overview of two intriguing applications of local restrictions: the first one is for the Isomorphism Conjecture and the second one is for moderately exponential time algorithms for the Boolean formula satisfiability problem.

We construct a counterexample that disproves the claim of Theorem 0.2 of the paper “Injective mappings and solvable vector fields of Euclidean spaces”, which appeared in Topology Appl. 136 (2004), 261–274.

We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length $mn$ for all $n$, and certain $\12-$order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.

This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of ; - many examples, e.g., , where pn is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.

This article is intended to indicate and discuss some errors in N. Lavi’s paper “A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions”.

A relation, established by Andras Schubert (Scientometrics 78(3): 559–565, 2009) on the relation between a paper’s h-index and its total number of received citations, is explained. The relation is a concavely increasing power law and is explained based on the Lotkaian model for the h-index, proved by Egghe and Rousseau.

This article calculates probabilities for the occurrence of different types of papers such as genius papers, basic papers, ordinary papers or insignificant papers. The basis of these calculations are the formulae for the cumulative n-th citation distribution, being the cumulative distribution of times at which articles receive their n-th (n=1,2,3,...) citation. These formulae (proved in previous papers) are extended to allow for different aging rates of the papers. These new results are then used to define different importance classes of papers according to the different values of n, in function of time t. Examples are given in case of a classification into four parts: genius papers, basic papers, ordinary papers and (almost) insignificant papers. The fact that, in these examples, the size of each class is inversely related to the importance of the journals in this class is proved in a general mathematical context in which we have an arbitrary number of classes and where the threshold values of n in each class are defined according to the natural law of Weber-Fechner.

The Kalman-Yakubovich-Popov (KYP) Lemma, giving the frequency-domain criteria for solvability of LQR problems and feasibility of related LMIs and Lur'e-Riccati equations, is undoubtedly one of the cornerstone results in modern control theory. Numerous applications of the KYP lemma in nonlinear and robust control motivated its extension to systems with distributed parameters. Unlike the finite-dimensional case, where the KYP lemma admits elegant proofs by means of algebraic techniques and methods from convex analysis, a prerequisite for its infinite-dimensional extensions is feasibility of the corresponding LQR problem, resulting on assumptions of exponential or L 2 -stabilizability. This property is restrictive and not easily verifiable for general infinite-dimensional systems. Being quite natural in the problems of absolute stability, it seems unnecessary in other applications of the KYP lemma which require only solvability of the operator inequality, but not positivity of its solution, such as e.g. instability or dichotomy criteria. In the present paper we show, that in the “strict” or coercive case the KYP lemma retains its validity, replacing stabilizability assumption with some technical assumption which holds, for instance, whenever the linear system is exponentially dichotomic.

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In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space. Note that the proof of multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent don't contained any mistakes. But at the proving of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in this paper. This result is assigned as Theorem 5 in noted paper. In other words, sufficient conditions for general weights ensuring the validity of the two-weight strong type inequalities for some sublinear operator was found. In this theorem the inequality (9) isn't true. In this note we give the details of the correct argument. We presume that the reader is familiar with the contents and notation of our original paper. At the heart of our correction is the following Theorem which replaces Theorem 5.

In this paper, we discuss numbers of downwards and upwards in generalized paper folding sequences. We compute the exact number of downwards and upwards in R n p and (RpRq) n by using the properties of recursive sequences where n;p and q are natural numbers with p 2 and q 2.

In 1935, Erdos proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai’s paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai’s paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai’s theorem using the Bombieri–Vinogradov theorem.

When objects are defined in terms of their use value, they serve as extensions of the body into the environment, but when objects are defined by the collection, such an extension is inverted, servi...

The proofs of Theorem 2.2 of K. J. Dykema and M. Rørdam, Purely infinite simple C*-algebras arising from free product constructions, Canad. J. Math. 50 (1998), 323–341 and of Theorem 3.1 of K J. Dykema, Purely infinite simple C*-algebras arising from free product constructions, II,Math. Scand. 90 (2002), 73–86 are corrected.

We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the observation of smaller graphs and basic structure of our heuristics. We also explain an evaluation function of each edge for efficient 2-opt local search. Using them, we found the best solutions for several graphs.

McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F ◦ f , where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F , and theory for the propagation of subgradients is presented. The generalization interprets the McCormick relaxation approach as a decomposition method for the auxiliary variable method. In addition to extending the framework, the new result provides a tool for the proof of relaxations of specific functions. Moreover, a direct consequence is an improved relaxation for the product of two functions, at least as tight as McCormicks result, and often tighter. The result also allows the direct relaxation of multilinear products of functions. Furthermore, the composition result is applied to obtain improved convex underestimators for the minimum/maximum and the division of two functions for which current relaxations are often weak. These cases can be extended to allow composition of a variety of functions for which relaxations have been proposed. Congratulations to the authors of the awardedpapers! Iwould also like to thankSpringer for sponsoring this award and the committee members for their active involvement. Nominations for the 2015 JOGO Best Paper Award should be emailed to butenko@tamu.edu. All JOGO papers published in 2015 (volumes 61–63) are eligible.

Given a propositional theory T and a proposition q , a sufficient condition of q is one that will make q true under T , and a necessary condition of q is one that has to be true for q to be true under T . In this paper, we propose a notion of strongest necessary and weakest sufficient conditions. Intuitively, the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory, and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory. We show that these two conditions are dual ones, and can be naturally extended to arbitrary formulas. We investigate some computational properties of these two conditions and discuss some of their potential applications.

2008年に創刊された学術雑誌Synthesiology（構成学）に掲載された70編の研究論文を対象にして、構成の方法論を分析した。その結果、研究分野ごとに構成方法に特色があり、バイオテクノロジー分野やナノテクノロジー・材料・製造分野ではブレークスルー型の構成に特徴があり、標準・計測分野で戦略的選択型が多いことが判明した。また、全体としては共通の構成方法として、本格研究においては「技術的な構成」と呼ぶべきものの方法論が重要であり、その研究成果を社会に導入させて行くためには、さらに「社会導入に向けた構成」と呼ぶべきものも連続して起こすことが特徴の一つであることが明らかになった。その際、前者においても後者においてもフィードバック・プロセスが見られるが、後者においては社会的試用によりフィードバック・プロセスを何回も回していくスパイラル・アップとも呼ぶべきダイナミックな構成方法が観察された。

These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds"., 216 pages, minor corrections made

Costa's celebrated ldquowriting on dirty paperrdquo (WDP) shows that the power-constrained channel Y=X+S+Z, with Gaussian Z, has the same capacity as the standard AWGN channel Y=X+Z, provided that the ldquointerferencerdquo S (no matter how strong it is) is known at the transmitter. While this ability for perfect interference cancelation is very appealing, it relies heavily on the Gaussianity of the (unknown) noise Z. We construct an example of ldquobadrdquo noise for writing on dirty paper, namely, ldquodifference set noiserdquo. If the interference S is strong, then difference-set noise limits the WDP capacity to at most 2 bits. At the same time, like in the AWGN case, the zero-interference capacity grows without bound with the input constraint. Thus almost 100% of the available capacity is lost in WDP in the presence of difference-set noise. This high capacity loss is due to the ldquoentropy amplification propertyrdquo (EAP) of noise with an aperiodic probability distribution. Using the EAP and the duality between WDP and Wyner-Ziv source coding, we also give an example of dramatic rate-loss in quantizing encrypted source.

This paper is concerned with construction of efficiently encodable nonbinary quasi-cyclic LDPC codes based on finite fields. Four classes of nonbinary quasi-cyclic LDPC codes are constructed. Experimental results show that codes constructed perform well with iterative decoding using a fast Fourier transform based q-ary sum-product algorithm and they achieve significant coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard- decision Berlekamp-Massey algorithm or algebraic soft-decision Kotter-Vardy algorithm.

It is shown that an old direct argument of Erdős and Heilbronn may be elaborated to yield a result of the current inverse type.

We point out that the proof of Theorem 3.3 of Bagchi and Sastry (2013) contains a serious flaw. Accordingly, this theorem needs to be modified. In consequence, we also have to retract Corollary 3.4, Corollary 3.6 and Theorem 3.8 of Bagchi and Sastry (2013).