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Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real‐world problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real‐world engineering problems. [ABSTRACT FROM AUTHOR]

Let r ≥ 2 and r be even. An r -hypergraph G on n vertices is called odd-colorable if there exists a map φ : [ n ] → [ r ] such that for any edge { j 1 , j 2 , … , j r } of G , we have φ ( j 1 ) + φ ( j 2 ) + ⋅ ⋯ ⋅ + φ ( j r ) ≡ r ∕ 2 ( mod r ) . In this paper, we first determine that, if r = 2 q ( 2 t + 1 ) and n ≥ 2 q ( 2 q − 1 ) r , then the maximum chromatic number in the class of the odd-colorable r -hypergraphs on n vertices is 2 q , which answers a question raised by V. Nikiforov recently in Nikiforov (2017). We also study some applications of the spectral symmetry of the odd-colorable r -hypergraphs given in the same paper by V. Nikiforov. We show that the Laplacian spectrum S p e c ( L ( G ) ) and the signless Laplacian spectrum S p e c ( Q ( G ) ) of an r -hypergraph G are equal if and only if r is even and G is odd-colorable. As an application of this result, we give an affirmative answer for the remaining unsolved case r ⁄ ≡ 0 ( m o d 4 ) of a question raised in Shao et al. (2015) about whether S p e c ( L ( G ) ) = S p e c ( Q ( G ) ) implies that L ( G ) and Q ( G ) have the same H-spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system. [ABSTRACT FROM AUTHOR]

The notions of "mathematicalness" and "mathematicability" of nature appear in the context of attempts at explaining the effectiveness of mathematics in the description of the world. Mathematicalness of nature means that structures of the world are mathematical. But is this true? Is nature mathematical? In the paper some reasons for mathematicalness of nature are considered. Mathematical analysis is widely used in physics. Its application requires continuity of time and space. There are also different kinds of infinity in the mathematical theories used in physics. This raises the issue: whether the material world is continuous or we "impose" on nature certain properties in order to use convenient mathematical tools. Is mathematics a useful tool, or does it reflect nature? So, is nature mathematical or only mathematicable? The article shows that mathematicalness of nature is only a metaphysical hypothesis. [ABSTRACT FROM AUTHOR]

The paper presents some interesting aspects related to the biography and works of Romanian mathematician Caius Iacob (1912--1992). He was famous for his works in the fields of mathematical analysis, fluid mechanics, classical hydrodynamics and compressible-flow theory. At the age of 19, he graduated from the Mathematics Faculty in Bucharest, and then he went to Paris to continue his studies at the Faculty of Sciences, where he worked on a PhD thesis under the advice of famous French mathematician Henri Villat. On 24 June 1935, Caius Iacob successfully presented to the Sorbonne committee his PhD thesis about "Determination of conjugated harmonic functions with some limit conditions, and their applications in hydrodynamics". Returning to Romania, Caius Iacob had a long and successful career teaching mathematics and mechanics at the universities of Timişoara, Cluj and Bucharest. His most important work is considered the "Mathematical introduction to the mechanics of fluids". This book, providing original ways to work with classical hydrodynamics and compressibleflow theory, was published in Romanian in 1952 and in French in 1959. In 1955, he was elected a Corresponding Member of the Romanian Academy, becoming a titular Member in 1963. He was also President of the Mathematics Section of the Romanian Academy from 1980 until the end of his life, in 1992. In 1991, he initiated the foundation of the "Romanian Academy Institute of Applied Mathematics". In 2001 the institute merged with the "Centre for Mathematical Statistics", which had been created in 1964 by mathematician Gheorghe Mihoc, thus creating the "Gheorghe Mihoc -- Caius Iacob Institute of Mathematical Statistics and Applied Mathematics" of the Romanian Academy. [ABSTRACT FROM AUTHOR]

Creativity is a complex, multi-faceted concept encompassing a variety of related aspects, abilities, properties and behaviours. If we wish to study creativity scientifically, then a tractable and well-articulated model of creativity is required. Such a model would be of great value to researchers investigating the nature of creativity and in particular, those concerned with the evaluation of creative practice. This paper describes a unique approach to developing a suitable model of how creative behaviour emerges that is based on the words people use to describe the concept. Using techniques from the field of statistical natural language processing, we identify a collection of fourteen key components of creativity through an analysis of a corpus of academic papers on the topic. Words are identified which appear significantly often in connection with discussions of the concept. Using a measure of lexical similarity to help cluster these words, a number of distinct themes emerge, which collectively contribute to a comprehensive and multi-perspective model of creativity. The components provide an ontology of creativity: a set of building blocks which can be used to model creative practice in a variety of domains. The components have been employed in two case studies to evaluate the creativity of computational systems and have proven useful in articulating achievements of this work and directions for further research. [ABSTRACT FROM AUTHOR]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract Let g E H be the Eguchi–Hanson metric on the blow-up of ℂ 2 at the origin. In this paper we show that m g E H is not balanced for any positive integer m. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study the representation theory of the Fuss–Catalan algebras, FC n (a , b). We prove that this algebra is cellular with a cellular basis and forms a tower of recollement, as defined by Cox, Martin, Parker, and Xi [7] , and hence, it is quasi-hereditary algebra if a , b are non-zero complex numbers. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself is equal to a given element of the ring. [ABSTRACT FROM AUTHOR]

Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model. [ABSTRACT FROM AUTHOR]

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by 'enlightening'. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. [ABSTRACT FROM AUTHOR]

This is a survey or exposition of a particular collection of results and open problems involving snarks — simple “cubic” (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by László Kászonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems. [ABSTRACT FROM AUTHOR]

Text The aim of this paper is to present a method to calculate the rate of growth of divergent series. In the case of the harmonic series, we study an alternate of other classical methods presented by L. Comtet, S.M. Zeyman, W. DeTemple and S.-H. Wang. Moreover, the method presented in this paper is suitable for obtaining similar results on other divergent series, as we will show in the final part of our investigation. Video For a video summary of this paper, please visit http://youtu.be/SFR7zY4pvG4 . [ABSTRACT FROM AUTHOR]

It is a classic topic of social network analysis to evaluate the importance of nodes and identify the node that takes on the role of core or bridge in a network. Because a single indicator is not sufficient to analyze multiple characteristics of a node, it is a natural solution to apply multiple indicators that should be selected carefully. An intuitive idea is to select some indicators with weak correlations to efficiently assess different characteristics of a node. However, this paper shows that it is much better to select the indicators with strong correlations. Because indicator correlation is based on the statistical analysis of a large number of nodes, the particularity of an important node will be outlined if its indicator relationship doesn't comply with the statistical correlation. Therefore, the paper selects the multiple indicators including degree, ego-betweenness centrality and eigenvector centrality to evaluate the importance and the role of a node. The importance of a node is equal to the normalized sum of its three indicators. A candidate for core or bridge is selected from the great degree nodes or the nodes with great ego-betweenness centrality respectively. Then, the role of a candidate is determined according to the difference between its indicators' relationship with the statistical correlation of the overall network. Based on 18 real networks and 3 kinds of model networks, the experimental results show that the proposed methods perform quite well in evaluating the importance of nodes and in identifying the node role. [ABSTRACT FROM AUTHOR]

Bayesian network classifiers (BNCs) have demonstrated competitive classification performance in a variety of real-world applications. A highly scalable BNC with high expressivity is extremely desirable. This paper proposes Redundant Dependence Elimination (RDE) for improving the classification performance and expressivity of k-dependence Bayesian classifier (KDB). To demonstrate the unique characteristics of each case, RDE identifies redundant conditional dependencies and then substitute/remove them. The learned personalized k-dependence Bayesian Classifier (PKDB) can achieve high-confidence conditional probabilities, and graphically interpret the dependency relationships between attributes. Two thyroid cancer datasets and four other cancer datasets from the UCI machine learning repository are selected for our experimental study. The experimental results prove the effectiveness of the proposed algorithm in terms of zero-one loss, bias, variance and AUC. [ABSTRACT FROM AUTHOR]

Countries, research institutions, and scholars are interested in identifying and promoting high-impact and transformative scientific research. This paper presents a novel set of text- and citation-based metrics that can be used to identify high-impact and transformative works. The 11 metrics can be grouped into seven types: Radical-Generative, Radical-Destructive, Risky, Multidisciplinary, Wide Impact, Growing Impact, and Impact (overall). The metrics are exemplified, validated, and compared using a set of 10,778,696 MEDLINE articles matched to the Science Citation Index ExpandedTM. Articles are grouped into six 5-year periods (spanning 1983–2012) using publication year and into 6,159 fields constructed using comparable MeSH terms, with which each article is tagged. The analysis is conducted at the level of a field-period pair, of which 15,051 have articles and are used in this study. A factor analysis shows that transformativeness and impact are positively related (ρ = .402), but represent distinct phenomena. Looking at the subcomponents of transformativeness, there is no evidence that transformative work is adopted slowly or that the generation of important new concepts coincides with the obsolescence of existing concepts. We also find that the generation of important new concepts and highly cited work is more risky. Finally, supporting the validity of our metrics, we show that work that draws on a wider range of research fields is used more widely. [ABSTRACT FROM AUTHOR]

Inversive distance circle packing metric was introduced by P Bowers and K Stephenson [7] as a generalization of Thurston's circle packing metric [34] . They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo [22] proved the infinitesimal rigidity and then Luo [27] proved the global rigidity. In this paper, based on an observation of Zhou [37] , we prove this conjecture for inversive distance in ( − 1 , + ∞ ) by variational principles. We also study the global rigidity of a combinatorial curvature introduced in [14,16,19] with respect to the inversive distance circle packing metrics where the inversive distance is in ( − 1 , + ∞ ) . [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

Solving a well-known problem of Maharam, Talagrand [18] constructed an exhaustive non uniformly exhaustive submeasure, thus also providing the first example of a Maharam algebra that is not a measure algebra. To each exhaustive submeasure one can canonically assign a certain countable ordinal, its exhaustivity rank. In this paper, we use carefully constructed Schreier families and norms derived from them to provide examples of exhaustive submeasures of arbitrary high exhaustivity rank. This gives rise to uncountably many non isomorphic separable atomless Maharam algebras. [ABSTRACT FROM AUTHOR]

Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]

In this paper, a unique and more distinctive encryption algorithm is proposed. This is based on the complexity of highly nonlinear S box in Flesnelet domain. The nonlinear pattern is transformed further to enhance the confusion in the dummy data using Fresnelet technique. The security level of the encrypted image boosts using the algebra of Galois field in Fresnelet domain. At first level, the Fresnelet transform is used to propagate the given information with desired wavelength at specified distance. It decomposes given secret data into four complex subbands. These complex sub-bands are separated into two components of real subband data and imaginary subband data. At second level, the net subband data, produced at the first level, is deteriorated to non-linear diffused pattern using the unique S-box defined on the Galois field . In the diffusion process, the permuted image is substituted via dynamic algebraic S-box substitution. We prove through various analysis techniques that the proposed scheme enhances the cipher security level, extensively. [ABSTRACT FROM AUTHOR]

In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences. [ABSTRACT FROM AUTHOR]

In this paper we continue studying the independent transversal domination number in a graph, i.e., the cardinality of a smallest dominating set which intersects each maximum independent set. As our main result, we prove two upper bounds on the independent transversal domination number in terms of the order and minimum degree of a graph. [ABSTRACT FROM AUTHOR]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

In this paper, we establish some scaling invariant regularity criteria for the Navier–Stokes–Maxwell system. [ABSTRACT FROM AUTHOR]

In this paper we isolate a property for forcing notions, the *-Prikry condition, that is similar to the Prikry con- dition but that is topological: A forcing P satisfies it iff for every p ∈ P and for every open dense D ⊆ P, there are n ∈ ω and q ≤∗ p such that for any r ≤ q with l(r) = l(q) + n, r ∈ D, for some length notion l. This is implicit in many proofs in literature. We prove this for the tree Prikry forcing and the long extender Prikry forcing. [ABSTRACT FROM AUTHOR]

Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper, we define the concept of graded 2-absorbing and graded weakly 2-absorbing primary ideals of commutative G-graded rings with non-zero identity. A number of results and basic properties of graded 2-absorbing primary and graded weakly 2-absorbing primary ideals are given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of weak graded rings that are rings graded by a set G of coset representatives for the left action of a subgroup H on a group X. Moreover, a graded rings by using the product H × G are also discussed. A detailed example is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the expected number of points in F q 2 of multiplicity m , for 0 ≤ m ≤ q + 1 , with respect to a randomly chosen arrangement of q + 1 lines with different slopes, is ( 1 / ( m ! e ) ) q 2 + O ( q ) , as q → ∞ . We further state that the distance between the number of such points in a randomly chosen arrangement and ( 1 / ( m ! e ) ) q 2 is lower than q ln ⁡ q with probability close to 1 for large q . [ABSTRACT FROM AUTHOR]

This paper proposes a new measure for recommendation through integrating Triangle and Jaccard similarities. The Triangle similarity considers both the length and the angle of rating vectors between them, while the Jaccard similarity considers non co-rating users. We compare the new similarity measure with eight state-of-the-art ones on four popular datasets under the leave-one-out scenario. Results show that the new measure outperforms all the counterparts in terms of the mean absolute error and the root mean square error. [ABSTRACT FROM AUTHOR]

Let H be an atomic monoid. The set of distances Δ ( H ) of H is the set of all d ∈ N with the following property: there are irreducible elements u 1 , … , u k , v 1 … , v k + d such that u 1 ⋅ … ⋅ u k = v 1 ⋅ … ⋅ v k + d but u 1 ⋅ … ⋅ u k cannot be written as a product of ℓ irreducible elements for any ℓ ∈ N with k < ℓ < k + d . It is well-known (and easy to show) that, if Δ ( H ) is nonempty, then min ⁡ Δ ( H ) = gcd ⁡ Δ ( H ) . In this paper we show conversely that for every finite nonempty set Δ ⊂ N with min ⁡ Δ = gcd ⁡ Δ there is a finitely generated Krull monoid H such that Δ ( H ) = Δ . [ABSTRACT FROM AUTHOR]

In this paper, the homoclinic breather limit method is employed to find the breather wave and the rational rogue wave solutions of the ( 2 + 1 )-dimensional Ito equation. Moreover, based on its bilinear form, the solitary wave solutions of the equation are also presented with a detailed derivation. The dynamic behaviors of breather waves, rogue waves and solitary waves are analyzed with some graphics, respectively. The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the ( 2 + 1 )-dimensional Ito equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation − div ( A ( x ) ∇ u ) + b ( x ) ⋅ ∇ u = f ( u ) in exterior domains in R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]

In their role as second messengers, cyclic nucleotides such as cAMP have a variety of intracellular effects. These complex tasks demand a highly organized orchestration of spatially and temporally confined cAMP action which should be best achieved by compartmentalization of the latter. A great body of evidence suggests that cAMP compartments may be established and maintained by cAMP degrading enzymes, e.g. phosphodiesterases (PDEs). However, the molecular and biophysical details of how PDEs can orchestrate cAMP gradients are entirely unclear. In this paper, using fusion proteins of cAMP FRET-sensors and PDEs in living cells, we provide direct experimental evidence that the cAMP concentration in the vicinity of an individual PDE molecule is below the detection limit of our FRET sensors (<100nM). This cAMP gradient persists in crude cytosol preparations. We developed mathematical models based on diffusion-reaction equations which describe the creation of nanocompartments around a single PDE molecule and more complex spatial PDE arrangements. The analytically solvable equations derived here explicitly determine how the capability of a single PDE, or PDE complexes, to create a nanocompartment depend on the cAMP degradation rate, the diffusive mobility of cAMP, and geometrical and topological parameters. We apply these generic models to our experimental data and determine the diffusive mobility and degradation rate of cAMP. The results obtained for these parameters differ by far from data in literature for free soluble cAMP interacting with PDE. Hence, restricted cAMP diffusion in the vincinity of PDE is necessary to create cAMP nanocompartments in cells. [ABSTRACT FROM AUTHOR]

In this paper we study the interval scoring rule as a mechanism to elicit subjective beliefs under varying degrees of uncertainty. In our experiment, subjects forecast the termination time of a time series to be generated from a given but unknown stochastic process. Subjects gradually learn more about the underlying process over time and hence the true distribution over termination times. We conduct two treatments, one with a high and one with a low volatility process. We find that elicited intervals are better when subjects are facing a low volatility process. In this treatment, participants learn to position their intervals almost optimally over the course of the experiment. This is in contrast with the high volatility treatment, where subjects, over the course of the experiment, learn to optimize the location of their intervals but fail to provide the optimal length. [ABSTRACT FROM AUTHOR]

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa. [ABSTRACT FROM AUTHOR]

In clinical studies, the period before an event occurs is frequently considered as an outcome. The general term used for this analytical method in clinical studies is "survival time analysis". The method employs Cox regression to compare hazards between groups. In this paper, we propose an index defined in the Bayesian framework to compare hazards. This index compares the sizes of the hazards directly. Further, we propose two methods to calculate the sizes of the hazards. One is an approximate method, by which we can easily calculate the size, and the other is an exact method. In addition, we apply the proposed index to two actual clinical studies to assess its usability. [ABSTRACT FROM AUTHOR]

In the paper, the authors find the logarithmically complete monotonicity of the Catalan-Qi function related to the Catalan numbers. [ABSTRACT FROM AUTHOR]

The present paper shows that for a given integer k ≥ 2 it is possible to construct an at least k -differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finslerian spheres as well. [ABSTRACT FROM AUTHOR]

Let A be any fixed cut-off restart algorithm running in parallel on multiple processors. If the algorithm is only allowed to run for up to time D, then it is no longer guaranteed that a result can be found. In this case, the probability of finding a solution within the time D becomes a measure for the quality of the algorithm. In this paper we address this issue and provide upper and lower bounds for the probability of A finding a solution before a deadline passes under varying assumptions. We also show that the optimal restart times for a fixed cut-off algorithm running in parallel is identical for the optimal restart times for the algorithm running on a single processor. Finally, we conclude that the odds of finding a solution scale superlinearly in the number of processors. [ABSTRACT FROM AUTHOR]

The generalized k-connectivity Kk(G) of a graph G, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized k-edge- connectivity λk(G). In this paper, graphs of order n such that Kk(G) = n -k/2- 1 and λk(G) = n -k/2- 1 for even k are characterized. [ABSTRACT FROM AUTHOR]

In this paper we give a complete classification of all n -dimensional non-Lie Malcev algebras with ( n − 4 ) -dimensional annihilator over an algebraically closed field of characteristic 0. We also show that such algebras are special. [ABSTRACT FROM AUTHOR]

An edge-coloured connected graph G is rainbow connected if each two vertices are connected by a path whose edges have distinct colours. If such a colouring uses k colours then G is called k -rainbow connected. The rainbow connection number of G , denoted by rc ( G ) , is the minimum k such that G is k -rainbow connected. Even the problem to decide whether rc ( G ) = 2 is NP-complete. It has been shown that if G is a connected graph of order n and size m with n − 2 2 + 2 ≤ m ≤ n − 1 2 , then 2 ≤ rc ( G ) ≤ 3 . In this paper we will present sufficient conditions for graphs G of this size to fulfil rc ( G ) = 2 depending on vertex degrees. [ABSTRACT FROM AUTHOR]

This paper investigates the structure of points u ∈ A N that are such that the omega-limit set ω ( u , σ ) is precisely X , where X ⊆ A N is an internally transitive shift space. We then use those results to study the possible structures of the omega-limit set of the turning point for a unimodal map. Examples are provided of unimodal maps f where no iterate of the turning point c is recurrent and ω ( c , f ) is either a minimal Cantor set or properly contains a minimal Cantor set. [ABSTRACT FROM AUTHOR]

The performance of device-to-device (D2D) communication in a cellular network depends on the resource sharing between D2D links and cellular users. Existing researches on resource sharing mainly focus on power control between the D2D users and cellular users that operate in the same frequency band. However, the D2D outage probability performance is hampered by the cellular interference to D2D links. Therefore, the D2D users may not achieve satisfactory SINR performance when D2D users and cellular users are geographically located in a small area; as a result, the outage probability performance would be significantly degraded. In this paper, we provide a novel resource sharing strategy to mitigate the interference from cellular users to D2D receivers by utilizing the low energy characteristics of signals in the guard band and analyze the D2D outage probability performance mathematically. Both the mathematical analysis and numerical results show that the proposed resource sharing strategy provides 1.2 dB SNR gain in D2D outage probability performance while guaranteeing the cellular throughputs. [ABSTRACT FROM AUTHOR]

Let M be a hyperbolizable, non-trivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of π 1 ( M ) into PSL ( 2 , C ) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the action of Out ( π 1 ( M ) ) on the PSL ( 2 , C ) -character variety of π 1 ( M ) . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the R package gendist that computes the probability density function, the cumulative distribution function, the quantile function and generates random values for several generated probability distribution models including the mixture model, the composite model, the folded model, the skewed symmetric model and the arc tan model. These models are extensively used in the literature and the R functions provided here are flexible enough to accommodate various univariate distributions found in other R packages. We also show its applications in graphing, estimation, simulation and risk measurements. [ABSTRACT FROM AUTHOR]