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Abstract: We show that paper-folding words contain arbitrarily large abelian powers. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Abstract: To meet always increasing safety requirements in car industry, design and safety assessment methods are developed in order to fit the complexity of new embedded mecatronic systems. Hybrid (discrete/continuous) and dynamic features, specific to these systems, require choosing a suitable formalism. These features should also be considered in safety studies made all through the system design. The aim of this paper is to propose a quantitative analysis method based on the construction of an aggregated Markov graph, which allows a limitation of the combinatorial expansion. This graph is directly deducted from the Petri net modelling of the system. It is composed by a set of functional modes and a set of transitions to which statistical information regarding the system dynamics has been added. [Copyright &y& Elsevier]

Abstract: We introduce a new combinatorial auction format based on a simple, transparent pricing mechanism tailored for the hierarchical package structure proposed by Rothkopf, Pekeč, and Harstad to avoid computational complexity [Rothkopf, M., Pekeč, A., Harstad, R., 1998, Computationally manageable combinatorial auctions. Manage. Sci. 44, 1131–1147]. This combination provides the feedback necessary for bidders in multi-round auctions to discern winning bidding strategies for subsequent rounds and to coordinate responses to aggressive package bids. The resulting mechanism is compared to two leading alternatives in a series of laboratory experiments involving varying degrees of value synergies. Based on these “wind tunnel” tests the FCC has decided to use hierarchical package bidding in a segment of the upcoming 700 MHz auction. [ABSTRACT FROM AUTHOR]

This paper extends the framework of soft set theory to directed graphs by introducing and analyzing the concepts of the normal product and restricted normal product of soft directed graphs. Building on Molodtsov’s foundational work in developing soft set theory to address uncertainty in data, this study presents new methods for modeling and understanding complex systems where uncertainty plays a significant role. Soft directed graphs, which enhance traditional graph models by incorporating parameters and uncertain relationships, serve as the foundation for this investigation. The normal product, defined as a combination of two soft directed graphs based on their respective parameter sets, and the restricted normal product, which combines soft directed graphs only where their parameter sets intersect, provide a comprehensive framework for these new operations. This paper also establishes the structural properties of these products, ensuring they are well-defined and retain the key features of soft directed graphs. Furthermore, we derive combinatorial identities related to vertex and arc counts, as well as degree sums, offering deeper insights into the composition and behavior of these graph products. [ABSTRACT FROM AUTHOR]

This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to the setting of simple graphs. This paper considers the set of functions from the vertices of our graph to N, which assign a fixed number of 1's to some vertices and assign higher numbers to other vertices by adding up their neighbors' assignments. The stepping stone solution is defined as an element obtained from the argmax of the maxima of these functions, and the maxima as its growth. This work is organized into work on the bounded and unbounded degree graph cases. In the bounded case, sufficient conditions are obtained for superlinear and sublinear stepping stone solution growth. Furthermore this paper demonstrates the existence of a basis of graphs which characterizes superlinear growth. In the unbounded case, properly sublinear and superlinear stepping stone solution growth are obtained. [ABSTRACT FROM AUTHOR]

The Minimum Score Separation Problem (MSSP) is a combinatorial problem that was introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting stock problem. During the process of producing boxes, flat papers are prepared for folding by being scored with knives. The problem is to determine whether and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. Introducing the concept of matching-based alternating Hamiltonian paths, this paper models the MSSP as the problem of finding an alternating Hamiltonian path on a graph that is the union of a matching and a type of graph known as a 'threshold graph'. On this basis, we find a heuristic that can quickly recognize a large percentage of feasible and infeasible instances of the MSSP. Detailed computational experiments demonstrate the efficiency of our approach. [ABSTRACT FROM AUTHOR]

This paper discusses the selection and design of heuristic procedures for solving one-dimensional roll trim problems. These are well-defined combinatorial problems which are too large to optimize. Five different roll trim problems from the paper and film industries are described along with the heuristic procedures that have been used successfully to improve the quality of the solutions generated. The paper concludes with some general guidelines for developing "industrial-grade" heuristic problem solving procedures. [ABSTRACT FROM AUTHOR]

The second multiplicative Zagreb eccentricity index E*2 (G) of a simple connected graph G is expressed as the product of the weights ε(a)εG(b) over all edges ab of G, where ε(a) stands for the eccentricity of the vertex a in G. In this paper, some extremal problems on the E*2 index over some special graph classes including trees, unicyclic graphs and bicyclic graphs are examined, and the corresponding extremal graphs are characterized. Besides, the relationships between this vertex-eccentricity-based graph invariant and some well-known parameters of graphs and existing graph invariants such as the number of vertices, number of edges, minimum vertex degree, maximum vertex degree, eccentric connectivity index, connective eccentricity index, first multiplicative Zagreb eccentricity index and second multiplicative Zagreb index are investigated. [ABSTRACT FROM AUTHOR]

The Gödel–Dummett logic and Łukasiewicz one are two main many-valued logics used by the fuzzy logic community. Our goal is a quantitative comparison of these two. In this paper, we will mostly consider the 3-valued Gödel–Dummett logic as well as the 3-valued Łukasiewicz one. We shall concentrate on their implicational-negation fragments which are limited to formulas formed with a fixed finite number of variables. First, we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length built with exactly one variable. Then, we investigate such proportion for satisfiable formulas. Second, we generalise our investigation on formulas written with $ k\ge 1 $ k ≥ 1 variables. The primary goal of the paper is the research on the asymptotic behaviour of these fractions when the length n tends to infinity. If such limits exists, they are real numbers between 0 and 1, which are called the density of truth or the density of SAT. To compare the density of truth and the density of satisfiable formulas for both fragments of 3-valued Gödel–Dummett's and Łukasiewicz's logics we use the powerful theory of analytic combinatorics. This paper is a natural continuation of the previous brief conference note by Kostrzycka and Zaionc (2020) as well as enriched with some previous results from Kostrzycka and Zaionc (2003). In the conference note we computed analytically the density of truth and the density of SAT (with a determined precision) for 3-valued Łukasiewicz's logic restricted to a language with only one variable. In Kostrzycka and Zaionc (2003) we computed the same values for exactly the same fragment of the 3-valued Gödel–Dummett logic. This paper answers the more general questions of the existence of density of truth and density of SAT for both many-valued logics with an arbitrary finite number of variables. Therefore this paper gives an an interesting picture of two main families of finite-valued fuzzy logics problems treated quantitatively. This picture is taken from the perspective of classical logic. It shows that unexpectedly there is quantitatively a little distance between these two approaches. [ABSTRACT FROM AUTHOR]

In this short note we generalize, complement and improve recent result on multiplicative metric spaces established by R.P. Agarwal et al. [Ravi P. Agarwal, Erdal Karapinar and Bessem Samet: An essential remark on fixed point results on multiplicative metric spaces. [ABSTRACT FROM AUTHOR]

This paper describes a full-scale physical model and its application to investigate the effectiveness/performance of small-bore sewers for a range of operational and design parameters. The implementation methodology involves observing the movement of synthetic gross solids in three small bore sewers (150, 100 and 75 mm diameter) for different volumes of simulated flush waves and gradients. The simulated flush waves were generated, using an automated wave sequencer, for three different flush volumes (3, 4.5 and 6 likes). To investigate the impact of solid shape factor, a number of tests were carried out using synthetic solids in combination with toilet tissue paper. In total, more than 1,000 tests were performed for different operational and design parameter combinations. Results obtained to date have confirmed earlier studies, particularly with respect to the role of flush volume in solids transport, and identified the impact of gradient variation and its significance particularly in small-bore sewers receiving low flush volume. Results from the physical model application exercise will be used to propose new design guidelines for wastewater collection systems with specific consideration to new developments and inform the decision support system, currently being developed as pan of a research project on water cycle management for new developments (WAND). [ABSTRACT FROM AUTHOR]

Population Based Algorithms (PBAs) are excellent search tools that allow searching space of parameters defined by problems under consideration. They are especially useful when it is difficult to define a differentiable evaluation criterion. This applies, for example, to problems that are a combination of continuous and discrete (combinatorial) problems. In such problems, it is often necessary to select a certain structure of the solution (e.g. a neural network or other systems with a structure usually selected by the trial and error method) and to determine the parameters of such structure. As PBAs have great application possibilities, the aim is to develop more and more effective search formulas used in them. An interesting approach is to use multiple populations and process them with separate PBAs (in a different way). In this paper, we propose a new multi-population-based algorithm with: (a) subpopulation evaluation and (b) replacement of the associated PBAs subpopulation formulas used for their processing. In the simulations, we used a set of typical CEC2013 benchmark functions. The obtained results confirm the validity of the proposed concept. [ABSTRACT FROM AUTHOR]

Enumeration of the problem space for the multiple-outage missed-thrust problem is a significant factor for determining what types of analysis is feasible to conduct. An exhaustive examination of the multiple-outage problem is one method for conducting missed-thrust analysis. In this paper, we explore the combinatorics of the problem, providing methods of calculating and estimating the number of possible missed-thrust cases when discretizing a trajectory to consider the effects of multiple missed-thrust events. We examine the difficulties of enumerating all possible cases, and examine when it may be desirable to conduct an exhaustive enumeration rather than a stochastic Monte-Carlo-type analysis. For missions which cover large time scales or feature high resolutions for their analysis, the combinatorics of the problem quickly grow excessively large, but the exhaustive formulation can still provide useful insight for smaller problems or with the right assumptions. We also explore various sub-problems, and their enumeration, such as the partial-thrust problem and the consideration of only critical regions of the trajectory, their potential applicability to the field of missed-thrust analysis, and connections to mathematical topics. [ABSTRACT FROM AUTHOR]

A reaction system is a computational model motivated by the functioning of living cells. In previous studies, Ehrenfeucht et al. have classified the functions specified by minimal reaction systems. Several studies have focused on the reaction system ranks of functions specified by minimal reaction systems, where the rank pertains to the minimum size of a specifying reaction system. This paper focuses on reaction system rank for a class of union-additive functions specified by minimal reaction systems introduced by Salomaa, which are closed under composition. More precisely, we establish a sufficient condition for the equality of reaction system ranks for functions belonging to the class. Then we study the reaction system ranks of such functions with signature sizes one and two, as well as those with one-to-one signatures, specifically over ternary and quaternary alphabets. Lastly, we establish a lower upper bound of reaction system ranks of such functions with one-to-one signatures for | S | ≥ 5. [ABSTRACT FROM AUTHOR]

Linear codes play a crucial role in various fields of engineering and mathematics, including data storage, communication, cryptography, and combinatorics. Minimal linear codes, a subset of linear codes, are particularly essential for designing effective secret sharing schemes. In this paper, we introduce several classes of minimal binary linear codes by carefully selecting appropriate Boolean functions. These functions belong to a renowned class of Boolean functions, namely, the general Maiorana–McFarland class. We employ a method first proposed by Ding et al. (IEEE Trans Inf Theory 64(10):6536–6545, 2018) to construct minimal codes violating the Ashikhmin–Barg bound (wide minimal codes) by using Krawtchouk polynomials. The lengths, dimensions, and weight distributions of the obtained codes are determined using the Walsh spectrum distribution of the chosen Boolean functions. Our findings demonstrate that a vast majority of the newly constructed codes are wide minimal. Furthermore, our proposed codes exhibit a significantly larger minimum distance, in some cases, compared to some existing similar constructions. Finally, we address this method, based on Krawtchouk polynomials, more generally, and highlight certain generic properties related to it. These general results offer insights into the scope of this approach. [ABSTRACT FROM AUTHOR]

The article presents information on the 2005 Information Theory Society Paper Award, which is given annually to for a valuable publication in the field of information theory. This year the award was jointly awarded to researchers Shuo-Yen Robert Li, Raymond W. Yeung, and Ning Cai for their paper "Linear Network Coding" which appeared in the February 2003 issue of the journal "IEEE Transactions on Information Theory." Shuo-Yen Robert Li has done his B.S. in mathematics from National Taiwan University in 1970 and Ph.D. in mathematics from the University of California, Berkeley, in 1974. Yeung was born in Hong Kong on June 3, 1962. He has done B.S., M.Eng., Ph.D. in electrical engineering from Cornell University in Ithaca, New York. His research work include information theory and network coding. Ning Cai has done his B.S. in mathematics from the Normal College of Beijing in Beijing, China in 1982. He completed his Ph.D. in mathematics from the University of Bielefeld in Bielefeld, Germany in 1988. He has done research in the field of combinatorics, information theory and their applications.

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