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Link Residual Closeness of Harary Graphs
No full textThe study of networks characteristics is an important subject in differentfields, like math, chemistry, transportation, social network analysis etc. Theresidual closeness is one of the most sensitive measure of graphsvulnerability. In this article we calculate the link residual closeness ofHarary graphs.Comment: 15 page
Associated Permutations of Complete Non-Ambiguous Trees
No full textWe explore new connections between complete non-ambiguous trees (CNATs) andpermutations. We give a bijection between tree-like tableaux and a specificsubset of CNATs. This map is used to establish and solve a recurrence relationfor the number of tree-like tableaux of a fixed size without occupied corners,proving a conjecture by Laborde-Zubieta. We end by establishing a row/columnswapping operation on CNATs and identify new areas for future research
Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian
No full textIn this paper we establish the existence and uniqueness of global solutions(in time), as well as the existence, regularity and stability (uppersemicontinuity) of the attractor for the semigroup generated by the solutionsof a two-dimensional nonlinear hyperbolic-parabolic coupled system withfractional Laplacian. In addition, we also obtain the existence of anexponential attractor and show that this attractor has a finite fractaldimension in a space containing the phase space of the dynamical system
revTPL: The Reversible Temporal Process Language
No full textReversible debuggers help programmers to find the causes of misbehaviours inconcurrent programs more quickly, by executing a program backwards from thepoint where a misbehaviour was observed, and looking for the bug(s) that causedit. Reversible debuggers can be founded on the well-studied theory ofcausal-consistent reversibility, which only allows one to undo an actionprovided that its consequences, if any, are undone beforehand.Causal-consistent reversibility yields more efficient debugging by reducing thenumber of states to be explored when looking backwards. Till now,causal-consistent reversibility has never considered time, which is a keyaspect in real-world applications. Here, we study the interplay betweenreversibility and time in concurrent systems via a process algebra. TheTemporal Process Language (TPL) by Hennessy and Regan is a well-understoodextension of CCS with discrete-time and a timeout operator. We define revTPL, areversible extension of TPL, and we show that it satisfies the propertiesexpected from a causal-consistent reversible calculus. We show that,alternatively, revTPL can be interpreted as an extension of reversible CCS withtime
Waiting Nets: State Classes and Taxonomy
No full textIn time Petri nets (TPNs), time and control are tightly connected: timemeasurement for a transition starts only when all resources needed to fire itare available. Further, upper bounds on duration of enabledness can forcetransitions to fire (this is called urgency). For many systems, one wants todecouple control and time, i.e. start measuring time as soon as a part of thepreset of a transition is filled, and fire it after some delay \underline{and}when all needed resources are available. This paper considers an extension ofTPN called waiting nets that dissociates time measurement and control. Theirsemantics allows time measurement to start with incomplete presets, and canignore urgency when upper bounds of intervals are reached but all resourcesneeded to fire are not yet available. Firing of a transition is then allowed assoon as missing resources are available. It is known that extending boundedTPNs with stopwatches leads to undecidability. Our extension is weaker, and weshow how to compute a finite state class graph for bounded waiting nets,yielding decidability of reachability and coverability. We then compareexpressiveness of waiting nets with that of other models w.r.t. timed languageequivalence, and show that they are strictly more expressive than TPNs
The bipartite Ramsey numbers
No full textFor the given bipartite graphs , the multicolor bipartiteRamsey number is the smallest positive integer such that any -edge-coloring of contains a monochromatic subgraphisomorphic to , colored with the th color for some . Wecompute the exact values of the bipartite Ramsey numbers for
Action of the automorphism group on the Jacobian of Klein's quartic curve II: Invariant theta functions
No full textBernstein-Schwarzman conjectured that the quotient of a complex affine spaceby an irreducible complex crystallographic group generated by reflections is aweighted projective space. The conjecture was proved by Schwarzman andTokunaga-Yoshida in dimension 2 for almost all such groups, and for allcrystallographic reflection groups of Coxeter type by Looijenga,Bernstein-Schwarzman and Kac-Peterson in any dimension. We prove that theconjecture is true for the crystallographic reflection group in dimension 3 forwhich the associated collineation group is Klein's simple group of order 168.In this case the quotient is the 3-dimensional weighted projective space withweights 1, 2, 4, 7. The main ingredient in the proof is the computation of thealgebra of invariant theta functions. Unlike the Coxeter case, the invariantalgebra is not free polynomial, and this was the major stumbling block.Comment: 21 pages, 1 figure. Final version typeset in the EPIGA styl
Twin-width and permutations
No full textInspired by a width invariant on permutations defined by Guillemot and Marx,Bonnet, Kim, Thomass\'e, and Watrigant introduced the twin-width of graphs,which is a parameter describing its structural complexity. This invariant hasbeen further extended to binary structures, in several (basically equivalent)ways. We prove that a class of binary relational structures (that is:edge-colored partially directed graphs) has bounded twin-width if and only ifit is a first-order transduction of a~proper permutation class. As aby-product, we show that every class with bounded twin-width contains at most pairwise non-isomorphic -vertex graphs
Diagonal F-splitting and Symbolic Powers of Ideals
No full textLet be any ideal in a strongly -regular, diagonally -split ring essentially of finite type over an -finite field. We show that for all for which the formula makes sense. We use this to show a number of novelcontainments between symbolic and ordinary powers of prime ideals in thissetting, which includes all determinantal rings and a large class of toricrings in positive characteristic. In particular, we show that for all prime ideals of height in such rings.Comment: Copy edited and formatted in the EpiGA journal's styleshee
Plato, Aristotle, and Locke on the accumulation of wealth and natural law
No full textThe possibility of a growing accumulation of wealth, what we now refer to as economic growth, was something already considered by Plato, Aristotle and Locke, under the concept of chrematistics. In this paper we show how the economic thinking of these authors cannot be fully understood without considering the intimate relationship they establish between politics and property accumulation. In addition to continuities and ruptures in the arguments, there can be seen a growing understanding of the phenomenon of economic growth in such a way that, when we arrive at Locke, an evident paradigm shift can be appreciated. This change is rooted in the contributions of scholastic thinking for which the acquisition of property through human labour or industry enjoys legitimacy according to natural law