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A Categorical Framework for Program Semantics and Semantic Abstraction
No full textCategorical semantics of type theories are often characterized asstructure-preserving functors. This is because in category theory both thesyntax and the domain of interpretation are uniformly treated as structuredcategories, so that we can express interpretations as structure-preservingfunctors between them. This mathematical characterization of semantics makes itconvenient to manipulate and to reason about relationships betweeninterpretations. Motivated by this success of functorial semantics, we addressthe question of finding a functorial analogue in abstract interpretation, ageneral framework for comparing semantics, so that we can bring similarbenefits of functorial semantics to semantic abstractions used in abstractinterpretation. Major differences concern the notion of interpretation that isbeing considered. Indeed, conventional semantics are value-based whereasabstract interpretation typically deals with more complex properties. In thispaper, we propose a functorial approach to abstract interpretation and studyassociated fundamental concepts therein. In our approach, interpretations areexpressed as oplax functors in the category of posets, and abstractionrelations between interpretations are expressed as lax natural transformationsrepresenting concretizations. We present examples of these formal concepts frommonadic semantics of programming languages and discuss soundness.Comment: MFPS 202
Derivation of Painlev\'e type system with affine Weyl group symmetry in a self-similarity limit
No full textWe show how the zero-curvature equations based on a loop algebra of with a principal gradation reduce via self-similarity limit to a polynomialHamiltonian system of coupled Painlev\'e III models with four canonicalvariables and affine Weyl group symmetry.Comment: 14 page
On Insecure Uses of BGN for Privacy Preserving Data Aggregation Protocols
No full textThe notion of aggregator oblivious (AO) security for privacy preserving dataaggregation was formalized with a specific construction of AO-secure blindingtechnique over a cyclic group by Shi et al. Some of proposals of dataaggregation protocols use the blinding technique of Shi et al. for BGNcryptosystem, an additive homomorphic encryption. Previously, there have beensome security analysis on some of BGN based data aggregation protocols in thecontext of integrity or authenticity of data. Even with such security analysis,the BGN cryptosystem has been a popular building block of privacy preservingdata aggregation protocol. In this paper, we study the privacy issues in theblinding technique of Shi et al. used for BGN cryptosystem. We show that theblinding techniques for the BGN cryptosystem used in several protocols are notprivacy preserving against the recipient, the decryptor. Our analysis is basedon the fact that the BGN cryptosystem uses a pairing e:GxG-->G_T and theexistence of the pairing makes the DDH problem on G easy to solve. We alsosuggest how to prevent such privacy leakage in the blinding technique of Shi etal. used for BGN cryptosystem.Comment: 11 page
Distinct Angles and Angle Chains in Three Dimensions
No full textIn 1946, Erd\H{o}s posed the distinct distance problem, which seeks to findthe minimum number of distinct distances between pairs of points selected fromany configuration of points in the plane. The problem has since beenexplored along with many variants, including ones that extend it into higherdimensions. Less studied but no less intriguing is Erd\H{o}s' distinct angleproblem, which seeks to find point configurations in the plane that minimizethe number of distinct angles. In their recent paper "Distinct Angles inGeneral Position," Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolfuse a logarithmic spiral to establish an upper bound of on the minimumnumber of distinct angles in the plane in general position, which prohibitsthree points on any line or four on any circle. We consider the question of distinct angles in three dimensions and providebounds on the minimum number of distinct angles in general position in thissetting. We focus on pinned variants of the question, and we examine explicitconstructions of point configurations in which useself-similarity to minimize the number of distinct angles. Furthermore, westudy a variant of the distinct angles question regarding distinct angle chainsand provide bounds on the minimum number of distinct chains in and .Comment: 16 pages, 7 figure
Almost Kenmotsu Manifolds
No full textThe object of this paper is to study generalized φ-recurrent almost Kenmotsu manifolds with characteristic vector field ξ belonging to (k, µ)-nullity distribution. We have showed that these manifolds reduce to Kenmotsu manifolds with scalar curvature-1. Further we establish the relations among the associated 1-forms and proved the conditions under which gradient Ricci almost soliton reduce to gradient Ricci soliton
Towards a Theory of Conversation in Political Economy
No full textThe paper analyzes the nature of Political Economy as a modern conversational style, by defining its logical and rhetoric features. Successively, a wider historical and political context linked to the birth of the discipline is taken into account and thoroughly introduced in its implications for the interpretation of the role of such a discipline in modern life. Finally Political Economy is examined under the light of the educational effort it requires, as an anti- rhetoric method of inquiry and dialogue
On the long time behaviour of single stochastic Hodgkin-Huxley neurons with constant signal, and a construction of circuits of interacting neurons showing self-organized rhythmic oscillations
No full textThe stochastic Hodgkin-Huxley neurons considered in this paper replacetime-constant deterministic input of the classical deterministic modelby increments of a stochastic process: isOrnstein-Uhlenbeck with volatility and backdriving force ,and we call the signal. We have ergodicity and strong laws oflarge numbers for various functionals of the process, and characterize 'quietbehaviour' and 'regular spiking' as events whose probability depends on theparameters and on the signal . The notions of quietbehaviour and regular spiking allow for a construction of circuits ofinteracting stochastic Hodgkin-Huxley neurons, combining excitation withinhibition according to a bloc structure along the circuit, on whichself-organized rhythmic oscillations can be observed.Comment: 53 pages, 8 figure
Geodesic Growth of Numbered Graph Products
No full textIn this paper, we study geodesic growth of numbered graph products; these area generalization of right-angled Coxeter groups, defined as graph products offinite cyclic groups. We first define a graph-theoretic condition calledlink-regularity, as well as a natural equivalence amongst link-regular numberedgraphs, and show that numbered graph products associated to link-regularnumbered graphs must have the same geodesic growth series. Next, we derive aformula for the geodesic growth of right-angled Coxeter groups associated tolink-regular graphs. Finally, we find a system of equations that can be used tosolve for the geodesic growth of numbered graph products corresponding tolink-regular numbered graphs that contain no triangles and have constant vertexnumbering.Comment: 35 pages, published in journal of Groups, Complexity, Cryptolog
Buddhist economics as a return to rational model of economic management
No full textThe concept of Buddhist economics is gaining increased appeal in a world where external factors are once again becoming more of a threat than a salvation. Buddhist economy is a return to the values of agricultural production, but taking into account the experience and achievements of the industrial and post-industrial economy. Care for the environment, personal development, community development, especially spiritual development – these are the priorities of the Buddhist economy. In particular, agricultural production appears as only the most convenient means for achieving these goals. However, Buddhist economics is not a rejection of the achievements of modern and postmodern society – it is an attempt to use these experiences and achievements for a more intelligent and effective implementation of the goals of the economy, which were defined by Aristotle. The rational model of economic management according to these views consists in thrifty but full consumption and restrained production with environmentally friendly aims
Token Swapping on Trees
No full textThe input to the token swapping problem is a graph with vertices , and tokens with labels , one on each vertex.The goal is to get token to vertex for all using aminimum number of swaps, where a swap exchanges the tokens on the endpoints ofan edge. We present some results about token swapping on a tree, also known as"sorting with a transposition tree": 1. An optimum swap sequence may need to perform a swap on a leaf vertex thathas the correct token (a "happy leaf"), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves -- as all known approximationalgorithms for the problem do -- has approximation factor at least .Furthermore, the two best-known 2-approximation algorithms have approximationfactor exactly 2. 3. A generalized problem -- weighted coloured token swapping -- isNP-complete on trees, even when they are restricted to be subdivided stars, butsolvable in polynomial time on paths and stars. In this version, tokens andvertices have colours, and colours have weights. The goal is to get every tokento a vertex of the same colour, and the cost of a swap is the sum of theweights of the two tokens involved.Comment: 37 pages, Discrete Mathematics and Theoretical Computer Science, DMTCS vol. 24:2, 2022, #