10,298 research outputs found

    Probabilistic Programming Interfaces for Random Graphs::Markov Categories, Graphons, and Nominal Sets

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    We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way.We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers 'black-and-white' graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons

    UMSL Bulletin 2023-2024

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    The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp

    The infrared structure of perturbative gauge theories

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    Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders. © 2022 Elsevier B.V

    The development of an international model for technology adoption: the case of Hong Kong

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    The purpose of this study is to examine the causal relationships between the internal beliefs formation of a decision-maker on technology adoption and the extent of the development of a technology adoptive behaviour. In particular, this study aims to develop an International Model For Technology Adoption (IMTA), which builds upon the Theory of Planned Behaviour (Ajzen 1992) and improves on the framework of the Technology Acceptance Model (Davis 1986). The development of such a model requires an understanding of the environmental factors which shape the cognitive processes of the decision maker. Hence, this is a behavioural model which investigates the constructs influencing the adoption behaviour and how the interaction between these constructs and the external variables can impact on the decision making process at the level of the firm. Previous research on technology transfer and innovation diffusion has classified factors affecting the diffusion process into two dimensions: 1) external-influence and 2) internal-influence. Hence, in this research, the International Model For Technology Adoption looks at how the endogenous and exogenous factors enter into the cognitive process of a technology adoption decision through which attitudes and behavioural intentions are shaped. Under the IMTA, the behavioural intention to adopt is a function of two exogenous variables, 1) Strategic Choice, and 2) Environmental Control. The Environmental Control factor is further categorised by two exogenous factors, namely, 1) Government Influence, and 2) Competitive Influence. In addition, the Competitive Influence factor is, in turn, classified into five forces: namely, 1) Industry Structure, 2) Price Intensity, 3) Demand Uncertainty, 4) Information Exposure, 5) Domestic Availability. Regarding the cognitive process which forms the attitude to adopt, it is hypothesised to be affected by six other endogenous beliefs: 1) Compatibility; 2) Enhanced Value; 3) Perceived Benefits; 4)Adaptative Experiences, 5) Perceived Difficulty; and 6) Suppliers’ Commitment. A survey research method was utilised in this study and the research instrument was developed after a comprehensive review of the relevant literature and an expert interview. A total of 298 completed questionnaires were returned; giving a response rate of 13.56%. Of the 298 questionnaires, 39 of the responses were unusable with missing date. This gives a total of 259 usable questionnaires and an effective response rate of 11.78%. The results of the analysis suggested that the fitness of the International Model For Technology Adoption was good and the data of this study supported the overall structure of the IMTA. When compared with the null model, which was used by the EQS as a baseline model to judge to overall fitness for the IMTA, the IMTA yielded a value of 0.914 in the Comparative Fit index; hence, indication of a good fit model. In addition, the results of the principal component analysis also illustrated that the 16-factor International Model For Technology Adoption was an adequate model to capture the information collected during the survey. The results shown that this 16-factor structure represented nearly 77% of the total variance of all items. A further analysis into the factor structure, again, revealed that there existed a perfect match between the conceptual dimensionality of the International Model For Technology Adoption and the empirical data collected in the survey. However, the results of the hypotheses testing on the individual constructs were mixed. While not all the magnitude of these ten hypotheses was statistically significant, almost all pointed to the direction conceptualised by the IMTA. From these results, it can be interpreted that while the results of the structural equation modelling analysis provided overall support to the International Model For Technology Adoption, the results of individual constructs of the Model revealed that some constructs were forming a larger impact than others in the decision making process to adopt foreign technology. In particular, the intention to adopt was greatly affected by the attitude of the prospective adopters, the influence of the government and the degree of industry rivalry. However, the impact of the overall competitive influence factor on the intention to adopt was not supported by the results. Again, the existence of investment alternative was also not a serious concern for the prospective adopters

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    UMSL Bulletin 2022-2023

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    The 2022-2023 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1087/thumbnail.jp

    Operands and instances

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    Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself

    Polynomial Identity Testing and the Ideal Proof System: PIT is in NP if and only if IPS can be p-simulated by a Cook-Reckhow proof system

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    The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable systems of polynomial equations. One potential drawback of IPS is that verifying an IPS proof is only known to be doable using Polynomial Identity Testing (PIT), which is solvable by a randomized algorithm, but whose derandomization, even into NSUBEXP, is equivalent to strong lower bounds. However, the circuits that are used in IPS proofs are not arbitrary, and it is conceivable that one could get around general PIT by leveraging some structure in these circuits. This proposal may be even more tempting when IPS is used as a proof system for Boolean Unsatisfiability, where the equations themselves have additional structure. Our main result is that, on the contrary, one cannot get around PIT as above: we show that IPS, even as a proof system for Boolean Unsatisfiability, can be p-simulated by a deterministically verifiable (Cook-Reckhow) proof system if and only if PIT is in NP. We use our main result to propose a potentially new approach to derandomizing PIT into NP

    Aspects of Gravitational and Cosmological Scattering Amplitudes

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    This thesis presents three distinct aspects of scattering amplitudes research along with background material on the concepts underpinning them. The first of these is the study of on-shell diagrams for \cN=7 supergravity and an associated recursion relation automatically encorporating the bonus relations. This is used to produce momentum twistor expressions which in the case of six-point NMHV use different `coordinate patches' with different ordering of external legs to get compact results and see the cancellation of spurious poles through momentum twistors. The second is the study of colour/kinematics duality of Yang-Mills amplitudes in four-dimensional Anti-de Sitter (AdS) space. By applying a generalised gauge transformation the kinematic numerators can be made to obey a Jacobi relation and these shifted numerators also obey a deformed AdS version of the Bern-Carrasco-Johansson relations. Finally we study wavefunction coefficients of scalar effective field theories (EFTs) in de Sitter space using a representation involving boundary conformal generators acting on contact diagrams and the cosmological scattering equations. Through this representation, we show that four-point wavefunction coefficients of EFTs exhibit double copy relations analogous to those in flat space with additional curvature corrections with unfixed coefficients. Imposing enhanced soft limits analogous to the EFTs in flat space allows these to be unambiguously fixed and also recovers Lagrangians with hidden shift symmetries. This is explored at four- and six-point

    A mixed-mode dependent interface and phase-field damage model for solids with inhomogeneities

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    The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular situation of a solid with inhomogeneities. Description of the fracture processes are based on the theory of material damage. It introduces two independent damage parameters to distinguish between interface and internal cracks. The parameter responsible for interface cracks is defined in a thin adhesive layer of the interface and renders relation between stress and strain quantities in fashion of cohesive zone models.The second parameter is defined inside material domains and it is founded on the theory of phase-field fracture guaranteeing the material damage to occur in a thin material strip introducing a regularised model of internal cracks. Additional property of both interface and phase-field damage is their capability to distinguish between fracture modes which is useful if the structures is subjected to combined loading. The solution methodology is based on a variational approach which allows implementation of non-linear programming optimisation into standard methods of finite-element discretisation and time stepping method.Computational implementation is prepared in MATLAB whose numerical data validate developed formulation for analysis of problems of fracture in multi-domain elements of structures.Comment: 24 pages, 19 figures, to be published in Theoretical and Applied Fracture Mechanic
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