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A computational Approach to Developing Mathematical Models of Polyploid Meiosis

GENETICS 2013年第4期193卷 1083-+页

作者： Rehmsmeier, Marc Gregor Mendel Inst Mol Plant Biol GmbH A-1030 Vienna Austria Uni Res Uni Comp Computat Biol Unit N-5008 Bergen Norway

Mathematical models of meiosis that relate offspring to parental genotypes through parameters such as meiotic recombination frequency have been difficult to develop for polyploids. Existing models have limitations wit... 详细信息

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Play-Hysteresis in the Joint Dynamics of Employment and Investment

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mathematics IN COMPUTER SCIENCE 2022年第1期16卷 1-13页

作者： Mota, P. R. Vasconcelos, P. B. Univ Porto Sch Econ & Business Rua Dr Roberto Frias S-N P-4200464 Porto Portugal CEF UP Rua Dr Roberto Frias S-N P-4200464 Porto Portugal

The slow recovery of many developed economies to the recent financial crisis, and the largest fall in aggregate demand since WWII caused by the COVID-19 Pandemic with its foreseeable negative and persistent effects on the aggregate supply, has generated renewed interest in the subject of hysteresis. The presence of significant hysteresis effects has important theoretical and policy implications. First, there is no unique and predetermined long-run equilibrium level of aggregate employment, as the equilibrium is permanently changed by temporary shocks. Second, as the economic system is not self-adjusting, substantial, timely, and sustained expansionary monetary and fiscal policy should be applied to mitigate the impact of shocks, including the temporary ones. Although it is not possible to quantify hysteresis effects in real time, we can use historical data to shed some light on the possible long-term economic consequences of the COVID-19 pandemic. For that purpose, we use the linear play-hysteresis model in the context of two equation system to analyses the join hysterical dynamics of aggregate employment and investment. We implement the model empirically by means of a new algorithm for the simultaneous equations system applied to Portuguese data that separates the effects of large and small changes in aggregate demand on aggregate employment and investment using an endogenous determined switching parameter as reference.

关键词： Play hysteresis modeling computational mathematics Switching regression Employment Investment

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Estimating the Employment Band of Inaction with Multiple Breaks due to Labor Market Reforms

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mathematics IN COMPUTER SCIENCE 2021年第1期15卷 121-133页

作者： Mota, P. R. Vasconcelos, P. B. Univ Porto Fac Econ Ctr Econ & Finance Rua Dr Roberto Frias S-N P-4200464 Porto Portugal Univ Porto Fac Econ Ctr Math Rua Dr Roberto Frias S-N P-4200464 Porto Portugal

This paper proposes a new way of testing the effect of labor market reforms in the employment adjustment at the macro level. Following the approach to hysteresis based on the presence of non-convex costs of adjustment, a switching aggregate employment equation is estimated, with an unknown splitting factor, from a computational implementation of the linear play hysteresis operator. The play hysteresis operator describes a dynamics where non-convex adjustment costs create intervals of weak reaction of employment to small variations in forcing variables, while spurts in employment adjustment may occur as a consequence of a large, or cumulative small shocks. The main contribution of this paper is to extend an existing approach for the case where there are disruptive breaks, by accommodating changes in the value of the switching parameter of the employment equation whenever labor market reforms are present. Numerical experiments on the Portuguese economy are performed.

关键词： Play hysteresis modeling computational mathematics Switching regression

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A Unified Formal Description of Arithmetic and Set Theoretical Data Types

A Unified Formal Description of Arithmetic and Set Theoretic...

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17th Symposium on the Integration of Symbolic Computation and Mechanised Reasoning

作者： Tarau, Paul Univ N Texas Dept Comp Sci & Engn Denton TX 76203 USA

ISBN: (纸本)9783642141270

We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type classes with examples of instances converging to an efficient implementation in terms of arbitrary length integers and bit operations. As an instance, we derive algorithms to perform arithmetic operations efficiently directly with hereditarily finite sets. The self-contained source code of the paper is available at http://***/tarau/research/2010/***

关键词： formal description of arithmetic and set theoretical data types Peano arithmetic and hereditarily finite sets bijective base-2 arithmetic software refinement with Haskell type classes computational mathematics

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On Computing Sparse Generalized Inverses And Sparse-Inverse/Low-Rank Decompositions

On Computing Sparse Generalized Inverses And Sparse-Inverse/...

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作者： Victor Fuentes University of Michigan

学位级别：博士

Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using 1-norm minimization and linear programming. We introduce several new sparse generalized inverses by using 1-norm minimization on a subset of the linear Moore-Penrose properties, again leading to linear programming. computationally, we demonstrate the usefulness of our approach in the context of application to least-squares problems and minimum 2-norm problems. One of the Moore-Penrose properties is nonlinear (in fact, quadratic), and so developing an effective convex relaxation for it is nontrivial. We develop a variety of methods for this, in particular a nonsymmetric lifting which is more efficient than the usual symmetric lifting that is normally applied to non-convex quadratic equations. In this context, we develop a novel and computationally effective âdiving procedureâ to find a path of solutions trading off sparsity against the nice properties of the Moore- Penrose pseudoinverse. Next, we consider the well-known low-rank/sparse decomposition problem min {

关键词： Sparse Optimization computational mathematics Moore-Penrose Pseudoinverse Convex Relaxation Matrix Decomposition Industrial and Operations Engineering Engineering

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Extending the Generalized Fermat Prime Number Search Beyond One Million Digits Using GPUs

Extending the Generalized Fermat Prime Number Search Beyond ...

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10th International Conference on Parallel Processing and Applied mathematics (PPAM)

作者： Bethune, Iain Goetz, Michael Univ Edinburgh EPCC James Clerk Maxwell BldgKings BldgMayfield Rd Edinburgh EH9 3JZ Midlothian Scotland PrimeGrid Ardsley NY USA

ISBN: (纸本)9783642552243

Great strides have been made in recent years in the search for ever larger prime Generalized Fermat Numbers (GFN). We briefly review the history of the GFN prime search, and describe new implementations of the 'Genefer' software (now available as open source) using CUDA and optimised CPU assembler which have underpinned this unprecedented progress. The results of the ongoing search are used to extend Gallot and Dubner's published tables comparing the theoretical predictions with actual distributions of primes, and we report on recent discoveries of GFN primes with over one million digits.

关键词： Generalized Fermat Numbers Primality testing Volunteer computing computational mathematics GPU computing CUDA

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Mathematical and Statistical Frameworks Fostering Advances in AI Systems and Computing 24th

Mathematical and Statistical Frameworks Fostering Advances i...

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24th International Conference on computational Science and Its Applications (ICCSA)

作者： Oliveira, Teresa A. Teodoro, Maria Filomena Univ Aberta Dept Ciencias & Tecnol P-1269001 Lisbon Portugal Univ Lisbon Fac Ciencias CEAUL P-1649014 Lisbon Portugal Naval Acad Ctr Naval Res CINAV Portuguese Navy P-2810001 Almada Portugal Lisbon Univ Ctr Computat & Stochast Math Inst Super Tecn CEMAT P-1048001 Lisbon Portugal

ISBN: (纸本)9783031652226;9783031652233

The rapid expansion of artificial intelligence (AI) areas and applications has become an everyday social reality and the development of computing methods and of technology, in order to accomplish for the respective needs, emerge as one of the biggest challenges of this century. However, a strong background in mathematics and Statistical fundamentals is crucial to foster the robustness of AI Systems and to attain for the correspondent generalization capabilities. Thus, recognizing the importance and benefits of integrate multiple mathematical methodologies that can leverage the unique strengths of each to create synergistic effects, is here discussed. In the literature it is possible to find diverse connections of Mathematical and Statistical frameworks with AI Systems and Computing. For illustration: Algebra - can be used to manipulate data in high-dimensional spaces;Statistical Analysis - helps on providing confidence in decision-making;Linear Regression- can be used on data modelling and accuracy assessment;and Bayesian statistics - can be used in probabilistic programming for AI applications. This work particularly highlights the evolving role of Hadamard Matrices and Coding Theory, illustrating their synergy with AI Systems and Computing, and how such synergy is driving innovation in various fields and approaching the new reality of Quantic paradigms.

关键词： computational mathematics geometric modeling incomplete block designs combinatorial optimization hadamard matrices AI quantum computing

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The Interface of Computer Science and Statistics: An Historical Perspective

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American Statistician 1968年第3期22卷 17-20页

作者： Goodman, A.F. Douglas Missile and Space Systems Division United States

Provides a historical perspective on the interface of computer science and statistics. Country tracing the connection between the two professions; Mathematician making substantial contributions to computer science and... 详细信息

关键词： Probabilities Statistics Computer science Calculus Calculators Biological sciences Gambling Astronomy computational mathematics

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