Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among individuals and resource distribution, the model exhibits some of the main features of evolutionary branching processing. The model can be extended to include spatial effects, different genetic loci, sexual mating and recombination, etc.
In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be shown. These transforms have interesting properties that led to new series expansions, representation of functions in terms of operators, connection between different series and operators, etc. By converting the power series into the Newton series, useful identities can be derived.
A. H. González, A. L. Anderson, A. Ferramosca
et al.
Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets (particularly the COVID-19), few of them present a formal dynamic characterization in terms of equilibrium sets and stability. Such concepts can be crucial to understand not only how the virus spreads in a population, but also how to tailor government interventions such as social distancing, isolation measures, etc. The objective of this work is to provide a full dynamic characterization of SIR-type systems under single-interval control actions and, based on it, to find the control action that produces the smallest number of infected individuals at the end of the epidemic that avoids second wave outbreaks. %Because of its simplicity, the latter result is intended to be just a reference/baseline for more complex control strategies related to general nonpharmaceutical measure (\textit{i.e}., those accounting for the health system capacity, the number of deaths, etc.). Simulations illustrate the benefits of the aforementioned results in terms of the herd immunity threshold.
In the past decade, blockchain has shown a promising vision greatly to build the trust without any powerful third party in a secure, decentralized and salable manner. However, due to the wide application and future development from cryptocurrency to Internet of Things, blockchain is an extremely complex system enabling integration with mathematics, finance, computer science, communication and network engineering, etc. As a result, it is a challenge for engineer, expert and researcher to fully understand the blockchain process in a systematic view from top to down. First, this article introduces how blockchain works, the research activity and challenge, and illustrates the roadmap involving the classic methodology with typical blockchain use cases and topics. Second, in blockchain system, how to adopt stochastic process, game theory, optimization, machine learning and cryptography to study blockchain running process and design blockchain protocol/algorithm are discussed in details. Moreover, the advantage and limitation using these methods are also summarized as the guide of future work to further considered. Finally, some remaining problems from technical, commercial and political views are discussed as the open issues. The main findings of this article will provide an overview in a methodology perspective to study theoretical model for blockchain fundamentals understanding, design network service for blockchain-based mechanisms and algorithms, as well as apply blockchain for Internet of Things, etc.
Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and the flat topology. By using these topologies, Tarizadeh and Aghajani obtained recently new characterizations of various classes of rings: Gelfand rings, clean rings, absolutely flat rings, $mp$ - rings,etc. The aim of this paper is to generalize some of their results to quantales, structures that constitute a good abstractization for lattices of ideals, filters and congruences. We shall study the flat and the patch topologies on the prime, the maximal and the minimal prime spectra of a coherent quantale. By using these two topologies one obtains new characterization theorems for hyperarchimedean quantales, normal quantales, B-normal quantales, $mp$ - quantales and $PF$ - quantales. The general results can be applied to several concrete algebras: commutative rings, bounded distributive lattices, MV-algebras, BL-algebras, residuated lattices, commutative unital $l$ - groups, etc.
Many interesting problems in the Internet industry can be framed as a two-sided marketplace problem. Examples include search applications and recommender systems showing people, jobs, movies, products, restaurants, etc. Incorporating fairness while building such systems is crucial and can have a deep social and economic impact (applications include job recommendations, recruiters searching for candidates, etc.). In this paper, we propose a definition and develop an end-to-end framework for achieving fairness while building such machine learning systems at scale. We extend prior work to develop an optimization framework that can tackle fairness constraints from both the source and destination sides of the marketplace, as well as dynamic aspects of the problem. The framework is flexible enough to adapt to different definitions of fairness and can be implemented in very large-scale settings. We perform simulations to show the efficacy of our approach.
We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider these problems in bounded domains, exterior domains, and in annular domains and we show that under suitable conditions, the domains and solutions are both radially symmetric. Our method uses both analytic and probabilistic tools.
There is a natural question to ask whether the rich mathematical theory of the hyperelliptic curves can be extended to all superelliptic curves. Moreover, one wonders if all of the applications of hyperelliptic curves such as cryptography, mathematical physics, quantum computation, diophantine geometry, etc can carry over to the superelliptic curves. In this short paper we make the case that the superelliptic curves are exactly the curves that one should study.
This paper comments on the published work dealing with robustness and regularization of support vector machines (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2009) [arXiv:0803.3490] by H. Xu, etc. They proposed a theorem to show that it is possible to relate robustness in the feature space and robustness in the sample space directly. In this paper, we propose a counter example that rejects their theorem.
Our system illustrates how information retrieved from social networks can be used for suggesting experts for specific tasks. The system is designed to facilitate the task of finding the appropriate person(s) for a job, as a conference committee member, an advisor, etc. This short description will demonstrate how the system works in the context of the HCIR2012 published tasks.
Anuj Mehra, Anupam Shukla, Mahender Kumawat
et al.
Biometric authentication techniques are more consistent and efficient than conventional authentication techniques and can be used in monitoring, transaction authentication, information retrieval, access control, forensics, etc. In this paper, we have presented a detailed comparative analysis between Principle Component Analysis (PCA) and Independent Component Analysis (ICA) which are used for feature extraction on the basis of different Artificial Neural Network (ANN) such as Back Propagation (BP), Radial Basis Function (RBF) and Learning Vector Quantization (LVQ). In this paper, we have chosen "TULIPS1 database, (Movellan, 1995)" which is a small audiovisual database of 12 subjects saying the first 4 digits in English for the incorporation of above methods. The six geometric lip features i.e. height of the outer corners of the mouth, width of the outer corners of the mouth, height of the inner corners of the mouth, width of the inner corners of the mouth, height of the upper lip, and height of the lower lip which extracts the identity relevant information are considered for the research work. After the comprehensive analysis and evaluation a maximum of 91.07% accuracy in speaker recognition is achieved using PCA and RBF and 87.36% accuracy is achieved using ICA and RBF. Speaker identification has a wide scope of applications such as access control, monitoring, transaction authentication, information retrieval, forensics, etc.
The Classical-map Hyper-Netted-Chain (CHNC) technique is a simple method of calculating quantum pair-distribution functions, spin-dependent energies, etc., of strongly-interacting {\it uniform} systems. We present CHNC calculations of charge densities and energies of {\it non-uniform} systems, viz., quantum dots, and compare with quantum Monte Carlo and density -functional results. Results for up to 210 electrons are reported.
We construct the non-standard complex (and real) numbers using the ultrapower method in the spirit of Cauchy's construction of the real numbers. We show that the non-standard complex numbers are a non-archimedean, algebraically closed field, and that the non-standard real numbers are a totally ordered, real-closed, non-archimedean field. We explore the various types of non-standard numbers, and develop the non-standard completeness results (Saturation Principle, Supremum Completeness of Bounded Internal Sets, etc) for $\starr$. We give non-standard characterizations for such usual topological objects as open, closed, bounded, and compact sets in terms of monads. We also consider such traditional topics of real analysis as limits, continuity, uniform continuity, convergence, uniform convergence, etc. in a non-standard setting. In both topology and real analysis we reduce (and in some cases eliminate) the number of quantifiers in the non-standard setting.
S. N. Balashov, K. Green, M. G. D. van der Grinten
et al.
This document is a copy of the original 2003 proposal for the construction grant for the CryoEDM Experiment at ILL, Grenoble. It is here made publicly available as a technical reference source for interested parties. It does not necessarily represent the final configuration of the experiment. Items pertaining to costs, personnel etc. have been removed.
Real thermal motion of gas molecules, free electrons, etc., at long time intervals (much greater than mean free-flight time) possesses, contrary to its popular mathematical models, essentially non-Gaussian statistics. A simple proof of this statement is suggested basing on only the determinism and reversibility of microscopic dynamics and besides incidentally derived virial expansion of a path probability distribution of molecular Brownian particle.
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional physical laws), rather than by the four-dimensional one, is explored in order to evade the most awkward problems of higher-dimensional theories with compact extra time-like dimensions: violation of causality and of unitarity.
In the present report, a set of theoretical results obtained in the period from 1991 to 2005 are reviewed. The physical systems under study include quark models of hadrons, inert atom clusters, atomic traps, and electrons and excitons confined in quantum dots. They contain three or more particles, and are described by nonrelativistic Quantum Mechanics. In the smallest systems (6 particles or less), exact diagonalization complemented with the Lanczos algorithm, and some analytical approaches (1/D-expansion, improved semiclassical quantization, etc.) are used. In the larger systems (from 7 to hundreds of particles), we employ approximate methods, such as two-point Pade approximants, variational Monte Carlo estimations, Hartree - Fock and RPA schemes, BCS functions and the Bethe - Goldstone algorithm, etc. With the help of these methods, a variety of physical properties have been computed, i.e., energy spectra, particle densities, spin textures, light absorption and emission, inelastic light scattering, and some dynamical features.
This work describes underlying features of the universe such as fundamental constants and cosmological parameters, conservation laws, baryon and lepton asymmetries, etc. in the context of local gauge theories for fundamental forces under the constraint of the flat universe. Conservation laws for fundamental forces are related to gauge theories for fundamental forces, their resulting fundamental constants are quantitatively analyzed, and their possible violations at different energy scales are proposed based on experimental evidences.
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.