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Articles 5881 - 5910 of 7997
Full-Text Articles in Physical Sciences and Mathematics
Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore
Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore
Masters Theses & Specialist Projects
No abstract provided.
Modeling In Microbial Batch Culture And Its Parameter Identification, Zhaohua Gong, Chongyang Liu, Enmin Feng
Modeling In Microbial Batch Culture And Its Parameter Identification, Zhaohua Gong, Chongyang Liu, Enmin Feng
Chongyang Liu
In this paper, the nonlinear dynamical system of batch fermentation is investigated in the bioconversion of glycerol to 1,3-propanediol(1,3-PD) by Klebsiella pneumoniae. Taking account of the kinetic behavior and experimental results in the batch cultures, we propose a two-stage dynamical system to formulate the fermentation process. Then some properties of the proposed system are proved. In view of the big errors between observations and numerical simulation results, we subsequently establish a parameter identification model to identify parameters in the system. The identifiability of the model is also discussed. Finally, in order to find the optimal parameters of the identification model, …
Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge
Electromagnetic Scattering Solutions For Digital Signal Processing, Jonathan Blackledge
Other resources
Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the …
Random Graphs: From Paul Erdős To The Internet, Michał Karoński
Random Graphs: From Paul Erdős To The Internet, Michał Karoński
Dalrymple Lecture Series
Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of …
Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris
Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris
Department of Mathematics: Faculty Publications
Neural representations of even temporally unstructured stimuli can show complex temporal dynamics. In many systems, neuronal population codes show “progressive differentiation,” whereby population responses to different stimuli grow further apart during a stimulus presentation. Here we analyzed the response of auditory cortical populations in rats to extended tones. At onset (up to 300 ms), tone responses involved strong excitation of a large number of neurons; during sustained responses (after 500 ms) overall firing rate decreased, but most cells still showed a statistically significant difference in firing rate. Population vector trajectories evoked by different tone frequencies expanded rapidly along an initially …
Hybrid Proximal Methods For Equilibrium Problems, Boris S. Mordukhovich, Barbara Panicucci, Mauro Passacantando, Massimo Pappalardo
Hybrid Proximal Methods For Equilibrium Problems, Boris S. Mordukhovich, Barbara Panicucci, Mauro Passacantando, Massimo Pappalardo
Mathematics Research Reports
This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions.
The Symmetric Positive Solutions Of Four-Point Problems For Nonlinear Boundary Value Second-Order Differential Equations, Qu Haidong
qu haidong
In this paper, we are concerned with the existence of symmetric positive solutions for second-order differential equations. Under the suitable conditions, the existence and symmetric positive solutions are established by using Krasnoselskii’s fixed-point theorems.
The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou
The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou
Mathematics and Statistics Faculty Publications
We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),...,M*(G29),R15,R16. Here G1,...,G29 are the vertically 2-connected excluded minors for the class of projective-planar graphs and R15 and R16 are two regular matroids that we will define in the article.
Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque
Logically Rectangular Finite Volume Methods With Adaptive Refinement On The Sphere, Marsha Berger, Donna Calhoun, Christiane Helzel, Randall Leveque
Donna Calhoun
The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GEOCLAW software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.
The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu
The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu
Physics and Astronomy Publications
We present some applications of the Lambert W function (W function) to the formalism of quantum statistics (QS). We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then present some applications of this formula including Bose–Einstein systems in d dimensions, Maxwell–Boltzmann systems, and black body radiation. We also show that for the appropriate parameter values, this formula reduces to an analytic expression in connection with Wien’s displacement law that was found in a previous study. In addition, we …
A Radical Transformation, Michael Castelbuono
A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin
A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch Hsu, Dongsheng Yin
Scholarship
Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.
A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin
A Pair Of Operator Summation Formulas And Their Applications, Tian-Xiao He, Leetsch C. Hsu, Dongsheng Yin
Tian-Xiao He
Two types of symbolic summation formulas are reformulated using an extension of Mullin–Rota’s substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167–213], and several applications involving various special formulas and identities are presented as illustrative examples.
Electron Self-Injection And Trapping Into An Evolving Plasma Bubble, Serguei Y. Kalmykov, Sunghwan A. Yi, Vladimir N. Khudik, Gennady Shvets
Electron Self-Injection And Trapping Into An Evolving Plasma Bubble, Serguei Y. Kalmykov, Sunghwan A. Yi, Vladimir N. Khudik, Gennady Shvets
Serge Youri Kalmykov
The blowout (or bubble) regime of laser wakefield acceleration is promising for generating monochromatic high-energy electron beams out of low-density plasmas. It is shown analytically and by particle-in-cell simulations that self-injection of the background plasma electrons into the quasistatic plasma bubble can be caused by slow temporal expansion of the bubble. Sufficient criteria for the electron trapping and bubble’s expansion rate are derived using a semianalytic nonstationary Hamiltonian theory. It is further shown that the combination of bubble’s expansion and contraction results in monoenergetic electron beams.
The Capacity For Multistability In Small Gene Regulatory Networks, Dan Siegal-Gaskins, Erich Grotewold, Gregory D. Smith
The Capacity For Multistability In Small Gene Regulatory Networks, Dan Siegal-Gaskins, Erich Grotewold, Gregory D. Smith
Arts & Sciences Articles
Background
Recent years have seen a dramatic increase in the use of mathematical modeling to gain insight into gene regulatory network behavior across many different organisms. In particular, there has been considerable interest in using mathematical tools to understand how multistable regulatory networks may contribute to developmental processes such as cell fate determination. Indeed, such a network may subserve the formation of unicellular leaf hairs (trichomes) in the model plant Arabidopsis thaliana.
Results
In order to investigate the capacity of small gene regulatory networks to generate multiple equilibria, we present a chemical reaction network (CRN)-based modeling formalism and describe …
On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue
On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue
Scholarship
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a generalmethod to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.
Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle
Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle
Conference papers
This paper discusses a new approach to ‘watermarking’ digital signals using linear frequency modulated or ‘chirp’ coding. The principles underlying this approach are based on the use of a matched filter to provide a reconstruction of a chirped code that is uniquely robust in the case of signals with very low signal-to-noise ratios. Chirp coding for authenticating data is generic in the sense that it can be used for a range of data types and applications (the authentication of speech and audio signals, for example). The theoretical and computational aspects of the matched filter and the properties of a chirp …
On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter J.-S. Shiue
On Sequences Of Numbers And Polynomials Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter J.-S. Shiue
Tian-Xiao He
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a generalmethod to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.
A Finite Volume Method For Solving Parabolic Equations On Curved Surfaces, Donna Calhoun
A Finite Volume Method For Solving Parabolic Equations On Curved Surfaces, Donna Calhoun
Donna Calhoun
No abstract provided.
Targeted Maximum Likelihood Estimation: A Gentle Introduction, Susan Gruber, Mark J. Van Der Laan
Targeted Maximum Likelihood Estimation: A Gentle Introduction, Susan Gruber, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
This paper provides a concise introduction to targeted maximum likelihood estimation (TMLE) of causal effect parameters. The interested analyst should gain sufficient understanding of TMLE from this introductory tutorial to be able to apply the method in practice. A program written in R is provided. This program implements a basic version of TMLE that can be used to estimate the effect of a binary point treatment on a continuous or binary outcome.
Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids. The basic governing equations are solved by means of a finite-volume scheme that is faithful, accurate, and conservative. Furthermore, this scheme is compatible with thermodynamics through the identification of the notions of numerical fluxes (a notion from numerics) and of excess quantities (a notion from irreversible thermodynamics). A selection of one-dimensional wave propagation problems is presented, the simulation of which exploits the designed numerical scheme. This selection of exemplary problems includes (i) waves in periodic media for weakly nonlinear waves with …
Computing Sequences And Series By Recurrence, Stephen J. Sugden
Computing Sequences And Series By Recurrence, Stephen J. Sugden
Stephen Sugden
Extract: Many commonly-used mathematical functions may be computed via carefully-constructed recurrence formulas. Sequences are typically defined by giving a formula for the general term. Series is the mathematical name given to partial sums of sequences. In either case we may often take advantage of the great expressive power of recurrence relations to create code which is both lucid and compact. Further, this does not necessarily mean that we must use recursive code. In many instances, iterative code is adequate, and often more efficient.
Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne
Qualitative Models Of Neural Activity And The Carleman Embedding Technique., Azamed Yehuala Gezahagne
Electronic Theses and Dissertations
The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain approximate solutions of the Fitzhugh Nagumo model and …
Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel
Shrinkage Estimation Of Expression Fold Change As An Alternative To Testing Hypotheses Of Equivalent Expression, Zahra Montazeri, Corey M. Yanofsky, David R. Bickel
COBRA Preprint Series
Research on analyzing microarray data has focused on the problem of identifying differentially expressed genes to the neglect of the problem of how to integrate evidence that a gene is differentially expressed with information on the extent of its differential expression. Consequently, researchers currently prioritize genes for further study either on the basis of volcano plots or, more commonly, according to simple estimates of the fold change after filtering the genes with an arbitrary statistical significance threshold. While the subjective and informal nature of the former practice precludes quantification of its reliability, the latter practice is equivalent to using a …
A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott
A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott
Department of Mathematics: Dissertations, Theses, and Student Research
Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperature-dependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate …
Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda
Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda
Undergraduate Research Opportunities Program (UROP)
We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.
Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich
Infimal Convolutions And Lipschitzian Properties Of Subdifferentials For Prox-Regular Functions In Hilbert Spaces, Miroslav Bačák, Jonathan M. Borwein, Andrew Eberhard, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to a rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new sub differential properties of infima! convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) sub differentials …
A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, Alun L. Lloyd
A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. T. Banks, Alex Capaldi, Alun L. Lloyd
Mathematics and Computer Science Faculty Publications
We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …
Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan
Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan
All Dissertations
Factoring polynomials is a central problem in computational algebra and number theory and is a basic routine in most
computer algebra systems (e.g. Maple, Mathematica, Magma, etc). It has been extensively studied
in the last few decades by many mathematicians and computer scientists. The main approaches include Berlekamp's method
(1967) based on the kernel of Frobenius map, Niederreiter's method (1993) via an ordinary differential equation,
Zassenhaus's modular approach (1969), Lenstra, Lenstra and Lovasz's lattice reduction (1982), and Gao's method via a partial differential equation (2003). These methods and their recent improvements due to van Hoeij (2002) and
Lecerf et al …
Variations On Graph Products And Vertex Partitions, Jobby Jacob
Variations On Graph Products And Vertex Partitions, Jobby Jacob
All Dissertations
In this thesis we investigate two graph products called double vertex graphs and complete double vertex graphs, and two vertex partitions called dominator partitions and rankings.
We introduce a new graph product called the complete double vertex graph and study its properties. The complete double vertex graph is a natural extension of the Cartesian product and a generalization of the double vertex graph.
We establish many properties of complete double vertex graphs, including results involving the chromatic number of a complete double vertex graph and the characterization of planar complete double vertex graphs. We also investigate the important problem of …