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2002

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Full-Text Articles in Applied Mathematics

Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek Dec 2002

Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We study the feedback group action on two-inputs non-linear control systems. We follow an approach proposed by Kang and Krener which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes that obtained in the single-input case. We also give homogeneous m-invariants of the action of the group of homogeneous transformations on the homogeneous systems of the same degree. We illustrate our results by analyzing the normal form and invariants of homogeneous systems of degree two.

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Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman Dec 2002

Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman

Arts & Sciences Articles

Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic “integrate-and-fire-or-burst” TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca 2+ current, IT, and …

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An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan Oct 2002

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

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Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden Oct 2002

Fixed Point And Two-Cycles Of The Discrete Logarithm, Joshua Holden

Mathematical Sciences Technical Reports (MSTR)

We explore some questions related to one of Brizolis: does every prime p have a pair (g, h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not only fixed points but also two-cycles. Campbell and Pomerance have not only answered the fixed point question for sufficiently large p but have also rigorously estimated the number of such pairs given certain conditions on g and h. We attempt to give heuristics for similar estimates given other conditions on g and h and also in the case …

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A Review Of Selected Works On Crack Indentification, Kurt M. Bryan Oct 2002

A Review Of Selected Works On Crack Indentification, Kurt M. Bryan

Mathematical Sciences Technical Reports (MSTR)

We give a short survey of some of the results obtained within the last 10 years or so concerning crack identification using impedance imaging techniques. We touch upon uniqueness results, continuous dependence results, and computational algorithms.

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Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah Sep 2002

Characterizing A Defect In A One-Dimensional Bar, Cynthia Gangi, Sameer Shah

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of locating and describing an internal point defect in a one­ dimensional rod W by controlling the heat inputs and measuring the subsequent temperatures at the boundary of W. We use a variation of the forward heat equation to model heat flow through W, then propose algorithms for locating an internal defect and quantifying the effect the defect has on the heat flow. We implement these algorithms, analyze the stability of the procedures, and provide several computational examples.

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Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela Sep 2002

Reconstruction Of Cracks With Unknown Transmission Condition From Boundary Data, F Ronald Ogborne Iii, Melissa E. Vellela

Mathematical Sciences Technical Reports (MSTR)

We examine the problem of Identifying both the location and constitutive law governing electrical current flow across a one-dimensional linear crack in a two dimensional region when the crack only partially blocks the flow of current. We develop a a constructive numerical procedure for solving the inverse problem and provide computational examples.

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Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell Sep 2002

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …

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A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga Sep 2002

A Posteriori Error Estimates Based On Polynomial Preserving Recovery, Zhimin Zhang, Ahmed Naga

Mathematics Research Reports

Superconvergence of order O(h1+rho), for some rho is greater than 0, is established for gradients recovered using Polynomial Preserving Recovery technique when the mesh is mildly structured. Consequently this technique can be used in building a posteriori error estimator that is asymptotically exact.

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Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty Sep 2002

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty

Mathematics and Statistics Faculty Publications

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

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The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt Sep 2002

The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt

All HMC Faculty Publications and Research

We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.

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Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman Sep 2002

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

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Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang Aug 2002

Gradient Recovery And A Posteriori Estimate For Bilinear Element On Irregular Quadrilateral Meshes, Zhimin Zhang

Mathematics Research Reports

A polynomial preserving gradient recovery method is proposed and analyzed for bilinear element under general quadrilateral meshes. It has been proven that the recovered gradient converges at a rate O(h1+rho) for rho = min(alpha, 1) when the mesh is distorted O(h1+alpha) (alpha > 0) from a regular one. Consequently, the a posteriori error estimator based on the recovered gradient is asymptotically exact.

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Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger Jul 2002

Fast Reconstruction Of Cracks Using Boundary Measurements, Nicholas A. Trainor, Rachel M. Krieger

Mathematical Sciences Technical Reports (MSTR)

This paper develops a fast algorithm for locating one or more perfectly insulating, pair-wise disjoint, linear cracks in a homogeneous two-dimensional electrical conductor, using boundary measurements.

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Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang Jul 2002

Analysis Of Recovery Type A Posteriori Error Estimators For Mildly Structured Grids, Jinchao Xu, Zhimin Zhang

Mathematics Research Reports

Some recovery type error estimators for linear finite element method are analyzed under O(h1+alpha) (alpha greater than 0) regular grids. Superconvergence is established for recovered gradients by three different methods when solving general non-self-adjoint second-order elliptic equations. As a consequence, a posteriori error estimators based on those recovery methods are asymptotically exact.

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The Order At 2 Of The Odd-Partition Function, Chris Mehelich Jun 2002

The Order At 2 Of The Odd-Partition Function, Chris Mehelich

Mathematical Sciences Technical Reports (MSTR)

Abstract. We evaluate the odd-partition function p2(n) modulo 4 by elementary methods and analyze the asymptotic distribution of p2(n) modulo 4. We use the theory of modular forms to obtain necessary and sufficient conditions for the order at 2 of p2(n) to equal any given value between 0 and 4 inclusive.

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On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li May 2002

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=N\ω is an exterior domain in N, ω⊂N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈Cαloc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

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Nonlinear Dynamics Of Mode-Locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, J Nathan Kutz May 2002

Nonlinear Dynamics Of Mode-Locking Optical Fiber Ring Lasers, Kristin M. Spaulding, Darryl H. Yong, Arnold D. Kim, J Nathan Kutz

All HMC Faculty Publications and Research

We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature …

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Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli Mar 2002

Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli

CMC Faculty Publications and Research

A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.

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A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga Feb 2002

A Meshless Gradient Recovery Method Part I: Superconvergence Property, Zhiming Zhang, Ahmed Naga

Mathematics Research Reports

A new gradient recovery method is introduced and analyzed. It is proved that the method is superconvergent for translation invariant finite element spaces of any order. The method maintains the simplicity, efficiency, and superconvergence properties of the Zienkiewicz-Zhu patch recovery method. In addition, under uniform triangular meshes, the method is superconvergent for the Chevron pattern, and ultraconvergence at element edge centers for the regular pattern.

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A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan Feb 2002

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

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Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He Jan 2002

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He

Scholarship

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.

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On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang Jan 2002

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C1,1 solution to the uniformly elliptic equation F(D2u) = 0 must belong to C2,α, if the equation has the Liouville property.

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Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller Jan 2002

Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller

Mathematics and Statistics Faculty Publications

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.

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Absolutely Continuous Jacobi Operators, Steen Pedersen Jan 2002

Absolutely Continuous Jacobi Operators, Steen Pedersen

Mathematics and Statistics Faculty Publications

No abstract provided.

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An Analysis Of The Development And Application Of Orthogonal Polynomials With An Emphasis On The Legendre Polynomials, Francis Radnoti Jan 2002

An Analysis Of The Development And Application Of Orthogonal Polynomials With An Emphasis On The Legendre Polynomials, Francis Radnoti

Senior Research Projects

No abstract provided.

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Parameters Affecting Partitioning Of 6 Pcb Congeners In Natural Sediments, Eid A. Alkhatib, Carl Weigand Jan 2002

Parameters Affecting Partitioning Of 6 Pcb Congeners In Natural Sediments, Eid A. Alkhatib, Carl Weigand

Chemistry & Physics Faculty Publications

Polychlorinated biphenyls (PCBs) released by bottom sediments were determined by experiments in which the sediments were artificially resuspended using sediment contaminated with PCBs in a particle entrainment simulator (PES). Sediment cores, spiked with PCBs, were collected from the Housatonic River in Connecticut and run in the PES at simulated shear stresses from 0 to 0.6 N m(-2). Experimental results from these simulations have shown that mean concentration of PCBs in the solid phase for sites with high volatile organic carbon (VOC) were significantly greater than samples with low VOC; the reverse was true for the water phase. In addition, on …

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Tuberculosis Models With Fast And Slow Dynamics: The Role Of Close And Casual Contacts, Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio Jan 2002

Tuberculosis Models With Fast And Slow Dynamics: The Role Of Close And Casual Contacts, Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our …

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Dynamics Of A Granular Particle On A Rough Surface With A Staircase Profile, J. J. P. Veerman, F. V. Cunha Jr., G. L. Vasconcelos Jan 2002

Dynamics Of A Granular Particle On A Rough Surface With A Staircase Profile, J. J. P. Veerman, F. V. Cunha Jr., G. L. Vasconcelos

Mathematics and Statistics Faculty Publications and Presentations

A simple model is presented for the motion of a grain down a rough inclined surface with a staircase profile. The model is an extension of an earlier model of ours where we now allow for bouncing, i.e., we consider a non-vanishing normal coefficient of restitution. It is shown that in parameter space there are three regions of interest: (i) a region of smaller inclinations where the orbits are always bounded (and we argue that the particle always stops); (ii) a transition region where halting, periodic and unbounded orbits co-exist; and (iii) a region of large inclinations where no halting …

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Single-Particle Model For A Granular Ratchet, Albert J. Bae, Welles Antonio Martinez Morgado, J. J. P. Veerman, Giovani L. Vasconcelos Jan 2002

Single-Particle Model For A Granular Ratchet, Albert J. Bae, Welles Antonio Martinez Morgado, J. J. P. Veerman, Giovani L. Vasconcelos

Mathematics and Statistics Faculty Publications and Presentations

A simple model for a granular ratchet corresponding to a single grain bouncing off a vertically vibrating sawtooth-shaped base is studied. Depending on the model parameters, horizontal transport is observed in both the preferred and unfavoured directions. A phase diagram is presented indicating the regions in parameter space where the different regimes (no current, normal current, and current reversal) occur.

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