Applied Mathematics Commons^™

A Fast And Simple Algorithm For Computing M Shortest Paths In Stage Graph, M. Sherwood, Laxmi P. Gewali, Henry Selvaraj, Venkatesan Muthukumar

Electrical & Computer Engineering Faculty Research

We consider the problem of computing m shortest paths between a source node s and a target node t in a stage graph. Polynomial time algorithms known to solve this problem use complicated data structures. This paper proposes a very simple algorithm for computing all m shortest paths in a stage graph efficiently. The proposed algorithm does not use any complicated data structure and can be implemented in a straightforward way by using only array data structure. This problem appears as a sub-problem for planning risk reduced multiple k-legged trajectories for aerial vehicles.

On The Dressing Method For The Generalised Zakharov-Shabat System, Rossen Ivanov

Articles

The dressing procedure for the Generalised Zakharov-Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax potentials, representing the soliton solutions for some important nonlinear evolution equations.

Studying Effects Of Primary Care Physicians And Patients On The Trade-Off Between Charges For Primary Care And Specialty Care Using A Hierarchical Multivariate Two-Part Model, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan.

Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads.

Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for …

A Hierarchical Multivariate Two-Part Model For Profiling Providers' Effects On Healthcare Charges, John W. Robinson, Scott L. Zeger, Christopher B. Forrest

Johns Hopkins University, Dept. of Biostatistics Working Papers

Procedures for analyzing and comparing healthcare providers' effects on health services delivery and outcomes have been referred to as provider profiling. In a typical profiling procedure, patient-level responses are measured for clusters of patients treated by providers that in turn, can be regarded as statistically exchangeable. Thus, a hierarchical model naturally represents the structure of the data. When provider effects on multiple responses are profiled, a multivariate model rather than a series of univariate models, can capture associations among responses at both the provider and patient levels. When responses are in the form of charges for healthcare services and sampled …

Direct Least-Squares Ellipse Fitting, Jane Courtney, Annraoi Depaor

Conference Papers

Many biological and astronomical forms can be best represented by ellipses. While some more complex curves might represent the shape more accurately, ellipses have the advantage that they are easily parameterised and define the location, orientation and dimensions of the data more clearly. In this paper, we present a method of direct least-squares ellipse fitting by solving a generalised eigensystem. This is more efficient and more accurate than many alternative approaches to the ellipse-fitting problem such as fuzzy c-shells clustering and Hough transforms. This method was developed for human body modelling as part of a larger project to design a …

Non-Parametric Estimation Of Roc Curves In The Absence Of A Gold Standard, Xiao-Hua Zhou, Pete Castelluccio, Chuan Zhou

UW Biostatistics Working Paper Series

In evaluation of diagnostic accuracy of tests, a gold standard on the disease status is required. However, in many complex diseases, it is impossible or unethical to obtain such the gold standard. If an imperfect standard is used as if it were a gold standard, the estimated accuracy of the tests would be biased. This type of bias is called imperfect gold standard bias. In this paper we develop a maximum likelihood (ML) method for estimating ROC curves and their areas of ordinal-scale tests in the absence of a gold standard. Our simulation study shows the proposed estimates for the …

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N-Dimensions, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

We consider the inverse problem of determining the shape of some inacces­ sible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples

Determining The Length Of A One-Dimensional Bar, Natalya Yarlikina, Holly Walrath

Mathematical Sciences Technical Reports (MSTR)

In this paper we examine the inverse problem of determining the length of a one-dimensional bar from thermal measurements (temperature and heat flux) at one end of the bar (the "accessible" end); the other inaccessible end of the bar is assumed to be moving. We develop two different approaches to estimating the length of the bar, and show how one approach can also be adapted to find unknown boundary conditions at the inaccessible end of the bar.

Asymptotic Solutions Of Semilinear Stochastic Wave Equations, Pao-Liu Chow

Mathematics Research Reports

Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution, in mean-square and the almost sure sense, are studied. Then, under some sufficient conditions, the existence of a unique invariant measure is proved. Two examples are presented to illustrate some applications of the theorems.

A Liouville-Gelfand Equation For K-Hessian Operators, Jon T. Jacobsen

All HMC Faculty Publications and Research

In this paper we establish existence and multiplicity results for a class of fully nonlinear elliptic equations of k-Hessian type with exponential nonlinearity. In particular, we characterize the precise dependence of the multiplicity of solutions with respect to both the space dimension and the value of k. The choice of exponential nonlinearity is motivated by the classical Liouville-Gelfand problem from combustible gas dynamics and prescribed curvature problems.

Review Of The Product Development Process And Information Flow In The Manufacturing Industry: Problems And A Possible Wav Forward, E Opiyo

Tanzania Journal of Engineering and Technology (TJET)

No abstract provided.

Derivation And Analysis Of Maximum And Conditional Work Of An Electromagnet In Relays With Small Gaps And Constant Armature Load, Dominic Chambega

Tanzania Journal of Engineering and Technology (TJET)

No abstract provided.

Mathematical Simulation Of The Influence Of Volatile Ma•Rrer Cloud On Heterogeneous Ignition Of Single Coal Particles, Hassan Ratal Ambula

Tanzania Journal of Engineering and Technology (TJET)

Asimple model has been developed to predict the heterogeneous ignition temperature for single coal particles under conditions of negligible, natural and forced convections. These conditions cause different sizes Of volatile matter cloud that surround the coal particle. The model is based on the ignition Of a single coal particle heated by irradiation from spot heaters in a cold (ambient) surrounding. Energy from the particle surface oxidation, volatile matter combustion and physical heating from the spot heaters are all included in rhe particle energv balance. General ignüion criterion is used to determine the ignition point. The agreement between the experimental and …

Probabilistic Load Flow For Mv Radial Distribution Networks Supplying Statistical Loads, B Kundy

Tanzania Journal of Engineering and Technology (TJET)

Aecurate load models are required Jör 'he computation OJ' load on Medium Voltage (MV) distribution net•.vovk.s_ Modern microprocessors in recent times have enabled researchers stunple and log domestic loads. The findings show that domestic loads are stochastic in nonwe and are best described bv u beta probability distribution [Herman et al. 1999]. The statistical evaluafion lhe consumer voltages requires description load currents al rhe lime e/ lhe system maximum demand. In this paper. an analytical 1001 computing voltage vegulation on MV distribution net-norks fi•eding statistical louds is presenled. To deal beta- distributed currents on MV distribution networks, new scaling factors …

Differential Expression With The Bioconductor Project, Anja Von Heydebreck, Wolfgang Huber, Robert Gentleman

Bioconductor Project Working Papers

A basic, yet challenging task in the analysis of microarray gene expression data is the identification of changes in gene expression that are associated with particular biological conditions. We discuss different approaches to this task and illustrate how they can be applied using software from the Bioconductor Project. A central problem is the high dimensionality of gene expression space, which prohibits a comprehensive statistical analysis without focusing on particular aspects of the joint distribution of the genes expression levels. Possible strategies are to do univariate gene-by-gene analysis, and to perform data-driven nonspecific filtering of genes before the actual statistical analysis. …

A Graph Theoretic Approach To Testing Associations Between Disparate Sources Of Functional Genomic Data, Raji Balasubramanian, Thomas Laframboise, Denise Scholtens, Robert Gentleman

Bioconductor Project Working Papers

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology.

We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics …

Absolutely Continuous Representations And A Kaplansky Density Theorem For Free Semigroup Algebras, Kenneth R. Davidson, Jiankui Li, David R. Pitts

Department of Mathematics: Faculty Publications

We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a ∗-extendible represen- tation . A ∗-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known examples are regular. Absolutely continuous func- tionals are intimately related to maps which intertwine a given ∗-extendible representation with the left regular representation. A simple application of these ideas extends reflexivity and hyper-reflexivity results. Moreover the use of absolute continuity is …

Statistical Analyses And Reproducible Research, Robert Gentleman, Duncan Temple Lang

Bioconductor Project Working Papers

For various reasons, it is important, if not essential, to integrate the computations and code used in data analyses, methodological descriptions, simulations, etc. with the documents that describe and rely on them. This integration allows readers to both verify and adapt the statements in the documents. Authors can easily reproduce them in the future, and they can present the document's contents in a different medium, e.g. with interactive controls. This paper describes a software framework for authoring and distributing these integrated, dynamic documents that contain text, code, data, and any auxiliary content needed to recreate the computations. The documents are …

Optimal Control Of Delay Systems With Differential And Algebraic Dynamic Constraints, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper concerns constrained dynamic optimization problems governed by delay control systems whose dynamic constraints are described by both delay-differential inclusions and linear algebraic equations. This is a new class of optimal control systems that, on one hand, may be treated as a specific type of variational problems for neutral functional-differential inclusions while, on the other hand, is related to a special class of differential-algebraic systems with a general delay-differential inclusion and a linear constraint link between "slow" and "fast" variables. We pursue a two-hold goal: to study variational stability for this class of control systems with respect to discrete …

Resampling Methods For Estimating Functions With U-Statistic Structure, Wenyu Jiang, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define suitable studentized versions of such estimating functions and consider asymptotic approximations as well as an estimating function bootstrap (EFB) method based on resampling the estimated terms in the estimating functions. These methods are justified asymptotically and lead to confidence intervals produced directly from the studentized estimating functions. Particular examples in this class of estimating functions arise in La estimation as well as Wilcoxon rank regression and other related estimation problems. The proposed methods are …

Optimal Boundary Control Of Hyperbolic Equations With Pointwise State Constraints, Boris S. Mordukhovich, Jean-Pierre Raymond

Mathematics Research Reports

In this paper we consider dynamic optimization problems for hyperbolic systems with boundary controls and pointwise state constraints. In contrast to parabolic dynamics, such systems have not been sufficiently studied in the literature. The reason is the lack of regularity in the case of hyperbolic dynamics. We present necessary optimality conditions for both Neumann and Dirichlet boundary control problems and discuss differences and relationships between them.

Miscellaneous Publication 8/2004 - Midas User Manual. Version 1, Ross Kingwell, Felicity Flugge, Emma Kopke, Michael O'Connell

Farm Systems and Economics published reports

What is MIDAS?

It's a computer model of dryland farming in Western Australia. MIDAS is an acronym (Model of an Integrated Dryland Agricultural System). Currently there are five versions of MIDAS, each describes a representative farm in a particular farming region of Western Australia. Versions exist for the following regions (see Figure 1):

• the Eastern Wheatbelt;
• the Central Wheatbelt;
• the West Midlands;
• the Great Southern; and,
• the South Coast.

Each of these versions is a mathematical programming model of a representative farm.

Interacting Near-Solutions Of A Hamiltonian System, Gregory S. Spradlin

Publications

A Hamiltonian system with a superquadratic potential is examined. The system is asymptotic to an autonomous system. The difference between the Hamiltonian system and the “problem at infinity,” the autonomous system, may be large, but decays exponientially. The existence of a nontrivial solution homoclinic to zero is proven. Many results of this type rely on a monotonicity condition on the nonlinearity, not assumed here, which makes the problem resemble in some sense the special case of homogeneous (power) nonlinearity. The proof employs variational, minimax arguments. In some similar results requiring the monotonicity condition, solutions inhabit a manifold homeomorphic to the …

An Analysis Of Electromagnetic Interference (Emi) Of Ultra Wideband(Uwb) And Ieee 802.11a Wireless Local Area Network (Wlan) Employing Orthogonal Frequency Division Multiplexing (Ofdm), Juan Lopez Jr.

Theses and Dissertations

Military communications require the rapid deployment of mobile, high-bandwidth systems. These systems must provide anytime, anywhere capabilities with minimal interference to existing military, private, and commercial communications. Ultra Wideband (UWB) technology is being advanced as the next generation radio technology and has the potential to revolutionize indoor wireless communications. The ability of UWB to mitigate multipath fading, provide high-throughput data rates (e.g., greater than 100 Mbps), provide excellent signal penetration (e.g., through walls), and low implementation costs makes it an ideal technology for a wide range of private and public sector applications. Preliminary UWB studies conducted by The Institute for …

Loss-Based Cross-Validated Deletion/Substitution/Addition Algorithms In Estimation, Sandra E. Sinisi, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In van der Laan and Dudoit (2003) we propose and theoretically study a unified loss function based statistical methodology, which provides a road map for estimation and performance assessment. Given a parameter of interest which can be described as the minimizer of the population mean of a loss function, the road map involves as important ingredients cross-validation for estimator selection and minimizing over subsets of basis functions the empirical risk of the subset-specific estimator of the parameter of interest, where the basis functions correspond to a parameterization of a specified subspace of the complete parameter space. In this article we …

An Analysis Of Coast Guard Hh-65 Engine Reliability: A Comparison Of Malfunctions To Component Removals, Donna L. Cottrell

Theses and Dissertations

The Coast Guard HH-65 helicopter experienced 31 in-flight loss of power incidents during FY 2003 and 21 during the first two months of FY 2003. Concurrent with this apparent decrease in reliability, the Coast Guard seeks ways to expand the HH- 65’s Airborne Use of Force capabilities as a result of the September 11th, 2001 terrorists’ attacks. This study is an exploratory, empirical analysis of engine and airframe component replacements as related to engine mishaps and reliability in the HH-65. We use contingency table analysis, ordinary least squares regression, and logistic regression to examine the mishap history and component replacement …

An Orthogonal Scaling Vector Generating A Space Of $C^1$ Cubic Splines Using Macroelements, Bruce Kessler

Mathematics Faculty Publications

The main result of this paper is the creation of an orthogonal scaling vector of four differentiable functions, two supported on $[-1,1]$ and two supported on $[0,1]$, that generates a space containing the classical spline space $\s_{3}^{1}(\Z)$ of piecewise cubic polynomials on integer knots with one derivative at each knot. The author uses a macroelement approach to the construction, using differentiable fractal function elements defined on $[0,1]$ to construct the scaling vector. An application of this new basis in an image compression example is provided.

Computing Isotypic Projections With The Lanczos Iteration, David K. Maslen, Michael E. Orrison, Daniel N. Rockmore

Dartmouth Scholarship

When the isotypic subspaces of a representation are viewed as the eigenspaces of a symmetric linear transformation, isotypic projections may be achieved as eigenspace projections and computed using the Lanczos iteration. In this paper, we show how this approach gives rise to an efficient isotypic projection method for permutation representations of distance transitive graphs and the symmetric group.

Finite Horizon Riemann Structures And Ergodicity, Victor J. Donnay, Charles Pugh

Mathematics Faculty Research and Scholarship

In this paper we show that any surface in R-3 can be modified by gluing on small 'focusing caps' so that its geodesic flow becomes ergodic. A new concept, finite horizon cap geometry, is what makes the construction work.

Incorporating Death Into Health-Related Variables In Longitudinal Studies, Paula Diehr, Laura Lee Johnson, Donald L. Patrick, Bruce Psaty

UW Biostatistics Working Paper Series

Background: The aging process can be described as the change in health-related variables over time. Unfortunately, simple graphs of available data may be misleading if some people die, since they may confuse patterns of mortality with patterns of change in health. Methods have been proposed to incorporate death into self-rated health (excellent to poor) and the SF-36 profile scores, but not for other variables.

Objectives: (1) To incorporate death into the following variables: ADLs, IADLs, mini-mental state examination, depressive symptoms, body mass index (BMI), blocks walked per week, bed days, hospitalization, systolic blood pressure, and the timed walk. (2) To …