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Articles 1 - 30 of 139
Full-Text Articles in Physical Sciences and Mathematics
Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus
Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus
Mathematics
Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly noncommutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of noncommutative computer algebra in a particular area of control theory-singularly perturbed dynamic systems-where working with the noncommutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. For example, the methods introduced here take the most standard textbook singular perturbation calculation, [KK086], one step further than had …
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Mathematics and Statistics Faculty Publications
Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …
Self-Consistency Algorithms, Thaddeus Tarpey
Self-Consistency Algorithms, Thaddeus Tarpey
Mathematics and Statistics Faculty Publications
The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.
The Weyr Characteristic, Helene Shapiro
The Weyr Characteristic, Helene Shapiro
Mathematics & Statistics Faculty Works
No abstract provided.
Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su
Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su
All HMC Faculty Publications and Research
No abstract provided in this article.
Computational Geometry Column 36, Joseph O'Rourke
Computational Geometry Column 36, Joseph O'Rourke
Computer Science: Faculty Publications
Two results in "computational origami" are illustrated.
A Hierarchy Of Maps Between Compacta, Paul Bankston
A Hierarchy Of Maps Between Compacta, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …
Interior-Point Methods And Modern Optimization Codes, Goran Lesaja
Interior-Point Methods And Modern Optimization Codes, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
During the last fifteen years we have witnessed an explosive development in the area of optimization theory due to the introduction and development of interior-point methods. This development has quickly led to the development of new and more efficient optimization codes. In this paper, the basic elements of interior-point methods for linear programming will be discussed as well as extensions to convex programming, complementary problems, and semidefinite programming. Interior-point methods are polynomial and effective algorithms based on Newton 's method. Since they have been introduced, the classical distinction between linear programming methods, based on the simplex algorithm, and those methods …
Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group
Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group
Computer Science: Faculty Publications
We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open.
A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler
A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler
Mathematics Faculty Publications
This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Mathematics and Statistics Faculty Publications
For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Mathematics, Statistics and Computer Science Faculty Research and Publications
A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5<HS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for …
Recounting Fibonacci And Lucas Identities, Arthur T. Benjamin, Jennifer J. Quinn
Recounting Fibonacci And Lucas Identities, Arthur T. Benjamin, Jennifer J. Quinn
All HMC Faculty Publications and Research
No abstract provided in this article.
Interior Weyl-Type Solutions To The Einstein-Maxwell Field Equations, Brendan Guilfoyle
Interior Weyl-Type Solutions To The Einstein-Maxwell Field Equations, Brendan Guilfoyle
Preprints
Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, …
Peak-To-Mean Power Control In Ofdm, Golay Complementary Sequences, And Reed–Muller Codes, James A. Davis, Jonathan Jedwab
Peak-To-Mean Power Control In Ofdm, Golay Complementary Sequences, And Reed–Muller Codes, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets ℤ2h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed–Muller code into cosets such that codewords with large values of PMEPR are isolated. …
Intersecting Chains In Finite Vector Spaces, Eva Czabarka
Intersecting Chains In Finite Vector Spaces, Eva Czabarka
Faculty Publications
We prove an Erdős–Ko–Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following.
For c = 0, 1, consider k-chains of subspaces of an n-dimensional vector space over GF(q), such that the smallest subspace in any chain has dimension at least …
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Mathematics and Statistics Faculty Publications
Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.
Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder
Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder
Mathematics and Statistics Faculty Publications
In this paper, we examine a random version of the lattice point problem.
Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton
Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Let p be a reflection on a closed Riemann Surface S, i.e., an anti-conformal involutary isometry of S with a non-empty fixed point subset. Let Sp denote the fixed point subset of p, which is also called the mirror of p. If S −Sp has two components, then p is called separating and we say that S splits at the mirror Sp. Otherwise p is called non-separating. We assume that the system of mirrors, Sq, as q varies over all reflections in the isometry group Aut*(S) defines a tiling of the surface, consisting of triangles. In turn, the tiling determines …
Dini-Campanato Spaces And Applications To Nonlinear Elliptic Equations, Jay Kovats
Dini-Campanato Spaces And Applications To Nonlinear Elliptic Equations, Jay Kovats
Mathematics and System Engineering Faculty Publications
We generalize a result due to Campanato [C] and use this to obtain regularity results for classical solutions of fully nonlinear elliptic equations. We demonstrate this technique in two settings. First, in the simplest setting of Poisson's equation Delta u=f in B, where f is Dini continuous in B, we obtain known estimates on the modulus of continuity of second derivatives D2u in a way that does not depend on either differentiating the equation or appealing to integral representations of solutions. Second, we use this result in the concave, fully nonlinear setting F(D^2u,x)=f(x) to obtain estimates on the modulus of …
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Stochastic Functional Differential Equations On Manifolds (Conference On Probability And Geometry), Salah-Eldin A. Mohammed
Miscellaneous (presentations, translations, interviews, etc)
We prove an existence theorem for solutions of stochastic functional differential equations under smooth constraints in Euclidean space. The initial states are semimartingales on a compact Riemannian manifold. It is shown that, under suitable regularity hypotheses on the coefficients, and given an initial semimartingale, a sfde on a compact manifold admits a unique solution living on the manifold for all time. We also discuss the Chen-Souriau regularity of the solution of the sfde in the initial process. The results are joint work with Remi Leandre.
Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker
Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker
Department of Mathematics: Faculty Publications
We construct certain error-correcting codes over finite rings and estimate their parameters. These codes are constructed using plane curves and the estimates for their parameters rely on constructing “lifts” of these curves and then estimating the size of certain exponential sums.
THE purpose of this paper is to construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably, an estimate for the dimension of trace codes over rings (generalizing work of van der Vlugt over fields and some results on lifts of affin curves from field of characteristic p …
Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald
Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald
Mathematics and Statistics Faculty Publications
Let D be a smoothly bounded domain in Euclidean space and let Xt be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by Xt, where the average is taken overall starting points in D.
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
All HMC Faculty Publications and Research
Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”
A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab
A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U. The initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for four distinct pairs (G, U).
On The Semivalues And The Power Core Of Cooperative Tu Games, Juan-Enrique Martínez-Legaz, Irinel C. Dragan
On The Semivalues And The Power Core Of Cooperative Tu Games, Juan-Enrique Martínez-Legaz, Irinel C. Dragan
Mathematics Technical Papers
The Semivalues were introduced axiomatically by P.Dubey, A.Neyman and R.J.Weber (1981) as an important class of values for cooperative TU games. This class contains the Shapley value, the Banzhaf value, and many other values. For the Shapley value characterizations of games for which the Shapley value is coalitionally rational are due to Inarra and Usategui (1993), Izawa and Takahashi (1998), and Marin-Solano and Rafels (1999). In this paper the same problem of coalitional rationality is discussed for Semivalues, by using special formulas for the computation of Semivalues. The characterization shows that this is a prosperity property as defined by Van …
Almost Periodic Factorization Of Certain Block Triangular Matrix Functions, Ilya M. Spitkovsky, Darryl H. Yong
Almost Periodic Factorization Of Certain Block Triangular Matrix Functions, Ilya M. Spitkovsky, Darryl H. Yong
All HMC Faculty Publications and Research
Let
where , and . For rational such matrices are periodic, and their Wiener-Hopf factorization with respect to the real line always exists and can be constructed explicitly. For irrational , a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible and commuting , was disposed of earlier-it was discovered that an almost periodic factorization of such matrices does not always exist, and a necessary and sufficient condition for its existence was found. This paper is devoted mostly to the situation when is not invertible but the commute pairwise (). The complete description is …
Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith
Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith
Mathematical Sciences Technical Reports (MSTR)
We consider triangle-quadrilateral pairs in the hyperbolic plane which "kaleidoscopically" tile the plane simultaneously. In this case the tiling by quadrilaterals is called a divisible tiling. All possible such divisible tilings are classified. There are a finite number of 1,2, and 3 parameter families as well as a finite number of exceptional cases.
Mathematical Modelling Of Extracellular Matrix Dynamics Using Discrete Cells: Fiber Orientation And Tissue Regeneration, J. C. Dallon, J. A. Sherratt, P. K. Maini
Mathematical Modelling Of Extracellular Matrix Dynamics Using Discrete Cells: Fiber Orientation And Tissue Regeneration, J. C. Dallon, J. A. Sherratt, P. K. Maini
Faculty Publications
Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modeled as a continuum. Using numerical simulations, we investigate the effect on alignment of changing cell properties and of varying cell interactions with collagen and fibrin.
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.