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- Convex body (9)
- Brunn-Minkowski inequality (4)
- Poisson process (4)
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- Bilinear operators (3)
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- Bilinear pseudodifferential operators (3)
- Busemann-Petty problem (3)
- Calderon-Zygmund theory (3)
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- Connectivity (3)
- Definitizable operator (3)
- Geometric tomography (3)
- Indefinite Sturm-Liouville problem (3)
- Intersection body (3)
- Random geometric graph (3)
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- Singular integrals (3)
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- Bilinear Hörmander classes (2)
- Calderón–Zygmund theory (2)
- Covariogram (2)
- Critical points of polynomials (2)
- Isoperimetric inequality (2)
- LU factorization (2)
- Lattice polygon (2)
- Least squares (2)
- Modulation space (2)
- Newton's method (2)
- Nonlinear Schrödinger equation (2)
Articles 1 - 30 of 108
Full-Text Articles in Physical Sciences and Mathematics
Isolating And Quantifying The Role Of Developmental Noise In Generating Phenotypic Variation, Maria Kiskowski, Tilmann Glimm, Nickolas Moreno, Tony Gamble, Ylenia Chiari
Isolating And Quantifying The Role Of Developmental Noise In Generating Phenotypic Variation, Maria Kiskowski, Tilmann Glimm, Nickolas Moreno, Tony Gamble, Ylenia Chiari
Mathematics Faculty Publications
Genotypic variation, environmental variation, and their interaction may produce variation in the developmental process and cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity in cellular and molecular processes when genotype and environment are fixed, also contributes to phenotypic variation. While evolutionary biology has long focused on teasing apart the relative contribution of genes and environment to phenotypic variation, our understanding of the role of developmental noise has lagged due to technical difficulties in directly measuring the contribution of developmental noise. The influence of developmental noise is likely underestimated in studies of phenotypic variation due to …
Modeling Cross-Border Regions, Place-Making, And Resource Management: A Delphi Analysis, Amy D. Anderson, Patrick H. Buckley, John Belec
Modeling Cross-Border Regions, Place-Making, And Resource Management: A Delphi Analysis, Amy D. Anderson, Patrick H. Buckley, John Belec
Mathematics Faculty Publications
Along international borders, spillover of resource management issues is a growing challenge. Development of cross-border regions (CBRs) is seen as an emerging means of addressing these issues. A set of theoretical models, geo-economic mobilization and a resource-focused territorial program of place-making have been proposed as a lens for understanding why such change could occur. From this theory, we identify three C’s as critical initial or necessary conditions to start the process: common territorial identity, convergence of knowledge and values, willingness for cooperation. We then utilize results of a Delphi study in the Fraser Lowland, a sub-district of the American-Canadian Cascadia …
Rainbow Turán Problems For Paths And Forests Of Stars, Daniel Johnston, Cory Palmer, Amites Sarkar
Rainbow Turán Problems For Paths And Forests Of Stars, Daniel Johnston, Cory Palmer, Amites Sarkar
Mathematics Faculty Publications
For a fixed graph F, we would like to determine the maximum number of edges in a properly edge-colored graph on n vertices which does not contain a rainbow copy of F, that is, a copy of F all of whose edges receive a different color. This maximum, denoted by ex∗ (n, F), is the rainbow Turán number of F, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstraëte [Combinatorics, Probability and Computing 16 (2007)]. We determine ex∗ (n, F) exactly when F is a forest of stars, and …
Weierstrass Points On X 0+(P) And Supersingular J-Invariants, Stephanie Treneer
Weierstrass Points On X 0+(P) And Supersingular J-Invariants, Stephanie Treneer
Mathematics Faculty Publications
We study the arithmetic properties of Weierstrass points on the modular curves X0+(p) for primes p. In particular, we obtain a relationship between the Weierstrass points on X0+(p) and the j-invariants of supersingular elliptic curves in characteristic p.
Deep Phylogenomics Of A Tandem-Repeat Galectin Regulating Appendicular Skeletal Pattern Formation, Ramray Bhat, Mahul Chakraborty, Tilmann Glimm, Thomas A. Stewart, Stuart (Stuart A.) Newman
Deep Phylogenomics Of A Tandem-Repeat Galectin Regulating Appendicular Skeletal Pattern Formation, Ramray Bhat, Mahul Chakraborty, Tilmann Glimm, Thomas A. Stewart, Stuart (Stuart A.) Newman
Mathematics Faculty Publications
Background: A multiscale network of two galectins Galectin-1 (Gal-1) and Galectin-8 (Gal-8) patterns the avian limb skeleton. Among vertebrates with paired appendages, chondrichthyan fins typically have one or more cartilage plates and many repeating parallel endoskeletal elements, actinopterygian fins have more varied patterns of nodules, bars and plates, while tetrapod limbs exhibit tandem arrays of few, proximodistally increasing numbers of elements. We applied a comparative genomic and protein evolution approach to understand the origin of the galectin patterning network. Having previously observed a phylogenetic constraint on Gal-1 structure across vertebrates, we asked whether evolutionary changes of Gal-8 could have …
Quantum Mock Modular Forms Arising From Eta–Theta Functions, Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Holly Swisher, Stephanie Treneer
Quantum Mock Modular Forms Arising From Eta–Theta Functions, Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Holly Swisher, Stephanie Treneer
Mathematics Faculty Publications
In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even characters, such that the shadows of these mock modular forms are given by the eta–theta functions with odd characters. In addition, we prove that our mock modular forms are quantum modular forms. As corollaries, we establish simple finite hypergeometric expressions which may be used to evaluate Eichler integrals of the odd eta–theta functions, as well as some curious algebraic identities.
The Role Of Sister Cities’ Staff Exchanges In Developing “Learning Cities”: Exploring Necessary And Sufficient Conditions In Social Capital Development Utilizing Proportional Odds Modeling, Patrick H. Buckley, Akio Takahashi, Amy D. Anderson
The Role Of Sister Cities’ Staff Exchanges In Developing “Learning Cities”: Exploring Necessary And Sufficient Conditions In Social Capital Development Utilizing Proportional Odds Modeling, Patrick H. Buckley, Akio Takahashi, Amy D. Anderson
Mathematics Faculty Publications
In the last half century former international adversaries have become cooperators through networking and knowledge sharing for decision making aimed at improving quality of life and sustainability; nowhere has this been more striking then at the urban level where such activity is seen as a key component in building “learning cities” through the development of social capital. Although mega-cities have been leaders in such efforts, mid-sized cities with lesser resource endowments have striven to follow by focusing on more frugal sister city type exchanges. The underlying thesis of our research is that great value can be derived from city-to-city exchanges …
On The Probabilistic Cauchy Theory Of The Cubic Nonlinear Schrödinger Equation On Rd, D≥3, Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
On The Probabilistic Cauchy Theory Of The Cubic Nonlinear Schrödinger Equation On Rd, D≥3, Árpád Bényi, Tadahiro Oh, Oana Pocovnicu
Mathematics Faculty Publications
We consider the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS) : i∂tu + Δu = ±|u|2u on R d, d ≥ 3, with random initial data and prove almost sure well-posedness results below the scaling-critical regularity scrit = d-2/2. More precisely, given a function on R d, we introduce a randomization adapted to the Wiener decomposition, and, intrinsically, to the so-called modulation spaces. Our goal in this paper is three-fold. (i) We prove almost sure local well-posedness of the cubic NLS below the scaling-critical regularity …
Directionally Bounded Utility And The Executive Pay Puzzle, Edoh Y. Amiran, Daniel Andreas Hagen
Directionally Bounded Utility And The Executive Pay Puzzle, Edoh Y. Amiran, Daniel Andreas Hagen
Mathematics Faculty Publications
The pay of CEOs and other top executives has risen disproportionately relative to other earnings. We provide a supply-side explanation based on utility theory using directionally bounded utility functions. As overall income levels have grown, the amount of compensation required to induce top executives to sacrifice a quiet life has risen. We show that directionally bounded utility functions predict a general rise in compensation for stress. More importantly, such utility functions can be used to explain why the CEO pay ratio has risen at an increasing rate, something which other approaches have difficulty explaining.
Compactness Properties Of Commutators Of Bilinear Fractional Integrals, Árpád Bényi, Wendolin Damián, Kabe Moen, Rodolfo H. (Rodolfo Humberto) Torres
Compactness Properties Of Commutators Of Bilinear Fractional Integrals, Árpád Bényi, Wendolin Damián, Kabe Moen, Rodolfo H. (Rodolfo Humberto) Torres
Mathematics Faculty Publications
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional integral versions of the bilinear Hilbert transform yield separately compact operators.
Somewhat Stochastic Matrices, Branko Ćurgus, Robert I. Jewett
Somewhat Stochastic Matrices, Branko Ćurgus, Robert I. Jewett
Mathematics Faculty Publications
The standard theorem for stochastic matrices with positive entries is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the positivity condition is replaced by a condition on the distances between columns.
Smoothing Of Commutators For A Hörmander Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
Smoothing Of Commutators For A Hörmander Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
Commutators of bilinear pseudodifferential operators with symbols in the Hörmander class BS11,0 and multiplication by Lipschitz functions are shown to be bilinear Calderón-Zygmund operators. A connection with a notion of compactness in the bilinear setting for the iteration of the commutators is also made.
A Squeeze For Two Common Sequences That Converge To E, Branko Ćurgus
A Squeeze For Two Common Sequences That Converge To E, Branko Ćurgus
Mathematics Faculty Publications
In this note, we give a direct proof that {Sn} and {Pn} converge to the same limit. The main tool in our proof is the squeeze theorem, which is probably the easiest to prove among the limit theorems. However, to use it, we need to establish a relevant squeeze, which is the main result of this note.
A Proof Of The Main Theorem On Bezoutians, Branko Ćurgus, Aad Dijksma
A Proof Of The Main Theorem On Bezoutians, Branko Ćurgus, Aad Dijksma
Mathematics Faculty Publications
We give a self-contained proof that the nullity of the Bezoutian matrix associated with a pair of polynomials f and g equals the number of their common zeros counting multiplicities.
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Mathematics Faculty Publications
A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Calderon-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.
Percolation In The Secrecy Graph, Amites Sarkar, Martin Haenggi
Percolation In The Secrecy Graph, Amites Sarkar, Martin Haenggi
Mathematics Faculty Publications
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the …
Comprehensive Analysis Of Escape-Cone Losses From Luminescent Waveguides, Stephen R. Mcdowall, Tristan Butler, Edward Bain, Kelsey Scharnhorst, David L. Patrick
Comprehensive Analysis Of Escape-Cone Losses From Luminescent Waveguides, Stephen R. Mcdowall, Tristan Butler, Edward Bain, Kelsey Scharnhorst, David L. Patrick
Mathematics Faculty Publications
Luminescent waveguides (LWs) occur in a wide range of applications, from solar concentrators to doped fiber amplifiers. Here we report a comprehensive analysis of escape-cone losses in LWs, which are losses associated with internal rays making an angle less than the critical angle with a waveguide surface. For applications such as luminescent solar concentrators, escape-cone losses often dominate all others. A statistical treatment of escape-cone losses is given accounting for photoselection, photon polarization, and the Fresnel relations, and the model is used to analyze light absorption and propagation in waveguides with isotropic and orientationally aligned luminophores. The results are then …
On A Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
On A Class Of Bilinear Pseudodifferential Operators, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We provide a direct proof for the boundedness of pseudodifferential operators with symbols in the bilinear Hörmander class BS10,ƍ, 0 ≤ ƍ
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
On The Hörmander Classes Of Bilinear Pseudodifferential Operators, Ii, Árpád Bényi, Frederic Bernicot, Diego Maldonado, Rodolfo H. (Rodolfo Humberto) Torres, Virginia Naibo
Mathematics Faculty Publications
Boundedness properties for pseudodifferential operators with symbols in the bilinear Hörmander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces, and in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
The Sobolev Inequality On The Torus Revisited, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We revisit the Sobolev inequality for periodic functions on the d-dimensional torus. We provide an elementary Fourier analytic proof of this inequality which highlights both the similarities and differences between the periodic setting and the classical d-dimensional Euclidean one.
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Compact Bilinear Operators And Commutators, Árpád Bényi, Rodolfo H. (Rodolfo Humberto) Torres
Mathematics Faculty Publications
A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear Caldeŕon-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact.
Iterative Scheme For Solving Optimal Transportation Problems Arising In Reflector Design, Tilmann Glimm, Nick Henscheid
Iterative Scheme For Solving Optimal Transportation Problems Arising In Reflector Design, Tilmann Glimm, Nick Henscheid
Mathematics Faculty Publications
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it has been shown previously that this problem is equivalent to an infinite-dimensional linear programming (LP) problem. Here we investigate techniques for constructing the two reflectors numerically by considering the finite dimensional LP problems which arise as approximations to the infinite dimensional problem. A straightforward discretization has the disadvantage that the number of constraints increases rapidly with the mesh size, so only very coarse meshes are …
Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik
Anisotropic Classes Of Inhomogeneous Pseudodifferential Symbols, Árpád Bényi, Marcin Bownik
Mathematics Faculty Publications
We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class Smγ,δ of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class S0δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S01,0(A) are bounded on L p spaces, 1 < p < ∞.
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
The Riesz Basis Property Of An Indefinite Sturm-Liouville Problem With Non-Separated Boundary Conditions, Branko Ćurgus, Andreas Fleige, Aleksey Kostenko
Mathematics Faculty Publications
We consider a regular indefinite Sturm–Liouville eigenvalue problem −f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in …
Solving Separable Nonlinear Equations Using Lu Factorization, Yun-Qiu Shen, Tjalling Ypma
Solving Separable Nonlinear Equations Using Lu Factorization, Yun-Qiu Shen, Tjalling Ypma
Mathematics Faculty Publications
Separable nonlinear equations have the form F(y,z) ≡ A (y)z + b(y) = 0, where the matrix A(y)∈ R m × N and the vector b(y) ∈ Rmare continuously differentiable functions of y ∈ Rn and z ∈ RN. We assume that m ≥ N + n, and F'(y,z) has full rank. We present a numerical method to compute the solution (y∗, z∗) for fully determined systems (m = N+ n) and compatible overdetermined systems (m …
Secrecy Coverage, Amites Sarkar, Martin Haenggi
Secrecy Coverage, Amites Sarkar, Martin Haenggi
Mathematics Faculty Publications
Motivated by information-theoretic secrecy, geometric models for secrecy in wireless networks have begun to receive increased attention. The general question is how the presence of eavesdroppers affects the properties and performance of the network. Previously, the focus has been mostly on connectivity. Here we study the impact of eavesdroppers on the coverage of a network of base stations. The problem we address is the following. Let base stations and eavesdroppers be distributed as stationary Poisson point processes in a disk of area n. If the coverage of each base station is limited by the distance to the nearest eavesdropper, …
Maximum Likelihood Estimation Of Individual Inbreeding Coefficients And Null Allele Frequencies, Nathan Hall, Laina Mercer, Daisy Phillips, Jonathan Shaw, Amy D. Anderson
Maximum Likelihood Estimation Of Individual Inbreeding Coefficients And Null Allele Frequencies, Nathan Hall, Laina Mercer, Daisy Phillips, Jonathan Shaw, Amy D. Anderson
Mathematics Faculty Publications
In this paper, we developed and compared several expectation-maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the …
Intersections Of Dilatates Of Convex Bodies, Stefano Campi, Richard J. Gardner, Paolo Gronchi
Intersections Of Dilatates Of Convex Bodies, Stefano Campi, Richard J. Gardner, Paolo Gronchi
Mathematics Faculty Publications
We initiate a systematic investigation into the nature of the function ∝K(L,ρ) that gives the volume of the intersection of one convex body K in Rn and a dilatate ρL of another convex body L in Rn, as well as the function ηK(L, ρ) that gives the (n - 1)-dimensional Hausdorff measure of the intersection of K and the boundary ∂(ρ L) of ρL. The focus is on the concavity properties of αK (L, ρ). Of particular interest is the …
On The Reproducing Kernel Of A Pontryagin Space Of Vector Valued Polynomials, Branko Ćurgus, Aad Dijksma
On The Reproducing Kernel Of A Pontryagin Space Of Vector Valued Polynomials, Branko Ćurgus, Aad Dijksma
Mathematics Faculty Publications
We give necessary and sufficient conditions under which the reproducing kernel of a Pontryagin space of d×1 vector polynomials is determined by a generalized Nevanlinna pair of d×d matrix polynomials.
Triangles And Groups Via Cevians, Árpád Bényi, Branko Ćurgus
Triangles And Groups Via Cevians, Árpád Bényi, Branko Ćurgus
Mathematics Faculty Publications
For a given triangle T and a real number ρ we define Ceva’s triangle Cρ(T) to be the triangle formed by three cevians each joining a vertex of T to the point which divides the opposite side in the ratioρ: (1 – ρ). We identify the smallest interval MT⊂R such that the family Cρ(T),ρ∈MT, contains all Ceva’s triangles up to similarity. We prove that the composition of operators Cρ,ρ∈R, acting on triangles is governed by a certain group structure on R. We use this structure to prove that two triangles have the same Brocard angle if and …