The Effect Of Regional Analgesia On Vascular Tone In Hip Arthroplasty Patients,
2016
Hospital for Special Surgery
The Effect Of Regional Analgesia On Vascular Tone In Hip Arthroplasty Patients, Enrique A. Goytizolo, Ottokar Stundner, Sandra M. Hurtado Rua, Dorothy Marcello, Valeria Buschiazzo, Ansara M. Vaz, Stavros G. Memtsoudis
Mathematics and Statistics Faculty Publications
Background: While it is assumed that neuraxial analgesia and pain management may beneficially influence perioperative hemodynamics, few studies provided data quantifying such effects and none have assessed the potential contribution of the addition of a nerve block. Questions/purposes: This clinical trial compared the visual analog scale (VAS) scores and measurement of arterial tone using augmentation index of patients who received combined spinal-epidural (CSE) only to patients who received both CSE and lumbar plexus block. Methods: After obtaining written consent, 92 patients undergoing total hip arthroplasty were randomized to receive either CSE or CSE with lumbar plexus block (LPB). Perioperative pain …
Characterization Of Completely K-Magic Regular Graphs,
2016
Ateneo de Manila University
Characterization Of Completely K-Magic Regular Graphs, Arnold A. Eniego, Ian June L. Garces
Mathematics Faculty Publications
Let k ∈ N and c ∈ Zk. A graph G is said to be c-sum k-magic if there is a labeling ` : E(G) → Zk \ {0} such that P u∈N(v) `(uv) ≡ c (mod k) for every vertex v of G, where N(v) is the neighborhood of v in G. We say that G is completely k-magic whenever it is c-sum k-magic for every c ∈ Zk. In this paper, we characterize all completely k-magic regular graphs.
The Characterization Of Vectors In RN With The Haar Property,
2016
Bridgewater State University
The Characterization Of Vectors In RN With The Haar Property, Terrence Kelleher
Undergraduate Review
Introduction:
As modern communication becomes more digital than ever, infrastructure tries to maintain an equal pace. Unfortunately, this is not always possible. Therefore, computer scientists and mathematicians alike have endeavored to invent ways to store, send and retrieve data, even if transmitted signals are severely damaged. One such way is by using what is called an error-correcting code, or an ECC. An ECC is a method of encoding information such that a signal that possesses a message can be significantly altered and still be decoded. There are many different types of ECCs. The type that is of interest in this …
Graph Cohomology,
2016
Harvey Mudd College
Graph Cohomology, Matthew Lin
HMC Senior Theses
What is the cohomology of a graph? Cohomology is a topological invariant and encodes such information as genus and euler characteristic. Graphs are combinatorial objects which may not a priori admit a natural and isomorphism invariant cohomology ring. In this project, given any finite graph G, we constructively define a cohomology ring H*(G) of G. Our method uses graph associahedra and toric varieties. Given a graph, there is a canonically associated convex polytope, called the graph associahedron, constructed from G. In turn, a convex polytope uniquely determines a toric variety. We synthesize these results, and describe the …
Convexity Of Neural Codes,
2016
Harvey Mudd College
Convexity Of Neural Codes, Robert Amzi Jeffs
HMC Senior Theses
An important task in neuroscience is stimulus reconstruction: given activity in the brain, what stimulus could have caused it? We build on previous literature which uses neural codes to approach this problem mathematically. A neural code is a collection of binary vectors that record concurrent firing of neurons in the brain. We consider neural codes arising from place cells, which are neurons that track an animal's position in space. We examine algebraic objects associated to neural codes, and completely characterize a certain class of maps between these objects. Furthermore, we show that such maps have natural geometric implications related to …
On The Similarity Of Ab And Ba For Normal And Other Matrices,
2016
Pomona College
On The Similarity Of Ab And Ba For Normal And Other Matrices, Stephan Ramon Garcia, David Sherman, Gary Weiss
Pomona Faculty Publications and Research
It is known that AB and BA are similar when A and B are Hermitian matrices. In this note we answer a question of F. Zhang by demonstrating that similarity can fail if A is Hermitian and B is normal. Perhaps surprisingly, similarity does hold when A is positive semidefinite and B is normal.
Methods For Quantized Compressed Sensing,
2016
University of California, Los Angeles
Methods For Quantized Compressed Sensing, Hao-Jun Michael Shi, Mindy Case, Xiaoyi Gu, Shenyinying Tu, Deanna Needell
CMC Faculty Publications and Research
In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for reconstruction: Quantized Compressed Sampling Matching Pursuit (QCoSaMP) and Adaptive Outlier Pursuit for Quantized Iterative Hard Thresholding (AOP-QIHT). We compare the performance of greedy quantized compressed sensing algorithms for a given bit-depth, sparsity, and noise level.
Lattices From Tight Equiangular Frames,
2016
Claremont McKenna College
Lattices From Tight Equiangular Frames, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj, Deanna Needell
CMC Faculty Publications and Research
We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular (k,n) frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the k-dimensional Euclidean space. We show that this is not the case if the cosine of the angle of the frame is irrational. We also prove that the set is a lattice for n=k+1 and that there are infinitely many k such that a lattice emerges for n=2k. We dispose of all cases in dimensions k at most 9. In …
Lattice Theory And Toeplitz Determinants,
2016
Technische Universitat Chemnitz
Lattice Theory And Toeplitz Determinants, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
CMC Faculty Publications and Research
This is a survey of our recent joint investigations of lattices that are generated by finite Abelian groups. In the case of cyclic groups, the volume of a fundamental domain of such a lattice is a perturbed Toeplitz determinant with a simple Fisher-Hartwig symbol. For general groups, the situation is more complicated, but it can still be tackled by pure matrix theory. Our main result on the lattices under consideration states that they always have a basis of minimal vectors, while our results in the other direction concern exact and asymptotic formulas for perturbed Toeplitz determinants. The survey is a …
On Arithmetic Lattices In The Plane,
2016
Claremont McKenna College
On Arithmetic Lattices In The Plane, Lenny Fukshansky, Pavel Guerzhoy, Florian Luca
CMC Faculty Publications and Research
We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes, semi-stable arithmetic similarity classes, and well-rounded arithmetic similarity classes of bounded height as the bound tends to infinity. We also briefly discuss some properties of the j-invariant corresponding to similarity classes of planar lattices.
Decomposition Of Finite Schmidt Rank Bounded Operators On The Tensor Product Of Separable Hilbert Spaces,
2016
Nova Southeastern University
Decomposition Of Finite Schmidt Rank Bounded Operators On The Tensor Product Of Separable Hilbert Spaces, Abdelkrim Bourouihiya
Mathematics Faculty Articles
Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are reflected by the operators involved in its Schmidt decomposition. These properties include compactness of FSR bounded operators and convergence of sequences whose terms are FSR bounded operators.
Energy-Conserving Numerical Scheme For The Poisson-Nerst-Plank Equations,
2016
Illinois Institute of Technology
Energy-Conserving Numerical Scheme For The Poisson-Nerst-Plank Equations, Julienne Kabre
Mathematics Faculty Proceedings, Presentations, Speeches, Lectures
Preliminary report.
The Poisson-Nernst-Planck equations are a system of nonlinear partial differential equations that describe flow of charged particles in solution. In particular, we are interested in the transport of ions in the biological membrane proteins (ion channels). This work is about the design of numerical schemes that preserve exactly (up to roundoff error) a discretized form of the energy dynamics of the system. We will present a scheme that achieves the goal of preserving the energy dissipation law and some preliminary numerical results.
Global Regularity For Unsteady Flow Of Third Grade Fluid In An Annular Region,
2016
TÜBİTAK
Global Regularity For Unsteady Flow Of Third Grade Fluid In An Annular Region, Saeed Ur Rahman, Tasawar Hayat, Hamed H. Alsulami
Turkish Journal of Mathematics
This article develops global regularity criteria for unsteady and magnetohydrodynamic flow of third grade fluid in terms of bounded mean oscillations. Uniqueness of the solution is also verified.
The Mystery Of The Non-Transitive Grime Dice,
2016
Bridgewater State University
The Mystery Of The Non-Transitive Grime Dice, Nicholas Pasciuto
Undergraduate Review
No abstract provided.
4. Dragging Along,
2016
Illinois Mathematics and Science Academy
Bc 1 Rate Of Change Activity Sheet Teacher Notes,
2016
Illinois Mathematics and Science Academy
Bc 1 Rate Of Change Activity Sheet Teacher Notes, Ruth Dover
A Simple Introduction to Rates
Before beginning this section of handouts, students will be introduced to a variety of vocabulary words often associated with calculus. These words will be used in an intuitive sense only and will not have been formally defined. Vocabulary should include graphical terms such as continuous, increasing, decreasing, maximum and minimum points, concave up, concave down, and point of inflection. In addition, discussion of the concept of "rate of change" should begin. It should be mentioned that many quantities change – population, cost, and temperature, to name just a few. All that is specifically required at this point can be related …
The Kretschmann Scalar,
2016
Department of Physics, Utah State University
The Kretschmann Scalar, Charles G. Torre
How to... in 10 minutes or less
On a pseudo-Riemannian manifold with metric g, the "Kretschmann scalar" is a quadratic scalar invariant of the Riemann R tensor of g, defined by contracting all indices with g. In this worksheet we show how to calculate the Kretschmann scalar from a metric.
What's In A Name? A Critical Review Of Definitions Of Quantitative Literacy, Numeracy, And Quantitative Reasoning,
2016
Pomona College
What's In A Name? A Critical Review Of Definitions Of Quantitative Literacy, Numeracy, And Quantitative Reasoning, Gizem Karaali, Edwin H Villafane Hernandez '18, Jeremy Alexander Taylor '18
Pomona Faculty Publications and Research
This article aims to bring together various threads in the eclectic literature that make up the scholarship around the theme of Quantitative Literacy. In investigating the meanings of terms like "quantitative literacy," "quantitative reasoning," and "numeracy," we seek common ground, common themes, common goals and aspirations of a community of practitioners. A decade ago, these terms were relatively new in the public sphere; today policy makers and accrediting agencies are routinely inserting them into general education conversations. Having good, representative, and perhaps even compact and easily digestible definitions of these terms might come in handy in public relations contexts as …
A Mathematical Model For Feral Cat Ecology With Application To Disease.,
2016
University of Central Florida
A Mathematical Model For Feral Cat Ecology With Application To Disease., Jeff Sharpe
Electronic Theses and Dissertations
We formulate and analyze a mathematical model for feral cats living in an isolated colony. The model contains compartments for kittens, adult females and adult males. Kittens are born at a rate proportional to the population of adult females and mature at equal rates into adult females and adult males. Adults compete with each other in a manner analogous to Lotka-Volterra competition. This competition comes in four forms, classified by gender. Native house cats, and their effects are also considered, including additional competition and abandonment into the feral population. Control measures are also modeled in the form of per-capita removal …
Structure-Preserving Finite Difference Methods For Linearly Damped Differential Equations,
2016
University of Central Florida
Structure-Preserving Finite Difference Methods For Linearly Damped Differential Equations, Ashish Bhatt
Electronic Theses and Dissertations
Differential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical integrators generally result in undesirable quantitative and qualitative errors . Standard numerical integrators aim to reduce quantitative errors, whereas geometric (numerical) integrators aim to reduce or eliminate qualitative errors, as well, in …
