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Articles 31 - 59 of 59
Full-Text Articles in Physical Sciences and Mathematics
Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu
Using Slow-Fast Dynamical Systems To Understand Regime Shifts In Ecology, Ting-Hao Hsu
Mathematics Colloquium Series
In ecology, regime shifts are continual rapid change between different long-lasting dynamics. For instance, rapid evolutionary changes have been observed in a wide variety of organisms, both in predators and in prey. Another example is disease outbreak, where a system exhibits qualitative changes after long periods of apparent quiescence. Using the theory of slow-fast dynamics, for systems of differential equations with sufficiently large separation of time scales we derive conditions under which regime shifts occur. This is joint work with Shigui Ruan and Gail Wolkowicz.
Mathematical Modeling Of Lung Cancer Screening Studies, Deborah L. Goldwasser
Mathematical Modeling Of Lung Cancer Screening Studies, Deborah L. Goldwasser
Mathematics Colloquium Series
Lung cancer has the second highest cancer incidence, second only to prostate cancer in men and breast cancer in women. Furthermore, more cancer deaths are attributable to lung cancer than any other cancer for both genders. There is a high public health need for effective secondary prevention in the form of early detection and early treatment, complementary to smoking cessation efforts. The U.S. National Lung Screening Trial (NLST) demonstrated that non-small cell lung cancer (NSCLC) mortality can be reduced by 20% through a program of annual CT screening in high-risk individuals. However, CT screening regimens and adherence vary, potentially impacting …
Preserver Problems On Matrices, Zejun Huang
Preserver Problems On Matrices, Zejun Huang
Mathematics Colloquium Series
Preserver problems on matrices concern the characterization of linear or nonlinear maps or operators on matrices that preserve properties of the space of matrices or leave certain functions, subsets, and relations invariant. In this talk, I will present some results on both linear and nonlinear preserver problems on matrices.
Relativity From Mathematics Or Why Newton Could Have Beaten Einstein To The Punch, Diego Castano
Relativity From Mathematics Or Why Newton Could Have Beaten Einstein To The Punch, Diego Castano
Mathematics Colloquium Series
Special Relativity was developed by Albert Einstein and relied crucially on Electromagnetism, a theory not fully developed until 1873. Yet there is nothing in the basic theory's development that requires physics beyond what Newton knew. A derivation of the theory based on Newton's laws and mathematical consistency is presented.
Using Multivariate Statistical Techniques To Aid In A Sports Index Construction, Tiffany Kelly
Using Multivariate Statistical Techniques To Aid In A Sports Index Construction, Tiffany Kelly
Mathematics Colloquium Series
Within a quantitative career, you are/will soon be challenged to create an overall value to explain a situational status. For example, socio-economic status, well-being, and in this specific example, happiness among sports fans. This talk seeks to discuss my previous work developed out from student research performed at NSU in its application to my first project for ESPN Sports Analytics, the College Football Fan Happiness Index (http://es.pn/2vmParA) . I will dive into the multivariate statistical techniques of principal component analysis and hierarchal clustering to create this happiness index from a slew of variables.
Harnack Inequalities: From Poincare Conjecture To Matrix Determinant, Fuzhen (Frank) Zhang
Harnack Inequalities: From Poincare Conjecture To Matrix Determinant, Fuzhen (Frank) Zhang
Mathematics Colloquium Series
With a brief survey on the Harnack inequalities in various forms in Functional Analysis, in Partial Differential Equations, and in Perelman’s solution of the Poincare Conjecture, we discuss the Harnack inequality in Linear Algebra and Matrix Analysis. We present an extension of Tung’s inequality of Harnack type and study the equality case.
Power Means Of Matrices, Jose Franco
Power Means Of Matrices, Jose Franco
Mathematics Colloquium Series
In this talk we will study the different ways the power means of positive numbers can be extended to means of positive definite matrices. Then, we will analyze the properties these means satisfy. Among these properties, we will be interested in analytic properties such as monotonicity and convexity. Using these results, we will compare the power means with other interpolations between the Arithmetic-Geometric-Harmonic means.
Heart Valve Tissue Engineering: Mathematical Modeling For Bioreactor Studies, Manuel Salinas
Heart Valve Tissue Engineering: Mathematical Modeling For Bioreactor Studies, Manuel Salinas
Mathematics Colloquium Series
Mechanical conditioning has been shown to promote tissue formation in a wide variety of tissue engineering studies, but the underlying mechanisms by which external mechanical stimuli regulate cells and tissues are not fully understood. This is particularly relevant in the area of heart valve tissue engineering (HVTE) due to the intense hemodynamic environments that surround native valves. Some studies suggest that oscillatory shear stress (OSS) caused by steady flow and scaffold flexure play a critical role in engineered tissue formation derived from bone marrow derived stem cells (BMSCs). In addition, scaffold flexure may enhance the transport of nutrients such as …
Mathematical Relativity And The Nature Of The Universe, Priscila Reyes
Mathematical Relativity And The Nature Of The Universe, Priscila Reyes
Mathematics Colloquium Series
In this talk, I will be discussing certain space-times, which can be used to model celestial objects and events in the universe. These are solutions to Einstein's field equations, which roughly describe the relation between matter, energy and the geometry of the universe. The concept of time in relation to an observer will be demonstrated. I will also include some interesting phenomena that arise out of the unusual mathematical structure of space-times , such as Lorentz contraction, reverse Cauchy-Schwarz, and the twin paradox.
Mathematical Optimization And Applications, Teodora Suciu
Mathematical Optimization And Applications, Teodora Suciu
Mathematics Colloquium Series
This talk centers on mathematical optimization in the context of Calculus of Variations. Optimization involves choosing the best element from a set of choices, usually through mathematical approaches. Solving these kinds of problems is considered an essential tool in many areas of science and engineering. Additionally, various mathematics and business applications are discussed. Also explored is a real-life example with a detailed algorithm that is closely related to the Traveling Salesman problem.
Minimum Number Of Distinct Eigenvalues Of Graphs, Shahla Nasserasr
Minimum Number Of Distinct Eigenvalues Of Graphs, Shahla Nasserasr
Mathematics Colloquium Series
For a simple graph G on n vertices, a real symmetric nxn matrix A is said to be compatible with G, if for different i and j, the (i; j) entry of A is nonzero whenever there is an edge between the vertices i and j, it is zero otherwise. The minimum number of distinct eigenvalues, when minimum is taken over all compatible matrices with G, is denoted by q(G). In this talk, a survey of some known and new results about q(G) is presented.
Continuous Dependence And Differentiating Solutions Of A Second Order Boundary Value Problem With Average Value Condition, Samantha A. Major
Continuous Dependence And Differentiating Solutions Of A Second Order Boundary Value Problem With Average Value Condition, Samantha A. Major
Mathematics Colloquium Series
Using a few conditions, continuous dependence, and a result regarding smoothness of initial conditions, we show that derivatives, with respect to each of the boundary data, of solutions to a second order boundary value problem with an average value integral condition solve the associated variational equation with interesting boundary conditions.
Spatial Population Models With Fitness Based Dispersal, Chris Cosner
Spatial Population Models With Fitness Based Dispersal, Chris Cosner
Mathematics Colloquium Series
Traditional continuous time models in spatial ecology typically describe movement in terms of linear diffusion and advection, which combine with nonlinear population dynamics to produce semi-linear parabolic equations and systems. In environments that are favorable everywhere in the sense that the local population growth rate is always positive, organisms can use linear advection and diffusion to achieve an optimal spatial distribution. (Here optimal means evolutionarily stable.) In regions where there are environmental “sinks” where the local growth rate is negative, it does not seem possible to achieve an optimal distribution via linear dispersal. It is possible for organisms using advection …
Modeling And Methods Of Signal Separations With Applications In Spectroscopic Sensing, Yuanchang Sun
Modeling And Methods Of Signal Separations With Applications In Spectroscopic Sensing, Yuanchang Sun
Mathematics Colloquium Series
Spectroscopic sensing is a powerful and a widely used family of techniques for detecting and identifying chemical and biological substances. For example, nuclear magnetic resonance (NMR) relies on the magnetic properties of the atomistic nucleus to determine the molecular structures. Raman spectroscopy (RS) uses laser light scattering and the resulting energy shift of photons to sense the vibrational modes of a sample. In remote sensing, hyperspectral imaging (HSI) makes use of hundreds of contiguous spectral bands to identify nearly invisible objects at subpixel level. Differential optical absorption spectroscopy (DOAS) is based on the light absorption property of matter to identify …
Geometric Flows, Ming-Liang Cai
Geometric Flows, Ming-Liang Cai
Mathematics Colloquium Series
A geometric flow is a process which is defined by a differential equation and is used to evolve a geometric object from a general shape to a one with more symmetries. For example, the curve-shortening flow deforms a simple closed curve to a round one ; the Ricci flow deforms a simply connected surface (say, a football shaped one) to a round sphere. In this talk, we will give an overview of some of these geometric flows, in particular, some discussions on singularities that these flows often run into.
Asymptotic Stability Of Non-Unique Solutions Of Initial Value Problems, Muhammad Islam
Asymptotic Stability Of Non-Unique Solutions Of Initial Value Problems, Muhammad Islam
Mathematics Colloquium Series
We consider an initial value problem (I. V. P.) of a first order nonlinear ordinary differential equations. We assume that the I. V. P. can have more than one solution. We study a new type of stability property of these solutions. This stability is not the standard Liapunov stability, commonly studied in the field of differential equations.
Periodicity In Quantum Calculus, Jeffrey T. Neugebauer
Periodicity In Quantum Calculus, Jeffrey T. Neugebauer
Mathematics Colloquium Series
After a brief introduction to time scales, we will explore periodic functions on time scales. We will discuss how periodicity is defined on time scales that are not periodic. In particular, we will look at periodicity in the quantum case. Two definitions of periodicity have recently been introduced. One definition is based on the equality of areas lying below the graph of the function at each period; the other regards a periodic function to be one that repeats its values after a certain number of steps. We will show a relation between these two definitions and then use this relation …
Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali
Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali
Mathematics Colloquium Series
Time scale, arbitrary nonempty closed subset of the real numbers (with the topology and ordering inherited from the real numbers) is an efficient and general framework to study different types of problems to discover the commonalities and highlight the essential differences. Sometimes, we may need to choose an appropriate time scale to establish parallels to known results. We present a few recent results from existence theory of funcational dynamic equations including a few (counter) examples. In particular, we discuss first order functional dynamic equations with delay xDelta(t)=f(t,xt) on a time scale. Here, xt is in Crd([-tau,0],Rn) and is given by …
Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy
Curvature: A Geometric Villain That Ruins Our Instinctive Perception Of Nature, Vehbi Emrah Paksoy
Mathematics Colloquium Series
Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that can only be explained by the ultimate abstraction that is embedded in mathematics. In this talk, I will discuss the concept of curvature and argue how it explains the “unexplainable”. We will see how the curvature proves that the earth is rotating, how good the soap bubbles are at proving profound mathematical results, and if the two dimensional residents can determine the shape of their …
Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu
Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu
Mathematics Colloquium Series
This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with …
Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz
Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz
Mathematics Colloquium Series
An appealing hypothesis suggests that neurons represent inputs in a coordinate system that is matched to the statistical structure of images in the natural environment. I discuss theoretical work on unsupervised learning of statistical regularities in natural images. In the model, Bayesian inference amounts to a generalized form of divisive normalization, a canonical computation that has been implicated in many neural areas. In our framework, divisive normalization is flexible: it is recruited only when the image is inferred to contain dependencies, and muted otherwise. I particularly focus on recent work in which we have applied this approach to understanding spatial …
Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston
Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston
Mathematics Colloquium Series
Simulating marine invaded systems requires broad consideration of physical oceanographic processes, such as ocean circulation patterns and temperature, and biological traits of the invader, such as their reproductive strategy and tolerances to their environment. Through this understanding of baseline biological and oceanographic function, models can be developed in order to forecast the incursion patterns of marine invasive species - helpful both to predict their spread as well as forewarn of impacts. To facilitate this understanding, computer simulation is useful in order to quickly and efficiently assimilate large biological and oceanographic datasets into digestible products. Data derived from such simulations are …
Life As An Nfl Statistician, Dennis Lock
Life As An Nfl Statistician, Dennis Lock
Mathematics Colloquium Series
Over the last few years, the fields of statistics and mathematics have become more prevalent and popular in professional sports (with the help of mainstream books and movies like Moneyball). The use of advanced (and non-advanced) statistical methods is growing across the sporting landscape from the front office to the media, and even into business and ticket sales. This talk will discuss Lock’s experiences building an analytics department with the Miami Dolphins as well as the general role of statistics in sports today. It will also including the recent analytics boom in the front office framework, the coinciding need for …
Computing Invariant Dynamics For Differential Equations: Spectral Methods, Errors, And Computer Assisted Proof, J. D. Mireles James
Computing Invariant Dynamics For Differential Equations: Spectral Methods, Errors, And Computer Assisted Proof, J. D. Mireles James
Mathematics Colloquium Series
The qualitative theory of dynamical systems is concerned with studying the long time behavior discrete and continuous time models such as nonlinear differential equations. The long time behavior of such models is organized by landmarks called invariant sets. For complicated nonlinear equations these invariant sets are difficult to study via pen and paper analysis, and we typically employ numerical simulations to gain insights into the dynamics. If we now think of these computer assisted insights as mathematical conjectures, then it is natural to ask how we might obtain proofs. Since the conjectures themselves originate with the computer it is not …
Arithmagons, Jose Franco
Arithmagons, Jose Franco
Mathematics Colloquium Series
Arithmagons are polygonal graphs whose vertices and edges are numbered by natural numbers in such a way that the product of the labels of two adjacent vertices equals the label on the edge that connects them. During the talk, Franco will briefly explore the conditions for solvability. The remainder of the talk will focus on counting the number of arithmagons that can be constructed so that the multiplication of all the values on the edges equals a fixed natural number.
Differentiation Of Solutions Of Second-Order Bvps With Integral Boundary Conditions, Alfredo Janson, Bibi Juman
Differentiation Of Solutions Of Second-Order Bvps With Integral Boundary Conditions, Alfredo Janson, Bibi Juman
Mathematics Colloquium Series
Janson’s and Juman’s research involves differentiating solutions of boundary value problems with integral conditions, as well as showing that the resulting functions solve an associated boundary value problem—called the variational equation—with new integral boundary values.
Disconjugacy And Differentiation For Solutions Of Boundary Value Problems For Second-Order Dynamic Equations On A Time Scale, Jeffrey W. Lyons
Disconjugacy And Differentiation For Solutions Of Boundary Value Problems For Second-Order Dynamic Equations On A Time Scale, Jeffrey W. Lyons
Mathematics Colloquium Series
On the specific time scale—given as integer multiples of a fixed, positive real number h—and under certain conditions, solutions of a nonlinear second-order dynamic equation with conjugate boundary conditions are differentiated with respect to the boundary values and delta differentiated with respect to the boundary points. Lyons will also present two corollaries of the result.
Fractional Calculus And Smallest Eigenvalues, Jeffrey T. Neugebauer
Fractional Calculus And Smallest Eigenvalues, Jeffrey T. Neugebauer
Mathematics Colloquium Series
This talk will introduce the subject of fractional calculus, which involves taking integrals and derivatives of arbitrary order. Neugebauer will show how the definitions of fractional derivatives and fractional integrals are natural extensions of the definitions of the derivative and the integral. In addition to showing some examples, Neugebauer will explore ongoing research on the comparison of smallest eigenvalues of a fractional-boundary-value problem with conjugate boundary conditions.
Existence Of A Positive Solution For A Right-Focal Dynamic Boundary Value Problem, Jeffrey Lyons
Existence Of A Positive Solution For A Right-Focal Dynamic Boundary Value Problem, Jeffrey Lyons
Mathematics Colloquium Series
This talk presents an application made from an extension of the Leggett-Williams fixed-point theorem—which requires neither of the functional boundaries to be invariant—to a second-order right focal dynamic boundary value problem on a time scale. To conclude, Lyons will provide a non-trivial example.