Physical Sciences and Mathematics Commons^™

Fibonacci Or Quasi-Symmetric Phyllotaxis. Part Ii: Botanical Observations, Stéphane Douady, Christophe Golé

Mathematics Sciences: Faculty Publications

Historically, the study of phyllotaxis was greatly helped by the simple description of botanical patterns by only two integer numbers, namely the number of helices (parastichies) in each direction tiling the plant stem. The use of parastichy num- bers reduced the complexity of the study and created a proliferation of generaliza- tions, among others the simple geometric model of lattices. Unfortunately, these simple descriptive method runs into difficulties when dealing with patterns pre- senting transitions or irregularities. Here, we propose several ways of addressing the imperfections of botanical reality. Using ontogenetic analysis, which follows the step-by-step genesis of the pattern, …

Fibonacci Or Quasi-Symmetric Phyllotaxis. Part I: Why?, Christophe Golé, Jacques Dumais, Stéphane Douady

Mathematics Sciences: Faculty Publications

The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions. Using the disk-accretion model, first introduced by Schwendener and justified by modern biological studies, we observe two dis- tinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square pack- ing, the quasi-symmetric ones, which are a generalization of the whorled patterns. Defining new geometric tools allowing to work with irregular patterns and local transitions, we provide simple …

Minimization And Eulerian Formulation Of Differential Geometry Based Nonpolar Multiscale Solvation Models, Zhan Chen

Department of Mathematical Sciences Faculty Publications

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while …

Mode-Sum Prescription For The Vacuum Polarization In Odd Dimensions, Peter Taylor, Cormac Breen

Articles

We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$. In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots …

An Indefinite Kähler Metric On The Space Of Oriented Lines, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space T of oriented affine lines in R3 with the tangent bundle of S2. Thus the round metric on S2 induces a Kähler structure on T which turns out to have a metric of neutral signature. It is shown that the identity component of the isometry group of this metric is isomorphic to the identity component of the isometry group of the Euclidean metric on R3.

The geodesics of this metric are either planes or helicoids in R3. The signature …

Creating The Perfect Nba Team: A Look At Per And How It Affects Wins, Gregory Hamalian

Honors Program Theses and Projects

Ever since Oakland Athletics’ general manager Billy Beane began applying analytical tools to compose a baseball team, professional sports teams have used advanced metrics to build competitive rosters. We use an exploratory data analysis strategy to find what statistics best predict team wins. Finding that the Player Efficiency Rating (PER) statistic best correlate with wins, we investigate the statistic to find its strengths and weaknesses. We look for ways to improve the statistic and adjust it to better evaluate player effectiveness. We also look for methods to best predict how the PER will change from one season to the next …

Diet And Lifetyle Factors Associated With Mirna Expression In Colorectal Tissue, Martha L. Slattery, Jennifer S. Herrick, Lila E. Mullany, John R. Stevens, Roger K. Wolff

Mathematics and Statistics Faculty Publications

MicroRNAs (miRNAs) are small non-protein-coding RNA molecules that regulate gene expression. Diet and lifestyle factors have been hypothesized to be involved in the regulation of miRNA expression. In this study it was hypothesized that diet and lifestyle factors are associated with miRNA expression. Data from 1,447 cases of colorectal cancer to evaluate 34 diet and lifestyle variables using miRNA expression in normal colorectal mucosa as well as for differential expression between paired carcinoma and normal tissue were used. miRNA data were obtained using an Agilent platform. Multiple comparisons were adjusted for using the false discovery rate q-value. There were 250 …

Extension Groups For Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups ExtiA(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtiA(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

An Examination Of The Neural Unreliability Thesis Of Autism, John Butler, Sophie Molholm, Gizely Andrade, John J. Foxe

Articles

An emerging neuropathological theory of Autism, referred to here as “the neural unreliability thesis,” proposes greater variability in moment-to-moment cortical representation of environmental events, such that the system shows general instability in its impulse response function. Leading evidence for this thesis derives from functional neuroimaging, a methodology ill-suited for detailed assessment of sensory transmission dynamics occurring at the millisecond scale. Electrophysiological assessments of this thesis, however, are sparse and unconvincing. We conducted detailed examination of visual and somatosensory evoked activity using high-density electrical mapping in individuals with autism (N = 20) and precisely matched neurotypical controls (N = 20), recording …

Discovery Of An Enzyme And Substrate Selective Inhibitor Of Adam10 Using An Exosite-Binding Glycosylated Substrate, Franck Madoux, Daniela Dreymuller, Jean-Phillipe Pettiloud, Radleigh Santos, Christoph Becker-Pauly, Andreas Ludwig, Gregg B. Fields, Thomas Bannister, Timothy P. Spicer, Mare Cudic, Louis D. Scampavia, Dmitriy Minond

Mathematics Faculty Articles

ADAM10 and ADAM17 have been shown to contribute to the acquired drug resistance of HER2-positive breast cancer in response to trastuzumab. The majority of ADAM10 and ADAM17 inhibitor development has been focused on the discovery of compounds that bind the active site zinc, however, in recent years, there has been a shift from active site to secondary substrate binding site (exosite) inhibitor discovery in order to identify non-zinc-binding molecules. In the present work a glycosylated, exosite-binding substrate of ADAM10 and ADAM17 was utilized to screen 370,276 compounds from the MLPCN collection. As a result of this uHTS effort, a selective, …

Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde

Mathematics Faculty Research

In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the conditional …

Privacy Protection And Aggregate Health Data: A Review Of Tabular Cell Suppression Methods (Not) Employed In Public Health Data Systems, Gregory J. Matthews, Ofer Harel, Robert H. Aseltine Jr.

Mathematics and Statistics: Faculty Publications and Other Works

Public health research often relies on individuals’ confidential medical data. Therefore, data collecting entities, such as states, seek to disseminate this medical data as widely as possible while still maintaining the privacy of the individual for legal and ethical reasons. One common way in which this medical data is released is through the use of Web-based Data Query Systems (WDQS). In this article, we examined WDQS listed in the National Association for Public Health Statistics and Information Systems (NAPHSIS) specifically reviewing them for how they prevent statistical disclosure in queries that produce a tabular response. One of the most common …

A Scalable Preconditioner For A Primal Dpg Method, Andrew T. Barker, Veselin A. Dobrev, Jay Gopalakrishnan, Tzanio Kolev

Portland Institute for Computational Science Publications

We show how a scalable preconditioner for the primal discontinuous Petrov-Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence which allows us to exploit existing AMG algorithms and software. We show how these algebraic preconditioners can be applied directly to a Schur complement system arising from the DPG method. One of our intermediate results shows that a generic stable decomposition implies a stable decomposition for the Schur complement. This justifies the application of algebraic solvers directly to the interface degrees of freedom. Combining such results, we …

Density-Dependent Leslie Matrix Modeling For Logistic Populations With Steady-State Distribution Control, Bruce Kessler, Andrew Davis

Mathematics Faculty Publications

The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity (see [1], [2], [4], [5], and [6]), with mixed results. In this paper we provide a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and the desired steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same …

The Conjugacy Problem For Automorphism Groups Of Countable Homogeneous Structures, Samuel Coskey, Paul Ellis

Mathematics Faculty Publications and Presentations

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.

The Decay Of Disease Association With Declining Linkage Disequilibrium: A Fine Mapping Theorem, Mehdi Maadooliat, Naveen K. Bansal, Jibal Upadhya, Manzur R. Farazi, Xiang Li, Max M. He, Scott J. Hebbring, Zhan Ye, Steven J. Schrodi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise …

The History Of Algorithmic Complexity, Audrey A. Nasar

Publications and Research

This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus.

Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou

Mathematics and Statistics Faculty Research & Creative Works

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …

Asymptotic Behavior Of Even-Order Damped Differential Equations With P-Laplacian Like Operators And Deviating Arguments, Qingmin Liu, Martin Bohner, Said R. Grace, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed.

An Efficient And Long-Time Accurate Third-Order Algorithm For The Stokes–Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

A third order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. a novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. the scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. the scheme is also unconditionally stable and, with …

Why Most Bright Stars Are Binary But Most Dim Stars Are Single: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that most visible stars are binary: they have a nearby companion star, and these two stars orbit around each other. Based on this fact, until recently, astronomers believed that, in general, most stars are binary. A few years ago, a surprising paper showed that while most bright stars are indeed binary, most dim stars are single. In this paper, we provide a simple qualitative explanation for this empirical fact.

When Invading, Cancer Cells Do Not Divide: A Geometric (Symmetry-Based) Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, malignant tumors are known to grow fast, cancer cells that form these tumors divide and spread around. Tumors also experience the process of metastasis, when cancer cells invade neighboring organs. A recent experiment has shown that, contrary to the previous assumptions, when cancer cells are invading, they stop dividing. In this paper, we provide a geometric explanation for this empirical phenomenon.

Towards An Algebraic Description Of Set Arithmetic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To describe the state of the world, we need to describe the values of all physical quantities. In practice, due to inevitable measurement inaccuracy, we do not know the exact values of these quantities, we only know the sets of possible values for these quantities. On the class of such uncertainty-related sets, we can naturally define arithmetic operations that transform, e.g., uncertainty in a and b into uncertainty with which we know the sum a + b.

In many applications, it has been useful to reformulate the problem in purely algebraic terms, i.e., in terms of axioms that the basic …

Yes- And No-Gestures Explained By Symmetry, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most cultures, "yes" is indicate by a vertical head movement (nod), while "no" is indicated by a left-right movement (shake). In this paper, we show that basic symmetries can explain this cultural phenomenon.

What Is The Best Way To Add Large Number Of Integers: Number-By-Number As Computers Do Or Lowest-Digits-Than-Next-Digits-Etc As We Humans Do?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we need to add several integers, computers add them one by one, while we usually add them digit by digit: first, we add all the lowest digits, then we add all next lowest digits, etc. Which way is faster? Should we learn from computers or should we teach computers to add several integers our way?

In this paper, we show that the computer way is faster. This adds one more example to the list of cases when computer-based arithmetic algorithms are much more efficient than the algorithms that we humans normally use.

Why Product "And"-Operation Is Often Efficient: One More Argument, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is an empirical fact that the algebraic product is one the most efficient "and"-operations in fuzzy logic. In this paper, we provide one of the possible explanations of this empirical phenomenon.

How To Make Machine Learning Robust Against Adversarial Inputs, Gerardo Muela, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been recently shown that it is possible to "cheat" many machine learning algorithms -- i.e., to perform minor modifications of the inputs that would lead to a wrong classification. This feature can be used by adversaries to avoid spam detection, to create a wrong identification allowing access to classified information, etc. In this paper, we propose a solution to this problem: namely, instead of applying the original machine learning algorithm to the original inputs, we should first perform a random modification of these inputs. Since machine learning algorithms perform well on random data, such a random modification ensures …

A Simple Geometric Explanation Of Occam's Razor, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Occam's razor states that out of possible explanations, plans, and designs, we should select the simplest one. It turns out that in many practical situations, the simplest explanation indeed turns out to be the correct one, the simplest plan is often the most successful, etc. But why this happens is not very clear. In this paper, we provide a simple geometric explanation of Occam's razor.

Why Growth Of Cancerous Tumors Is Gompertzian: A Symmetry-Based Explanation, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the growth of a cancerous tumor is well described by the Gompertz's equation. The existing explanations for this equation rely on specifics of cell dynamics. However, the fact that for many different types of tumors, with different cell dynamics, we observe the same growth pattern, make us believe that there should be a more fundamental explanation for this equation. In this paper, we show that a symmetry-based approach indeed leads to such an explanation: indeed, out of all scale-invariant growth dynamics, the Gompertzian growth is the closest to the linear-approximation exponential growth model.

Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.