Physical Sciences and Mathematics Commons^™

Nonparametric Copula Density Estimation In Sensor Networks, Leming Qu, Hao Chen, Yicheng Tu

Mathematics Faculty Publications and Presentations

Statistical and machine learning is a fundamental task in sensor networks. Real world data almost always exhibit dependence among different features. Copulas are full measures of statistical dependence among random variables. Estimating the underlying copula density function from distributed data is an important aspect of statistical learning in sensor networks. With limited communication capacities or privacy concerns, centralization of the data is often impossible. By only collecting the ranks of the data observed by different sensors, we estimate and evaluate the copula density on an equally spaced grid after binning the standardized ranks at the fusion center. Without assuming any …

A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, Grady Wright, Robert D. Guy, Jian Du, Aaron L. Fogelson

Mathematics Faculty Publications and Presentations

An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material parameters …

On The K-Theory And Homotopy Theory Of The Klein Bottle Group, Jens Harlander, Andrew Misseldine

Mathematics Faculty Publications and Presentations

We construct infinitely many chain homotopically distinct algebraic 2-complexes for the Klein bottle group and give various topological applications. We compare our examples to other examples in the literature and address the question of geometric realizability.

Combinatorial Bounds On Hilbert Functions Of Fat Points In Projective Space, Susan Cooper, Brian Harbourne, Zach Teitler

Mathematics Faculty Publications and Presentations

We study Hilbert functions of certain non-reduced schemes A supported at finite sets of points in P^N, in particular, fat point schemes. We give combinatorially defined upper and lower bounds for the Hilbert function of A using nothing more than the multiplicities of the points and information about which subsets of the points are linearly dependent. When N = 2, we give these bounds explicitly and we give a sufficient criterion for the upper and lower bounds to be equal. When this criterion is satisfied, we give both a simple formula for the Hilbert function and combinatorially defined …

The Monodromy Conjecture For Hyperplane Arrangements, Nero Budur, Mircea Mustaţă, Zach Teitler

Mathematics Faculty Publications and Presentations

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane arrangements. Furthermore, we reduce the strong version to the following conjecture: −n/d is always a root of the Bernstein-Sato polynomial of an indecomposable essential central hyperplane arrangement …

Flow-Induced Channel Formation In The Cytoplasm Of Motile Cells, Robert D. Guy, Toshiyuki Nakagaki, Grady Wright

Mathematics Faculty Publications and Presentations

A model is presented to explain the development of flow channels within the cytoplasm of the plasmodium of the giant amoeba Physarum polycephalum. The formation of channels is related to the development of a self-organizing tubular network in large cells. Experiments indicate that the flow of cytoplasm is involved in the development and organization of these networks, and the mathematical model proposed here is motivated by recent experiments involving the observation of development of flow channel in small cells. A model of pressure-driven flow through a polymer network is presented in which the rate of flow increases the rate …

Elliptic Pairs Of Primes In Cryptography And Their Effects On Rsa Security, Suzanne Craig, Liljana Babinkostova

College of Arts and Sciences Poster Presentations

Cryptography is a constantly evolving field – elliptic curve groups have been a major part of this field since 1987 when Koblitz and Miller separately proposed their use in cryptosystems such as RSA.

• Elliptic Curve: A curve defined by the equation: where A and B are less than a prime p, and where the discriminant is not equal to zero. We are concerned with the curves where A = 0.
• Elliptic Curve Group (ECG): A group whose elements are defined by the elliptic curve and the operation in question. Elliptic curves naturally qualify as groups due simply to their nature. …

Linear Feedback Shift Registers: Pseudo-Random Number Generators And Their Use In Cryptosystems, Michael Perez, Marion Scheepers

College of Arts and Sciences Poster Presentations

Cryptology is the study and application of encrypting and decrypting data so that only the intended recipient and senders can view data. This is important in applications such as online banking and military operations. Linear Feedback Shift Registers, or LFSRs for short, create a pseudo-random number stream that is computationally efficient. LFSRs are used (in conjunction with other methods) to encrypt items such as DVD’s and many wireless signals, including digital TV and radio. Using random methods, a seed value can be created to create a strong random number stream.

Numerical Solutions For A Model Of Tissue Invasion And Migration Of Tumour Cells, Mikhail Kolev, Barbara Zubik-Kowal

Mathematics Faculty Publications and Presentations

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.