Mathematics Commons^™

Modeling State Transitions With Automata, Egor Dolzhenko

USF Tampa Graduate Theses and Dissertations

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of …

How Ideas Grow: Critical Mass In The Linear Threshold Model, Hossein Alidaee

Mathematics, Statistics, and Computer Science Honors Projects

We study how ideas spread through a social network using the Linear Threshold Model. Each node i on the complete graph K_n is given a threshold Ɵ_i chosen uniformly at random from (0, 1]. This threshold indicates the fraction of the social network that must be active (or believe the idea) prior to node i becoming active. We start with an activated group of early adopters, called the seed set. Considering various scenarios, we use the probabilistic method to find lower bounds on size of a seed set which guarantees that all nodes become active with high …

A Convex Optimization Algorithm For Sparse Representation And Applications In Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. Any test sample is represented in an overcomplete dictionary with the training sample as base elements. A given test sample can be expressed as a linear combination of only those training …

Coding Theory-Based Cryptopraphy: Mceliece Cryptosystems In Sage, Christopher Roering

Honors Theses, 1963-2015

Unlike RSA encryption, McEliece cryptosystems are considered secure in the presence of quantum computers. McEliece cryptosystems leverage error-correcting codes as a mechanism for encryption. The open-source math software Sage provides a suitable environment for implementing and exploring McEliece cryptosystems for undergraduate research. Using our Sage implementation, we explored Goppa codes, McEliece cryptosystems, and Stern’s attack against a McEliece cryptosystem.

Introduction To Neutrosophic Measure, Neutrosophic Integral, And Neutrosophic Probability, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples.

It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Neutrosophics study the indeterminacy. Indeterminacy is different from randomness. It can be caused by physical space materials and type of construction, by items involved in the space, etc.

Nominal Computation Theory (Dagstuhl Seminar 13422), Mikołaj Bojanczyk, Bartek Klin, Alexander Kurz, Andrew M. Pitts

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 13422 “Nominal Computation Theory”. The underlying theme of the seminar was nominal sets (also known as sets with atoms or Fraenkel-Mostowski sets) and they role and applications in three distinct research areas: automata over infinite alphabets, program semantics using nominal sets and nominal calculi of concurrent processes.

Dynamic Sequent Calculus For The Logic Of Epistemic Actions And Knowledge, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

"Dynamic Logics (DLs) form a large family of nonclassical logics, and perhaps the one enjoying the widest range of applications. Indeed, they are designed to formalize change caused by actions of diverse nature: updates on the memory state of a computer, displacements of moving robots in an environment, measurements in models of quantum physics, belief revisions, knowledge updates, etc. In each of these areas, DL-formulas express properties of the model encoding the present state of affairs, as well as the pre- and post-conditions of a given action. Actions are semantically represented as transformations of one model into another, encoding the …

Epistemic Updates On Algebras, Alexander Kurz, Alessandra Palmigiano

Engineering Faculty Articles and Research

We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss-Solecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. This dual characterization naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). As an application of this dual characterization, we …

Nominal Coalgebraic Data Types With Applications To Lambda Calculus, Alexander Kurz, Daniela Petrişan, Paula Severi, Fer-Jan De Vries

Engineering Faculty Articles and Research

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.

A Pointwise Estimate For The Fourier Transform And The Number Of Maxima Of A Function, Ryan Berndt

Mathematics Faculty Scholarship

We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the derivative of a function.

Solution Of Fuzzy System Of Linear Equations With Polynomial Parametric Form, Diptiranjan Behera, S. Chakraverty

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposed two new and simple solution methods to solve a fuzzy system of linear equations having fuzzy coefficients and crisp variables using a polynomial parametric form of fuzzy numbers. Related theorems are stated and proved. The proposed methods are used to solve example problems. The results obtained are also compared with the known solutions and are found to be in good agreement.

Radar Signal Delay In The Dvali-Gabadadze-Porrati Gravity In The Vicinity Of The Sun, Ioannis Haranas, Omiros Ragos, Ioannis Gkigkitzis

Physics and Computer Science Faculty Publications

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use the space time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects we derive expressions for the signal time delays in the vicinity of the sun, and for various angles of the signal approach. We use the corresponding numerical value for the parameter r₀ to be equal to 5 Mpc, and from that we calculate that the time contribution due to DGP correction to the metric is proportional to b^{3/2 …}

Zadeh's Vision Of Going From Fuzzy To Computing With Words: From The Idea's Origin To Current Successes To Remaining Challenges, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

G-Cimp Status Prediction Of Glioblastoma Samples Using Mrna Expression Data, Mehmet Baysan, Serdar Bozdag, Margaret C. Cam, Svetlana Kotliarova, Susie Ahn, Jennifer Walling, Jonathan K. Killian, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma Multiforme (GBM) is a tumor with high mortality and no known cure. The dramatic molecular and clinical heterogeneity seen in this tumor has led to attempts to define genetically similar subgroups of GBM with the hope of developing tumor specific therapies targeted to the unique biology within each of these subgroups. Recently, a subset of relatively favorable prognosis GBMs has been identified. These glioma CpG island methylator phenotype, or G-CIMP tumors, have distinct genomic copy number aberrations, DNA methylation patterns, and (mRNA) expression profiles compared to other GBMs. While the standard method for identifying G-CIMP tumors is based on …

An Optimal Lower Bound On The Communication Complexity Of Gap-Hamming-Distance, Amit Chakrabarti, Oded Regev

Dartmouth Scholarship

We prove an optimal Ω(n) lower bound on the randomized communication complex- ity of the much-studied gap-hamming-distance problem. As a consequence, we obtain essentially optimal multipass space lower bounds in the data stream model for a number of fundamental prob- lems, including the estimation of frequency moments. The gap-hamming-distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively. They are promised that the Hamming distance between x and y is either at least n/2 + √n or at most n, and their goal is to decide which of these is the case. Since …

The Sense-Isomorphism Theoretical Image Voxel Estimation (Sense-Itive) Model For Reconstruction And Observing Statistical Properties Of Reconstruction Operators, Iain P. Bruce, M. Muge Karaman, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show …

On Lattices Of Varieties Of Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the …

Mathematical Problem Posing As A Measure Of Curricular Effect On Students' Learning, Jinfa Cai, John Moyer, Ning Wang, Stephen Hwang, Bikai Nie, Tammy Garber

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of …

Analyzing Multiple-Probe Microarray: Estimation And Application Of Gene Expression Indexes, Mehdi Maadooliat, Jianhua Z. Huang, Jianhua Hu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that …

On Order Statistics For Gs-Distributions, M. M. Mohie El-Din, M. M. Amein, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, a class of distributions is used to establish several recurrence relations satisfied by single and product moments of order statistics and progressive Type-II right censoring. The recurrence relations for moments of some specific distributions including uniform (a, b); exponential (λ); generalized exponential (α, λ, ν); beta (1, b); beta (b, 1); logistic (α, β) and other distributions from order statistics and progressive Type-II right censoring can be obtained as special cases. A short explanation of GS-distribution can be found in reference [27]. As an example, means, variances and covariances …

H-Coloring Tori, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is a function from the vertices of G to the vertices of H that preserves adjacency. H-colorings encode graph theory notions such as independent sets and proper colorings, and are a natural setting for the study of hard-constraint models in statistical physics. We study the set of H-colorings of the even discrete torus View the MathML source, the graph on vertex set {0,…,m−1}d (m even) with two strings adjacent if they differ by 1 (mod m) on one coordinate and agree on all others. This is a bipartite graph, with bipartition …

Role Of Glutathione In Lung Retention Of 99mtc-Hexamethylpropyleneamine Oxime In Two Unique Rat Models Of Hyperoxic Lung Injury, Said H. Audi, David L. Roerig, Steven Thomas Haworth, Anne V. Clough

Biomedical Engineering Faculty Research and Publications

Rat exposure to 60% O₂ for 7 days (hyper-60) or to >95% O₂ for 2 days followed by a 24-hour in room air (hyper-95R) confers susceptibility or tolerance, respectively, of the otherwise lethal effects of subsequent exposure to 100% O₂. The objective of this study was to determine if lung retention of the radiopharmaceutical agent ^99mTc-HMPAO (hexamethylpropyleneamine oxime) is differentially altered in hyper-60 and hyper-95R rats. Tissue retention of HMPAO is dependent on intracellular content of the antioxidant glutathione (GSH) and mitochondrial function. HMPAO was injected i.v. in anesthetized rats and planar images were acquired. …

Orders On Intervals Over Partially Ordered Sets: Extending Allen's Algebra And Interval Graph Results, Francisco Zapata, Vladik Kreinovich, Cliff Joslyn, Emilie Hogan

Departmental Technical Reports (CS)

To make a decision, we need to compare the values of quantities. In many practical situations, we know the values with interval uncertainty. In such situations, we need to compare intervals. Allen's algebra describes all possible relations between intervals on the real line which are generated by the ordering of endpoints; ordering relations between such intervals have also been well studied. In this paper, we extend this description to intervals in an arbitrary partially ordered set (poset). In particular, we explicitly describe ordering relations between intervals that generalize relation between points. As auxiliary results, we provide a logical interpretation of …

Kansei Engineering: Towards Optimal Set Of Designs, Van-Nam Huynh, Octavio Lerma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many engineering situations, we need to take into account subjective user preferences; taking such preference into account is known as {\em Kansei Engineering}. In this paper, we formulate the problem of selecting optimal set of designs in Kansei engineering as a mathematical optimization problem, and we provide an explicit solution to this optimization problem.

How To Define Mean, Variance, Etc., For Heavy-Tailed Distributions: A Fractal-Motivated Approach, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, we encounter heavy-tailed distributions for which the variance -- and even sometimes the mean -- are infinite. We propose a fractal-motivated approach that enables us to gauge the mean and variance of such distributions.

A Survey Of Classical And Recent Results In Bin Packing Problem, Yoga Jaideep Darapuneni

UNLV Theses, Dissertations, Professional Papers, and Capstones

In the classical bin packing problem one receives a sequence of n items 1, 2,..., n with sizes s1, s2, . . . ,sn where each item has a fixed size in (0, 1]. One needs to find a partition of the items into sets of size1, called bins, so that the number of sets in the partition is minimized and the sum of the sizes of the pieces assigned to any bin does not exceed its capacity. This combinatorial optimization problem which is NP hard has many variants as well as online and offline versions of the problem. Though …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …

Generating Minimal T-Wise Test Suites, Luis C. Gutierrez, Carlos Nieto, Francisco Zapata, Martine Ceberio

COURI Symposium Abstracts, Summer 2012

As the use of computing devices increases every day, users rely on the adequate functioning of software. When software is not tested properly, it can yield erroneous information or a complete failure of the system. The NIST estimates that defective software cost the United States economy close to $60 billion a year. Therefore, there is a need to develop software testing techniques that are time and cost effective. Fully testing software under all possible combinations of parameters values cannot be reduced. However, testing can focus on covering all combinations of subsets of parameters and empirical data shows that doing so …

An Intelligent System To Manage Soft Constraints, Gabriel Higareda, Eduardo Breijo, Martine Ceberio

COURI Symposium Abstracts, Summer 2012

Most problems can be expressed in terms of requirements that must be met by their expected solutions. Constraints are requirements and constraint programming is a declarative programming paradigm that simply consists in modeling problems as lists of their requirements. Many constraint solvers exist that provide solutions to such list of requirements.

However, constraint solvers are stiff: if a problem was ill modeled, no solution will be returned and the original problem called over-constrained. Nevertheless there is hope even in these cases: such overconstrained problems can be handled as soft constraints, meaning that their processing will not be stiff anymore and …

Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is either completely unable to select one of these alternatives, or selects one of the alternatives only "to some extent". How can we extend the traditional decision theory to such realistic interval and fuzzy cases? In their previous papers, the first two authors proposed a natural generalization of the usual decision theory axioms to interval and fuzzy cases, and described decision coming from this generalization. …