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Articles 1 - 30 of 71
Full-Text Articles in Applied Mathematics
Analysis Of A Quantum Attack On The Blum-Micali Pseudorandom Number Generator, Tingfei Feng
Analysis Of A Quantum Attack On The Blum-Micali Pseudorandom Number Generator, Tingfei Feng
Mathematical Sciences Technical Reports (MSTR)
In 2012, Guedes, Assis, and Lula proposed a quantum attack on a pseudorandom number generator named the Blum-Micali Pseudorandom number generator. They claimed that the quantum attack can outperform classical attacks super-polynomially. However, this paper shows that the quantum attack cannot get the correct seed and provides another corrected algorithm that is in exponential time but still faster than the classical attack. Since the original classical attacks are in exponential time, the Blum-Micali pseudorandom number generator would be still quantum resistant.
The Primitive Root Problem: A Problem In Bqp, Shixin Wu
The Primitive Root Problem: A Problem In Bqp, Shixin Wu
Mathematical Sciences Technical Reports (MSTR)
Shor’s algorithm proves that the discrete logarithm problem is in BQP. Based on his algorithm, we prove that the primitive root problem, a problem that verifies if some integer g is a primitive root modulo p where p is the largest prime number smaller than 2n for a given n, which is assumed to be harder than the discrete logarithm problem, is in BQP by using an oracle quantum Turing machine.
Structure Of Number Theoretic Graphs, Lee Trent
Structure Of Number Theoretic Graphs, Lee Trent
Mathematical Sciences Technical Reports (MSTR)
The tools of graph theory can be used to investigate the structure
imposed on the integers by various relations. Here we investigate two
kinds of graphs. The first, a square product graph, takes for its vertices
the integers 1 through n, and draws edges between numbers whose product
is a square. The second, a square product graph, has the same vertex set,
and draws edges between numbers whose sum is a square.
We investigate the structure of these graphs. For square product
graphs, we provide a rather complete characterization of their structure as
a union of disjoint complete graphs. For …
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu
Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu
Mathematical Sciences Technical Reports (MSTR)
Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.
Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun
Mathematical Sciences Technical Reports (MSTR)
Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.
Modeling Braids With Space-Varying And Time-Varying Stranded Cellular Automata, Brian Chan
Modeling Braids With Space-Varying And Time-Varying Stranded Cellular Automata, Brian Chan
Mathematical Sciences Technical Reports (MSTR)
Braids in a traditional sense and braids in a mathematical sense are wildly different outlooks on the same concept. Using cellular automata to represent and analyze braids is a way to bridge the gap between them. Joshua and Lana Holden and Hao Yang have previously worked on developing and expanding upon a Stranded Cellular Automata (SCA) model capable of representing many different braids and weaves. Continuing their work, we were able to devise a more user-friendly method for interacting with the model such that even those without a mathematical background can construct and analyze braids of their own. This paper …
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
Mathematical Sciences Technical Reports (MSTR)
In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.
Forward Selection Via Distance Correlation, Ty Adams
Forward Selection Via Distance Correlation, Ty Adams
Mathematical Sciences Technical Reports (MSTR)
No abstract provided.
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Mathematical Sciences Technical Reports (MSTR)
A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and …
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Modeling Of Quadcopter Dynamics, Qikai Huang (Bruce Wingo)
Mathematical Sciences Technical Reports (MSTR)
Recently, Google, Amazon and others are attempting to develop delivery drones for commercial use, in particular Amazon Prime Air promising 30 minute delivery. One type of commonly used drone proposed for such purposes is a quadcopter. Quadcopters have been around for some time with original development in the 1920’s. They are popular now because they are mechanically simple and provide a good vehicle for unmanned flight. By controlling the speed of the four propellers, a quadcopter can roll, change pitch, change yaw, and accelerate. This research will focus on the study of classical mechanics theories on rigid body motion using …
Variance Of Clusterings On Graphs, Thomas Vlado Mulc
Variance Of Clusterings On Graphs, Thomas Vlado Mulc
Mathematical Sciences Technical Reports (MSTR)
Graphs that represent data often have structures or characteristics that can represent some relationships in the data. One of these structures is clusters or community structures. Most clustering algorithms for graphs are deterministic, which means they will output the same clustering each time. We investigated a few stochastic algorithms, and look into the consistency of their clusterings.
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Mathematical Sciences Technical Reports (MSTR)
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader
Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader
Mathematical Sciences Technical Reports (MSTR)
A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Mathematical Sciences Technical Reports (MSTR)
In this paper, we explore the mathematical inverse problem of detecting corroded material on the reverse side of a partially accessible metal plate. We will show how a linearization can be used to simplify the initial problem and explain a regularization method used to obtain acceptable results for the corrosion profile. We will also state and perform some calculations for the full three-dimensional problem for possible future work.
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Mathematical Sciences Technical Reports (MSTR)
In certain situations it is useful to identify an unknown sample of metal without contact or visual inspection. We wish to do this by inducing a current in a coil and placing the sample in the resulting magnetic field. For the special case in which the sample is an infinite slab, we have a model that gives the change in impedance of the coil based on the properties of the sample. In this paper we analyze the inverse problem of finding the metal properties from impedance measurements over a wide range of frequencies.
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Mathematical Sciences Technical Reports (MSTR)
Flux Balance Analysis (FBA) is a widely used computational model for studying the metabolic pathways of cells and the role individual metabolites and reactions play in maintaining cell function. However, the successes of FBA have been limited by faulty biological assumptions and computational imperfections. We introduce Robust Analysis of Metabolic Pathways (RAMP) to provide a more theoretically sound and computationally accurate model of cellular metabolism. RAMP overcomes the faulty assumptions of traditional FBA by allowing deviation from steady-state and accounting for variability across a cellular culture. Computationally, RAMP more successfully predicts the lethality of gene knockouts and reduces degeneracy in …
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Mathematical Sciences Technical Reports (MSTR)
Nondestructive testing and imaging plays an important role in many industries, e.g., the monitoring and maintenance of corrosion in aircraft. The general technique is to input energy in some form into an object, observe the object’s response, and from this input-output information determine the internal structure. New techniques are always being explored, and recently there has been much interest in methods that use multiple forms of energy. In this vein, we examine a new technique for imaging corrosion or material loss in an object by combining electrical and thermal measurements on some accessible portion of the object’s outer boundary. The …
Cloaking Against Thermal Imaging, Maple So
Cloaking Against Thermal Imaging, Maple So
Mathematical Sciences Technical Reports (MSTR)
There has been a lot of recent interest in cloaking and invisibility in the mathematics and science communities, and in fact physically plausible mechanisms have been proposed (some built) for cloaking an object against detection using a variety of electromagnetic methods. The ideas are very general, however, and should allow one to design cloaks that work against other forms of imaging. We examine the possibility of cloaking an object to make it invisible to an observer using thermal energy (heat) as the imaging tool. Specifically, we desire to cloak an object inside a two-dimensional disk by cutting a small hole …
Computational Biology, Harvey Greenberg, Allen Holder
Computational Biology, Harvey Greenberg, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species.
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
Mathematical Sciences Technical Reports (MSTR)
We look at the Pure Parsimony problem and the Perfect Phylogeny Haplotyping problem. From the Pure Parsimony problem we consider structures of genotypes called g-lattices. These structures either provide solutions or give bounds to the pure parsimony problem. In particular, we investigate which of these structures supports an unrooted perfect phylogeny, a condition that adds biological interpretation. By understanding which g-lattices support an unrooted perfect phylogeny, we connect two of the standard biological inference rules used to recreate how genetic diversity propagates across generations.
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
We present two algorithms that use spectral methods to align protein folds. One of the algorithms is suitable for database searches, the other for difficult alignments. We present computational results for 780 pairwise alignments used to classify 40 proteins as well as results for a separate set of 36 protein alignments used for comparison to four other alignment algorithms. We also provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach.
Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine
Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine
Mathematical Sciences Technical Reports (MSTR)
Proteins are a primary functional component of organic life, and understanding their function is integral to many areas of research in biochemistry. The three-dimensional structure of a protein largely determines this function. Protein structure alignment compares the structure of a protein with known function to that of a protein with unknown function. A protein’s three-dimensional structure can be transformed through a smooth piecewise-linear sigmoid function to a real symmetric contact matrix that represents the functional significance of certain parts of the protein. We address the protein alignment problem as a minimization of the 2-norm difference of two proteins’ contact matrices. …
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Mathematical Sciences Technical Reports (MSTR)
We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …
Parametric Lp Analysis, Allen Holder
Parametric Lp Analysis, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it is important since it highlights how a problem changes as what is often estimated data varies. We present what is a modern perspective on the classical analysis of the objective value's response to parametrizations in the right-hand side and cost vector. We also mention a few applications and provide citations for further study
Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz
Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz
Mathematical Sciences Technical Reports (MSTR)
We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the amount of corrosion on an inaccessible surface of a two-dimensional region. Using numerical methods, we develop an algorithm for approximating corrosion profile using measurements of electrical potential along the accessible portion of the region. We also evaluate the effect of error on the problem, address the issue of ill-posedness, and develop a method of regularization to correct for this error. An examination of solution uniqueness is also presented.
Anti-Cloaking: The Mathematics Of Disguise, Theresa C. Anderson, Brooke E. Phillips
Anti-Cloaking: The Mathematics Of Disguise, Theresa C. Anderson, Brooke E. Phillips
Mathematical Sciences Technical Reports (MSTR)
Recent developments in cloaking, the ability to selectively bend electromagnetic waves so as to render an object invisible, have been abundant. Based on cloaking principles, we will describe several ways to mathematically disguise objects in the context of electrical impedance imaging. Through the use of a change-of-variables scheme we show how one can make an object appear enlarged, translated, or rotated by surrounding it with a suitable "metamaterial," a man-made material that selectively redirects current. Analysis of eigenvectors and eigenvalues, which describe how current flows, follow. We prove that in order to disguise an object, a metamaterial must encompass both …
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Mathematical Sciences Technical Reports (MSTR)
Developing methods for the nondestructive testing of materials is an important area of research for industry. Situations often arise in which the integrity of an object is questioned, but testing it is very difficult. For example, a support bar may be embedded in a larger structure so that testing the bar’s integrity directly would require the impractical task of breaking down the larger structure. Instead, the ends of the bar might be accessible without dismantling the enclosing structure. The goal of nondestructive testing is to use methods that require taking measurements at the ends of the bar alone to give …
Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones
Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones
Mathematical Sciences Technical Reports (MSTR)
Impedance imaging has received a lot of attention in the past two decades, as a means for non-destructively imaging the interior of a conductive object. One injects a known electrical current pattern into an object at the exterior boundary, then measures the induced potential (voltage) on some portion of the boundary. The goal is to recover information about the interior conductivity of the object, which (we hope) influences the voltages we measure. Of course one can also use multiple input currents and measured voltages. A variation on this problem is that of "boundary identification," in which some portion of the …
Optimization In The Undergraduate Curriculum, Allen Holder
Optimization In The Undergraduate Curriculum, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
A discussion of how an optimization course fits into the undergraduate mathematics curriculum