Browsing Research by Department "MATH / Applied Mathematics"
Now showing items 120 of 59

ADAPTIVE COVERING CODES IN THE QARY HYPERCUBE
(201112)We investigate a generalized version of the Pathological Liar Game of Ellis and Yan. In our version, there are nonnegative integer parameters M; n; e; a; q with 0 < a < q. The player (Carole) is equipped with M messages, ... 
ADAPTIVE QUASIMONTE CARLO CUBATURE
(201612)In some definite integral problems the analytical solution is either unknown or hard to compute. As an alternative, one can approximate the solution with numerical methods that estimate the value of the integral. However, ... 
ANALYSIS OF THE APPLICATION OF THE LIAR MACHINE TO THE QARY PATHOLOGICAL LIAR GAME WITH A FOCUS ON LOWER DISCREPANCY BOUNDS
(201112)The binary pathological liar game, as described by Ellis and Yan in [Ellis and Yan, 2004], is a variation of the original liar game, as described by Berlekamp, R enyi, and Ulam in [Berlekamp, 1964], [R enyi, 1961], and ... 
ANALYSIS OF VARIATION IN MULTISTAGE MANUFACTURING PROCESS BASED ON TREE REGRESSION
(201405)In a multistage manufacturing process, variation propagates in the process when we produce products from stage to stage. Since there are limits of reducing variation through process in traditional industrial management and ... 
ANALYZING REPRODUCING KERNEL APPROXIMATION METHODS VIA A GREEN FUNCTION APPROACH
(201205)In this thesis, we use Green functions (kernels) to set up reproducing kernels such that their related reproducing kernel Hilbert spaces (native spaces) are isometrically embedded into or even are isometrically equivalent ... 
APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH NONGAUSSIAN NOISE AND APPLICATION TO A VOLATILITY MODEL
(201505)In recent decades, stochastic processes with nonGaussian noise are widely utilized in financial models. The astable Levy motion, one type of nonGaussian noise processes, provides robust data ts and events simulations ... 
A BOUNDARY INTEGRAL METHOD FOR SOLVING THE BRINKMAN'S EQUATION IN 3DIMENSIONAL FLOW
(201412)In this paper, we consider the boundary integral equation (BIE) corresponding to the Brinkmans equation. We compute the velocities of the interacting particles when the pointwise forces acting on them are known. We ... 
THE CHANGE OF KURTOSIS IN IMPORTANCE SAMPLING FOR MONTE CARLO
(201312)The Mont e Carlo (II IC) Method is commonly used to approximat e mult ivariat e integrals, which can be interpreted as means of random variab les. The IIIC method uses th e sample mean to estimate the tr ue mean. In this ... 
Comprehending the Menger Sponge
(20120131)This poster, created by undergraduate students at the Illinois Institute of Technology (IIT), details Karl Menger's 1926discovered fractal curve currently known as the Menger sponge. Menger is a former IIT faculty member. 
COMPUTATION AND ANALYSIS OF TUMOR GROWTH
(201605)The ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment. Parameters that control tumor morphology may also contribute to its invasive ... 
COMPUTATIONAL COST OF SIMULATING MEAN EXIT TIME USING STOCHASTIC DIFFERENTIAL EQUATIONS
(201605)Stochastic di erential equations play an important role in modern science, including engineering, physics, computer science and nance. It has been shown that numerically solving stochastic di erential equation is a ... 
CONSTRUCTIONS IN NONADAPTIVE GROUP TESTING STEINER SYSTEMS AND LATIN SQUARES
(201405)This thesis explores and introduces new constructions for nonadaptive group testing which are particulary important for the parameter range we encounter in real life problems. After a summary of existing results, the ... 
CONTRIBUTIONS TO ALGORITHMIC MATROID PROBLEMS
(201507)In this thesis, we obtain several algorithms for problems related to matroids, a structure that generalizes the concept of linear independence in a vector space and an acyclic subgraph structure in a graph. Matroids have ... 
COORDINATEEXCHANGE ALGORITHM CONSTRUCTION OF UNIFORM SPACE FILLING DESIGN
(201405)Many scientific phenomena are now investigated by complex computer models. A computer experiment is a sequence of runs with various inputs. The uniform experimental design seeks its design points to be uniformly scattered ... 
DISJUNCTNESS PROPERTIES RESULTING FROM CONCATENATION OF GROUP TESTING MATRICES
(201505)This thesis discusses matrix properties as they relate to the idea of nonadaptive group testing. This is accomplished by first considering the history of group testing and then exploring existing results. The next chapter ... 
DYNAMIC COHERENT ACCEPTABILITY INDICES AND THEIR APPLICATIONS IN FINANCE
(201105)This thesis presents a unified framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures. In particular, we establish a ... 
DYNAMIC CONIC FINANCE VIA BACKWARD STOCHASTIC DIFFERENCE EQUATIONS AND RECURSIVE CONSTRUCTION OF CONFIDENCE REGIONS
(201607)This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics. The contribution to mathematical finance is made via developing new theoretical results in the area of ... 
DYNAMIC CONIC FINANCE: NOARBITRAGE PRICING AND NOGOODDEAL PRICING FOR DIVIDENDPAYING SECURITIES IN DISCRETETIME MARKETS WITH TRANSACTION COSTS
(201207)This thesis studies noarbitrage pricing and dynamic conic nance for dividendpaying securities in discretetime markets with transaction costs. The rst part investigates noarbitrage pricing for dividendpaying ... 
DYNAMICS OF A THREEDIMENSIONAL FOURBAR LINKAGE SUBJECT TO RANDOM EXTERNAL FORCING
(201112)This thesis explores the dynamics of a threedimensional fourbar mechanical linkage subject to random external forcing. The Lagrangian formulation of the equations of motion are index3 stochastic di erentialalgebraic ... 
DYNAMICS OF VESICLES IN VISCOUS FLUID
(201412)Modeling vesicle dynamics involves a complicated moving boundary problem where uids, thermal uctuations, and vesicle morphology are intimately coupled. In this thesis, we study the dynamics of a twodimensional ...