Mathematics Commons^™

3d Building Internal Structural Component Segmentation From Point Cloud Data Using Dbscan And Modified Ransac With Normal Deviation Conditions, Thanapon Doougphummet

Chulalongkorn University Theses and Dissertations (Chula ETD)

Nowadays, the laser scanner plays an important role as a tool to capture building structure in a form of point cloud which can be used to draw a blueprint or a floor plan for reconstruction or renovation of an existing building. The point cloud data represent a shape or an object in three dimensions. This point cloud together with the utilization of Building Information Modeling (BIM) which is a workflow that provides information about the foundation and structure measurement of a building, make a planning and design to construction more convenient and efficient in several aspects than the traditional way. …

Connected Size Ramsey Numbers Of Matching And Some Graphs, Jirawat Mungtumklang

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Valuation Of American Commodity Options, Piyapoom Nonsoong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we present analytical option pricing formulas for European and American options in which the price dynamics of a risky asset follows a meanreverting process with time-dependent parameter. The process can be adapted to describe both nonseasonal and seasonal variation in price, especially, in commodity markets such as agricultural commodities. The formulas are derived based on the solutions of partial differential equations showing that the values of both European and American options can be decomposed into two parts: the payoff of the option at initial time and the time-integral over the lifetime of the option, which is driven …

Random Forest Algorithm Using Quartile-Patternbootstrapping For Class Imbalanced Problem, Worawit Jitpakdeebodin

Chulalongkorn University Theses and Dissertations (Chula ETD)

Nowadays, classification in machine learning serves as a valuable tool for extracting and analyzing real-world datasets. However, an important issue in classification is the problem of class imbalance, which significantly impacts the performance of classifiers. In 2019, a novel approach for a decision tree induction was introduced to address This problem—the Minority Condensation Entropy (MCE) measure that can effectively handle imbalanced datasets. Subsequently, in 2021, a new outlier factor called the Mass ratio - variance Outlier Factor (MOF) was presented that can rank instances based on the dataset density. This thesis proposes a random forest algorithm using quartile-pattern Bootstrapping that …

Nidus Idearum. Scilogs, Viii: Painting By Numbers, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this eighth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, – in email messages to research colleagues, or replies, and personal notes handwritten on the planes to, and from international conferences, about all kind of topics, centered mostly on Paradoxism and Neutrosophy.

Exchanging ideas with: Robert Neil Boyd, Joseph Brenner, Ahmed Cevik, Victor Christianto, Adrian Curaj, Jean Dezert, Andrei-Lucian Drăgoi, Ervin Goldfain, Young Bae Jun, Yale Landsberg, Radu Munteanu, Paul Piștea, Viorel Roman, Ridvan Sahin, Said Broumi, Selcuk Topal, Eric W. Weisstein, Xiaohing Zhang.

Solutions For Fermi Questions, October 2022 Cloud Ripple Pattern, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Robust Testing Of Paired Outcomes Incorporating Covariate Effects In Clustered Data With Informative Cluster Size, Sandipan Dutta

Mathematics & Statistics Faculty Publications

Paired outcomes are common in correlated clustered data where the main aim is to compare the distributions of the outcomes in a pair. In such clustered paired data, informative cluster sizes can occur when the number of pairs in a cluster (i.e., a cluster size) is correlated to the paired outcomes or the paired differences. There have been some attempts to develop robust rank-based tests for comparing paired outcomes in such complex clustered data. Most of these existing rank tests developed for paired outcomes in clustered data compare the marginal distributions in a pair and ignore any covariate effect on …

Multicolor Ramsey And List Ramsey Numbers For Double Stars, Jake Ruotolo

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For a graph H, the k-color Ramsey number r(H; k) of H is the smallest integer n such that every k-edge-coloring of K_n contains a monochromatic copy of H. Despite active research for decades, very little is known about Ramsey numbers of graphs. This is especially true for r(H; k) when k is at least 3, also known as the multicolor Ramsey number of …

Totally Multicolored Rado Numbers For The Equation X_1 + X_2 + X_3 + ... + X_(M−1) = X_M, Skylar Halverson

Electronic Theses and Dissertations

A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all natural numbers t, m, let R(t, m) be the least natural number n such that for every t-coloring of the set {1, 2, 3, ..., R(t, m)} there exist a solution set {x_1, x_2, . . ., x_m} to L(m), x_1 + x_2 + x_3 + ... + x_(m−1) = x_m such that x_i does not equal x_j for all i that does not equal j, that avoids being Totally Multicolored. This paper shows a function to find R(t,m) for any …

The Efficacy Of The South Dakota State University Summer Jacks Leap Program, Tessa M. Sundermann

Electronic Theses and Dissertations

Today, several studies detail the continuing struggle many students have with college mathematics courses at universities across the United States. The South Dakota State University Summer Jacks LeaP program is a summer bridge mathematics program aimed at improving incoming students’ mathematics success. This analysis used a mixed methods research design to examine the efficacy of the Summer Jacks LeaP program. First, we analyzed the LeaP students’ homework averages, exam 1 scores, final exam scores, and overall grade scores to determine if they were finding success in their fall semester mathematics courses. We also used hypothesis testing to compare LeaP participants …

On Flow Polytopes, Nu-Associahedra, And The Subdivision Algebra, Matias Von Bell

Theses and Dissertations--Mathematics

This dissertation studies the geometry and combinatorics related to a flow polytope F_car(ν) constructed from a lattice path ν, whose volume is given by the ν-Catalan numbers. It begins with a study of the ν-associahedron introduced by Ceballos, Padrol, and Sarmiento in 2019, but from the perspective of Schröder combinatorics. Some classical results for Schröder paths are extended to the ν-setting, and insights into the geometry of the ν-associahedron are obtained by describing its face poset with two ν-Schröder objects. The ν-associahedron is then shown to be dual to a framed triangulation of F_car(ν), which is a …

Geometric Properties Of Weighted Projective Space Simplices, Derek Hanely

Theses and Dissertations--Mathematics

A long-standing conjecture in geometric combinatorics entails the interplay between three properties of lattice polytopes: reflexivity, the integer decomposition property (IDP), and the unimodality of Ehrhart h*-vectors. Motivated by this conjecture, this dissertation explores geometric properties of weighted projective space simplices, a class of lattice simplices related to weighted projective spaces.

In the first part of this dissertation, we are interested in which IDP reflexive lattice polytopes admit regular unimodular triangulations. Let Delta_(1,q)denote the simplex corresponding to the associated weighted projective space whose weights are given by the vector (1,q). Focusing on the case where Delta …

Batch Normalization Preconditioning For Neural Network Training, Susanna Luisa Gertrude Lange

Theses and Dissertations--Mathematics

Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this work, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during training. This is designed to improve the Hessian matrix of the loss …

Tropical Geometry Of T-Varieties With Applications To Algebraic Statistics, Joseph Cummings

Theses and Dissertations--Mathematics

Varieties with group action have been of interest to algebraic geometers for centuries. In particular, toric varieties have proven useful both theoretically and in practical applications. A rich theory blending algebraic geometry and polyhedral geometry has been developed for T-varieties which are natural generalizations of toric varieties. The first results discussed in this dissertation study the relationship between torus actions and the well-poised property. In particular, I show that the well-poised property is preserved under a geometric invariant theory quotient by a (quasi-)torus. Conversely, I argue that T-varieties built on a well-poised base preserve the well-poised property when the base …

The V1-Periodic Region In Complex Motivic Ext And A Real Motivic V1-Selfmap, Ang Li

Theses and Dissertations--Mathematics

My thesis work consists of two main projects with some connections. In the first project we establish a v₁ periodicity theorem in Ext over the complex motivic Steenrod algebra. The element h₁ of Ext, which detects the homotopy class \eta in the motivic Adams spectral sequence, is non-nilpotent and therefore generates h₁-towers. Our result is that, apart from these h₁-towers, v₁ periodicity operators give isomorphisms in a range near the top of the Adams chart. This result generalizes well-known classical behavior.

In the second project we consider a nontrivial action of C_{2 …}

Local Finiteness And Automorphism Groups Of Low Complexity Subshifts, Ronnie Pavlov, Scott Schmieding

Mathematics: Faculty Scholarship

We prove that for any transitive subshift X with word complexity function c_n(X), if lim inf(log(c_n(X)/n)/(log log log n)) = 0, then the quotient group Aut(X, σ)/〈 σ〉 of the automorphism group of X by the subgroup generated by the shift σ is locally finite. We prove that significantly weaker upper bounds on c_n(X) imply the same conclusion if the gap conjecture from geometric group theory is true. Our proofs rely on a general upper bound for the number of automorphisms of X of range n in terms of word complexity, which may be …

Measure-Theoretically Mixing Subshifts With Low Complexity, Darren Creutz, Ronnie Pavlov, Shaun Rodock

Mathematics: Faculty Scholarship

We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any f : N → N with f (n)/n increasing and ∑ 1/f (n) < ∞, that there exists an extremely elevated staircase with word complexity p(n) = o(f (n)). This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.

Finding An Effective Shape Parameter Strategy To Obtain The Optimal Shape Parameter Of The Oscillatory Radial Basis Function Collocation In 3d, Quinnlan Aiken, Annika Murray, Ar Lamichhane

Undergraduate Mathematics Day: Past Content

Recent research into using the Method of Approximate Particular Solutions to numerically solve partial differential equations, has shown promising results. High levels of accuracy can be obtained when implementing this method, however the success of this collocation method is dependent on a shape parameter that is found in nearly all radial basis functions. If the shape parameter is not appropriately chosen, then it can provide an unacceptable result. Two shape parameter strategies are considered, a random variable shape parameter strategy and a leave-one-out cross validation strategy. The main objective of this work is to assess the viability of using these …

Fixed Points Of Functions Below The Line Y = X, Grace Fryling, Harrison Rouse

Undergraduate Mathematics Day: Past Content

This paper concerns fixed points of functions whose graphs lie on or below the line y = x. Using the Monotone Convergence Theorem, we show that positive fixed points of such functions are “attracting on the right” so long as we include a couple of further assumptions about these functions near their fixed points. As an illustrative example, we confirm that this is the case for the function y = x sin x; the positive fixed points of this function “attract on the right” and “repel on the left.” Further, we generalize by showing that differentiability is in fact not …

Efficient Conformal Binary Classification Under Nearest Neighbor, Maxwell Lovig

Undergraduate Mathematics Day: Past Content

There are many types of statistical inferences that can be used today: Frequentist, Bayesian, Fiducial, and others. However, Vovk introduced a new version of statistical inference known as Conformal Predictions. Conformal Predictions were designed to reduce the assumptions of standard prediction methods. Instead of assuming all observations are drawn independently and identically distributed, we instead assume exchangeability. Meaning, all N! possible orderings of our N observations are equally likely. This is more applicable to fields such as machine learning where assumptions may not be easily satisfied. In the case of binary classification, Vovk provided the nearest neighbors (NN) measure which …