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2024

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Full-Text Articles in Mathematics

The Exponential Function In Discrete Fractional Calculus Under The Delta Operator, Brayton James Link Jan 2024

The Exponential Function In Discrete Fractional Calculus Under The Delta Operator, Brayton James Link

Masters Theses

"Previously the exponential problem in discrete fractional calculus under the nabla operator was solved with the discrete Mittag--Leffler function. We now show the solution to the exponential problem in discrete fractional calculus under the delta operator, providing multiple derivations of the solution with recursion and Laplace transforms. We also share some computational and numerical results of experiments with different orders of difference to display the nature of the solution" -- Abstract, p. iii

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Linear Topological Space, Vi Nguyen Jan 2024

Linear Topological Space, Vi Nguyen

UNF Graduate Theses and Dissertations

This thesis begins with an introduction to linear and topological spaces and then defines linear topological spaces. It studies key properties such as neighborhoods, convexity, reflexivity, and weak and weak* topologies. Finally, it concludes with solving non-linear partial differential equations.

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Dynamics And Inverse Problems For Nonlinear Schrödinger Equations, Christopher Hogan Jan 2024

Dynamics And Inverse Problems For Nonlinear Schrödinger Equations, Christopher Hogan

Doctoral Dissertations

"The cubic nonlinear Schrödinger equation (NLS) is a model of interest in the study of physical problems including nonlinear optics and Bose-Einstein condensates. Of particular interest is the study of cubic NLS with inhomogeneities such as localizations of the nonlinearity or terms introducing potential barriers. We first address some preliminaries and techniques useful in the study of the cubic NLS and its variations. We then consider the cubic NLS with a localized nonlinearity in dimensions d ≥ 2. We show that solutions with data given by small-amplitude wave packets accrue a nonlinear phase that determines the X-ray transform of the …

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Prime Intersection Graphs Of Ideals Of Commutative Artinian Rings, Nuttawut Sangjaer Jan 2024

Prime Intersection Graphs Of Ideals Of Commutative Artinian Rings, Nuttawut Sangjaer

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study prime intersection graphs of ideals of commutative Artinian rings. We work on the connectedness, completeness and planarity of the graphs and characterize the star graphs for these graphs. We calculate graph \linebreak parameters and find the radius and a center of the graphs. Moreover, we determine the degree of each vertex when the vertex set is finite, and characterize the Eulerian and Hamiltonian properties of the graphs.

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Prediction Of Optimal Binding Constraints Of Linear Programming Problem Using Deep Learning, Natdanai Kafakthong Jan 2024

Prediction Of Optimal Binding Constraints Of Linear Programming Problem Using Deep Learning, Natdanai Kafakthong

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis presents innovative deep learning models designed to enhance the efficiency of solving linear programming, transportation, and traveling salesman problems. The first model, LP-Net, predicts the binding optimal constraints in linear programming problems, achieving faster solution times compared to traditional solvers like CPLEX. The second model, Transport-Net, predicts optimal basic feasible arcs for transportation problems, demonstrating significant speedups and superior scalability over both CPLEX and Gurobi in large-scale instances. The third model, TSP-Net, addresses the traveling salesman problem by predicting an initial near-optimal tour, outperforming Gurobi and genetic algorithms in computational efficiency. Collectively, these deep learning approaches offer transformative …

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Fuzzy Digital Signature Scheme For Binary Noisy Strings With Respect To Hamming Distance, Ittanee Srikham Jan 2024

Fuzzy Digital Signature Scheme For Binary Noisy Strings With Respect To Hamming Distance, Ittanee Srikham

Chulalongkorn University Theses and Dissertations (Chula ETD)

One of the risks associated with public key infrastructure (PKI) pertains to the security of the user's private key. Given the imperative for stringent protection of this key, a proposed solution to mitigate this risk involves the utilization of biometric information. Although biometric information is fuzzy, it cannot be used directly as a cryptographic key. Thus, our investigation commenced into the exploration of ``Signature Scheme with a Fuzzy Private Key" by Takahashi et al. They introduced a new concept of digital signature called ``fuzzy signature" for real vectors with $L_{\infty}$ metric. A fuzzy signature is a signature scheme that uses …

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Adjustment Of Ridge Estimator For Linear Regression Model With Multicollinearity, Sittinon Pumpuang Jan 2024

Adjustment Of Ridge Estimator For Linear Regression Model With Multicollinearity, Sittinon Pumpuang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Linear regression model is one of important statistical tools applied in many different problems. Therefore, several studies in developing tools for linear regression models have brought interests from statisticians. One such problem is to find an efficient method for parameter estimation. Several different methods have been proposed in literature such as the ordinary least square method which has been widely used in application. However, the least square estimator has high error when there exists a multicollinearity problem. This, statisticians have developed alternative parameter estimation methods for linear regression models with multicollinearity such as the ridge regression. In this thesis, we …

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Fixed Point And Periodic Cycle Of Sequence Arises From Number Of Factors, Thanapong Jaitrakoon Jan 2024

Fixed Point And Periodic Cycle Of Sequence Arises From Number Of Factors, Thanapong Jaitrakoon

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let. {an} and {bn} be sequences of positive integers. For each positive integer n., define an+1 to be the eube of the number of positive factors of an and define bn+1 to be the forth power of the number of positive factors of bn. This thesis proves that (i) if a1 > 1, then (an) eventually becomes the fixed point, namely 21952 or 64000, or {an}eventually becomes a sequence having periodie cycle of prime period 2, namely (64, 343) or (343, 64); (ii) if b1 > 1, then {bn} is eventually the fixed point, namely 625, 6561 or 4100625.

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Some Properties Of S-Multiplication Modules And S-Comultiplication Modules, Kanrop Hukaew Jan 2024

Some Properties Of S-Multiplication Modules And S-Comultiplication Modules, Kanrop Hukaew

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let R be an associative ring with identity, and all modules be unitary right R- modules. In 2020, D. D. Anderson et al. introduced the concept of S-multiplication modules, which is a generalization of multiplication modules. Two years later, E. Yildiz et al. introduced the dual notion of S-multiplication modules called S- comultiplication modules. Moreover, S-comultiplication modules are also a gen- eralization of comultiplication modules. In this thesis, we will explore several properties of both S-multiplication modules and S-comultiplication modules. We will provide examples of S-multiplication modules and S-comultiplication modules. Additionally, we demonstrate that the concepts of S-multiplication modules, sim- …

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Spatial Data Analysis For Household Income And Expenditure In Thailand, Jirayut Rattana Jan 2024

Spatial Data Analysis For Household Income And Expenditure In Thailand, Jirayut Rattana

Chulalongkorn University Theses and Dissertations (Chula ETD)

Poverty has been a serious problem for many countries throughout the world, particularly during the COVID-19 pandemic. Due to the pandemic, many people lost their jobs and encountered economic. Therefore, the government and policy planners need an effective strategy to improve the country's economy. An essential component of these strategies involves analyzing socio-economic indicators, a field extensively explored by statisticians, economists, and policymakers. In Thailand, methodologies such as the World Bank method, Empirical Bayes, and Hierarchical Bayes have been applied to tackle poverty. However, these approaches often overlook the integration of spatial information in their analyses. In this study, we …

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System Of Stochastic Grey Differential Equations With Singular Spectrum Analysis For Precious Metal Prices Forecasting, Rammarat Panadsako Jan 2024

System Of Stochastic Grey Differential Equations With Singular Spectrum Analysis For Precious Metal Prices Forecasting, Rammarat Panadsako

Chulalongkorn University Theses and Dissertations (Chula ETD)

โลหะมีค่าเป็นกลุ่มโลหะที่มีมูลค่าทางเศรษฐกิจสูงกว่าโลหะทั่วไป ดังนั้นการพยากรณ์ราคาของโลหะมีค่าจึงเป็นหนึ่งปัญหาที่น่าสนใจ ซึ่งการพยากรณ์ราคาของโลหะมีค่ามีหลากหลายวิธี โดยวิทยานิพนธ์ฉบับนี้มีจุดประสงค์เพื่อพัฒนาระบบสมการเชิงอนุพันธ์เกรย์สโตแคสติกกับการวิเคราะห์สเปกตรัมเอกฐาน (SGDE+SSA) ในการพยากรณ์ราคาของทองคำ เงิน แพลทินัม และแพลเลเดียม ในขั้นตอนแรกจะทำการสร้างแบบจำลอง SGDE+SSA แบบหนึ่งมิติ เพื่อพยากรณ์ราคาของโลหะมีค่าทั้งสี่ชนิดโดยไม่พิจารณาค่าสหสัมพันธ์ของโลหะเหล่านี้ แต่ในความเป็นจริงราคาของโลหะเหล่านี้มีความสัมพันธ์กัน ดังนั้นแบบจำลอง SGDE+SSA แบบหลายมิติจึงถูกสร้างขึ้น โดยมีการพิจารณาค่าสหสัมพันธ์ที่เกิดจากการวิเคราะห์ข้อมูลราคาในอดีตเพื่อให้แบบจำลองมีความเหมาะสมกับสถานการณ์จริงมากยิ่งขึ้น สำหรับการวิเคราะห์ความอ่อนไหวจะศึกษาโดยการพัฒนาวิธีการคัดเลือกค่าพารามิเตอร์เพื่อเพิ่มประสิทธิภาพของแบบจำลอง นอกจากนี้ค่าคาดหวังและค่าความแปรปรวนของผลเฉลยทางตัวเลขถูกแสดงโดยคำนวณจากแบบจำลอง ความแม่นยำของแบบจำลอง SGDE+SSA แบบหนึ่งมิติ และแบบจำลอง SGDE+SSA แบบหลายมิติ จะถูกแสดงผ่านค่า MAPE ซึ่งเป็นการเปรียบเทียบระหว่างราคาจากแบบจำลองและราคาของโลหะมีค่าในอดีตตั้งแต่เดือนมกราคม พ.ศ. 2548 ถึง เดือนมกราคม พ.ศ. 2567 ผลการศึกษาครั้งนี้พบว่าแบบจำลอง SGDE+SSA แบบหนึ่งมิติสำหรับราคาการพยากรณ์ในช่วงชุดการเรียนรู้ และสำหรับสำหรับราคาที่พยากรณ์ในช่วงข้อมูลชุดทดสอบ แบบจำลอง SGDE+SSA แบบหนึ่งมิติมีความเชี่ยวชาญในการคาดการณ์ราคาของเงิน ในขณะที่แบบจำลอง SGDE+SSA แบบหลายมิติมีประสิทธิภาพในการทำนายราคาของทองคำและแพลทินัม โดยรวมแล้วแบบจำลองเหล่านี้มีประสิทธิภาพในการทำนายราคาทองคำ เงินและแพลทินัม

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Homotopy Conjugate Of Continuous Map, Thitipon Phuksawad Jan 2024

Homotopy Conjugate Of Continuous Map, Thitipon Phuksawad

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce the concept of homotopy conjugate, which is weaker than topological conjugate, for continuous maps. We study the properties of a homotopy conjugate related to the fixed space, the orbit space, and the mapping cylinder. Moreover, we prove that affine maps on R™ with at least one fixed point are all homotopy conjugate.

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Logistic Stochastic Differential Equation Driven By Fractional Brownian Motion, Thanayuth Promkong Jan 2024

Logistic Stochastic Differential Equation Driven By Fractional Brownian Motion, Thanayuth Promkong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, the logistic stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) is proposed. We derive the exact solution of this SDE using the fractional Itô's formula with respect to FBM and investigate the probabilistic properties of the solution, namely the mean and the $k$-th moment, using Taylor series approximation. The simulation of sample paths using the direct formula of the exact solution of this SDE driven by FBM with various Hurst parameters, along with that of the corresponding SDE driven by standard Brownian motion, is performed to demonstrate the behaviors of these SDEs and affirm our …

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Pricing Option On Commodity Under Schwartz Model By Using Finite Difference Method, Peerawit Kalaphakdee Jan 2024

Pricing Option On Commodity Under Schwartz Model By Using Finite Difference Method, Peerawit Kalaphakdee

Chulalongkorn University Theses and Dissertations (Chula ETD)

This work aims for finding prices of options with underlying assets considered as commodities, where the price of commodity is assumed to follow a mean-reverting Ornstein-Uhlenbeck process, namely, the Schwartz one-factor model. The prices of both European and American options are obtained by employing the finite different methods (FDMs) for solving parabolic partial differential equations (PDEs) generated from Feynman-Kac theorem. In this work, we construct three FDMs to solve PDEs, namely FTCS, BTCS and CN methods. The accuracy of FDMs are validated and confirmed by numerical examples for European options by comparing with analytical results from Black-Scholes type formula and …

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Perfect Codes On T-Cayley Graphs, Kantapong Wannatong Jan 2024

Perfect Codes On T-Cayley Graphs, Kantapong Wannatong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let G be a finite group with the identity e and t ∈ N. In this dissertation, we study perfect codes in a t-Cayley graph of G. Let H be a subgroup of G and k ∈ {1, . . . , t}. We have a necessary and sufficient condition for a collection Ω of subsets of G such that H × {1, . . . , k} is a perfect code in t-Cayley graph Cay(G× {1, . . . , t}, Ω). In addition, we obtain criterions for determining if H × {1, . . . , t} is …

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Stochastic And Fuzzy Unit Commitment Models To Accommodate Solar Energy And Electric Vehicle Charging Penetration, Sukita Kaewpasuk Jan 2024

Stochastic And Fuzzy Unit Commitment Models To Accommodate Solar Energy And Electric Vehicle Charging Penetration, Sukita Kaewpasuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

This dissertation investigates the integration of renewable energy and electric vehicle (EV) consumption in the power system of Thailand. As the country moves towards sustainability, the production sector is experiencing a significant penetration of renewable energy sources, while the consumption sector is observing an increasing adoption of EVs. The unit commitment model is commonly used for electricity production planning to minimize costs and ensure system stability. However, the uncertainties associated with renewable energy output and EV charging consumption challenge the characteristic of the net load demand prediction. This study focuses on developing robust unit commitment models that consider the high …

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A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen Jan 2024

A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen

Mathematics, Physics, and Computer Science Faculty Articles and Research

As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …

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Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng Jan 2024

Symmetries And Integrable Systems, Sen-Yue Lou, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

Symmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries. In addition to the fundamental role to find exact group invariant solutions via Lie point symmetries, some important new developments on symmetries and conservation laws are reviewed. The recursion operator method is important to find infinitely many local and nonlocal symmetries of (1+1)-dimensional integrable systems. In this paper, it is pointed out that a recursion operator may be obtained from one key symmetry, say, a residual symmetry. For (2+1)-dimensional integrable systems, the master-symmetry approach …

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Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury Jan 2024

Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.

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Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai Jan 2024

Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.

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Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi Jan 2024

Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared …

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Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant Jan 2024

Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant

School of Mathematical & Statistical Sciences Faculty Publications

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were …

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Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton Jan 2024

Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members' understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators' understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that …

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Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield Jan 2024

Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

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Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba Jan 2024

Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …

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Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota Jan 2024

Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota

School of Mathematical & Statistical Sciences Faculty Publications

Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher …

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Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington Jan 2024

Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants 𝜆 and 𝜇 usually vanish for imaginary quadratic fields where p is non-split.

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On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva Jan 2024

On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

For the queer Lie superalgebra Q(1), we explicitly describe the center of the super-Yangian Y Q(1) of Q(1) in terms of generators of Y Q(1). We also describe the square of the antipodal map on Y Q(1) and use the antipode to construct an involutive automorphism of Y Q(1).

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Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen Jan 2024

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

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Self-Exciting Point Processes In Real Estate, Ian Fraser Jan 2024

Self-Exciting Point Processes In Real Estate, Ian Fraser

Theses and Dissertations (Comprehensive)

This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …

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