Physical Sciences and Mathematics Commons^™

New Algorithmic Support For The Fundamental Theorem Of Algebra, Vitaly Zaderman

Dissertations, Theses, and Capstone Projects

Univariate polynomial root-finding is a venerated subjects of Mathematics and Computational Mathematics studied for four millenia. In 1924 Herman Weyl published a seminal root-finder and called it an algorithmic proof of the Fundamental Theorem of Algebra. Steve Smale in 1981 and Arnold Schonhage in 1982 proposed to classify such algorithmic proofs in terms of their computational complexity. This prompted extensive research in 1980s and 1990s, culminated in a divide-and-conquer polynomial root-finder by Victor Pan at ACM STOC 1995, which used a near optimal number of bit-operations. The algorithm approximates all roots of a polynomial p almost as fast as one …

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

Machine Learning In Finances, Elma Kastrat, Akinyemi Apampa, Satyanand Singh

Publications and Research

In our study we work on an optimization of an appropriate stock portfolio base on available information. Our work takes into consideration the average return and any associated risk. We produce an investment strategy that predictively allows a portfolio to grow with high yields.

Models For Decision-Making - Second Edition, Steven Cosares, Fred Rispoli

Open Educational Resources

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.

We provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use …

Symmetry-Inspired Analysis Of Biological Networks, Ian Leifer

Dissertations, Theses, and Capstone Projects

The description of a complex system like gene regulation of a cell or a brain of an animal in terms of the dynamics of each individual element is an insurmountable task due to the complexity of interactions and the scores of associated parameters. Recent decades brought about the description of these systems that employs network models. In such models the entire system is represented by a graph encapsulating a set of independently functioning objects and their interactions. This creates a level of abstraction that makes the analysis of such large scale system possible. Common practice is to draw conclusions about …

Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, Troy Smith

Dissertations, Theses, and Capstone Projects

For much of American history, literacy has been prioritized in K-12 education and society, at large, at the expense of numeracy. This lack of numerical emphasis has established innumeracy as an American cultural norm that has resulted in America not producing a sufficient number of numerate citizens, and ranking poorly on mathematical performance in international comparisons. This paper investigates the decisions and circumstances that led to this under prioritization, along with the public and cultural impact of said actions. Toward this end, literature regarding contemporary and historical influences on American mathematics education (e.g., civic, policy, and parental) was reviewed. The …

Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong

Dissertations and Theses

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass …

An Analysis Of Comparison-Based Sorting Algorithms, Jacob M. Gomez, Edgar Aponte, Brad Isaacson

Publications and Research

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest.

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

The Exact Factorization Equations For One- And Two-Level Systems, Bart Rosenzweig

Theses and Dissertations

Exact Factorization is a framework for studying quantum many-body problems. This decomposes the wavefunctions of such systems into conditional and marginal components. We derive corresponding evolution equations for molecular systems whose conditional electronic subsystems are described by one or two Born-Oppenheimer levels and develop a program for their mathematical study.

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

Open Educational Resources

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

Publications and Research

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

Discovering Kepler’S Third Law From Planetary Data, Boyan Kostadinov, Satyanand Singh

Publications and Research

In this data-inspired project, we illustrate how Kepler’s Third Law of Planetary Motion can be discovered from fitting a power model to real planetary data obtained from NASA, using regression modeling. The power model can be linearized, thus we can use linear regression to fit the model parameters to the data, but we also show how a non-linear regression can be implemented, using the R programming language. Our work also illustrates how the linear least squares used for fitting the power model can be implemented in Desmos, which could serve as the computational foundation for this project at a lower …

The Beauty Of Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

It is very difficult for ordinary people to become excellent painters like Picasso. In contemporary society, everyone has a computer, but no one associates painting with computers. This project aims to show that one can use computer tools to connect mathematics with art. We use Krita, which is a professional free, and open-source painting program made by artists to create digital art. We demonstrate how the Bezier curve pen tool in Krita can help anyone to ́ draw paintings such as Picasso’s cubist oil paintings on a computer in a relatively short time.

Bézier Curves, Qing Chen, Ariane Masuda

Publications and Research

Drawing on a computer using a mouse is quite different than drawing by hand. It can be challenging to use a mouse to even simply trace a line. If the drawing involves several lines and curves, the task becomes more complicated. The goal of this project is to show how to design beautiful artworks using Bézier curves. A Bézier curve is a smooth parametric curve produced by the coordinates of certain points. To draw a specific curve, one needs to select multiple control points positioned in strategic places. By changing these positions, one can draw different curves to produce the …

Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev

Dissertations, Theses, and Capstone Projects

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.

We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number …

A New Mathematical Theory For The Dynamics Of Large Tumor Populations, A Potential Mechanism For Cancer Dormancy & Recurrence And Experimental Observation Of Melanoma Progression In Zebrafish, Adeyinka A. Lesi

Dissertations and Theses

Cancer, a family of over a hundred disease varieties, results in 600,000 deaths in the U.S. alone. Yet, improvements in imaging technology to detect disease earlier, pharmaceutical developments to shrink or eliminate tumors, and modeling of biological interactions to guide treatment have prevented millions of deaths. Cancer patients with initially similar disease can experience vastly different outcomes, including sustained recovery, refractory disease or, remarkably, recurrence years after apparently successful treatment. The current understanding of such recurrences is that they depend on the random occurrence of critical mutations. Clearly, these biological changes appear to be sufficient for recurrence, but are they …

Parametric Art, Shaun Pollard, Daanial Ahmad, Satyanand Singh

Publications and Research

Lissajous curves, named after Jules Antoine Lissajous (1822-1880) are generated by the parametric equations ��=��������(����) and ��=��������(����) in its simplistic form. Others have studied these curves and their applications like Nathaniel Bowditch in 1815, and they are often referred to as Bowditch curves as well. Lissajous curves are found in engineering, mathematics, graphic design, physics, and many other backgrounds. In this project entitled “Parametric Art” this project will focus on analyzing these types of equations and manipulating them to create art. We will be investigating these curves by answering a series of questions that elucidate their purpose. Using Maple, which …

Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang

Publications and Research

As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology exhibits …

Matrix Low Rank Approximation At Sublinear Cost, Qi Luan

Dissertations, Theses, and Capstone Projects

A matrix algorithm runs at sublinear cost if the number of arithmetic operations involved is far fewer than the number of entries of the input matrix. Such algorithms are especially crucial for applications in the field of Big Data, where input matrices are so immense that one can only store a fraction of the entire matrix in memory of modern machines. Typically, such matrices admit Low Rank Approximation (LRA) that can be stored and processed at sublinear cost. Can we compute LRA at sublinear cost? Our counter example presented in Appendix C shows that no sublinear cost algorithm can compute …

An Accurate Solution Of The Self-Similar Orbit-Averaged Fokker-Planck Equation For Core-Collapsing Isotropic Globular Clusters: Properties And Application, Yuta Ito

Dissertations, Theses, and Capstone Projects

Hundreds of dense star clusters exist in almost all galaxies. Each cluster is composed of approximately ten thousand through ten million stars. The stars orbit in the clusters due to the clusters' self-gravity. Standard stellar dynamics expects that the clusters behave like collisionless self-gravitating systems on short time scales (~ million years) and the stars travel in smooth continuous orbits. Such clusters temporally settle to dynamically stable states or quasi-stationary states (QSS). Two fundamental QSS models are the isothermal- and polytropic- spheres since they have similar structures to the actual core (central part) and halo (outskirt) of the clusters. The …

Analysis Of Surface Temperature Trends Of Global Lakes Using Satellite Remote Sensing And In Situ Observations, Christal Jean Soverall, Zahida Yasmin, Mahoutin Godnou, Wen Yong Huang, Ryan Chen, Abdou Bah, Hamidreza Norouzi, Reginald Blake

Publications and Research

Even though lakes make up a small percentage of the water bodies on the global land surface, lakes provide critically important ecosystem services. Unfortunately, however, several lake surface areas around the globe have been changing with many of them drastically decreasing due to climate variability and local mismanagement at the basin-scale level. Lake Surface Water Temperature (LSWT) is recognized as a critical indicator of climate change in lakes. The changes in water and the surrounding land temperatures may be an indicator of climate variability if there is consistency between changes in both temperatures. This project focuses on the application of …

Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton

Publications and Research

Data analysis and Machine Learning are destined to evolve the current technology infrastructure by solving technology and economy demands present mainly in developed cities like New York. This research proposes a machine learning (ML) based solution to alleviate one of the main issues that big buildings such as CUNY campuses have, that is the waste of energy resources. The analysis of data coming from the readings of different deployed sensors such as CO2, humidity and temperature can be used to estimate occupancy in a specific room and building in general. The outcome of this research established a relationship between the …

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.

A Study Of Cholera Transmission, Urmi Ghosh-Dastidar

Open Educational Resources

A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this …

Mechanisms Of Value-Biased Prioritization In Fast Sensorimotor Decision Making, Kivilcim Afacan-Seref

Dissertations and Theses

In dynamic environments, split-second sensorimotor decisions must be prioritized according to potential payoffs to maximize overall rewards. The impact of relative value on deliberative perceptual judgments has been examined extensively, but relatively little is known about value-biasing mechanisms in the common situation where physical evidence is strong but the time to act is severely limited. This research examines the behavioral and electrophysiological indices of how value biases split-second perceptual decisions and the possible mechanisms underlying the process. In prominent decision models, a noisy but statistically stationary representation of sensory evidence is integrated over time to an action-triggering bound, and value-biases …

Tropical Cyclone Hazards In Relation To Propagation Speed, Jiehao Huang

Dissertations and Theses

As the population and infrastructure along the US East Coast increase, it becomes increasingly important to study the characteristics of tropical cyclones that can impact the coast. A recent study shows that the propagation speed of tropical cyclones has slowed over the past 60 years, which can lead to greater accumulation of precipitation and greater storm surge impacts. The study presented herein is meant to examine and analyze the relationships that exist between the propagation speed of tropical cyclones, their surface wind strength, displacement angles, and cyclone averaged winds. This analysis is focused on tropical cyclones spanning from 1950-2015 in …

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

Publications and Research

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.