Physical Sciences and Mathematics Commons^™

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 …

Three Imprimitive Character Sums, Brad Isaacson

Publications and Research

We express three imprimitive character sums in terms of generalized Bernoulli numbers. These sums are generalizations of sums introduced and studied by Arakawa, Berndt, Ibukiyama, Kaneko and Ramanujan in the context of modular forms and theta function identities. As a corollary, we obtain a formula for cotangent power sums considered by Apostol.

Distributed Cross-Community Collaboration For The Cloud-Based Energy Management Service, Yu-Wen Chen, J. Morris Chang

Publications and Research

Customers’ participation is a critical factor for inte-grating the distributed energy resources via demand response and demand-side management programs, especially when customers become prosumers. Incentives need to be delivered by the energy management service to attract prosumers to operate their distributed energy resources and electricity loads grid-friendly actively. The cloud-based energy management service enables virtual trading for customers within the same community to minimize cost and smooth the fluctuation. With the potential fast-growing number of service providers and customers, the needs exist for efficiently collaborating across multiple service providers and customers. This paper proposes the distributed cross-community collaboration (XCC) for …

Amm Problem #12219, Brad Isaacson

Publications and Research

No abstract provided.

A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson

Publications and Research

In this paper, we express three different, yet related, character sums in terms of generalized Bernoulli numbers. Two of these sums are generalizations of sums introduced and studied by Berndt and Arakawa–Ibukiyama–Kaneko in the context of the theory of modular forms. A third sum generalizes a sum already studied by Ramanujan in the context of theta function identities. Our methods are elementary, relying only on basic facts from algebra and number theory.

A Review Of Measuring Ecosystem Resilience To Disturbance, Chuixiang Yi, Nathan Jackson

Publications and Research

Resilience is the central concept for understanding how an ecosystem responds to a strong perturbation, and is related to other concepts used to analyze system properties in the face of change such as resistance, recovery, sustainability, vulnerability, stability, adaptive capacity, regime shift, and tipping point. It is extremely challenging to formulate resilience thinking into practice. The current state-of-art approaches of assessing ecosystem resilience may be useful for policy makers and ecosystem resource managers to minimize climatological or natural disaster related impacts. Here, we review the methods of assessing resilience and classify and limit them to three cases: (1) forest resilience …

Transmission Zeros With Topological Symmetry In Complex Systems, Yuhao Kang, Azriel Genack

Publications and Research

Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media, has advanced the understanding and applications of wave interactions. Here we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and by adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss …

Math 111: Introduction To Statistics And Probability, Yu Wang

Open Educational Resources

Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.

Dimers, Orientifolds And Stability Of Supersymmetry Breaking Vacua, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.

Jazz Colors: Pigment Identification In The Gouaches Used By Henri Matisse, Ana Martins, Anne Catherine Prud’Hom, Maroussia Duranton, Abed Haddad, Celine Daher, Anne Genachte-Le Bail, Tiffany Tang

Publications and Research

Jazz, the illustrated book by Henri Matisse, is a testament to the vitality of the artist in the last decade of his career. The book consists of twenty illustrations reproduced in 370 copies using a stencil-based printing technique and the same Linel gouaches the artist had used for the original maquettes. This study reports on the comprehensive analysis carried out to identify the pigments in the gouaches used in Jazz by transmitted and reflectance infrared, Raman, SERS, and X-ray fluorescence spectroscopies, and describes the lightfastness of these gouaches as evaluated by microfaedometry. This study also highlights the necessity of …

Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

We study 4d N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians, Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar

Publications and Research

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J⁽ⁿ⁾ of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator …

Color Charge Correlations In The Proton At Nlo: Beyond Geometry Based Intuition, Adrian Dumitru, Heikki Mäntysaari, Risto Paatelainen

Publications and Research

Color charge correlators provide fundamental information about the proton structure. In this Letter, we evaluate numerically two-point color charge correlations in a proton on the light cone including the next-to-leading order corrections due to emission or exchange of a perturbative gluon. The non-perturbative valence quark structure of the proton is modelled in a way consistent with high-x proton structure data. Our results show that the correlator exhibits startlingly non-trivial behavior at large momentum transfer or central impact parameters, and that the color charge correlation depends not only on the impact parameter but also on the relative transverse momentum of …

Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus, Sebastián Franco, Azeem Hasan

Publications and Research

The open string sector of the topological B-model on CY (m + 2)-folds is described by m-graded quivers with superpotentials. This correspondence generalizes the connection between CY (m + 2)-folds and gauge theories on the worldvolume of D(5 − 2m)-branes for m = 0, . . . , 3 to arbitrary m. In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CY_m+2 and CY_n+2 produces the quiver theory for a related CY_{m+n+3 …}

Exclusion Statistics For Particles With A Discrete Spectrum, Stéphane Ouvry, Alexios P. Polychronakos

Publications and Research

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a …

Wavefront-Selective Fano Resonant Metasurface, Adam C. Overvig, Andrea Alù

Publications and Research

Fano resonances are conventionally understood as sharp spectral features with selectivity in the momentum-frequency domain, implying that they can be excited only by plane waves with specific frequencies and incident angles. We demonstrate that Fano resonances can be made generally selective in the space-frequency domain. They can be tailored to resonate only when excited by a frequency, polarization, and wavefront of choice. This generalization reveals that Fano systems are characterized by eigenwaves that scatter to their time-reversed image upon reflection. Although in conventional Fano systems this trivially occurs for normally incident plane waves, we show that, in general, the selected …

African Land Mammal Ages, John Van Couvering, Eric Delson

Publications and Research

We define 17 African land mammal ages, or AFLMAs, covering the Cenozoic record of the Afro-arabian continent, the planet’s second largest land mass. While fossiliferous deposits are absent on the eroded plateau of the continent’s interior, almost 800 fossil genera from over 350 locations have now been identified in coastal deposits, karst caves, and in the Neogene rift valleys. Given a well-developed geochronologic framework, together with continuing revision to the fossil record—both stimulated by the story of human evolution in Africa—and also to compensate for the variation in fossil ecosystems across such great distances, the AFLMAs are biochronological units defined …

Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra

Publications and Research

No abstract provided.

Variation In Personality Among Semi-Wild Myanmar Timber Elephants, Sateesh Venkatesh

Theses and Dissertations

This study examines two personality traits: exploration and neophobia, which could influence human-elephant conflicts. Thirty-one semi-wild elephants were tested over two trials using a custom novel puzzle tube containing three tasks and three rewards. Our studies show that elephants do vary significantly between individuals in both exploration and neophobia.

Applying The Food-Energy-Water Nexus Approach To Urban Agriculture: From Few To Fewp (Food-Energy- Water-People), Silvio Caputo, Victoria Schoen, Kathrin Spect, Baptiste Grard, Chris Blythe, Nevin Cohen, Runrid Fox-Kämper, Jason Hawes, Joshua Newell, Lidia Poniży

Publications and Research

Many studies examine the correlation between the use of resources such as water, energy and land, and the production of food. These nexus studies focus predominantly on large scale systems, often considering the social dimensions only in terms of access to resources and participation in the decision- making process, rather than individual attitudes and behaviours with respect to resource use. Such a concept of the nexus is relevant to urban agriculture (UA), but it requires customisation to the particular characteristics of growing food in cities, which is practiced mainly at a small scale and produces not only food but also …

Extending Import Detection Algorithms For Concept Import From Two To Three Biomedical Terminologies, Vipina K. Keloth, James Geller, Yan Chen, Julia Xu

Publications and Research

Background: While enrichment of terminologies can be achieved in different ways, filling gaps in the IS-A hierarchy backbone of a terminology appears especially promising. To avoid difficult manual inspection, we started a research program in 2014, investigating terminology densities, where the comparison of terminologies leads to the algorithmic discovery of potentially missing concepts in a target terminology. While candidate concepts have to be approved for import by an expert, the human effort is greatly reduced by algorithmic generation of candidates. In previous studies, a single source terminology was used with one target terminology.

Methods: In this paper, we are extending …

Nyc Communities Battle Flooding, But Not From Coastal Storms, Danielle C. Cruz

Capstones

A look at the impact high-tide flooding and inland flooding has on various communities in New York City. This article also looks into what city officials are doing and not doing to address the concerns of residents who have had to deal with recurring flooding in their community.

Link to Capstone: https://danielle-cruz.format.com/nyc-communities-battle-flooding

An Enticing Study Of Prime Numbers Of The Shape �� = ��^2 + ��^2, Xiaona Zhou

Publications and Research

We will study and prove important results on primes of the shape ��² + ��² using number theoretic techniques. Our analysis involves maps, actions over sets, fixed points and involutions. This presentation is readily accessible to an advanced undergraduate student and lay the groundwork for future studies.

Driven Dipolariton Transistors In Y-Shaped Channels, Patrick Serafin, Tim Byrnes, German Kolmakov V

Publications and Research

Exciton-dipolaritons are investigated as a platform for realizing working elements of a polaritronic transistor. Exciton-dipolaritons are three-way superposition of cavity photons, direct and indirect excitons in a bilayer semiconducting system embedded in an optical microcavity. Using the forced diffusion equation for dipolaritons, we study the room-temperature dynamics of dipolaritons in a transition-metal dichalcogenide (TMD) heterogeneous bilayer. Specifically, we considered a MoSe₂-WS₂ heterostructure, where a Y-shaped channel guiding the dipolariton propagation is produced. We demonstrate that polaritronic signals can be redistributed in the channels by applying a driving voltage in an optimal direction. Our findings open a route …

Data Analysis And Visualizations Of Drosophila Behavioral Phases, Xiaona Zhou

Publications and Research

We analyze drosophila behavioral data from the neuroscience labs of Professor Maria de la Paz Fernandez, Barnard College of Columbia University, and Professor Orie Shafer, the Neuroscience Initiative of the CUNY Advanced Science Research Center. The main goal of this project is to create algorithms for analyzing and visualizing the average activity of drosophila across a specified number of days and across all live flies and use this analysis to calibrate a smoothing filter to be applied to the raw fly activity so that the drosophila behavioral phases can be computed and visualized. We also investigate how to compute and …

Responsive Web Design, Ashley Varon, David Karlins

Publications and Research

Responsive web design is one of the most important topics in web. It can be one of the main reasons a website can be costing a business clients, and creating an effect on a business. The rise in popularity of mobile phones and tablets makes it crucial for a website to be designed to respond and adjust to different viewports. This project will research how important responsive web design is in 2020 and the positive or negative impacts it may have on the users, customers, and businesses. Companies must consider text size, layout, navigation, image sizes, and testing when designing …

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 …

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 …

Understanding Of Aerosol Transmission Of Covid 19 In Indoor Environments, Adama Barro, Cathal O'Toole, Jacob S. Lopez, Matthew Quinones, Sherene Moore

Publications and Research

Our reason for discussing severe acute respiratory syndrome corona virus 2 (SARS-CoV-2) or 2019 novel corona virus (Covid-19), is to understand its aerosol transmission characteristics in indoor spaces and to mitigate further spread of this disease by designing a new HVAC system. The problem that we are tackling is the spread of covid-19 droplets through aerosol transmission by looking at potential engineering solutions to the existing HVAC systems. The purpose is to eradicate the spread of the COVID-19 by testing indoor spaces in an effort to understand the effectiveness of ventilation controls. We believe that scientists and engineers have not …

Principal Component Analysis For Predicting The Party Of The Legislators, Afsana Mimi

Publications and Research

In Spring 2020, I did a project, "Decision Tree Predicting the Party of Legislators," and construct a decision tree model to predict legislators' parties' based on their votes. We also use this model to identify legislators who frequently voted against their parties. We used the legislators' roll call votes, Office of Clerk U.S. House of Representatives Data Sets (Categorical values) collected in 2018 and 2019. In this new project, We study the 2018 and 2019 vote data using Principal Component Analysis (PCA). The goal is to find a (compressed) model using unsupervised learning to distinguish the legislators' parties, and PCA …