2023-2024 Colloquia

Title: Divisor Functions: 1 Train-like Structure and Density Properties, 2 The theory of sets: Cantor and Kronecker
Speaker:  1 Evelina Dubovski (Staten Island Technical High School), 2 Stefon Sauers (Queensborough Community College, CUNY)
Date: Wednesday, May 1, 2024 
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)



Train-like Structure and Density Properties


We analyze if perfect numbers are really “special", within the lens of exploring divisor functions fs(n), depending on parameter s. The divisor function f is the sum of all factors of n divided by n. For example, f1(6)=2 (a perfect number). We extend the analysis from the already-proven density of s=1 to s>0. In 1977 D.Wolke proved that inequality |f(n)-a|<n- 0.4  has infinitely many solutions for any a>1 and conjectured that this estimate can be improved to |f(n)-a|<n- 1. In this research, we establish that fs is dense for 0<s≤1 and prove the Wolke's conjecture for points a from the range of fs Particularly, this result supports the hypothesis that there are infinitely many perfect numbers. Also, we extend Wolke's discovery to all 0<s≤1 and, thus, provide additional quantitative measures of density. The proof reveals the structure of fs as the union of infinitely many trains -specially organized collections of decreasing sequences, which we define. As parameter s increases, the train structures become more visible within chaos, forming ruptures at s>1. At the threshold s=1, the infinite product switches from divergence to convergence, leading to the loss of density. Furthermore, we prove that if we treat fs(n) as a random variable, then its expectation is Riemann function ς(s+1) and show that the variance drastically decreases with s. All results are supported by computations.





The talk is about the birth of mathematicians during the 19th Century. The presentation will focus on the history/ upbring of Cantor and Kronecker, bringing light to their accomplishments about math, then it will explain the logical principles of set theory, and finally doing a deep into understanding The Cantor Set. The presentation will go on to explain how groundbreaking all of these things were for the understanding standing of math, and how it gave meaning to the term infinity. 

Title: Introduction to Categorical Database Theory
Speaker:  Dr. Emilio Minichiello
Date: Wednesday, April 10, 2024 
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)


In this talk, the speaker will introduce categorical database theory, a subject that has received renewed attention in the applied category theory community. It will be explained how one can view categories as database schemas and functors F: C -> Set as database instances. The attribute problem will be discussed, which relates how data can be represented mathematically without losing its meaning, and how this problem is solved using the Algebraic model of databases.  Some recent work will be mentioned that deals with how to query categorical databases using profunctors and some surprising nuances that come about when working syntactically with profunctor presentations.

Title: Generalized Discriminants of Quadratics
Speaker:  Dr. Yusuf Z. Gurtas
Date: Wednesday, March 20, 2024 
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)


The discriminant Δ=𝑏2−4𝑎𝑐, of a quadratic 𝑎𝑥2+𝑏𝑥+𝑐 is a crucial parameter that provides definite information about the nature and number of solutions to the equation 𝑎𝑥2+𝑏𝑥+𝑐=0. For polynomials of degree higher than two the computation of discriminant becomes more complex and less informative. Therefore, it is natural to look for quantities that are simpler in nature and easier to compute to get partial information about the nature and number of solutions to polynomial equations. For example the cubic equation 𝑎𝑥3+𝑏𝑥2+𝑐𝑥+𝑑=0 has complex (non-real) solutions if 𝑏2−3𝑎𝑐<0 but 𝑏2−3𝑎𝑐>0 alone is not sufficient to conclude that the cubic equation must have only real solutions. In this talk we will present a method to generalize the discriminants of quadratics to polynomials of degree 𝑛>2 to obtain such partial information. Based on these generalized discriminants of quadratics we will see, for example, why there cannot be any quartic with four real roots having the last three terms ⋯+2𝑥2−𝑥+1 . Another application we will show is how to graph 𝑥4+(2𝑦2−4)𝑥2+𝑦4+4𝑦2+3=0 without using Calculus.

Title:  Edge Leveraged Artificial Intelligence for Traffic Anomaly Detection
Speaker:  Dr. Xiaohai Li (Department of Computer Engineering Technology

NYC College of Technology (City Tech))

Date: Wednesday, March 13, 2024 
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)



We will present one of our recent research works on applying deep learning in abnormal traffic pattern detection and leverage the latest edge computing tools to develop a portable terminal solution for the system deployment. 

Title:  Solving nonlinear optimal control problems using convex optimization techniques
Speaker:  Alexander Popov (Airbus Defense and Space in Stevenage, UK)
Date: Wednesday, March 6, 2024
Time: 12:30 pm - 1:30 pm
Room: zoom (see information below)



Optimal control problems aim to determine the optimal evolution of a dynamical system over some time interval, where the system’s behavior can be influenced by a trajectory of independent control variables. These problems are often composed of highly nonlinear algebraic and differential equations for which a closed-form solution does not exist. Over the past few decades, several efficient computational solution techniques have been developed. For many problems, the best approach is to use so-called direct transcription methods, which transcribe the problem onto a discrete time domain and then solve the resulting finite-dimensional optimization problem with well-established algorithms. While this strategy is extremely effective for many applications, the algorithms can be computationally expensive if the transcribed optimization problem remains very complicated. This talk will review some of the main features of direct transcription, and then focus on sequential convex programming techniques, in which the transcribed optimization problem is solved with a series of simpler convex optimization problems. This approach often works very well in practice, and it is well-suited to some common optimal control problem structures. We will see how these methods can be used to solve a lunar landing trajectory optimization problem. Finally, we will consider the practical considerations when trying to apply fast optimal control algorithms to real space missions.


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Title:  Randomized Reduced Basis Methods for Advection-Diffusion Problems
Speaker:  Mr. Charles Beall (Stevens Institute of Technology, Hoboken, NJ)
Date: Wednesday, November 29, 2023
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)



In this project, we develop randomized model reduction methods for advection-diffusion problems with sharply discontinuous source terms. To study such problems, we must solve the advection-diffusion equation, a partial differential equation (PDE) used to model systems such as a liquid dye being dissolved in a flowing fluid, or the combination of heat conduction and convection through a medium. This PDE arises often in the sciences, from fluid dynamics [1] to semiconductor physics [2], although in such contexts, the equation is almost always unsolvable by hand, so we rely on computer algorithms to efficiently obtain accurate approximations to the solutions. Our goal is to obtain a faster result than with direct numerical simulations like finite difference or finite element schemes. We employ randomized methods from data science to allow for parallel-in-time computation [3] and generation of a reduced order model. Compared to direct simulations, the reduced model produces a solution space of much lower dimension, meaning the computational complexity is greatly reduced. Thus, simulations with the reduced model allow for a further speedup in computational runtime, with the added benefit of maintaining accuracy. As a novel contribution, we consider the case of sharp discontinuities in source functions, partition the time domain into overlapping subintervals with overlap around the discontinuities, and construct a reduced basis on each subinterval. This allows for the construction of a reduced solution that combines information from the reduced bases, rather than relying on a single reduced basis to capture information throughout the time domain. We present a test case to show that this approach can provide significant improvements in accuracy compared to the construction of only one reduced basis over the whole-time domain. 


One-sentence summary: To solve a partial differential equation modeling, e.g., the dissolving of a liquid dye in a flowing fluid or the conduction and convection of heat, we employ randomized methods from data science to facilitate parallel-in-time computation and generate a reduced order model to reduce computational complexity.   



[1] Bird, R. B., Stewart, W. E. & Lightfoot, E. N. (2007). Transport Phenomena (Revised second). John Wiley & Sons.  

[2] New, O. (2004) Derivation and numerical approximation of the quantum drift diffusion model for semiconductors, Jour. Myan. Acini. Arts & Sc., Vol. II (Part Two), No. 5.  

[3] Schleuß, J., Smetana, K., & ter Maat, L. (2022). Randomized quasi-optimal local approximation spaces in time. arXiv preprint arXiv:2203.06276. To appear in SIAM J. Sci. Comput., 2023 

Title:  Missing Data Imputation – Use Cases from the Property Insurance Industry 
Speaker:  Dr. Iordan Slavov (Hunter College)  
Date: Wednesday, November 15, 2023
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)



Missing data imputation is a well-studied problem. Many of the methods solving this problem were developed and used in medical research. But the application of these methods is seen in many other areas, e.g., in property insurance underwriting. 

Apart from very basic approaches of using the mean, mode, or other statistics of the non-missing observations for imputations, there are two other main categories of methods. The first category is the iterative approach. It is based on the idea of estimating the conditional distribution of one feature using all other available features. In one iteration, a conditional distribution estimator is trained to predict the value of each feature. This process is repeated for many iterations until it converges. This approach has been studied extensively and one of the most well-known methods is Multiple Imputation by Chained Equations (MICE).  

Lately another approach using deep generative models was developed. In this approach, a generative model is trained to generate values in missing parts based on observed values. Review of the methods and specifically for tabular data (numeric and categorical) will be followed with examples of my industry experience with them. 

Title:  Generalized Fractional Maps
Speaker:  Dr. Mark Edelman (Yeshiva University). 
Date: Wednesday, October 4, 2023
Time: 12:30 pm - 1:30 pm
Room: S-213 (Dr. Joseph Bertorelli Classroom)



The persistence of fractional calculus is because it is a natural extension of regular calculus which has a rich history, associated with the names of many great mathematicians. The recent increase in interest in fractional calculus is due to its multiple applications in various areas of science and engineering. But general properties of fractional dynamics are poorly investigated. It is easier to start the investigation of general properties by using fractional maps which we define as the discreet Volterra equations of a convolution type with the diverging kernels and absolutely converging first differences of the kernels. We show that bifurcations on a single trajectory are typical features of discrete fractional dynamics, which may be used to model unstable systems with memory. For example, the fractional logistic map may be used to model biological systems with limited lifespans which have the Gompertz distribution. We derive the asymptotic stability conditions and the equations that define asymptotically periodic and bifurcation points in generalized fractional maps. We use those equations to draw bifurcation diagrams of the fractional logistic map and to show that the fractional Feigenbaum numbers may exist and have the same values as the regular Feigenbaum numbers.

Campus Cultural Centers

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Kupferberg Holocaust Center Opens in a new window

The KHC uses the lessons of the Holocaust to educate current and future generations about the ramifications of unbridled prejudice, racism and stereotyping.

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QPAC: Performing Arts CenterOpens in a new window

QPAC is an invaluable entertainment company in this region with a growing national reputation. The arts at QPAC continues to play a vital role in transforming lives and building stronger communities.

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QCC Art Gallery

The QCC Art Gallery of the City University of New York is a vital educational and cultural resource for Queensborough Community College, the Borough of Queens and the surrounding communities.