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We will discuss methods to craft your 1-page resume for effective industry job/internship searches. What are some of the essential ingredients that should be there in such a resume? Which of your experiences should you highlight? How should you talk about your teaching/TA experience? And what are some details best to avoid?

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Given a pair of time series over the same time period, we are interested in studying how the periodicity of one influences the periodicity of the other. For instance, consider the average amount of rainfall per day and the average number of umbrellas used per day over time. One would expect these series to occur at similar frequencies, while on the other hand, we'd expect the frequencies of average amount of rainfall and average number of cookies eaten over time to be less similar. There are several known methods to measure the similarity between a pair of time series. While many experimental results show robustness of these similarity measures, we have yet to find any measures with known theoretical stability results.

Persistence homology from the field of topological data analysis has been utilized to construct a scoring function with theoretical proofs of stability that quantifies the periodicity of a single univariate time series. Building on this concept, we propose a conditional periodicity score that quantifies the periodicity of one univariate time series given another. We introduce several mathematical statements we aim to prove that demonstrate theoretical stability of our conditional scoring function, as well as a pseudocode for computing our conditional periodicity score on pairs of discrete time series. We end with some preliminary findings.

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Continuation of the discussion from last week, and presentation of results.

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Motivated by the application of shuttle bus systems such as those at airports, and ride-sharing services like Uber, we propose a dynamic pricing control model by applying a strategic joining/balking scheme in which the fees for each customer and time of service commencement depend on their experienced waiting time cost in batch service (shuttle) systems. In this model, the monopolist sets the fee for each customer so that all customers on the same shuttle have equal utility (including waiting costs). If the total time cost for waiting customers exceeds a certain threshold, the monopolist allows the shuttle to depart, even if the number of customers is less than the full capacity (i.e., early departure) of the shuttle, enabling the fair determination of fees.

This study aims to verify the superiority of the dynamic pricing control model. We present a unique Nash equilibrium strategy, an algorithm for the transition probability, and effective approximations for the expected inter-arrival times of customers, conditional on the occurrence of early departure under the restriction that early departure can be executed only immediately before the arrival of the next customer. Then, we derive several performance measures to evaluate the dynamic pricing control model. Through numerical experiments, we confirm that our analytical results closely align with those of the general model, in which the timing of early departure is not restricted—implying the usefulness of our theoretical analysis. Moreover, we demonstrate that the dynamic pricing control model is superior to the conventional fixed pricing control model in terms of fairness to customers and performance efficiency. The proposed model benefits customers, society, and the monopolist in the long run, as it enhances the overall quality of services and customer satisfaction, reduces waiting costs, and improves revenue.

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We are at the crossroads of powerful currents in science and technology, spurred by recent advances in both neuroscience research, and neuromorphic engineering. A recent focus on brain studies has produced a wealth of new, multi-modal structural and functional neural data. At the same time, advances in electronics and the search for unconventional computational paradigms led to the creation of capable commercial neuromorphic systems. We see a natural match between hardware realizations of data-based neuronal models produced by the neuroscience research endeavor and the neuromorphic hardware abstractions forming the foundation of current and future neuromorphic chips. We also see a new paradigm in computing abstractions, possibly advancing beyond the von Neumann paradigm, and through Moore's scaling law.

One major unresolved question is the practical issue of programming neuromorphic systems. How can we efficiently combine neuromorphic modules to achieve specific dynamics, and later, specific tasks by that dynamics? As with the original development of computers, tools from applied math, with 70–80 years additional development past the complement of the 1940s will be crucial for this: dynamical systems theory; nonlinear optimization; linear and nonlinear control; sensitivity analysis; multi-scale cost functions. There is also a broader question: what is computable with these new systems? Neuromorphic system elements have their own dynamics, which is steerable to some degree. How close can such systems approximate dynamics of interest to us? What are appropriate cost functions to assess levels of approximation? Are there diffeomorphisms between neuromorphic systems and systems of interest?

I will report on our lab's work, mainly with Intel's Loihi along these questions and our plans for future work.

Abstract (click to read)

We are at the crossroads of powerful currents in science and technology, spurred by recent advances in both neuroscience research, and neuromorphic engineering. A recent focus on brain studies has produced a wealth of new, multi-modal structural and functional neural data. At the same time, advances in electronics and the search for unconventional computational paradigms led to the creation of capable commercial neuromorphic systems. We see a natural match between hardware realizations of data-based neuronal models produced by the neuroscience research endeavor and the neuromorphic hardware abstractions forming the foundation of current and future neuromorphic chips. We also see a new paradigm in computing abstractions, possibly advancing beyond the von Neumann paradigm, and through Moore's scaling law.

One major unresolved question is the practical issue of programming neuromorphic systems. How can we efficiently combine neuromorphic modules to achieve specific dynamics, and later, specific tasks by that dynamics? As with the original development of computers, tools from applied math, with 70–80 years additional development past the complement of the 1940s will be crucial for this: dynamical systems theory; nonlinear optimization; linear and nonlinear control; sensitivity analysis; multi-scale cost functions. There is also a broader question: what is computable with these new systems? Neuromorphic system elements have their own dynamics, which is steerable to some degree. How close can such systems approximate dynamics of interest to us? What are appropriate cost functions to assess levels of approximation? Are there diffeomorphisms between neuromorphic systems and systems of interest?

I will report on our lab's work, mainly with Intel's Loihi along these questions and our plans for future work.

Abstract (click to read)

When individuals express preferences using a ranking, a natural goal is to aggregate the data into an overall ranking of objects from best to worst. However, the inferred ranks associated with each object are often uncertain (or even indistinguishable). In this talk, I'll present a Bayesian statistical model for inferring rank-clusters from rankings that permits more interpretable and honest summaries of the observed data. The model is applied to real datasets on ranked-choice voting and social surveys.

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This presentation dives into the world of minimal homotopy in the plane, tracing its history and significance in math. We kick things off by defining homotopy and minimal homotopy, and why continuous paths and deformations are key to deeper understanding. We'll look at major breakthroughs, including Douglas and Radó's work on the Plateau problem, to show how minimal homotopy has evolved. Additionally, we will explore recent advancements, including new algorithms for computing minimal homotopy areas, and extend the conversation to higher dimensions, discussing the challenges and potential extensions of minimal homotopy. To wrap it up, we'll outline future research directions and open questions, emphasizing the ongoing relevance and potential applications of minimal homotopy in both theoretical and applied math. This overview aims to give researchers and enthusiasts alike a deeper understanding of minimal homotopy, its history, and future potential.

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Continuation and wrap-up of previous week's talk

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This presentation examines the stability and convergence of Neural Field Self-Organizing Maps (NFSOMs), which integrate neural field theory with the dynamic SOM algorithm. Using Lyapunov's stability theory, we derive local stability conditions for NFSOMs and validate them through numerical simulations. The findings emphasize the importance of balancing lateral excitation and inhibition to maintain stability. Theoretical results are applied to a computational model, providing testable stability criteria and insights into optimizing NFSOMs for computational neuroscience. Numerical experiments confirm that stability conditions are crucial for successful self-organization.

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For both voluntary action and regulatory compliance, large organizations need detailed information about their direct emissions (from their facilities and properties) and indirect emissions (attributable to their activities but occurring outside their facilities). However, estimating indirect emissions is costly and complex, often involving the environmental footprint of thousands of products and services within global supply chains. In response, we develop a heuristic approach to estimating Scope 3 emissions that combines life cycle assessment and data analytics. This approach leverages product-level information (unit cost, quantity consumed, and average lifecycle emissions of materials) to derive scientifically grounded estimates of aggregate and distributed emissions. We apply this approach to the healthcare sector, revealing different mitigation priorities compared to traditional methods.