Aninda Sinha’s Post

Here is a link to a paper by prof. Avi Berman and myself in spectral graph theory. We defined a new class of graphs and showed some interesting properties and results. https://lnkd.in/dfTdr6Un

“05C50 Online” Title: New results on graph partitions and Fiedler theory Speaker: Enide Andrade (University of Aveiro) Synopsis: In this seminar, we recall the spectral partitioning method based on a Fiedler vector, i.e., an eigenvector corresponding to the second smallest eigenvalue of the Laplacian matrix of a graph. This problem corresponds to the minimization of a quadratic form associated with this matrix, under a certain constraint. We introduce a similar problem using the $\ell_1$-norm to measure distances and compare the optimal solutions for both problems. Fri 01/26 at 11AM ET The World Wide Web, visit: https://lnkd.in/erP29fE6 P.S. @umanitoba

📃Scientific paper: A First Order Theory of Diagram Chasing;Une théorie du premier ordre pour la chasse au diagramme Abstract: International audience; This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order theory, and we study the models and decidability of this theory. The longer-term motivation of this work is the design of a computer-aided instrument for writing reliable proofs in homological algebra, based on interactive theorem provers. Continued on ES/IODE ➡️ https://etcse.fr/5N9vx ------- If you find this interesting, feel free to follow, comment and share. We need your help to enhance our visibility, so that our platform continues to serve you.

I am happy to share our latest paper titled "Towards All Categorical Symmetries in 2+1 Dimensions", which has been available on arXiv for a few weeks now. In this work, we investigate the most general gauging operations in 2+1 dimensional oriented field theories with finite symmetry groups, which correspond to gapped boundary conditions in 3+1 dimensional Dijkgraaf-Witten theory. The classification is achieved by enumerating 2+1 dimensional oriented topological quantum field theories that cancel the 't Hooft anomaly associated with the symmetry. This framework is rigorously formulated using twisted crossed extensions of modular fusion categories and projective 3-representations. Additionally, we explore the resulting fusion of 2-category symmetries and argue that this framework captures all possible categorical symmetries in 2+1 dimensional oriented field theories.

Second draft of my second paper (Co-authored with Krzysztof Krupiński) 'Maximal stable quotients of invariant types in NIP theories' is now published on arXiv and is to appear on the Journal of Symbolic Logic. La segunda versión de mi segundo artículo "Maximal stable quotients of invariant types in NIP theories" se encuentra ya en arXiv y será publicada en Journal of Symbolic Logic.

Here is our new work on Quantum Chaos from String scattering amplitudes. We show that while usual string amplitudes (Veneziano, Virasoro-Shapiro) show no chaotic behaviour, the generic highly excited string (dual to black holes in string theory through the string-Black hole correspondence as prescribed long ago by Susskind-Horowitz-Polchinski) scattering into multiple tachyons provide us with examples of scattering amplitudes, which can be characterized as Chaotic scattering amplitudes. We devise a way to study the complexity (in Krylov basis) for these scattering amplitudes and find the existence of a pronounced peak before saturation, which is a clear signature of chaos. More to be reported along these directions in the upcoming months. Done with Aneek Jana, an undergrad from Indian Institute of Science, Bangalore. https://lnkd.in/dA7bcdzG

I am pleased to share that our recent work, in collaboration with Xavier Bekaert and Hamid Afshar, is now available on arXiv: https://lnkd.in/djBqWb6K 👉 Due to a technical issue on arXiv, preprints scheduled to appear on October 1st were announced with a delay. As a result, many people may not have seen our paper, so I would appreciate it if you could share it with interested readers. 👈 In this work, we investigate all minimal conformal extensions of the Carroll algebra in arbitrary spacetime dimensions and identify their infinite-dimensional extensions. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.

Happy to share that our article https://lnkd.in/gp68j4ZX on Gaussian approximation was recently accepted at Annals of Statistics. I am very thankful to Soham Bonnerjee and my PhD adviser Wei Biao Wu for all their contributions with this article. What is a Gaussian approximation? The basic principle states that under large sample size, often certain statistic (read function of data) start behaving like normal distribution regardless of original distribution of the data. Generally this comes under the umbrella of invariance principle. It's funny how I used to motivate invariance principle in my talks by picking up the most basic coloring problem. "If you remove two opposite corners of a 8x8 chessboard, you cannot cover the rest with 31 Dominoes" Most popular amongst such approximations is Central Limit Theorem whereas the type of result we prove is more general under more moment assumptions. One of the main papers from my thesis proves such approximation however the result remained only existential. In this new article, thanks to some new technical innovation we were able to establish a construction strategy while keeping the sharp rate of the approximation intact.

Very proud to share my recent work in collaboration with Prof. D. L. Karabalis. In this work, we study the linear #SDOF and #MDOF problems for #StructuralDynamics in full mathematical rigor, and, as a result, we obtain a family of numerical methods that vastly outperform the classical Newmark-type time-step methods. In part I, we obtain the Weak Form of the equations of motion for both the SDOF and MDOF problems for #StructuralDynamics, and show how to obtain particular numerical algorithms and their bounds. In part II we construct a particular case of an algorithm for the SDOF problem, using Bernstein polynomials for interpolation. This algorithm has two free parameters contributing to convergence: the degree of approximation (unlike traditional timestep methods where interpolation is restricted to second-degree polynomials) and the timestep. The estimates provided in the article show very fast convergence both when the polynomial degree increases and/or the timestep goes to 0. The power of the algorithm can already be seen in the graph of the error in eigenperiod estimation. We consider an undamped SDOF system, for which initial displacement is set to 1, and initial velocity and external force are both set to 0. The time of the first full oscillation is then calculated for different degrees of polynomial approximation p and timestep h. We plot the error rate in the estimation of the eigenperiod. The error rate of Newmark-type methods is somewhere on the top left of the chart, which is in log-scale. We also calculate the amplitude at the estimated eigenperiod and plot the corresponding error rate. In part III, to appear soon, we will present an exhaustive numerical study using a codebase that will be made available on Gitlab. A first version of the codebase is already available on Github. The papers are on the arXiv: https://lnkd.in/drWzZv75 https://lnkd.in/d3fqmEGj The preliminary version of the codebase is on Github: https://lnkd.in/dd6iS8ex #CivilEngineering #MechanicalEngineering #research #opensource #numericalmethods #numericalmethod #numericalanalysis