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1. Discrete gravity

   https://doi.org/10.1007/JHEP11(2021)013  

   Chamseddine, Ali H.; Mukhanov, Viatcheslav (November 2021, Journal of High Energy Physics)

   A bstract We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced. 

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2. Locked fronts in a discrete time discrete space population model

   https://doi.org/10.1007/s00285-022-01802-7  

   Holzer, Matt; Richey, Zachary; Rush, Wyatt; Schmidgall, Samuel (January 2022, Journal of mathematical biology)
3. Discrete bulk reconstruction

   https://doi.org/10.1007/JHEP04(2023)037  

   Aaronson, Scott; Pollack, Jason (April 2023, Journal of High Energy Physics)

   A bstract According to the AdS/CFT correspondence , the geometries of certain spacetimes are fully determined by quantum states that live on their boundaries — indeed, by the von Neumann entropies of portions of those boundary states. This work investigates to what extent the geometries can be reconstructed from the entropies in polynomial time . Bouland, Fefferman, and Vazirani (2019) argued that the AdS/CFT map can be exponentially complex if one wants to reconstruct regions such as the interiors of black holes. Our main result provides a sort of converse: we show that, in the special case of a single 1D boundary divided into N “atomic regions”, if the input data consists of a list of entropies of contiguous boundary regions, and if the entropies satisfy a single inequality called Strong Subadditivity, then we can construct a graph model for the bulk in linear time. Moreover, the bulk graph is planar, it has O ( N 2 ) vertices (the information-theoretic minimum), and it’s “universal”, with only the edge weights depending on the specific entropies in question. From a combinatorial perspective, our problem boils down to an “inverse” of the famous min-cut problem: rather than being given a graph and asked to find a min-cut, here we’re given the values of min-cuts separating various sets of vertices, and need to find a weighted undirected graph consistent with those values. Our solution to this problem relies on the notion of a “bulkless” graph, which might be of independent interest for AdS/CFT. We also make initial progress on the case of multiple 1D boundaries — where the boundaries could be connected via wormholes — including an upper bound of O ( N 4 ) vertices whenever an embeddable bulk graph exists (thus putting the problem into the complexity class NP). 

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4. Bayesian Pyramids: identifiable multilayer discrete latent structure models for discrete data

   https://doi.org/10.1093/jrsssb/qkad010  

   Gu, Yuqi; Dunson, David B (March 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of identifiable multilayer (potentially deep) discrete latent structure models for discrete data, termed Bayesian Pyramids. We establish the identifiability of Bayesian Pyramids by developing novel transparent conditions on the pyramid-shaped deep latent directed graph. The proposed identifiability conditions can ensure Bayesian posterior consistency under suitable priors. As an illustration, we consider the two-latent-layer model and propose a Bayesian shrinkage estimation approach. Simulation results for this model corroborate the identifiability and estimatability of model parameters. Applications of the methodology to DNA nucleotide sequence data uncover useful discrete latent features that are highly predictive of sequence types. The proposed framework provides a recipe for interpretable unsupervised learning of discrete data and can be a useful alternative to popular machine learning methods. 

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5. Power Converter and Discrete Device Optimization Utilizing Discrete Time State-Space Modeling

   https://doi.org/10.1109/COMPEL52896.2023.10221030  

   Baxter, Jared A; Costinett, Daniel J (June 2023, 2023 IEEE 24th Workshop on Control and Modeling for Power Electronics (COMPEL))

   Broad-scale modeling and optimization play a vital role in the design of advanced power converters. Optimization is normally implemented via brute force iterations of design variables or utilizing metaheuristic techniques which are time consuming for a wide range of potential topologies, device implementations, and operating points. Recently, discrete time state-space modeling has shown merits in rapid analysis and generality to arbitrary circuit topologies but has not yet been utilized under rapid optimization techniques across multiple converter parameters. In this work, we investigate methods to incorporate rapid gradient-based optimization techniques to leverage discrete time state-space modeling and showcase the approach in the power converter design process. The method is validated on a 48-to-1V converter designed using the proposed techniques. 

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