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Future lepton colliders such as the FCC-ee, CEPC, ILC, or a muon collider will collect large data samples that allow precision physics studies with unprecedented accuracy, especially when the data is collected by innovative state-of-the-art detectors. An electromagnetic calorimeter based on scintillating crystals, designed to separately record Cherenkov and scintillation light, can achieve precision measurements of electrons and photons without sacrificing jet energy resolution, given adequate light collection efficiency and separation. This paper presents initial measurements from a program aimed at developing such a calorimeter system for future colliders. We focus on using PbF2 crystals to enhance the understanding of Cherenkov light collection, marking the first step in this endeavor., Comment: 10 pages

We establish a recursive relation for the bipartition number $p_2(n)$ which might be regarded as an analogue of Euler's recursive relation for the partition number $p(n)$. Two proofs of the main result are proved in this article. The first one is using the generating function, and the second one is using combinatoric objects (called ``symbols'') created by Lusztig for studying representation theory of finite classical groups.

This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both geometric control theory and statistical shape data analysis. Our work encompasses a rigorous proof for the existence of global solutions in H\"{o}lder spaces for the gradient flow. The asymptotic limits of these solutions establish the existence of the spline interpolation versus least-squares fitting problem on smooth Riemannian manifolds, offering a comprehensive solution. Notably, the constructive nature of the proof suggests potential numerical schemes for finding solutions., Comment: the article is merged into another one of the authors' papers, arXiv:2312.10513

In this paper, we resolve problems of spline interpolation, regardless of whether least-squares fitting is incorporated, on smooth Riemannian manifolds. Our approach leverages the concept of gradient flows for successively connected curves or networks, offering a fresh perspective on addressing such challenges. Notably, this method extends to the problem of spline interpolation on Lie groups, commonly encountered in mechanical optimal control theory formulations, thus contributing to both geometric control theory and statistical shape data analysis. We rigorously establish the existence of global solutions in H\"{o}lder spaces for the gradient flow, with the asymptotic limits of these solutions confirming the existence to the problem of spline interpolation. This comprehensive solution underscores the constructive nature of our proof, hinting at potential numerical schemes for discovering solutions.

An almost $k$-cover of the hypercube $Q^n = \{0,1\}^n$ is a collection of hyperplanes that avoids the origin and covers every other vertex at least $k$ times. When $k$ is large with respect to the dimension $n$, Clifton and Huang asymptotically determined the minimum possible size of an almost $k$-cover. Central to their proof was an extension of the LYM inequality, concerning a weighted count of hyperplanes. In this paper we completely characterise the hyperplanes of maximum weight, showing that there are $\binom{2n-1}{n}$ such planes. We further provide stability, bounding the weight of all hyperplanes that are not of maximum weight. These results allow us to effectively shrink the search space when using integer linear programming to construct small covers, and as a result we are able to determine the exact minimum size of an almost $k$-cover of $Q^6$ for most values of $k$. We further use the stability result to improve the Clifton--Huang lower bound for infinitely many choices of $k$ in every sufficiently large dimension $n$., Comment: 15 pages

Binarized Neural Networks (BNNs) significantly reduce the computation and memory demands with binarized weights and activations compared to full-precision NNs. Executing a layer in a BNN on different devices of a heterogeneous multiprocessor platform consisting of CPU and GPU can affect the inference performance, i.e., accuracy and latency. Usually, a heterogeneous HW platform consisting of a CPU and a GPU is available to execute the BNN workloads. However, to use the heterogeneous HW effectively, it is necessary to find an efficient strategy for BNN workload mapping. In this work, we propose a framework that generates efficient BNN layer-to-device mappings (i.e. suitable parallel configuration for each layer of the model) for execution platforms comprised of CPU and CUDA-capable GPU. We evaluate our proposed framework with two BNN architectures using two well-known datasets, Fashion-MNIST and CIFAR-10, on three hardware platforms with different characteristics. The results show that compared to running a fully-parallelized GPU implementation, our framework generates an efficient configuration up to 2x, 2.6x and 11.8x faster on our tested hardware respectively., Comment: This paper has been accepted for presentation in the 5th Workshop on Accelerated Machine Learning (AccML), co-located with HiPEAC23. 8 Pages, 5 figures

We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, e.g., conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions.