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1. Can you hear the Planck mass?

   https://doi.org/10.1007/JHEP08(2024)123  

   De_Luca, G Bruno; De_Ponti, Nicolò; Mondino, Andrea; Tomasiello, Alessandro (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> For the Laplacian of ann-Riemannian manifoldX, the Weyl law states that thek-th eigenvalue is asymptotically proportional to (k/V)^2/n, whereVis the volume ofX. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification onXbehaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion onXis ergodic, for largekthe eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volumeV, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we callweighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only forp= 6,7,8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory. 

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2. Can one hear the shape of a crystal?

   https://doi.org/10.1103/PhysRevResearch.6.043124  

   Wang, Haina; Torquato, Salvatore (November 2024, Physical Review Research)

   Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question “Can one hear the shape of a drum?” concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in $d$-dimensional Euclidean space ${\mathbb{R}}^d$is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function $g_2\left(r\right)$. While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an $n$-particle basis ( $n\ge 2$). Here, we ask what is $n_{\text{min}}\left(d\right)$, the minimum value of $n$for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension $d$? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multiparticle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral four-, three- and two-particle bases in one, two, and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identically the same $g_2\left(r\right)$'s for all values of $r$. Based on our analyses, we conjecture that $n_{\text{min}}\left(d\right)=4$, 3, 2 for $d=1$, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with $n=3$, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radial pair information. Published by the American Physical Society2024 

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3. Look Hear: Gaze Prediction for Speech-Directed Human Attention

   https://doi.org/10.1007/978-3-031-72946-1_14  

   Mondal, Sounak; Ahn, Seoyoung; Yang, Zhibo; Balasubramanian, Niranjan; Samaras, Dimitris; Zelinsky, Gregory; Hoai, Minh (October 2024, Lecture notes in computer science)
4. SHAPER: can you hear the shape of a jet?

   https://doi.org/10.1007/JHEP06(2023)195  

   Ba, Demba; Dogra, Akshunna S.; Gambhir, Rikab; Tasissa, Abiy; Thaler, Jesse (July 2023, Journal of High Energy Physics)

   The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover’s Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (Shaper), which is a general framework for defining and computing shape-based observables. Shaper generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the Shaper framework by performing empirical jet substructure studies using several examples of new shape-based observables. 

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5. An Eocene insect could hear conspecific ultrasounds and bat echolocation

   https://doi.org/10.1016/j.cub.2023.10.040  

   Woodrow, Charlie; Celiker, Emine; Montealegre-Z, Fernando (November 2023, Current Biology)