We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each ti...
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We consider the construction of point processes from tilings, with equal-volume tiles, of d-dimensional Euclidean space Rd. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are “superhomogeneous” (or “hyperuniform”)—i.e., for which the structure factor S(k) vanishes when the wave vector k tends to zero. The exponent γ characterizing the leading small-k behavior, S(k→0)∝kγ, depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent γ=4 for any tiling in which the shapes and orientations of the tiles are short-range correlated. Smaller exponents in the range 4−d<γ<4 (and thus always superhomogeneous for d≤4) may be obtained in the case that the latter quantities have long-range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S(k) exactly. Our results provide an explicit analytical construction of point processes with γ>4. Applications to condensed matter physics, and also to cosmology, are briefly discussed.
The isothermal compressibility (i.e., the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal near ambient conditions. This anomalous non-monotonic temperature dependence is...
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In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatiall...
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In Table I and the caption of Fig. 8 of Ref. 1, the numerical value of the percolation threshold ηc of three-dimensional overlapping spheres as determined via t
In Table I and the caption of Fig. 8 of Ref. 1, the numerical value of the percolation threshold ηc of three-dimensional overlapping spheres as determined via t
Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using...
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The design and implementation of a new framework for adaptive mesh refinement calculations are described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design ...
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In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency osci...
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B. D. Coller, P. Holmes, John Lumley; Erratum: ‘‘Interaction of adjacent bursts in the wall region’’ [Phys. Fluids 6, 954 (1994)], Physics of Fluids, Volume 9,
B. D. Coller, P. Holmes, John Lumley; Erratum: ‘‘Interaction of adjacent bursts in the wall region’’ [Phys. Fluids 6, 954 (1994)], Physics of Fluids, Volume 9,
In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective...
In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.
We present BEAST DB, an open-source database comprised of ab initio electrochemical data computed using grand-canonical density functional theory in implicit solvent at consistent calculation parameters. The database ...
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