Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the se...
In this manuscript, we introduce a novel Decision Flow (DF) framework for sampling decisions from a target distribution while incorporating additional guidance from a prior sampler. DF can be viewed as an AI-driven al...
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In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-fr...
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The amygdala responds to a large variety of socially and emotionally salient environmental and interoceptive stimuli. The context in which these stimuli occur determines their social and emotional significance. In can...
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Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed...
An intelligent Levenberg-Marquardt Technique (LMT) with artificial neural network (ANN) backpropagation (BP) has been used to analyze the thermal heat and mass transfer of unsteady magnetohydrodynamics (MHD) thin film...
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Computational phenotyping is essential for biomedical research but often requires significant time and resources, especially since traditional methods typically involve extensive manual data review. While machine lear...
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Let be a collineation of PG (2, q3) of order 3 which fixes a plane of order q pointwise. The points of PG (2, q3) can be partitioned into three types with respect to orbits of : fixed points;points P with P, P, P2 dis...
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We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model b...
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We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained o...
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We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.
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