In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implici...
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Harmonic Path Integral Diffusion (H-PID) introduces a novel approach to sampling from complex, continuous probability distributions by creating a time-dependent "bridge" from an initial point to the target d...
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Harmonic Path Integral Diffusion (H-PID) introduces a novel approach to sampling from complex, continuous probability distributions by creating a time-dependent "bridge" from an initial point to the target distribution. Formulated as a Stochastic Optimal Control problem, H-PID balances control effort and accuracy through a unique three-level integrable structure: Top Level: Potential, force, and gauge terms combine to form a linearly solvable Path Integral Control system based on Green functions. Mid Level: With quadratic potentials and affine force/gauge terms, the Green functions reduce to Gaussian forms, mirroring quantum harmonic oscillators in imaginary time. Bottom Level: For a uniform quadratic case, the optimal drift/control reduces to a convolution of the target distribution with a Gaussian kernel, enabling efficient sampling. Implementation-wise the low-level H-PID operates without neural networks, allowing it to run efficiently on standard CPUs while achieving high precision. Validated on Gaussian mixtures and CIFAR-10 images, H-PID reveals a "weighted state" parameter as an order parameter in a dynamic phase transition, signaling early completion of the sampling process. This feature positions H-PID as a strong alternative to traditional methods sampling, such as simulated annealing, particularly for applications that demand analytical control, computational efficiency, and scalability. In this manuscript, we present a novel approach for sampling from a continuous multivariate probability distribution, which may either be explicitly known (up to a normalization factor) or represented via empirical samples. Our method constructs a time-dependent bridge from a delta function centered at the origin of the state space at t = 0, optimally transforming it into the target distribution at t = 1. We formulate this as a Stochastic Optimal Control problem of the Path Integral Control type, with a cost function comprising (in its basic form) a quadratic control term
Exploring various phenomena and issues related to leaf images is paramount, particularly in segmentation and classification of such images. This study employs bibliometric analysis to delve into two overarching themes...
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Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctu...
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Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple
In this paper, we ascertain the global λ-structure of the set of positive and negative solutions bifurcating from u=0 for the semilinear elliptic BVP −dΔu=λ〈a,∇u〉+u+λu2−uqinΩ,u=0on∂Ω,according to the values of d...
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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 paper, we investigate the weak convergence of an iterative method for solving classical variational inequalities problems with semistrictly quasimonotone and Lipschitz-continuous mappings in real Hilbert space...
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The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the l...
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A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...
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A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capaci...
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