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Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…
Pedestrian attribute recognition is an important multi-label classification problem. Although the convolutional neural networks are prominent in learning discriminative features from images, the data imbalance in multi-label setting for…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
Given a collection of points $S \subset \mathbb{R}^N$, which is partitioned into $M$ overlapping subsets $\{S_i\}_{i=1}^M$, and approximate data $\{D_i\}_{i=1}^M$ associated with the subsets, one may seek a consistent merged dataset $D$…
Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for…
Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. This property can be useful in constructing energy-stable discretizations of partial differential vequations. SBP operators are defined by a…
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties…
This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
Basic principles of set theory have been applied in the context of probability and binary computation. Applying the same principles on inequalities is less common but can be extremely beneficial in a variety of fields. This paper formulates…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can…
Differential privacy (DP) data synthesizers support public release of sensitive information, offering theoretical guarantees for privacy but limited evidence of utility in practical settings. Utility is typically measured as the error on…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The Piecewise Polynomial Interpolation (PPI) function approach is aimed at solving nonlinear programming problems with disjoint feasible regions. In such problems, disjointedness is generally associated with prohibited operating zones,…
The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…