相关论文: Doob's maximal identity, multiplicative decomposit…
Motivated by bases of representations compatible with the PBW filtration for basic Lie superalgebras by Kus and Fourier, we generalise the construction of degenerations of flag varieties via favourable modules to the super setup. In the…
Noisy gradient descent and its variants are the predominant algorithms for differentially private machine learning. It is a fundamental question to quantify their privacy leakage, yet tight characterizations remain open even in the…
Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference,…
We study tropicalization of symplectic flag varieties with respect to the Pl\"ucker embedding. We identify a particular maximal prime cone in this tropicalization by explicitly giving its facets. For every interior point of this maximal…
In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most…
Most methods of exact probability propagation in Bayesian networks do not carry out the inference directly over the network, but over a secondary structure known as a junction tree or a join tree (JT). The process of obtaining a JT is…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…
We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. This dual is widely used in decomposition methods for…
Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from shifting property of the…
We prove the $L^p$ boundedness of a maximal operator associated with a dyadic frequency decomposition of a Fourier multiplier, under a weak regularity assumption.
We study the problem of differentially private (DP) secure multiplication in distributed computing systems, focusing on regimes where perfect privacy and perfect accuracy cannot be simultaneously achieved. Specifically, N nodes…
Cross-modal image synthesis is a topical problem in medical image computing. Existing methods for image synthesis are either tailored to a specific application, require large scale training sets, or are based on partitioning images into…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators, for instance as local…
We argue how boundary B-type Landau-Ginzburg models based on matrix factorizations can be used to compute exact superpotentials for intersecting D-brane configurations on compact Calabi-Yau spaces. In this paper, we consider the dependence…
We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…
Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…
In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the…
When extending the Ehrhart lattice point enumerator $L_P(t)$ to allow real dilation parameters $t$, we lose the invariance under integer translations that exists when $t$ is restricted to be an integer. This paper studies this phenomenon;…