Related papers: Softmax as a Lagrangian-Legendrian Seam
Small-scale liquid flows on solid surfaces provide convincing details in liquid animation, but they are difficult to be simulated with efficiency and fidelity, mostly due to the complex nature of the surface tension at the contact front…
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric…
Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level…
A model, based on Gribov's Reggeon calculus, is proposed and applied to processes of soft diffraction at high energies. It is shown that by accounting for absorptive corrections for all legs of triple-Regge and loop diagrams a good…
Recent neural network sequence models with softmax classifiers have achieved their best language modeling performance only with very large hidden states and large vocabularies. Even then they struggle to predict rare or unseen words even if…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
Mixture-of-experts models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent gating mechanism. These models have become increasingly…
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as…
In a supersymmetric (SUSY) theory, the IR-contributions to the Higgs mass are calculable below the mediation scale $\Lambda_{\text{UV}}$ in terms of the IR field content and parameters. However, logarithmic sensitivity to physics at…
In this paper, we address the classical problem of maximum-likelihood (ML) detection of data in the presence of random phase noise. We consider a system, where the random phase noise affecting the received signal is first compensated by a…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the…
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system…
A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an…
We formulate a stochastic process, FiLex, as a mathematical model of lexicon entropy in deep learning-based emergent language systems. Defining a model mathematically allows it to generate clear predictions which can be directly and…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
We extend a heuristic method for automatic dimensionality selection, which maximizes a profile likelihood to identify "elbows" in scree plots. Our extension enables researchers to make automatic choices of multiple hyper-parameters…
Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…