Related papers: Collisions between kinks with long-range tails: a …
This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the…
Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which…
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to…
Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…
We analyse a generalised Fokker-Planck equation by making essential use of its linearisability through a Cole-Hopf transformation. We determine solutions of travelling wave and multi-kink type by resorting to a geometric construction in the…
We construct a modified non-BPS sine-Gordon theory which supports stable static kinks of arbitrary topological degree $N$. We use this toy model to study problems which are interesting for higher-dimensional soliton theories supporting…
In this work we present an approach which can be systematically used to construct nonlinear systems possessing analytical multi-kink profile configurations. In contrast with previous approaches to the problem, we are able to do it by using…
In this paper, kink scattering in the dimensional reduction of the bosonic sector of a one-parameter family of generalized Wess-Zumino models with three vacuum points is discussed. The value of the model parameter determines the specific…
We study the scattering of the $\varphi^8$ kinks off each other, namely, we consider those $\varphi^8$ kinks that have power-law asymptotics. The slow power-law fall-off leads to a long-range interaction between the kink and the antikink.…
Forecast combination has been proven to be a very important technique to obtain accurate predictions. In many applications, forecast errors exhibit heavy tail behaviors for various reasons. Unfortunately, to our knowledge, little has been…
We study a variety of supersymmetric systems describing sixth-order interactions between two coupled real superfields in 2+1 dimensions. We search for BPS domain ribbon solutions describing minimum energy static field configurations that…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…
Real-world datasets often exhibit a long-tailed distribution, where vast majority of classes known as tail classes have only few samples. Traditional methods tend to overfit on these tail classes. Recently, a new approach called Imbalanced…
Higher-order scalar field models in two dimensions, including the $\phi^8$ model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found.…
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the…
Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently representing…
Collision checking is a computational bottleneck in motion planning, requiring lazy algorithms that explicitly reason about when to perform this computation. Optimism in the face of collision uncertainty minimizes the number of checks…
The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…