Related papers: A new tool to study real dynamics: The Convergence…

The effectiveness of the machine learning methods for real-world tasks depends on the proper structure of the modeling pipeline. The proposed approach is aimed to automate the design of composite machine learning pipelines, which is…

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…

Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…

Modern deep models are trained on large real-world datasets, where data quality varies and redundancy is common. Data-centric approaches such as dataset pruning have shown promise in improving training efficiency and model performance.…

Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…

Event-driven molecular dynamics is a valuable tool in condensed and soft matter physics when particles can be modeled as hard objects or more generally if their interaction potential can be modeled in a stepwise fashion. Hard spheres model…

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…

Imitation learning is a paradigm to address complex motion planning problems by learning a policy to imitate an expert's behavior. However, relying solely on the expert's data might lead to unsafe actions when the robot deviates from the…

A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…

We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…

It has been known for some time that the topological entropy is a nondecreasing function of the parameter in the real quadratic family, which corresponds to the intuitive idea that more nonlinearity induces more complex dynamical behavior.…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…

Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…

Bifurcation diagram is a powerful tool that visually gives information about the behavior of the equilibrium points of a dynamical system respect to the varying parameter. This paper proposes an educational algorithm by which the local…

The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…