Related papers: Convex Environmental Contours for Non-Stationary P…
In this paper, we create optimal, collision-free, time-dependent trajectories through cluttered dynamic environments. The many spatial and temporal constraints make finding an initial guess for a numerical solver difficult. Graphs of Convex…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Being able to safely operate for extended periods of time in dynamic environments is a critical capability for autonomous systems. This generally involves the prediction and understanding of motion patterns of dynamic entities, such as…
Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…
The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…
The convex analytic method has proved to be a very versatile method for the study of infinite horizon average cost optimal stochastic control problems. In this paper, we revisit the convex analytic method and make three primary…
Turbulent convection models are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied in calculations of stellar structure and evolution. In order to…
In this work, the issue of obtaining consistent parameter estimators for nonlinear regression models where the regressors are second-order modulus functions is explored. It is shown that consistent instrumental variable estimators can be…
We present a framework to obtain valid inequalities for a reverse convex set: the set of points in a polyhedron that lie outside a given open convex set. Reverse convex sets arise in many models, including bilevel optimization and…
This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first…
Compositional convection is atmospheric mixing driven by density variations caused by compositional gradients. Previous studies have suggested that compositional gradients of atmospheric trace species within planetary atmospheres can impact…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
How ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environment. Here, we introduce a theoretical framework for…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We…
Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…