Related papers: Higher Order Rigidity and Energy
Constrained reinforcement learning is to maximize the expected reward subject to constraints on utilities/costs. However, the training environment may not be the same as the test one, due to, e.g., modeling error, adversarial attack,…
We obtain a full characterization of consistency with respect to higher-order stochastic dominance within the rank-dependent utility model. Different from the results in the literature, we do not assume any condition on the utility…
New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.'s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
This study presents the framework to perform a stability analysis of nonlocal solids whose response is formulated according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…
A successor-invariant first-order formula is a formula that has access to an auxiliary successor relation on a structure's universe, but the model relation is independent of the particular interpretation of this relation. It is well known…
The regularity of the solution of elliptic partial differential equa- tions in a polygonal domain with re-entrant corners is, in general, reduced compared to the one on a smooth convex domain. This results in a best approximation property…
In order to design tougher materials, it is crucial to understand the relationship between their composition and their resistance to fracture. To this end, we investigate the fracture toughness of usual sodium silicate glasses (NS) and…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
We study the coboundary expansion property of product codes called product expansion, which played a key role in all recent constructions of good qLDPC codes. It was shown before that this property is equivalent to robust testability and…
The $k$-dimensional functional order property ($\text{FOP}_k$) is a combinatorial property of a $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf, which identified $\text{NFOP}_2$ as a ternary analogue of stability in…
In this paper we criticize the robustness measure traditionally employed to assess the performance of machine learning models deployed in adversarial settings. To mitigate the limitations of robustness, we introduce a new measure called…
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern…
The development of instability in the dynamics of theories with higher derivatives is traced in detail in the framework of the Pais-Uhlenbeck fourth oder oscillator. For this aim the external friction force is introduced in the model and…