Related papers: Continuity conditions weaker than lower semi-conti…
Whether language models can systematically generalize remains actively debated. Yet empirical performance is jointly shaped by multiple factors such as training data, training paradigms, and inference-time strategies, making failures…
Typed feature structures are used extensively for the specification of linguistic information in many formalisms. The subsumption relation orders TFSs by their information content. We prove that subsumption of acyclic TFSs is well-founded,…
We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…
Stability results for extremum seeking control in $\mathbb{R}^n$ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets…
We study whether a logic based on team semantics can be enriched with a conditional satisfying minimal requirements--namely, preservation of the closure property of the logic, Modus Ponens, and the Deduction Theorem. We show that such…
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…
The standard approach to supervised classification involves the minimization of a log-loss as an upper bound to the classification error. While this is a tight bound early on in the optimization, it overemphasizes the influence of…
This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…
In this work, we study the external and internal stability of minimal solutions to set-valued optimization problems in a new functional framework. We consider perturbations on both the objective function and the admissible domain. To…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
We study the termination problem of the chase algorithm, a central tool in various database problems such as the constraint implication problem, Conjunctive Query optimization, rewriting queries using views, data exchange, and data…
In this paper, we further develop the coordination control framework for discrete-event systems with both complete and partial observation. A new weaker sufficient condition for the computation of the supremal conditionally controllable…
Three distinct phenomena complicate statistical causal analysis: latent common causes, causal cycles, and latent selection. Foundational works on Structural Causal Models (SCMs), e.g., Bongers et al. (2021, Ann. Stat., 49(5): 2885-2915),…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…
We present a lattice of distributed program specifications, whose ordering represents implementability/refinement. Specifications are modelled by families of subsets of relative execution traces, which encode the local orderings of state…
It is known that supercyclicity implies strong stability. It is not known whether weak l-sequential supercyclicity implies weak stability. In this paper we prove that weak l-sequential supercyclicity implies weak quasistability. Corollaries…