Related papers: On parametrization, optimization and triviality of…
Scherk-Schwarz compactification in string theory can be defined as orbifolding by an R symmetry, a symmetry that acts differently on bosons and fermions. Such a symmetry can arise in many situations, including toroidal and orbifold…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
Randomized smoothing, a method to certify a classifier's decision on an input is invariant under adversarial noise, offers attractive advantages over other certification methods. It operates in a black-box and so certification is not…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving…
Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Sz\'ekelyhidi, as the limit of the associated $\mathbb{C}^*$-actions. We show that there actually…
A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of MAOOAM, a coupled ocean-atmosphere model of intermediate complexity. Two physically-based parameterizations are investigated, the…
We prove various results involving arcs - which generalise test configurations - within the theory of K-stability. Our main result characterises coercivity of the Mabuchi functional on spaces of Fubini-Study metrics in terms of uniform…
Boardman, Johnson, and Wilson gave a precise formulation for an unstable algebra over a generalized cohomology theory. Modifying their definition slightly in the case of complex K-theory by taking into account its periodicity, we prove that…
In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
I review the basic idea of $k_{\perp}$-factorization and its relation to collinear factorization. Theoretical results in resummed perturbation theory are summarized and the example of the heavy-flavour structure functions is explicitly…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding…
This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of…