Related papers: Deterministic Genericity for Polynomial Ideals
Parametric Gr\"obner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case…
A theory of dissipative generalized continuum mechanics is presented in the framework of weakly nonlocal non-equilibrium thermodynamics. The evolution equation of microdeformation is obtained by thermodynamic principles. Conditions of…
A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
We use the theory of resultants of polynomials to study the stability of an arbitrary polynomial over a finite field, that is, the property of having all its iterates irreducible. This result partially generalises the quadratic polynomial…
In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of "generic stability" in arbitrary theories. Among other things, we show that the standard definition of generic…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…
We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical…
After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion…
For a given ergodic measure preserving transformation T of a standard measure space each finite labelled partition defines an ergodic stationary process. There is a complete metric on the space of partitions which is separable. Various…
In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…
We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…