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Model-theoretic imaginaries and coherent sheaves
Get PDFCategories of imaginaries (imaginary sorts are the objects and definable functions are the maps) defined using positive existential formulas are shown to be equivalent to categories of finitely presented / coherent functors on the category of models. Localised/relativised versions are also proved. This is linked with interpretation functors between categories of structures.
These results generalise what is already known in the additive case and include an alternative approach to an old result of Makkai and Reyes
Pure-injective modules
Get PDFThe pure-injective -modules are defined easily enough: as those
modules which are injective over all pure embeddings, where an
embedding is said to be pure if every finite
system of -linear equations with constants from and a
solution in has a solution in But the definition itself
gives no indication of the rich theory around purity and
pure-injectivity. The purpose of this survey is to present and
illustrate the definitions and a number of the results around
pure-injective modules
Language Invariance and Spectrum Exchangeability in Inductive Logic
Get PDFA sufficient condition is given for a probability function in Inductive Logic
(with relations of all arities) satisfying spectrum exchangeability to addition-
ally satisfy Language Invariance. This condition is shown to also be necessary
in the case of homogeneous probability functions
A Continuum of Inductive Methods arising from a Generalized Principle of Instantial Relevance
Get PDFIn this paper we consider a natural generalization of the Principle of In-
stantial Relevance and give a complete characterization of the probabilistic
belief functions satisfying this principle as a family of discrete probability
functions parameterized by a single real
Bounds on Sizes of Finite Bisimulations of Pfaffian Dynamical Systems
Get PDFWe study finite bisimulations of dynamical systems in ℝ n defined by Pfaffian maps. The pure existence of finite bisimulations for a more general class of o-minimal systems was shown in Brihaye et al. (Lecture Notes in Comput. Sci. 2993, 219–233, 2004), Davoren (Theor. Inf. Appl. 33(4/5), 357–382, 1999), Lafferriere et al. (Math. Control Signals Syst. 13, 1–21, 2000). In Lecture Notes in Comput. Sci. 3210, 2004, the authors proved a double exponential upper bound on the size of a bisimulation in terms of the size of description of the dynamical system. In the present paper we improve it to a single exponential upper bound, and show that this bound is tight, by exhibiting a parameterized class of systems on which it is attained
The probability that a slightly perturbed numerical analysis problem is difficult
Get PDFWe prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs. Several applications to linear and polynomial equation solving show that the estimates obtained in this way are easy to derive and quite accurate. The main theorem is based on a volume estimate of -tubular neighborhoods around a real algebraic subvariety of a sphere, intersected with a spherical disk of radius . Besides and , this bound depends only on the dimension of the sphere and on the degree of the defining equations
Solutions of affine stochastic functional differential equations in the state space
Get PDFdifferential
equations on Rd. The drift of these equations is specified by a
functional defined on a general function space B which is only described
axiomatically. The solutions are reformulated as stochastic processes in the
space B. By representing such a process in the bidual space of B we establish
that the transition functions of this process form a generalized Gaussian
Mehler semigroup on B. Thus the process is characterized completely on B since it is Markovian.
Moreover we derive a sufficient and necessary condition on the underlying
space B such that the transition functions are even an Ornstein-Uhlenbeck
semigroup. We exploit this result to associate a Cauchy problem in the
function space B to the finite-dimensional functional equation
On the free energy of a directed polymer in a Browian environment
No full textWe prove a formula conjectured in [14] for the free energy density
of a directed polymer in a Brownian environment in 1+1 dimensions
Generalized symmetric powers and a generalization of the Kolmogorov-Gel'fand-Buchstaber-Rees theory
Get PDFBASES, FILTRATIONS AND MODULE DECOMPOSITIONS OF FREE LIE ALGEBRAS
No full textWe use Lazard Elimination to devise some new bases of the free Lie
algebra which (like classical Hall bases) consist of Lie products of left
normed basic Lie monomials. Our bases yield direct decompositions
of the homogeneous components of the free Lie algebra with direct
summands that are particularly easy to describe: they are tensor
products of metabelian Lie powers. They also give rise to new
filtrations and decompositions of
free Lie algebras as modules for groups of graded
algebra automorphisms. In particular, we obtain some new
decompositions for free Lie algebras and free restricted free Lie
algebras over fields of positive characteristic