162,927 research outputs found
Certification of programs with computational effects
In purely functional programming languages imperative features, more
generally computational effects are prohibited. However, non-functional lan-
guages do involve effects. The theory of decorated logic provides a rigorous
for- malism (with a refinement in operation signatures) for proving program
properties with respect to computational effects. The aim of this thesis is to
first develop Coq libraries and tools for verifying program properties in
decorated settings as- sociated with several effects: states, local state,
exceptions, non-termination, etc. Then, these tools will be combined to deal
with several effects
Equidistribution of Zeros of Random Holomorphic Sections for Moderate Measures
We establish an equidistribution theorem for the zeros of random holomorphic
sections of high powers of a positive holomorphic line bundle. The
equidistribution is associated with a family of singular moderate measures. We
also give a convergence speed for the equidistribution.Comment: 18 page
Perverse Monodromic Sheaves
We introduce and study the category of modular (i.e. with coefficient of
positive characteristic) monodromic perverse sheaves on complex stratified
-varieties, with a complex algebraic torus. In particular, we show that
under appropriate assumptions this category has a natural highest weight
structure
Peripheral structures of relatively hyperbolic groups
In this paper, we introduce and characterize a class of parabolically
extended structures for relatively hyperbolic groups. A characterization of
relative quasiconvexity with respect to parabolically extended structures is
obtained using dynamical methods. Some applications are discussed. The class of
groups acting geometrically finitely on Floyd boundaries turns out to be easily
understood. However, we also show that Dunwoody's inaccessible group does not
act geometrically finitely on its Floyd boundary.Comment: 30 page
Sapo: Reachability Computation and Parameter Synthesis of Polynomial Dynamical Systems
Sapo is a C++ tool for the formal analysis of polynomial dynamical systems.
Its main features are: 1) Reachability computation, i.e., the calculation of
the set of states reachable from a set of initial conditions, and 2) Parameter
synthesis, i.e., the refinement of a set of parameters so that the system
satisfies a given specification. Sapo can represent reachable sets as unions of
boxes, parallelotopes, or parallelotope bundles (symbolic representation of
polytopes). Sets of parameters are represented with polytopes while
specifications are formalized as Signal Temporal Logic (STL) formulas
Uniform rationality of Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on exponential sums
This thesis contains some new results on the uniform rationality of
Poincar\'e series of p-adic equivalence relations and Igusa's conjecture on
exponential sumsComment: Doctoral thesis, University of Lill
A BSDE approach to stochastic differential games with incomplete information
We consider a two-player zero-sum stochastic differential game in which one
of the players has a private information on the game. Both players observe each
other, so that the non-informed player can try to guess his missing
information. Our aim is to quantify the amount of information the informed
player has to reveal in order to play optimally: to do so, we show that the
value function of this zero-sum game can be rewritten as a minimization problem
over some martingale measures with a payoff given by the solution of a backward
stochastic differential equation
Theories without the tree property of the second kind
We initiate a systematic study of the class of theories without the tree
property of the second kind - NTP2. Most importantly, we show: the burden is
"sub-multiplicative" in arbitrary theories (in particular, if a theory has TP2
then there is a formula with a single variable witnessing this); NTP2 is
equivalent to the generalized Kim's lemma and to the boundedness of ist-weight;
the dp-rank of a type in an arbitrary theory is witnessed by mutually
indiscernible sequences of realizations of the type, after adding some
parameters - so the dp-rank of a 1-type in any theory is always witnessed by
sequences of singletons; in NTP2 theories, simple types are co-simple,
characterized by the co-independence theorem, and forking between the
realizations of a simple type and arbitrary elements satisfies full symmetry; a
Henselian valued field of characteristic (0,0) is NTP2 (strong, of finite
burden) if and only if the residue field is NTP2 (the residue field and the
value group are strong, of finite burden respectively), so in particular any
ultraproduct of p-adics is NTP2; adding a generic predicate to a geometric NTP2
theory preserves NTP2.Comment: 35 pages; v.3: a discussion and a Conjecture 2.7 on the
sub-additivity of burden had been added; Section 3.1 on the SOPn hierarchy
restricted to NTP2 theories had been added; Problem 7.13 had been updated;
numbering of theorems had been changed and some minor typos were fixed;
Annals of Pure and Applied Logic, accepte
Compactified Spacelike Extra Dimension & Brane-Higgs Field
In the paradigm with a small warped Spacelike Extra Dimensions (SED), the
Higgs field is in general localized at a boundary of the SED (TeV-brane) where
the gravity scale is redshifted to the TeV by a warp factor. If the SM gauge
bosons and fermions propagate into the warped SED, one can generate the mass
hierarchy for fermions. It is thus crucial to treat carefully the TeV-brane
localized masses for such fermions, which is done in the literature by applying
a regularization process suffering from a lack of consistency and more
importantly being useless, as we demonstrate in detail in the present thesis.
The first part of the thesis is devoted to the treatment of brane localized
mass terms for 5D fermions, which requires the introduction of new Lagrangian
terms at the SED boundaries, similar to the Gibbons-Hawking terms in gravity.
The second part consists in applying different methods (function/distribution
fields, 4D/5D calculations, etc) to various brane localized terms (kinetic
terms, Majorana masses, etc), as well as a generalization to several classified
models (flat/warped dimensions, intervalle/orbifold, etc). In the third part,
we propose to compactify a flat SED on a star/rose graph with a large number of
identical small leaves/petals. We obtain a compactified space with a large
volume without a large compactification length to stabilize. We use the
approach of 5D fermions to build a toy model of small Dirac neutrino masses
(brane localized left-handed neutrinos and bulk right-handed ones).Comment: 244 pages. PhD thesis manuscript. Part I "State of the Art" in French
and Part II "Original Research Work" in Englis
Cohomological invariants of finite Coxeter groups
In this paper, we generalize Serre's splitting theorem for cohomological
invariants of the symmetric group to finite Coxeter groups, provided that the
ground field has characteristic zero. We then use this principle to determine
all the cohomological invariants of Weyl groups of classical type with
coefficients modulo 2.Comment: arXiv admin note: substantial text overlap with arXiv:1112.629
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