Related papers: QRB-Domains and the Probabilistic Powerdomain
We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures…
Bayesian networks provide a modeling language and associated inference algorithm for stochastic domains. They have been successfully applied in a variety of medium-scale applications. However, when faced with a large complex domain, the…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical omega-category. This also has the structure of connections in the sense of Brown and Higgins,…
We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category $X$. The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when $X$ is the category of…
We introduce a taxonomy for partially coherent optical fields spanning multiple degrees of freedom (DoFs) based on the rank of the associated coherence matrix (the number of non-zero eigenvalues). When DoFs comprise two spatial modes and…
We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of…
We present a unifying framework of residual domination for (expansions of) henselian valued fields of equicharacteristic zero, encompassing some valued fields with operators. We show that the class of residually dominated types coincides…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem…
We show that the category of categories with pullbacks and pullback preserving functors is cartesian closed.
We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…
We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined through a strongly recurrent self-similar local regular Dirichlet…
A new criterion is given for a semigroup to be the semigroup of a valuation dominating an equicharacteristic local domain. The criterion is used to construct examples of well ordered subsemigroups of the positive rational numbers which are…
We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem…
We give an elementary characterization of those quantaloids Q for which the category Cat(Q) of Q-enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using ad hoc methods) and we give…
We prove that the K-theory of an exact quasicategory can be computed via a higher categorical variant of the Q construction. This construction yields a quasicategory whose weak homotopy type is a delooping of the K-theory space. We show…
The metallic state of the underdoped high-Tc cuprates has remained an enigma: How may seemingly disconnected Fermi surface segments, observed in zero magnetic field as a result of the opening of a partial gap (the pseudogap), possess…
We describe a duality for quantale-enriched categories that extends the Lawson duality for continuous dcpos: for any saturated class J of modules that commute with certain weighted limits, and under an appropriate choice of morphisms, the…
A version of Gabor expansion over a lattice of critical density is shown to converge to an arbitrary function that belongs to domain of the oscillator operator. This expansion is used for approximation of an arbitrary function concentrated…