Related papers: The splitting principle and singularities
A 'process theory' is any theory of systems and processes which admits sequential and parallel composition. `Terminality' unifies normalisation of pure states, trace-preservation of CP-maps, and adding up to identity of positive operators…
We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsulates low-level analytic…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
A set $M$ of nonzero integers is said to split a finite abelian group $G$ if there exists a subset $S\subseteq G$ such that $M\cdot S = G\setminus\{0\}$. Such a splitting is called purely singular if every prime divisor of $|G|$ divides…
Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical Mechanics predicts such behaviour if one accepts that the configurational integral of a system of N colloids must be divided by N!.…
We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by…
In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal…
Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like "What distinguishes a clustering of data from other data partitioning?", "Are there any principles governing all…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
The axiom of countable choice for reals is one of the most basic fragments of the axiom of choice needed in many parts of mathematics. Descriptive choice principles are a further stratification of this fragment by the descriptive complexity…
We say that $M$ and $S$ form a \textsl{splitting} of $G$ if every nonzero element $g$ of $G$ has a unique representation of the form $g=ms$ with $m\in M$ and $s\in S$, while $0$ has no such representation. The splitting is called {\it…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite…
We extend the criterion of Kawatani and Okawa for indecomposability of the derived category of a smooth projective variety to arbitrary schemes. For relative schemes, we also give a criterion for the nonexistence of semiorthogonal…