相关论文: Uniqueness and order in sequential effect algebras
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based…
Let P be a quadratic operad. We determine an associated operad ~P such that for any P-algebra A and any ~P-algebra B then the tensor product $A \otimes B$ is a P-algebra.
Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the…
We consider the composition product of symmetric sequences in the case where the underlying symmetric monoidal structure does not commute with coproducts. Even though this composition product is not a monoidal structure on symmetric…
We show that the *-algebra of the product of two synchronous games is the tensor product of the corresponding *-algebras. We prove that the product game has a perfect C*-strategy if and only if each of the individual games does, and that in…
First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew braces, heaps, trusses). Then we analyse the concept of…
The recent years have seen interest into the possibility for (classical as well as quantum) causal structures that, while remaining logically consistent, feature a cyclic causal order between events, opening intriguing possibilities for new…
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…
If $\mathfrak{g}$ is a Frobenius Lie algebra, then the spectrum of $\mathfrak{g}$ is an algebraic invariant equal to the multiset of eigenvalues corresponding to a particular operator acting on $\mathfrak{g}$. In the case of Frobenius…
Categorical spectra are spectrum objects in pointed $(\infty,\infty)$-categories: sequences $(X_n)$ equipped with equivalences $X_n\simeq \Omega X_{n+1}$. This thesis develops foundations for categorical spectra and constructs their tensor…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We…
In this article a sequential theory in the category of spaces and proper maps is described and developed. As a natural extension a sequential theory for exterior spaces and maps is obtained.
We prove that there exists essentially one {\it minimal} differential algebra of distributions $\A$, satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l'impossibilit\'e de la multiplication des…
The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…
An attempt is made to define the concept of execution of an instruction sequence. It is found to be a special case of directly putting into effect of an instruction sequence. Directly putting into effect of an instruction sequences…