Related papers: Generalized Compare and Swap
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
The generalisation of proper time, as an alternative to models with extra dimensions of space, has been proposed as the source of the elementary structures of matter. Direct connections with the Standard Model of particle physics together…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
In this work, we investigate the relationship between model generalization and counterfactual explainability in supervised learning. We introduce the notion of $\varepsilon$-valid counterfactual probability ($\varepsilon$-VCP) -- the…
We introduce generalized filtration with which we can represent situations such as some agents forget information at some specific time. The filtration is defined as a functor to a category Prob whose objects are all probability spaces and…
Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable joint specification. We demonstrate that generic composite…
In this paper, we generalized the classical Fermat point, proved the sufficient and necessary condition for uniqueness and existence for the generalized Fermat point(GFP) theorem, and discuss some interesting geometric property of the…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…
We describe an Aldous--Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the…
We reconsider a well known problem of quantum theory, i.e. the so called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives…
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
We propose an alternative to the Turing test that removes the inherent asymmetry between humans and machines in Turing's original imitation game. In this new test, both humans and machines judge each other. We argue that this makes the test…
Generalized planning is about finding plans that solve collections of planning instances, often infinite collections, rather than single instances. Recently it has been shown how to reduce the planning problem for generalized planning to…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
We generalize the concept of disjunction.
We present a mathematical framework adapted to the comparison of atomic clocks remotely connected by a complex network of optical or microwave links. This framework facilitates the computation of frequency ratios using a generic set of…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In this essay, I wish to share a novel perspective based on the principle of universalization in arriving at the relativistic and quantum world from the classical world. I also delve on some insightful discussion on going ``beyond''.
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…