Related papers: Reply to comment by P.Markos [arXiv:1205.0689]
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
Given that machine learning algorithms are increasingly being deployed to aid in high stakes decision-making, uncertainty quantification methods that wrap around these black box models such as conformal prediction have received much…
Quantifying uncertainty in automatically generated text is important for letting humans check potential hallucinations and making systems more reliable. Conformal prediction is an attractive framework to provide predictions imbued with…
We propose a model theoretic interpretation of the theorems about the equivalence between mixed characteristic perfectoid spaces and their tilts.
Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining…
The problem of continuous machine learning is studied. Within the framework of the game-theoretic approach, when for calculating the next forecast, no assumptions about the stochastic nature of the source that generates the data flow are…
Topos theory has been suggested by Doring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular it has been used to reformulate standard quantum mechanics in such a way that a novel type…
This article is an overview of the "SP theory of intelligence". The theory aims to simplify and integrate concepts across artificial intelligence, mainstream computing and human perception and cognition, with information compression as a…
A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, D\'iaz-Madrigal, and Pommerenke. We also derive some consequences for…
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical…
The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A special case of relative categoricity is identified (almost…
We provide a self-contained proof to so-called Martio's conjecture in the class of mappings of bounded length distortion. Unlike the earlier proofs, our proof is not based on the modulus of continuity estimate of Martio from 1970.
Statistical shape analysis is a very useful tool in a wide range of medical and biological applications. However, it typically relies on the ability to produce a relatively small number of features that can capture the relevant variability…
Previous studies on sequence-based extraction of human movement trajectories have an issue of inadequate trajectory representation. Specifically, a pair of locations may not be lined up in a sequence especially when one location includes…
Fine population distribution both in space and in time is crucial for epidemic management, disaster prevention,urban planning and more. Human mobility data have a great potential for mapping population distribution at a high level of…
This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational…
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…
We introduce an interleaving operational semantics for describing the client-observable behaviour of atomic transactions on distributed key-value stores. Our semantics builds on abstract states comprising centralised, global key-value…