相关论文: Efficient Implementation and the Product State Rep…

We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…

Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of…

We introduce the idea that the knowable quantum reality depends not only on the state but also on measurements. Mathematically, we map the states from the ordinary Hilbert space into new states in what we call the measurement space. The…

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…

Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer…

Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a…

We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals' vNM preferences over the alternatives, assigns a unique number -- the social inefficiency -- to each alternative. These…

Notion of effective size of support (Ess) of a random variable is introduced. A small set of natural requirements that a measure of Ess should satisfy is presented. The measure with prescribed properties is in a direct (exp-) relationship…

The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification…

Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution…

We study the implementability problem for an expressive class of symbolic communication protocols involving multiple participants. Our symbolic protocols describe infinite states and data values using dependent refinement predicates.…

The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…

A network-based optimization approach, EEE, is proposed for the purpose of providing validation-viable state estimations to remediate the failure of pretrained models. To improve optimization efficiency and convergence, the most important…

The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…

In this paper, we first clarify the concepts of green AI versus frugal AI, positioning frugality as efficiency by design and green AI as transparency and accountability. We then argue that these approaches, while complementary, are…

Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…

Representation is a key notion in neuroscience and artificial intelligence (AI). However, a longstanding philosophical debate highlights that specifying what counts as representation is trickier than it seems. With this brief opinion paper…

We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of…