Search results for "Quantification"

On the Power of Non-adaptive Learning Graphs

2012

We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein. Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an optimal quantum query algorithm for it. For a special case of certificate structures generated by cer…

Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities

2016

One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parity-oblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such task…

Epistemic uncertainty in fault tree analysis approached by the evidence theory

2012

Abstract Process plants may be subjected to dangerous events. Different methodologies are nowadays employed to identify failure events, that can lead to severe accidents, and to assess the relative probability of occurrence. As for rare events reliability data are generally poor, leading to a partial or incomplete knowledge of the process, the classical probabilistic approach can not be successfully used. Such an uncertainty, called epistemic uncertainty, can be treated by means of different methodologies, alternative to the probabilistic one. In this work, the Evidence Theory or Dempster–Shafer theory (DST) is proposed to deal with this kind of uncertainty. In particular, the classical Fau…

A short proof of the self-improving regularity of quasiregular mappings

2005

. The theoryof quasiregular mappings is a central topic in modern analysis withimportant connections to a variety of topics as elliptic partial differen-tial equations, complex dynamics, differential geometry and calculus ofvariations [13] [10].A remarkable feature of quasiregular mappings is the self-improvingregularity. In 1957 [2], Bojarski proved that for planar quasiregularmappings, there exists an exponent

Some new Hadamard designs with 79 points admitting automorphisms of order 13 and 19

2001

Abstract We have proved that there exists at least 2091 mutually nonisomorphic symmetric (79,39,19)-designs. In particular, 1896 of them admit an action of the nonabelian group of order 57, and an additional 194 an action of the nonabelian group of order 39.

HBsAg quantification in HBeAg negative cirrhosis on nucleoside/nucleotide analogue (NA) and risk of development of HCC

2013

On Sets of Words of Rank Two

2019

Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …

Frequency Prediction of Functions

2012

Prediction of functions is one of processes considered in inductive inference. There is a "black box" with a given total function f in it. The result of the inductive inference machine F( ) is expected to be f(n+1). Deterministic and probabilistic prediction of functions has been widely studied. Frequency computation is a mechanism used to combine features of deterministic and probabilistic algorithms. Frequency computation has been used for several types of inductive inference, especially, for learning via queries. We study frequency prediction of functions and show that that there exists an interesting hierarchy of predictable classes of functions.

An urban drainage stormwater quality model: model development and uncertainty quantification

2010

Summary The evaluation of urban stormwater quality is of relevant importance for urban drainage, and mathematical models may be of great interest in this respect. To date, several detailed mathematical models are available to predict stormwater quantity–quality characteristics in urban drainage systems. However, only a few models take sewer sediments into account, considering their cohesive-like properties that influence the build-up process of the pollutant load. Furthermore, the model data requirements, especially for the quality aspects, are extensive, which limit their applicability and affect model results with large uncertainty. Uncertainty analysis provides a measure or index regardi…

Bayesian approach for uncertainty quantification in water quality modelling: The influence of prior distribution

2010

Summary Mathematical models are of common use in urban drainage, and they are increasingly being applied to support decisions about design and alternative management strategies. In this context, uncertainty analysis is of undoubted necessity in urban drainage modelling. However, despite the crucial role played by uncertainty quantification, several methodological aspects need to be clarified and deserve further investigation, especially in water quality modelling. One of them is related to the “a priori” hypotheses involved in the uncertainty analysis. Such hypotheses are usually condensed in “a priori” distributions assessing the most likely values for model parameters. This paper explores…