Search results for "probabilistic"
showing 10 items of 380 documents
Discontinuous, although “highly” differentiable, real functions and algebraic genericity
2021
Abstract We exhibit a class of functions f : R → R which are bounded, continuous on R ∖ Q , left discontinuous on Q , right differentiable on Q , and upper left Dini differentiable on R ∖ Q . Other properties of these functions, such as jump sizes and local extrema, are also discussed. These functions are constructed using probabilistic methods. We also show that the families of functions satisfying similar properties contain large algebraic structures (obtaining lineability, algebrability and coneability).
Contextuality is About Identity of Random Variables
2014
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force "one and the same" random variable to change "its" identity, any two random variables recorded under different conditions are considered different "automatically". They are never the…
Ultrametric Vs. Quantum Query Algorithms
2014
Ultrametric algorithms are similar to probabilistic algorithms but they describe the degree of indeterminism by p-adic numbers instead of real numbers. This paper introduces the notion of ultrametric query algorithms and shows an example of advantages of ultrametric query algorithms over deterministic, probabilistic and quantum query algorithms.
Quantum query algorithms for certain functions and general algorithm construction techniques
2007
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we concentrate on quantum query algorithm designing tasks. The main aim of research was to find new efficient algorithms and develop general algorithm designing techniques. We present several exact quantum query algorithms for certain problems that are better than classical counterparts. Next we introduce algorithm transformation methods that allow significant enlarging of sets of exactly computable functions. Finally, we propose quantum algorithm designing methods. G…
Models of Dynamical Modelling Under Uncertainty
1986
The objective of this work is to modelize the evolution of a Model-System to be adapted to a Random System. This evolution is described by means of the change of a probabilistic function, through deterministic rules and in function of the random responses of the modelized System. This probabilistic function can describe the relative weight of distinct submodels (deterministic or random Systems, with constant or variable stimulus), or the stimulus-response relation in the Model-System (Adaptative Random System). We conclude that the Adaptative Random Model permits a more precise, simple and economical modelling.
A Qualified Kolmogorovian Account of Probabilistic Contextuality
2014
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central principle contextuality-by-default is that the outputs indexed by mutually incompatible values of inputs are stochastically unrelated; but they can be coupled imposed a joint distribution on in a variety of ways. A system is characterized by a pattern of which outputs can be "directly influenced" by which inputs a primitive relation, hypothetical or normative, and by certain constraints imposed on the outputs such as Bell-type inequalities or their quantum analogues. The set of couplings compatible with these …
On Solving the Problem of Identifying Unreliable Sensors Without a Knowledge of the Ground Truth: The Case of Stochastic Environments.
2017
The purpose of this paper is to propose a solution to an extremely pertinent problem, namely, that of identifying unreliable sensors (in a domain of reliable and unreliable ones) without any knowledge of the ground truth. This fascinating paradox can be formulated in simple terms as trying to identify stochastic liars without any additional information about the truth. Though apparently impossible, we will show that it is feasible to solve the problem, a claim that is counterintuitive in and of itself. One aspect of our contribution is to show how redundancy can be introduced, and how it can be effectively utilized in resolving this paradox. Legacy work and the reported literature (for exam…
Assessment of building energy modelling studies to meet the requirements of the new Energy Performance of Buildings Directive
2020
Abstract The cost optimal method (COM) as applied in the Energy Performance of Buildings Directive (EPBD) uses “non-calibrated deterministic reference buildings (RBs)”. Such RBs are defined with single envelope and equipment parameter values, for which calibration with actual building stock energy performance (EP) is not undertaken. Thus, it is not possible to visualise the effect of uncertainties or diversity in the input parameters on cost-optimal level benchmarks and to verify the choice of RBs. The paper proposes an update to the COM via use of “Probabilistic Bayesian calibrated RBs” to handle uncertainties and produce more realistic cost optimal levels to support policy makers in devis…
Waiting time in quantum repeaters with probabilistic entanglement swapping
2019
The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters, calculating repeater rates has typically depended on approximations assuming sufficiently small probabilities. Here we propose an exact and systematic approach including an algorithm based on Markov chain theory to compute the average waiting time (and hence the transmission rates) of quantum repeaters with arbitrary numbers of links. For up to four repeater segments, we explicitly give the exact rate formulae for arbitrary entanglement swapping probabiliti…
Risk based Fatigue Inspection Planning – State of the Art
2013
AbstractThe present paper presents the methodology and the practical calculations for risk based inspection planning of fatigue cracks in welded offshore steel structures. Due to the uncertainty in the variables involved in the problem the planning has to be carried out by stochastic modeling and risk based assessments. Scatter in potential crack growth has to be analyzed by applied probabilistic facture mechanics and the uncertainty in the performance of the actual inspection technique has to be determined. With given risk acceptance criteria the practical outcome of the analyses is recommended inspection techniques and associated planned inspection time intervals. The classical theory is …