A probabilistic semi-metric space (S, F ) is said to be of class H ([5]) if there exists a metric d on S such that, for t > 0, d(p, q) < t ⇔ Fpq(t) > 1− t. We will prove that (S, F ) is of class H iff the mapping K, defined on S × S by K (p, q) = sup{t ≥ 0 | t ≤ 1− Fpq(t)} is a metric on S. Two fixed point theorems for multivalued contractions in probabilistic metric spaces are also proved. Inc...

In the previous lecture, we considered the following sparse approximations problem (w.r.t. Lp norm): For a vector x, find x′ such that x′ is k-sparse, i.e., ‖x‖0 ≤ k, and ‖x− x‖p ≤ C Err, where Err = Errpk = min‖x′′‖0≤k ‖x− x ‖p. We could maintain a linear sketch of x of length O(k logm) from which can recover k-sparse approximation of x (for some C > 1). The guarantee was probabilistic: for an...

Probabilistic Linear Discriminant Analysis (PLDA) has become state-of-the-art method for modeling i-vector space in speaker recognition task. However the performance degradation is observed if enrollment data size differs from one speaker to another. This paper presents a solution to such problem by introducing new PLDA scoring normalization technique. Normalization parameters are derived in a ...

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrödinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with the probab...

The probabilistic properties of R-valued Markov-Switching ARMA processes with a general state space parameter chain are analysed. Stationarity and ergodicity conditions are given and a feasible general stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negat...

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrödinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with the probab...

Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an involutive operator Ĵ which renders the Hamiltonian Ĵ-Hermitian leads to the unambiguous definition of an associated positive definite norm allowing for the standard...

We propose a norm-based agent-oriented model of decision-making of semi-autonomous vehicles in urban traffic scenarios. Computational norms are used to represent the driving rules and conventions that influence the distributed decisionmaking process of the vehicles. As norms restrict the admissible behaviour of the agents, we propose to represent them as constraints, and we express the agents’ ...

the current study investigated and compared data generation methods for groundwater modeling. thesemethods can be divided into two classes; geostatistic and probabilistic. by comparing geostatistic methods,the best method was chosen and the hydraulic conductivity of the aquifer was generated for a study area ina grid (9-cell) format. after observing weak spatial correlation between the data, th...

Causal selection is the cognitive process through which one or more elements in a complex causal structure are singled out as actual causes of a certain effect. In this paper, we report on an experiment in which we investigated the role of moral and temporal factors in causal selection. Our results are as follows. First, when presented with a temporal chain in which two human agents perform the...