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Probability distributions are commonly used for describing and modeling data in several different areas. There are a lot of well-known statistical distributions however they are inefficient for modeling data in many applied areas such as lifetime analysis, finance and insurance. The selection of the appropriate probability density distribution reduces the estimation error and also allows obtaining characteristics. Hence, there is a clear need for more flexible distributions. In this study, we propose a new probability distribution to model different data sets. After defining the new probability distribution named Poisson-Lindley (PL) distribution, an application to real data demonstrates that the new distribution can provide a better fit than other classical models. [ABSTRACT FROM AUTHOR]

The complex-classical short-range interaction Hamiltonian is used for the first time for solving spin glasses with consideration of relaxation effects. A system of recurrent equations is obtained on the nodes of the 1D lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of extended Sylvester conditions which allows node-by-node construct a huge number of stable spin chains in parallel. As a result of the simulation, distribution functions of different parameters of a spin glass are constructed from the first principles of complex-classical mechanics. Also, the critical properties of spin glass such as catastrophes in the Clausius-Mossotti equation are studied depending on the external field. It is shown that the developed approach excludes these catastrophes, which allows organize continuous parallel computation based on the whole-range values of the external field. A new representation of the partition function is suggested which, opposite to the usual definition, is a complex function with the derivatives defined everywhere, including at critical points. [ABSTRACT FROM AUTHOR]

We show that the contextual value of an observable coincides with the weak value of Aharonov and his colleagues on the basis of consistency of quantum mechanics with Kolmogorov's measure theory of probability and that this consistency also leads to Born's rule as the unique probability measure of events to be discovered by the post-selection. We will give a simple example for illustration. [ABSTRACT FROM AUTHOR]

An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The particles in this model must be self-organized repetitive structures. The dynamics of this model is a stochastic sequential growth dynamics. New vertexes are added one by one. The probability of this addition depends on the structure of existed graph. The particular case of the dynamics is considered. The numerical simulation provides some symptoms of self-organization. [ABSTRACT FROM AUTHOR]

I show that the classical coin tossing experiment involves two distinct definitions of probability, one ontological (the relative frequencies of initial deterministic states) and another empirical (the relative frequencies of observations). In quantum theory, I argue, only the latter definition can be invoked, since a single superposition state can give rise to multiple observation experiences. This difference explains why the present statistical quantum mechanics is an ontological dead end, despite its enormous pragmatic success. To get at the ontological content of quantum theory, I propose that the observations themselves can be interpreted on a different footing, without reference to determinate detector states. [ABSTRACT FROM AUTHOR]

A review of the probability representation of quantum and classical states is presented. Inequalities corresponding to nonnegativity of the states' density operators and the presence of quantum correlations are considered. Comparison with some classical correlations is discussed. Entropic uncertainty relations along with other uncertainty relations are studied. [ABSTRACT FROM AUTHOR]

We present an overview on some of the critical aspects of foundations of Quantum Mechanics, ranging from the concept of Realism to non-locality, random choice, macro-objectivation issue etc. [ABSTRACT FROM AUTHOR]

The distance dependence of the probability of observing two photons in a waveguide is investigated and the Glauber correlation functions of the entangled photons are considered. First the case of a hollow waveguide with modal dispersion is treated in detail: the spatial and temporal dependence of the correlation functions is evaluated and the distance dependence of the probability of observing two photons upper bounds and asymptotic expressions valid for large distances are derived. Second the generalization to a real fibre with both material and modal dispersion, allowing dispersion shift, is discussed. [ABSTRACT FROM AUTHOR]

Modal quantum theory (MQT) is a simplified cousin of ordinary Hilbert space quantum theory. We show that two important theorems of actual quantum theory, the Kochen-Specker theorem excluding non-contextual hidden variables and the Conway-Kochen "free will theorem" about entangled systems, have direct analogues in MQT. The structure of possible measurement results for an entangled system in MQT cannot be represented by probability assignments satisfying the no-signaling principle, such as those given by ordinary quantum theory. [ABSTRACT FROM AUTHOR]

We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of the key and remain undetected even if Alice and Bob are using 100% efficient detectors. The attack can be easily extended to Ekert protocol, with an efficiency as high as 85.3%. [ABSTRACT FROM AUTHOR]

The Pauli exclusion principle (PEP) is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the violation parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopical fast Silicon Drift Detectors. We also mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models. [ABSTRACT FROM AUTHOR]

This work considers the Hamilton equations of general relativity and quantum theory in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics, see [1], [2], [3]. The probability appears automatically, without apriori assumptions. Certain results and communications pertaining to solutions of these problems are also provided. [ABSTRACT FROM AUTHOR]