Application of mathematical probabilistic statistical model of base – FFCA financial data processing

In order to improve the detection and filtering ability for financial data, a data-filtering method based on mathematical probability statistical model, a descriptive statistical analysis model of big data filtering, probability density characteristic statistical design data filtering analysis combined with fuzzy mathematical reasoning, regression analysis according to probability density of financial data distribution, and threshold test and threshold judgment are conducted to realize data filtering. The test results show that the big data filtering and the reliability and convergence of the mathematical model are optimal.

Quantitative Risk Assessment and Application of Landslide Disaster in Chongqing

Chongqing is located in southwestern China, and geological disasters occur frequently. The amount of potential landslide disasters is far greater than the number of landslides that can be managed by government funds, so the risk assessment for potential landslide disasters is critical. In practical applications, risk assessment methods based on landslide stability and loss are restricted by various factors. These methods can be simplified to semi-empirical assessment methods, which are influenced by the discrimination factors near the limit values of the determined conditions, possibly leading to sudden changes in the evaluation results and distort the conclusions. To solve this problem, we propose a full quantitative risk assessment method according to the probability of landslide damage. The mathematical probability model is used to quantitatively describe the risk assessment impacting factors, weaken the boundary influence, and improve the accuracy of landslide risk assessment. Correspondingly, the software is developed to conduct quantitative risk assessment on six landslides in Feng jie County, Chongqing, which verifies the accuracy and reliability of the full quantitative risk assessment method, and provides an important reference for judging urban landslide geological disasters.

Quantitative Description for Sand Void Fabric with the Principle of Stereology

Based on the principle of stereology to describe void fabric, the fabric tensor is redefined by the idea of normalization, and a novel quantitative description method for the orthotropic fabric of granular materials is presented. The scan line is described by two independent angles in the stereo space, and the projection of the scan line on three orthogonal planes is used to determine the plane tensor. The second-order plane tensor can be described equivalently by two invariants, which describe the degree and direction of anisotropy of the material, respectively. In the three-dimensional orthogonal space, there are three measurable amplitude parameters on the three orthogonal planes. Due to the normalized definition of tensor in this paper, there are only two independent variations of the three amplitude parameters, and any two amplitude parameters can be used to derive the three-dimensional orthotropic fabric tensor. Therefore, the same orthorhombic anisotropy structure can be described by three fabrics, which enriches the theoretical description of orthotropy greatly. As the geometric relationship of the stereoscopic space scan line changes, the three sets of orthotropic fabrics degenerate into different forms of transversely isotropic and isotropic fabrics naturally and have a clear physical meaning. The novel fabric tensor is quantitatively determined based on mathematical probability and statistics. The discrete distribution of voids in space is projected as a scalar measurable parameter on a plane. This parameter is related to the macroscopic constitutive relationship directly and can be used to describe the effect of microscopic voids on the macroscopic phenomenon of materials.

Behavioral dynamics of pedestrian’s movements: Theoretical aspects of commercial arterial road frontage activities

The common scientific approaches to the reasoning of problems are mathematical reasoning or statistical reasoning. Mathematical or formal reasoning is usually deductive, therein one reason from general assumptions to specifics using symbolic logic and axioms for multi criteria decision-making. Mathematical probability, which is the basis of all statistical theories, had its beginning in the past. The aim of this paper is to explore a number of the mathematical and statistical aspects of the disposition and behavior of road frontage activities, which are of importance in pedestrian behavior as considered. It's shown that number of crossings from right to left is proportional to the pedestrian on the right (PXRL ∝ NR) and therefore, the number of crossings left to right is proportional to the pedestrians on the left (PXLR ∝ NL). Frequency distributions of the pedestrians generated for a given shopping string arterial were of 4 kinds, one related to pedestrians passing through not crossing the road, not going into and out of outlets. The second kind related to pedestrians crossing the road for the aim of going into and out of outlets, etc. the third kind related to pedestrian going into shops and eventually, the fourth kind related to others, e.g. Pedestrians generated from parking vehicles, buses, etc. A formula is given for the frequency with crossing from left to right and right to leave based on the land-use activities on the left and right. In considering the capacity of road systems it should be remembered that increases in traffic flow generally produce corresponding decreases in speed. However, it's an assumption that a rise in population generated along the footpath can cause the crossing the road, and usually produce corresponding decreases in vehicle speed. The paper concludes with a constatation of the pedestrian movements at a continuing rate that expressed in mathematical form.

The Paradigm of Complex Probability and Isaac Newton’s Classical Mechanics: On the Foundation of Statistical Physics

The concept of mathematical probability was established in 1933 by Andrey Nikolaevich Kolmogorov by defining a system of five axioms. This system can be enhanced to encompass the imaginary numbers set after the addition of three novel axioms. As a result, any random experiment can be executed in the complex probabilities set C which is the sum of the real probabilities set R and the imaginary probabilities set M. We aim here to incorporate supplementary imaginary dimensions to the random experiment occurring in the “real” laboratory in R and therefore to compute all the probabilities in the sets R, M, and C. Accordingly, the probability in the whole set C = R + M is constantly equivalent to one independently of the distribution of the input random variable in R, and subsequently the output of the stochastic experiment in R can be determined absolutely in C. This is the consequence of the fact that the probability in C is computed after the subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic experiment. We will apply this innovative paradigm to Isaac Newton’s classical mechanics and to prove as well in an original way an important property at the foundation of statistical physics.

The Paradigm of Complex Probability and Thomas Bayes’ Theorem

The mathematical probability concept was set forth by Andrey Nikolaevich Kolmogorov in 1933 by laying down a five-axioms system. This scheme can be improved to embody the set of imaginary numbers after adding three new axioms. Accordingly, any stochastic phenomenon can be performed in the set C of complex probabilities which is the summation of the set R of real probabilities and the set M of imaginary probabilities. Our objective now is to encompass complementary imaginary dimensions to the stochastic phenomenon taking place in the “real” laboratory in R and as a consequence to gauge in the sets R, M, and C all the corresponding probabilities. Hence, the probability in the entire set C = R + M is incessantly equal to one independently of all the probabilities of the input stochastic variable distribution in R, and subsequently the output of the random phenomenon in R can be evaluated totally in C. This is due to the fact that the probability in C is calculated after the elimination and subtraction of the chaotic factor from the degree of our knowledge of the nondeterministic phenomenon. We will apply this novel paradigm to the classical Bayes’ theorem in probability theory.

The Maxim of Probabilism, with special regard to Reichenbach

It is shown that by realizing the isomorphism features of the frequency and geometric interpretations of probability, Reichenbach comes very close to the idea of identifying mathematical probability theory with measure theory in his 1949 work on foundations of probability. Some general features of Reichenbach’s axiomatization of probability theory are pointed out as likely obstacles that prevented him making this conceptual move. The role of isomorphisms of Kolmogorovian probability measure spaces is specified in what we call the “Maxim of Probabilism”, which states that a necessary condition for a concept to be probabilistic is its invariance with respect to measure-theoretic isomorphisms. The functioning of the Maxim of Probabilism is illustrated by the example of conditioning via conditional expectations.

WAVE FUNCTION TO PARTITION FUNCTION: A CORRELATION

In this note the statistical thermodynamics is correlated to wave function through mathematical probability. The note can be subdivided into two following portions.STATISTICS -THE BASIC OF STATISTICAL THERMODYNAMICS: A CORRELATION and PROBABILITY -A THE BASICS OF WAVE FUNCTION .Randomisation , Wave Function , Probability Density Function , Multiplicative Probability , Partition function , Correlation ( K.P ) coefficient , Probability , Weights , Stirring’s Approximation