Monsoon, post monsoon rainy days analysis by using normal, binomial distribution and discrete probability for south Gujarat

The analysis will be conducted for standard weekly (SW) 22 to 47 of monsoon and post monsoon season at south Gujarat. The standard weekly rainy days analysis of binomial distribution for monsoon season of Navsari on chi-square test on binomial distribution was found in standard week (SW) 22 to 31, 33 and standard week (SW) 35 to 39 and post monsoon in standard week (SW) 41 to 44 shows significant. The result also reveals that the monsoon season SW 32 and 34 and post monsoon season SW 40, 45, 46 and 47 revealed non-significant result. Analysis reveals the rainfall is not equally distributed during SW 32, 34, 40, 45, 16 and 47, so that the test of binomial distribution is a good fit. Monsoon season rainfall data of Navsari, Bharuch and Valsad reveals that the normal distribution at 10, 20 and 30% probability levels for the month of June, July, August and September shows the possibility of increasing rainy days occurrence. The Navsari and Bharuch districts during post monsoon season rainfall of months of October and November reveals decreasing tendency except Valsad district. The binomial distribution fit only those standard weeks in which rainfall is not equally distributed. The standard weekly rainy days analysis of binomial distribution on chi-square test in Bharuch was found that standard week (SW) 25 only 10% of monsoon season and in post monsoon standard week (SW) 42 and 47 shows non significant (5 and 10% level of significant) result, but SW 25 found significant at 5% level. In case of Valsad district, standard week 22 to 39 of monsoon season and in post monsoon season 41, 42, 43 and 46 standard weeks shows significant result. The result reveals that the monsoon season of Bharuch standard weeks 22 to 39 except from 25 and post monsoon 40, 41, 43, 44, 45 and 46 shows significant result. Further, in Valsad district standard weeks 40, 44, 45 and 47 shows significant result. The trend analysis of rainy days shows that increasing trend in monsoon season and decreasing trend in post monsoon season of Navsari, Bharuch and Valsad districts. From above results observed that the rainfall distribution is not equally distributed so test of binomial distribution at above given standard week is a good fit. The data also shows that, decreasing tendency in rainfall was observed except Valsad district.

Crystallographic complexity partition analysis

We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.

On the Distributional Characterization of Graph Models of Water Distribution Networks in Wasserstein Spaces

This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.

Dynamic sampling from a discrete probability distribution with a known distribution of rates

In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance–Rejection method, the Complete Binary Tree and the Alias method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used, with the top level selecting a group of events, and the bottom level selecting an element from a group. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant when the rate distribution follows certain conditions. We show that for any distribution, combining a tree structure with the Acceptance–Rejection method, we have an expected time of sampling and update of $$O\left( \log \log {r_{max}}/{r_{min}}\right) $$ O log log r max / r min is possible, where $$r_{max}$$ r max is the maximum rate and $$r_{min}$$ r min the minimum rate. We also discuss an implementation of a Two Levels Acceptance–Rejection data structure, that allows expected constant time for sampling, and amortized constant time for updates, assuming that $$r_{max}$$ r max and $$r_{min}$$ r min are known and the number of events is sufficiently large. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting.

Analysis on Spatial Layout Model of Urban Road Green Landscape Based on Discrete Probability

The development issues about urban road greening design are constantly emerging in modern urban road construction. Therefore, a model of spatial layout of urban road green landscape based on discrete probability was built. The relevant urban road data was collected and the corresponding three-dimensional model of urban road was built. On this basis, the spatial layout and characteristics of urban road were analyzed. According to the analysis results, the greening modes and configuration methods that met the humanistic characteristics were established reasonably. Moreover, the green landscape vegetation was selected in consideration of the growth potential, height and seasonal phase of plants. Then, the discrete probability was used to determine the initial planting location and planting density of vegetation. Finally, following the principle of macro control and micro coordination respectively, the spatial layout of urban road green landscape was achieved from the horizontal and vertical directions. Based on the evaluation for the spatial layout model, it is concluded that the comprehensive score of the designed model is improved by 4.3 points compared with the traditional model.

Technical Perspective

The paper entitled "Probabilistic Data with Continuous Distributions" overviews recent work on the foundations of infinite probabilistic databases [3, 2]. Prior work on probabilistic databases (PDBs) focused almost exclusively on the finite case: A finite PDB represents a discrete probability distribution over a finite set of possible worlds [4]. In contrast, an infinite PDB models a continuous probability distribution over an infinite set of possible worlds. In both cases, each world is a finite relational database instance. Continuous distributions are essential and commonplace tools for reasoning under uncertainty in practice. Accommodating them in the framework of probabilistic databases brings us closer to applications that naturally rely on both continuous distributions and relational databases.

Probabilistic Data with Continuous Distributions

Statistical models of real world data typically involve continuous probability distributions such as normal, Laplace, or exponential distributions. Such distributions are supported by many probabilistic modelling formalisms, including probabilistic database systems. Yet, the traditional theoretical framework of probabilistic databases focuses entirely on finite probabilistic databases. Only recently, we set out to develop the mathematical theory of infinite probabilistic databases. The present paper is an exposition of two recent papers which are cornerstones of this theory. In (Grohe, Lindner; ICDT 2020) we propose a very general framework for probabilistic databases, possibly involving continuous probability distributions, and show that queries have a well-defined semantics in this framework. In (Grohe, Kaminski, Katoen, Lindner; PODS 2020) we extend the declarative probabilistic programming language Generative Datalog, proposed by (B´ar´any et al. 2017) for discrete probability distributions, to continuous probability distributions and show that such programs yield generative models of continuous probabilistic databases.