Application of logistic regression to simulate the influence of rainfall genesis on storm overflow operations: a probabilistic approach

Abstract. One of the key parameters constituting the basis for the operational assessment of stormwater systems is the annual number of storm overflows. Since uncontrolled overflows are a source of pollution washed away from the surface of the catchment area, which leads to imbalanced receiving waters, there is a need for their prognosis and potential reduction. The paper presents a probabilistic model for simulating the annual number of storm overflows. In this model, an innovative solution is to use the logistic regression method to analyze the impact of rainfall genesis on the functioning of a storm overflow (OV) in the example of a catchment located in the city of Kielce (central Poland). The developed model consists of two independent elements. The first element of the model is a synthetic precipitation generator, in which the simulation of rainfall takes into account its genesis resulting from various processes and phenomena occurring in the troposphere. This approach makes it possible to account for the stochastic nature of rainfall in relation to the annual number of events. The second element is the model of logistic regression, which can be used to model the storm overflow resulting from the occurrence of a single rainfall event. The paper confirmed that storm overflow can be modeled based on data on the total rainfall and its duration. An alternative approach was also proposed, providing the possibility of predicting storm overflow only based on the average rainfall intensity. Substantial simplification in the simulation of the phenomenon under study was achieved compared with the works published in this area to date. It is worth noting that the coefficients determined in the logit models have a physical interpretation, and the universal character of these models facilitates their easy adaptation to other examined catchment areas. The calculations made in the paper using the example of the examined catchment allowed for an assessment of the influence of rainfall characteristics (depth, intensity, and duration) of different genesis on the probability of storm overflow. Based on the obtained results, the range of the variability of the average rainfall intensity, which determines the storm overflow, and the annual number of overflows resulting from the occurrence of rain of different genesis were defined. The results are suited for the implementation in the assessment of storm overflows only based on the genetic type of rainfall. The results may be used to develop warning systems in which information about the predicted rainfall genesis is an element of the assessment of the rainwater system and its facilities. This approach is an original solution that has not yet been considered by other researchers. On the other hand, it represents an important simplification and an opportunity to reduce the amount of data to be measured

Real estate appraisals with Bayesian approach and Markov Chain Hybrid Monte Carlo Method: An application to a central urban area of Naples

This paper experiments an artificial neural networks model with Bayesian approach on a small real estate sample. The output distribution has been calculated operating a numerical integration on the weights space with the Markov Chain Hybrid Monte Carlo Method (MCHMCM). On the same real estate sample, MCHMCM has been compared with a neural networks model (NNs), traditional multiple regression analysis (MRA) and the Penalized Spline Semiparametric Method (PSSM). All four methods have been developed for testing the forecasting capacity and reliability of MCHMCM in the real estate field. The Markov Chain Hybrid Monte Carlo Method has proved to be the best model with an absolute average percentage error of 6.61%

On the Parity Problem in One-Dimensional Cellular Automata

We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices. We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can possibly solve the parity problem from arbitrary initial configurations. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and we formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Mesoscopic Casimir forces from effects of discrete particle number in the quantum vacuum

Traditionally it is assumed that the Casimir vacuum pressure does not depend on the ultraviolet cut-off. There are, however, some arguments that the effect actually depends on the regularization procedure and thus on the trans-Planckian physics. We provide the condensed matter example where the Casimir forces do explicitly depend on the microscopic (correspondingly trans-Planckian) physics due to the mesoscopic finite-N effects, where N is the number of bare particles in condensed matter (or correspondingly the number of the elements comprising the quantum vacuum). The finite-N effects lead to mesoscopic fluctuations of the vacuum pressure. The amplitude of the mesoscopic flustuations of the Casimir force in a system with linear dimension L is larger by the factor N^{1/3}\sim L/a than the traditional value of the Casimir force given by effective theory, where a is the interatomic distance which plays the role of the Planck length.Comment: LaTeX file, 13 pages, no figures, submitted to JETP Letter

Accelerated detectors in Dirac vacuum: the effects of horizon fluctuations

We consider an Unruh-DeWitt detector interacting with a massless Dirac field. Assuming that the detector is moving along an hyperbolic trajectory, we modeled the effects of fluctuations in the event horizon using a Dirac equation with random coefficients. First, we develop the perturbation theory for the fermionic field in a random media. Further we evaluate corrections due to the randomness in the response function associated to different model detectors.Comment: 19 pages, 1 figur

Ordering Quantiles through Confidence Statements

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of different populations using independent samples. This confidence may provide insights about possible differences among groups and yields a ranking of importance for the variables. Computations are efficient and use exact distributions with no need for asymptotic considerations. Experiments with simulated data and with multiple real -omics data sets are performed, and they show advantages and disadvantages of the method. Quor has no assumptions but independence of samples, thus it might be a better option when assumptions of other methods cannot be asserted. The software is publicly available on CRAN

Light-cone fluctuations and the renormalized stress tensor of a massless scalar field

We investigate the effects of light-cone fluctuations over the renormalized vacuum expectation value of the stress-energy tensor of a real massless minimally coupled scalar field defined in a ($d+1$)-dimensional flat space-time with topology ${\cal R}\times {\cal S}^d$. For modeling the influence of light-cone fluctuations over the quantum field, we consider a random Klein-Gordon equation. We study the case of centered Gaussian processes. After taking into account all the realizations of the random processes, we present the correction caused by random fluctuations. The averaged renormalized vacuum expectation value of the stress-energy associated with the scalar field is presented