Signatures of partition functions and their complexity reduction through the KP II equation

A statistical amoeba arises from a real-valued partition function when the positivity condition for pre-exponential terms is relaxed, and families of signatures are taken into account. This notion lets us explore special types of constraints when we focus on those signatures that preserve particular properties. Specifically, we look at sums of determinantal type, and main attention is paid to a distinguished class of soliton solutions of the Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures preserving the determinantal form, as well as the signatures compatible with the KP II equation, is provided: both of them are reduced to choices of signs for columns and rows of a coefficient matrix, and they satisfy the whole KP hierarchy. Interpretations in term of information-theoretic properties, geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of the paper has been change

Shrunken Locally Linear Embedding for Passive Microwave Retrieval of Precipitation

This paper introduces a new Bayesian approach to the inverse problem of passive microwave rainfall retrieval. The proposed methodology relies on a regularization technique and makes use of two joint dictionaries of coincidental rainfall profiles and their corresponding upwelling spectral radiative fluxes. A sequential detection-estimation strategy is adopted, which basically assumes that similar rainfall intensity values and their spectral radiances live close to some sufficiently smooth manifolds with analogous local geometry. The detection step employs a nearest neighborhood classification rule, while the estimation scheme is equipped with a constrained shrinkage estimator to ensure stability of retrieval and some physical consistency. The algorithm is examined using coincidental observations of the active precipitation radar (PR) and passive microwave imager (TMI) on board the Tropical Rainfall Measuring Mission (TRMM) satellite. We present promising results of instantaneous rainfall retrieval for some tropical storms and mesoscale convective systems over ocean, land, and coastal zones. We provide evidence that the algorithm is capable of properly capturing different storm morphologies including high intensity rain-cells and trailing light rainfall, especially over land and coastal areas. The algorithm is also validated at an annual scale for calendar year 2013 versus the standard (version 7) radar (2A25) and radiometer (2A12) rainfall products of the TRMM satellite

A traffic classification method using machine learning algorithm

Applying concepts of attack investigation in IT industry, this idea has been developed to design a Traffic Classification Method using Data Mining techniques at the intersection of Machine Learning Algorithm, Which will classify the normal and malicious traffic. This classification will help to learn about the unknown attacks faced by IT industry. The notion of traffic classification is not a new concept; plenty of work has been done to classify the network traffic for heterogeneous application nowadays. Existing techniques such as (payload based, port based and statistical based) have their own pros and cons which will be discussed in this literature later, but classification using Machine Learning techniques is still an open field to explore and has provided very promising results up till now

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results