Mathematical Basis for Physical Inference

While the axiomatic introduction of a probability distribution over a space is common, its use for making predictions, using physical theories and prior knowledge, suffers from a lack of formalization. We propose to introduce, in the space of all probability distributions, two operations, the OR and the AND operation, that bring to the space the necessary structure for making inferences on possible values of physical parameters. While physical theories are often asumed to be analytical, we argue that consistent inference needs to replace analytical theories by probability distributions over the parameter space, and we propose a systematic way of obtaining such "theoretical correlations", using the OR operation on the results of physical experiments. Predicting the outcome of an experiment or solving "inverse problems" are then examples of the use of the AND operation. This leads to a simple and complete mathematical basis for general physical inference.Comment: 24 pages, 4 figure

Astroinformatics of galaxies and quasars: a new general method for photometric redshifts estimation

With the availability of the huge amounts of data produced by current and future large multi-band photometric surveys, photometric redshifts have become a crucial tool for extragalactic astronomy and cosmology. In this paper we present a novel method, called Weak Gated Experts (WGE), which allows to derive photometric redshifts through a combination of data mining techniques. \noindent The WGE, like many other machine learning techniques, is based on the exploitation of a spectroscopic knowledge base composed by sources for which a spectroscopic value of the redshift is available. This method achieves a variance \sigma^2(\Delta z)=2.3x10^{-4} (\sigma^2(\Delta z) =0.08), where \Delta z = z_{phot} - z_{spec}) for the reconstruction of the photometric redshifts for the optical galaxies from the SDSS and for the optical quasars respectively, while the Root Mean Square (RMS) of the \Delta z variable distributions for the two experiments is respectively equal to 0.021 and 0.35. The WGE provides also a mechanism for the estimation of the accuracy of each photometric redshift. We also present and discuss the catalogs obtained for the optical SDSS galaxies, for the optical candidate quasars extracted from the DR7 SDSS photometric dataset {The sample of SDSS sources on which the accuracy of the reconstruction has been assessed is composed of bright sources, for a subset of which spectroscopic redshifts have been measured.}, and for optical SDSS candidate quasars observed by GALEX in the UV range. The WGE method exploits the new technological paradigm provided by the Virtual Observatory and the emerging field of Astroinformatics.Comment: 36 pages, 22 figures and 8 table

DroTrack: High-speed Drone-based Object Tracking Under Uncertainty

We present DroTrack, a high-speed visual single-object tracking framework for drone-captured video sequences. Most of the existing object tracking methods are designed to tackle well-known challenges, such as occlusion and cluttered backgrounds. The complex motion of drones, i.e., multiple degrees of freedom in three-dimensional space, causes high uncertainty. The uncertainty problem leads to inaccurate location predictions and fuzziness in scale estimations. DroTrack solves such issues by discovering the dependency between object representation and motion geometry. We implement an effective object segmentation based on Fuzzy C Means (FCM). We incorporate the spatial information into the membership function to cluster the most discriminative segments. We then enhance the object segmentation by using a pre-trained Convolution Neural Network (CNN) model. DroTrack also leverages the geometrical angular motion to estimate a reliable object scale. We discuss the experimental results and performance evaluation using two datasets of 51,462 drone-captured frames. The combination of the FCM segmentation and the angular scaling increased DroTrack precision by up to $9\%$ and decreased the centre location error by $162$ pixels on average. DroTrack outperforms all the high-speed trackers and achieves comparable results in comparison to deep learning trackers. DroTrack offers high frame rates up to 1000 frame per second (fps) with the best location precision, more than a set of state-of-the-art real-time trackers.Comment: 10 pages, 12 figures, FUZZ-IEEE 202

Financial Markets Analysis by Probabilistic Fuzzy Modelling

For successful trading in financial markets, it is important to develop financial models where one can identify different states of the market for modifying one???s actions. In this paper, we propose to use probabilistic fuzzy systems for this purpose. We concentrate on Takagi???Sugeno (TS) probabilistic fuzzy systems that combine interpretability of fuzzy systems with the statistical properties of probabilistic systems. We start by recapitulating the general architecture of TS probabilistic fuzzy rule-based systems and summarize the corresponding reasoning schemes. We mention how probabilities can be estimated from a given data set and how a probability distribution can be approximated by a fuzzy histogram. We apply our methodology for financial time series analysis and demonstrate how a probabilistic TS fuzzy system can be identified, assuming that a linguistic term set is given. We illustrate the interpretability of such a system by inspecting the rule bases of our models.time series analysis;data-driven design;fuzzy reasoning;fuzzy rule base;probabilistic fuzzy systems

Fuzzy-based Propagation of Prior Knowledge to Improve Large-Scale Image Analysis Pipelines

Many automatically analyzable scientific questions are well-posed and offer a variety of information about the expected outcome a priori. Although often being neglected, this prior knowledge can be systematically exploited to make automated analysis operations sensitive to a desired phenomenon or to evaluate extracted content with respect to this prior knowledge. For instance, the performance of processing operators can be greatly enhanced by a more focused detection strategy and the direct information about the ambiguity inherent in the extracted data. We present a new concept for the estimation and propagation of uncertainty involved in image analysis operators. This allows using simple processing operators that are suitable for analyzing large-scale 3D+t microscopy images without compromising the result quality. On the foundation of fuzzy set theory, we transform available prior knowledge into a mathematical representation and extensively use it enhance the result quality of various processing operators. All presented concepts are illustrated on a typical bioimage analysis pipeline comprised of seed point detection, segmentation, multiview fusion and tracking. Furthermore, the functionality of the proposed approach is validated on a comprehensive simulated 3D+t benchmark data set that mimics embryonic development and on large-scale light-sheet microscopy data of a zebrafish embryo. The general concept introduced in this contribution represents a new approach to efficiently exploit prior knowledge to improve the result quality of image analysis pipelines. Especially, the automated analysis of terabyte-scale microscopy data will benefit from sophisticated and efficient algorithms that enable a quantitative and fast readout. The generality of the concept, however, makes it also applicable to practically any other field with processing strategies that are arranged as linear pipelines.Comment: 39 pages, 12 figure