Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Intelligent Transportation Related Complex Systems and Sensors

Building around innovative services related to different modes of transport and traffic management, intelligent transport systems (ITS) are being widely adopted worldwide to improve the efficiency and safety of the transportation system. They enable users to be better informed and make safer, more coordinated, and smarter decisions on the use of transport networks. Current ITSs are complex systems, made up of several components/sub-systems characterized by time-dependent interactions among themselves. Some examples of these transportation-related complex systems include: road traffic sensors, autonomous/automated cars, smart cities, smart sensors, virtual sensors, traffic control systems, smart roads, logistics systems, smart mobility systems, and many others that are emerging from niche areas. The efficient operation of these complex systems requires: i) efficient solutions to the issues of sensors/actuators used to capture and control the physical parameters of these systems, as well as the quality of data collected from these systems; ii) tackling complexities using simulations and analytical modelling techniques; and iii) applying optimization techniques to improve the performance of these systems. It includes twenty-four papers, which cover scientific concepts, frameworks, architectures and various other ideas on analytics, trends and applications of transportation-related data

Deep Interpretability Methods for Neuroimaging

Brain dynamics are highly complex and yet hold the key to understanding brain function and dysfunction. The dynamics captured by resting-state functional magnetic resonance imaging data are noisy, high-dimensional, and not readily interpretable. The typical approach of reducing this data to low-dimensional features and focusing on the most predictive features comes with strong assumptions and can miss essential aspects of the underlying dynamics. In contrast, introspection of discriminatively trained deep learning models may uncover disorder-relevant elements of the signal at the level of individual time points and spatial locations. Nevertheless, the difficulty of reliable training on high-dimensional but small-sample datasets and the unclear relevance of the resulting predictive markers prevent the widespread use of deep learning in functional neuroimaging. In this dissertation, we address these challenges by proposing a deep learning framework to learn from high-dimensional dynamical data while maintaining stable, ecologically valid interpretations. The developed model is pre-trainable and alleviates the need to collect an enormous amount of neuroimaging samples to achieve optimal training. We also provide a quantitative validation module, Retain and Retrain (RAR), that can objectively verify the higher predictability of the dynamics learned by the model. Results successfully demonstrate that the proposed framework enables learning the fMRI dynamics directly from small data and capturing compact, stable interpretations of features predictive of function and dysfunction. We also comprehensively reviewed deep interpretability literature in the neuroimaging domain. Our analysis reveals the ongoing trend of interpretability practices in neuroimaging studies and identifies the gaps that should be addressed for effective human-machine collaboration in this domain. This dissertation also proposed a post hoc interpretability method, Geometrically Guided Integrated Gradients (GGIG), that leverages geometric properties of the functional space as learned by a deep learning model. With extensive experiments and quantitative validation on MNIST and ImageNet datasets, we demonstrate that GGIG outperforms integrated gradients (IG), which is considered to be a popular interpretability method in the literature. As GGIG is able to identify the contours of the discriminative regions in the input space, GGIG may be useful in various medical imaging tasks where fine-grained localization as an explanation is beneficial

Three Risky Decades: A Time for Econophysics?

Our Special Issue we publish at a turning point, which we have not dealt with since World War II. The interconnected long-term global shocks such as the coronavirus pandemic, the war in Ukraine, and catastrophic climate change have imposed significant humanitary, socio-economic, political, and environmental restrictions on the globalization process and all aspects of economic and social life including the existence of individual people. The planet is trapped—the current situation seems to be the prelude to an apocalypse whose long-term effects we will have for decades. Therefore, it urgently requires a concept of the planet's survival to be built—only on this basis can the conditions for its development be created. The Special Issue gives evidence of the state of econophysics before the current situation. Therefore, it can provide excellent econophysics or an inter-and cross-disciplinary starting point of a rational approach to a new era

Proceedings of the Second Joint Technology Workshop on Neural Networks and Fuzzy Logic, volume 2

Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by NASA and the University of Texas, Houston. Topics addressed included adaptive systems, learning algorithms, network architectures, vision, robotics, neurobiological connections, speech recognition and synthesis, fuzzy set theory and application, control and dynamics processing, space applications, fuzzy logic and neural network computers, approximate reasoning, and multiobject decision making

Comparative Analysis of Student Learning: Technical, Methodological and Result Assessing of PISA-OECD and INVALSI-Italian Systems .

PISA is the most extensive international survey promoted by the OECD in the field of education, which measures the skills of fifteen-year-old students from more than 80 participating countries every three years. INVALSI are written tests carried out every year by all Italian students in some key moments of the school cycle, to evaluate the levels of some fundamental skills in Italian, Mathematics and English. Our comparison is made up to 2018, the last year of the PISA-OECD survey, even if INVALSI was carried out for the last edition in 2022. Our analysis focuses attention on the common part of the reference populations, which are the 15-year-old students of the 2nd class of secondary schools of II degree, where both sources give a similar picture of the students

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters