874 research outputs found

    General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power

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    We study the general connectivity distribution functions for growing networks with preferential attachment of fractional power, Πikα\Pi_{i} \propto k^{\alpha}, using the Simon's method. We first show that the heart of the previously known methods of the rate equations for the connectivity distribution functions is nothing but the Simon's method for word problem. Secondly, we show that the case of fractional α\alpha the ZZ-transformation of the rate equation provides a fractional differential equation of new type, which coincides with that for PA with linear power, when α=1\alpha = 1. We show that to solve such a fractional differential equation we need define a transidental function Υ(a,s,c;z)\Upsilon (a,s,c;z) that we call {\it upsilon function}. Most of all previously known results are obtained consistently in the frame work of a unified theory.Comment: 10 page

    Taming neuronal noise with large networks

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    How does reliable computation emerge from networks of noisy neurons? While individual neurons are intrinsically noisy, the collective dynamics of populations of neurons taken as a whole can be almost deterministic, supporting the hypothesis that, in the brain, computation takes place at the level of neuronal populations. Mathematical models of networks of noisy spiking neurons allow us to study the effects of neuronal noise on the dynamics of large networks. Classical mean-field models, i.e., models where all neurons are identical and where each neuron receives the average spike activity of the other neurons, offer toy examples where neuronal noise is absorbed in large networks, that is, large networks behave like deterministic systems. In particular, the dynamics of these large networks can be described by deterministic neuronal population equations. In this thesis, I first generalize classical mean-field limit proofs to a broad class of spiking neuron models that can exhibit spike-frequency adaptation and short-term synaptic plasticity, in addition to refractoriness. The mean-field limit can be exactly described by a multidimensional partial differential equation; the long time behavior of which can be rigorously studied using deterministic methods. Then, we show that there is a conceptual link between mean-field models for networks of spiking neurons and latent variable models used for the analysis of multi-neuronal recordings. More specifically, we use a recently proposed finite-size neuronal population equation, which we first mathematically clarify, to design a tractable Expectation-Maximization-type algorithm capable of inferring the latent population activities of multi-population spiking neural networks from the spike activity of a few visible neurons only, illustrating the idea that latent variable models can be seen as partially observed mean-field models. In classical mean-field models, neurons in large networks behave like independent, identically distributed processes driven by the average population activity -- a deterministic quantity, by the law of large numbers. The fact the neurons are identically distributed processes implies a form of redundancy that has not been observed in the cortex and which seems biologically implausible. To show, numerically, that the redundancy present in classical mean-field models is unnecessary for neuronal noise absorption in large networks, I construct a disordered network model where networks of spiking neurons behave like deterministic rate networks, despite the absence of redundancy. This last result suggests that the concentration of measure phenomenon, which generalizes the ``law of large numbers'' of classical mean-field models, might be an instrumental principle for understanding the emergence of noise-robust population dynamics in large networks of noisy neurons

    FFT-Based Deep Learning Deployment in Embedded Systems

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    Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to thousands of neurons. Embedded platforms are now becoming essential for deep learning deployment due to their portability, versatility, and energy efficiency. The large model size of DNNs, while providing excellent accuracy, also burdens the embedded platforms with intensive computation and storage. Researchers have investigated on reducing DNN model size with negligible accuracy loss. This work proposes a Fast Fourier Transform (FFT)-based DNN training and inference model suitable for embedded platforms with reduced asymptotic complexity of both computation and storage, making our approach distinguished from existing approaches. We develop the training and inference algorithms based on FFT as the computing kernel and deploy the FFT-based inference model on embedded platforms achieving extraordinary processing speed.Comment: Design, Automation, and Test in Europe (DATE) For source code, please contact Mahdi Nazemi at <[email protected]

    Probabilistic Anomaly Detection in Natural Gas Time Series Data

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    This paper introduces a probabilistic approach to anomaly detection, specifically in natural gas time series data. In the natural gas field, there are various types of anomalies, each of which is induced by a range of causes and sources. The causes of a set of anomalies are examined and categorized, and a Bayesian maximum likelihood classifier learns the temporal structures of known anomalies. Given previously unseen time series data, the system detects anomalies using a linear regression model with weather inputs, after which the anomalies are tested for false positives and classified using a Bayesian classifier. The method can also identify anomalies of an unknown origin. Thus, the likelihood of a data point being anomalous is given for anomalies of both known and unknown origins. This probabilistic anomaly detection method is tested on a reported natural gas consumption data set

    Experiences of Historically Black and Traditionally Latino Fraternity and Sorority Members at a Predominately White Institution

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    Research on college students and student groups is so important because student populations are continuously changing and administrators must keep up to meet the needs of evolving students. In particular, African American and Latino fraternities and sororities are different from majority Greek organizations. Their differences are sometimes clustered together although these are two very different cultural groups. Through interviews with these two groups of students, the principal investigator attempted to better understand the experiences of African American and Latino fraternity and sorority members as well as their similarities and differences. The examination of results identify several themes outlining the experiences of these groups of students as well as explained the differences in the initial contact with the organization and the membership intake experiences

    Exploring Character Pattern Recognition Techniques: A case study for Greek Polytonic Machine-Printed Characters

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    Σε αυτη την διπλωματική εργασία εξερευνούμε διάφορες τεχνικές αναγνώρισης προτύπων για χαρακτήρες και παρουσιάζουμε μια μελέτη περίπτωσης για Ελληνικούς πολυτονικούς τυπωμένους χαρακτήρες όπου οι τεχνικές αυτές είναι εφαρμόσιμες. Υλοποιούμε και περιγράφουμε στατιστικές τεχνικές μηχανικής χαρακτηριστικών (feature engineering) όπως είναι ο διαχωρισμός του χαρακτήρα σε ζώνες, ο διαχωρισμός του χαρακτήρα σε προσαρμοστικές ζώνες, η εξαγωγή ιστογραμμάτων κάθετων και οριζόντιων προβολών καθώς και μια τεχνική εξαγωγής χαρακτηριστικών που βασίζεται σε αναδρομικές υποδιαιρέσεις του χαρακτήρα. Επιπλέον, υλοποιούμε και συζητάμε δύο τεχνικές κατηγοριοποίησης, η μια βασίζεται στο μοντέλο του ταιριάσματος προτύπου (template matching) και η άλλη βασίζεται στα τεχνητά νευρωνικά δίκτυα. Επιπρόσθετα, παρουσιάζουμε την υλοποιημένη σε python βιβλιοθήκη ανοικτού κώδικα που διεκπεραιώνει αυτές τις λειτουργίες μαζί με μια ενότητα για το πώς να την χρησιμοποιήσει κάποιος. Τέλος, αξιολογούμε τις προαναφερθείσες τεχνικές σε δύο διαφορετικά σύνολα δεδομένων που περιέχουν Ελληνικούς πολυτονικούς χαρακτήρες και παρουσιάζουμε τα αποτελέσματα μας για όσον αφορά την απόδοση των μεθόδων μας.In this thesis we explore various character pattern recognition techniques and we present a case study for Greek polytonic machine-printed characters where those techniques are applicable. We implement and describe statistical feature engineering techniques such as character zoning, adaptive character zoning, extraction of horizontal and vertical projection histograms as well as a feature extraction technique based on recursive subdivisions of the character. We also implement and discuss two classification techniques, one based on the template matching model and the other one based on artificial neural networks. Additionally, the python-based open source library that implements those functionalities is presented along with a how-to-use section. Finally, we evaluate the aforementioned techniques on two separate datasets that contain Greek polytonic characters and we present our results on the performance of our methods
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