scholarly journals Machine learning in spectral domain

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lorenzo Giambagli ◽  
Lorenzo Buffoni ◽  
Timoteo Carletti ◽  
Walter Nocentini ◽  
Duccio Fanelli
Keyword(s):  
Deep Neural Networks ◽  
Orthogonal Basis ◽  
Spectral Domain ◽  
Reservoir Computing ◽  
Eigenvalues And Eigenvectors ◽  
New Approach ◽  
Linear Classifiers ◽  
Spectral Learning ◽  
Identical Number ◽  
Free Parameters

AbstractDeep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvalues and eigenvectors of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non-linear classifiers. Adjusting the eigenvalues, when freezing the eigenvectors entries, yields performances that are superior to those attained with standard methods restricted to operate with an identical number of free parameters. To recover a feed-forward architecture in direct space, we have postulated a nested indentation of the eigenvectors. Different non-orthogonal basis could be employed to export the spectral learning to other frameworks, as e.g. reservoir computing.

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

scholarly journals FPGA-Based Stochastic Echo State Networks for Time-Series Forecasting

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Miquel L. Alomar ◽  
Vincent Canals ◽  
Nicolas Perez-Mora ◽  
Víctor Martínez-Moll ◽  
Josep L. Rosselló
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Power Dissipation ◽  
Hardware Implementation ◽  
Functional System ◽  
Time Series Forecasting ◽  
Reservoir Computing ◽  
New Approach ◽  
Echo State Networks ◽  
Learning Capabilities

Hardware implementation of artificial neural networks (ANNs) allows exploiting the inherent parallelism of these systems. Nevertheless, they require a large amount of resources in terms of area and power dissipation. Recently, Reservoir Computing (RC) has arisen as a strategic technique to design recurrent neural networks (RNNs) with simple learning capabilities. In this work, we show a new approach to implement RC systems with digital gates. The proposed method is based on the use of probabilistic computing concepts to reduce the hardware required to implement different arithmetic operations. The result is the development of a highly functional system with low hardware resources. The presented methodology is applied to chaotic time-series forecasting.

scholarly journals Caudate transcriptome implicates decreased presynaptic autoregulation as the dopamine risk factor for schizophrenia

2020 ◽  
Author(s):  
Kynon JM Benjamin ◽  
Arthur S Feltrin ◽  
André Rocha Barbosa ◽  
Andrew E Jaffe ◽  
Leonardo Collado-Torres ◽  
...  
Keyword(s):  
Caudate Nucleus ◽  
Deep Neural Networks ◽  
Psychotic Symptoms ◽  
Common Variants ◽  
D2 Dopamine Receptor ◽  
Risk Genes ◽  
New Approach ◽  
New Genes ◽  
Da Release

AbstractIncreased dopamine (DA) signaling in the striatum has been a cornerstone hypothesis about psychosis for over 50 years. Increased dopamine release results in psychotic symptoms, while D2 dopamine receptor (DRD2) antagonists are antipsychotic. Recent schizophrenia GWAS identified risk-associated common variants near the DRD2 gene, but the risk mechanism has been unclear. We performed RNA-sequencing in postmortem caudate nucleus from 444 individuals and identified many new genes associated with risk for schizophrenia through genetic modulation of expression. Genetic risk for schizophrenia is associated specifically with decreased expression of the short isoform of DRD2, which encodes the presynaptic autoreceptor, and not with expression of the long isoform postsynaptic receptor. These data implicate decreased control of presynaptic DA release as a genetic mechanism of schizophrenia risk. Using a new approach based on deep neural networks, we construct caudate gene expression networks that highlight interactions involving schizophrenia risk genes and uncover potential novel therapeutic targets.One Sentence SummaryA comprehensive analysis of schizophrenia risk and of the role of DRD2 signaling within the caudate nucleus.

A Quadratic Form-Based Approach to Identification of Kinematic Chains in Structural Analysis and Synthesis of Mechanisms

2001 ◽  
Author(s):  
Peiren He ◽  
Wenjun Zhang ◽  
Qing Li
Keyword(s):  
Structural Analysis ◽  
Quadratic Form ◽  
Test Cases ◽  
Eigenvalues And Eigenvectors ◽  
New Approach ◽  
Kinematic Chains ◽  
Synthesis Of Mechanisms ◽  
Adjacency Matrices ◽  
Analysis And Synthesis

Abstract Identification of kinematic chains is needed when studying in structural analysis and synthesis of mechanisms. Research on detection of isomorphism in graphs/kinematic chains has a long history. Many algorithms or methods have been proposed. However, these methods have only achieved success in restricted conditions. This paper proposes a new approach using the concept of quadratic form. Graphs/kinematic chains are first represented by their adjacency matrices, the eigenvalues and their eigenvectors corresponding to these adjacency matrices are then calculated. Two graphs are represented by two quadratic expressions. The comparison of two graphs reduces to the comparison of two quadratic expressions. Quadratic expressions are characterized by the eigenvalues and eigenvectors. An algorithm is developed to compare, correspondingly, eigenvalues and eigenvectors of two graphs, known test cases are used to verify the effectiveness of the approach.

Hardware-Based Framework of Photonic Reservoir Computing with Coupled SOAs Network

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Louiza Dehyadegari ◽  
Mohammad Reza Salehi ◽  
Maryam Sedigh Sarvestani ◽  
Ebrahim Abiri
Keyword(s):  
Time Series ◽  
Random Sequence ◽  
Reservoir Computing ◽  
Time Series Classification ◽  
Noisy Signal ◽  
Photonic Structure ◽  
New Approach ◽  
Triangular Wave ◽  
Wave Forms ◽  
One Step

AbstractIn this paper, a photonic structure for reservoir computing is presented. A new approach for photonic reservoir computing is proposed using a network of SOAs arranged in a waterfall topology and coupled by semi-transparent mirrors. The proposed method is then simulated in OptiSystem software. As this software is hardware framework-based, the simulation result is one step closer to fabrication than the previous works. A series of noisy and noise-free time-series signals are employed to evaluate the performance of the proposed method. The used time-series signals contain random sequence of both square and triangular wave forms. The results of this simulation show 92.14% recognition of a noise-free signal and 79.32% of a 60 dB noisy signal. The parameters of the simulated photonic reservoir network are also optimized to achieve higher accuracy in this time-series classification.

Accurate and efficient study of substrate-integrated waveguide devices using iterative wave method

2015 ◽  
Vol 9 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Jamel Ben Romdhan Hajri ◽  
Hafedh Hrizi ◽  
Noureddine Sboui
Keyword(s):  
Iterative Method ◽  
Iterative Process ◽  
Spectral Domain ◽  
Substrate Integrated Waveguide ◽  
Wave Method ◽  
Fast Analysis ◽  
New Approach ◽  
Waveguide Devices ◽  
Numerical Complexity ◽  
Good Agreement

This paper proposes an efficient and fast analysis of substrate integrated waveguide (SIW) components using a new approach of the iterative method called WCIP, i.e. “Wave Concept Iterative Process”. This method is based on the iterative resolution of waves between two domains. The first is the spectral domain. We use the Floquet–Bloch decomposition to describe all modes in the spectral domain. The second describes the configuration of the circuit in the spatial domain. It allows taking the exact structure according to the appropriate boundary conditions. This method permits to reduce numerical complexity. The convergence of this approach is always guaranteed. The theoretical suggested study is validated by the simulation of two different examples of SIW circuits. The obtained results are in good agreement with those of measurement and with software HFSS simulations, which prove the advantage of this method.

scholarly journals Complex Risk Statistics with Scenario Analysis

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fei Sun ◽  
Yichuan Dong
Keyword(s):  
Neural Networks ◽  
Risk Management ◽  
Scenario Analysis ◽  
Special Class ◽  
Intelligent Systems ◽  
Deep Neural Networks ◽  
Critical Factor ◽  
New Approach ◽  
Dual Representations

Complex risk is a critical factor for both intelligent systems and risk management. In this paper, we consider a special class of risk statistics, named complex risk statistics. Our result provides a new approach for addressing complex risk, especially in deep neural networks. By further developing the properties related to complex risk statistics, we are able to derive dual representations for such risk.

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