scholarly journals Minimization of Quadratic Binary Functional with Additive Connection Matrix

2009 ◽  
pp. 161-170
Author(s):  
Leonid Litinskii
Keyword(s):  
Connection Matrix

scholarly journals A computational framework for connection matrix theory

2021 ◽  
Author(s):  
Shaun Harker ◽  
Konstantin Mischaikow ◽  
Kelly Spendlove
Keyword(s):  
Matrix Theory ◽  
Connection Matrix ◽  
Computational Framework

scholarly journals Inverse Problem for Ising Connection Matrix with Long-Range Interaction

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1624
Author(s):  
Leonid Litinskii ◽  
Boris Kryzhanovsky
Keyword(s):  
Inverse Problem ◽  
Long Range ◽  
Random Number ◽  
Connection Matrix ◽  
Range Interaction ◽  
Connection Matrices ◽  
Ising Systems ◽  
Long Range Interaction ◽  
Matrix Spectrum ◽  
Analytical Expressions

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

scholarly journals GateRL: Automated Circuit Design Framework of CMOS Logic Gates Using Reinforcement Learning

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1032
Author(s):  
Hyoungsik Nam ◽  
Young In Kim ◽  
Jina Bae ◽  
Junhee Lee
Keyword(s):  
Reinforcement Learning ◽  
Circuit Design ◽  
Logic Gates ◽  
Connection Matrix ◽  
Design Framework ◽  
Network Layers ◽  
Learning Speed ◽  
Fully Connected ◽  
Automated Circuit Design ◽  
Circuit Configuration

This paper proposes a GateRL that is an automated circuit design framework of CMOS logic gates based on reinforcement learning. Because there are constraints in the connection of circuit elements, the action masking scheme is employed. It also reduces the size of the action space leading to the improvement on the learning speed. The GateRL consists of an agent for the action and an environment for state, mask, and reward. State and reward are generated from a connection matrix that describes the current circuit configuration, and the mask is obtained from a masking matrix based on constraints and current connection matrix. The action is given rise to by the deep Q-network of 4 fully connected network layers in the agent. In particular, separate replay buffers are devised for success transitions and failure transitions to expedite the training process. The proposed network is trained with 2 inputs, 1 output, 2 NMOS transistors, and 2 PMOS transistors to design all the target logic gates, such as buffer, inverter, AND, OR, NAND, and NOR. Consequently, the GateRL outputs one-transistor buffer, two-transistor inverter, two-transistor AND, two-transistor OR, three-transistor NAND, and three-transistor NOR. The operations of these resultant logics are verified by the SPICE simulation.

Convergence Theory for Unified Discrete-Time RNNs with Quasi-Symmetric Connection

2014 ◽  
Vol 538 ◽  
pp. 167-170
Author(s):  
Hui Zhong Mao ◽  
Chen Qiao ◽  
Wen Feng Jing ◽  
Xi Chen ◽  
Jin Qin Mao
Keyword(s):  
Neural Network ◽  
Global Convergence ◽  
Discrete Time ◽  
Recurrent Neural Network ◽  
Symmetric Matrix ◽  
Network Models ◽  
Convergence Theory ◽  
Connection Matrix ◽  
Neural Network Models ◽  
Symmetric Connection

This paper presents the global convergence theory of the discrete-time uniform pseudo projection anti-monotone network with the quasi–symmetric matrix, which removes the connection matrix constraints. The theory widens the range of applications of the discrete–time uniform pseudo projection anti–monotone network and is valid for many kinds of discrete recurrent neural network models.

scholarly journals Brain Networks Maintain a Scale-free Organization across Consciousness, Anesthesia, and Recovery

2010 ◽  
Vol 113 (5) ◽  
pp. 1081-1091 ◽  
Author(s):  
UnCheol Lee ◽  
GabJin Oh ◽  
Seunghwan Kim ◽  
GyuJung Noh ◽  
ByungMoon Choi ◽  
...  
Keyword(s):  
General Anesthesia ◽  
Minimum Spanning Tree ◽  
Essential Feature ◽  
Fundamental Principle ◽  
Temporal Organization ◽  
Cumulative Distribution ◽  
Connection Matrix ◽  
Scale Free ◽  
States Of Consciousness ◽  
Network Connections

Background Loss of consciousness is an essential feature of general anesthesia. Although alterations of neural networks during anesthesia have been identified in the spatial domain, there has been relatively little study of temporal organization. Methods Ten healthy male volunteers were anesthetized with an induction dose of propofol on two separate occasions. The duration of network connections in the brain was analyzed by multichannel electroencephalography and the minimum spanning tree method. Entropy of the connections was calculated based on Shannon entropy. The global temporal configuration of networks was investigated by constructing the cumulative distribution function of connection times in different frequency bands and different states of consciousness. Results General anesthesia was associated with a significant reduction in the number of network connections, as well as significant alterations of their duration. These changes were most prominent in the δ bandwidth and were also associated with a significant reduction in entropy of the connection matrix. Despite these and other changes, a global "scale-free" organization was consistently preserved across multiple subjects, anesthetic exposures, states of consciousness, and electroencephalogram frequencies. Conclusions Our data suggest a fundamental principle of temporal organization of network connectivity that is maintained during consciousness and anesthesia, despite local changes. These findings are consistent with a process of adaptive reconfiguration during general anesthesia.

Stable Assembly Sequence Planning Using a Genetic Algorithm

1999 ◽  
Author(s):  
Shiang-Fong Chen ◽  
Xiao-Yun Liao
Keyword(s):  
Genetic Algorithm ◽  
Simple Structure ◽  
Fitness Function ◽  
Assembly Sequence Planning ◽  
Connection Matrix ◽  
Assembly Sequence ◽  
Sequence Planning ◽  
Industry Standard ◽  
Planning Algorithm ◽  
The Stability

Abstract Stability problems in assembly sequence planning have drawn great research interest in recent years. Most proposed methodologies are based on graph theory and involve complex geometric and physical analyses. As a result, even for a simple structure, it is difficult to take all the criteria into account and to implement real world solutions. This paper uses a genetic algorithm (GA) to synthesize different criteria fo generating a stable assembl plan. Three matrices (Connection Matrix, Supporting Matrix, and Interference-Free Matrix) are generated from an input B-rep file to represent the CAD information of a given product. The stability of a given assembly plan and reorientation numbers are incorporated into the fitness function of the genetic assembly planner. The proposed planning algorithm has been successfull implemented. This paper also presents implemented planne performance as measured for two industry-standard structures.

Echo State Property Linked to an Input: Exploring a Fundamental Characteristic of Recurrent Neural Networks

2013 ◽  
Vol 25 (3) ◽  
pp. 671-696 ◽  
Author(s):  
G. Manjunath ◽  
H. Jaeger
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Statistical Characteristics ◽  
Connection Matrix ◽  
Reservoir Computing ◽  
Mathematical Methods ◽  
Network Response ◽  
Network Connection ◽  
Memory Content ◽  
Definition Of

The echo state property is a key for the design and training of recurrent neural networks within the paradigm of reservoir computing. In intuitive terms, this is a passivity condition: a network having this property, when driven by an input signal, will become entrained by the input and develop an internal response signal. This excited internal dynamics can be seen as a high-dimensional, nonlinear, unique transform of the input with a rich memory content. This view has implications for understanding neural dynamics beyond the field of reservoir computing. Available definitions and theorems concerning the echo state property, however, are of little practical use because they do not relate the network response to temporal or statistical properties of the driving input. Here we present a new definition of the echo state property that directly connects it to such properties. We derive a fundamental 0-1 law: if the input comes from an ergodic source, the network response has the echo state property with probability one or zero, independent of the given network. Furthermore, we give a sufficient condition for the echo state property that connects statistical characteristics of the input to algebraic properties of the network connection matrix. The mathematical methods that we employ are freshly imported from the young field of nonautonomous dynamical systems theory. Since these methods are not yet well known in neural computation research, we introduce them in some detail. As a side story, we hope to demonstrate the eminent usefulness of these methods.

A Study of Linear Joint and Tool Models in Spindle-Holder-Tool Receptance Coupling

2005 ◽  
Author(s):  
Timothy J. Burns ◽  
Tony L. Schmitz
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Nonlinear Least Squares ◽  
Analytical Models ◽  
Connection Matrix ◽  
Depth Of Cut ◽  
Combined System ◽  
Receptance Coupling ◽  
Overhang Length ◽  
Exponential Trend

The dynamics of a spindle-holder-tool (SHT) system during high-speed machining is sensitive to changes in tool overhang length. A well-known method for predicting the limiting depth of cut for avoidance of tool chatter requires a good estimate of the tool-point frequency response (FRF) of the combined system, which depends upon the tool length. In earlier work, a combined analytical and experimental method has been discussed, that uses receptance coupling substructure analysis (RCSA) for the rapid prediction of the combined spindle-holder-tool FRF. The basic idea of the method is to combine the measured direct displacement vs. force receptance (i.e., frequency response) at the free end of the spindle-holder (SH) system with calculated expressions for the tool receptances based on analytical models. The tool was modeled as an Euler-Bernoulli (EB) beam, the other three spindle-holder receptances were set equal to zero, and the model for the connection with the tool led to a diagonal matrix. The main conclusion of the earlier work was that there was an exponential trend in the dominant connection parameter, which enabled interpolation between tip receptance data for the longest and shortest tools in the combined SHT system. Thus, a considerable savings in time and effort could be realized for the particular SHT system. A question left open in the earlier work was: how general is this observed exponential trend? Here, to explore this question further, an analytical EB model is used for the SH system, so that all four of its end receptances are available, and the tool is again modeled as a free-free EB beam that is connected to the SH by a specified connection matrix, that includes nonzero off-diagonal terms. This serves as the “exact” solution. The approximate solution is once again formed by setting all but one SH receptance equal to zero, and the connection parameters are determined using nonlinear least squares software. Both diagonal and full connection matrices are investigated. The main result is that, for this system, in the case of a diagonal connecting matrix, there is no apparent trend in the dominant connecting spring stiffness with tool overhang length. However, in the full connecting matrix case, a general constant trend is observed, with some interesting exceptions.

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