scholarly journals Asymptotic Behavior of Memristive Circuits

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 789
Author(s):  
Francesco Caravelli
Keyword(s):  
Lyapunov Function ◽  
Spin Glasses ◽  
Optimization Problems ◽  
Strong Dependence ◽  
Mean Field ◽  
Stationary Points ◽  
Circuit Topology ◽  
Combinatorial Optimization Problems ◽  
The Matrix ◽  
Memristive Circuits

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors. Such a Lyapunov function can be asymptotically approximated with binary variables, and mapped to quadratic combinatorial optimization problems. This also shows a direct parallel between memristive circuits and the Hopfield-Little model. In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the projectors can be roughly approximated with a Gaussian distribution, and that it scales with the inverse square root of the number of elements. This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses. Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit. We estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only.

A GRADIENT SYSTEM SOLUTION TO POTTS MEAN FIELD EQUATIONS AND ITS ELECTRONIC IMPLEMENTATION

1993 ◽  
Vol 04 (01) ◽  
pp. 27-34 ◽  
Author(s):  
KIICHI URAHAMA ◽  
SHIN-ICHIRO UENO
Keyword(s):  
Solution Method ◽  
Optimization Problems ◽  
Mean Field ◽  
Gradient System ◽  
Field Equations ◽  
Combinatorial Optimization Problems ◽  
System Solution ◽  
Mean Field Equations ◽  
Optimum Solution ◽  
Winner Take All

A gradient system solution method is presented for solving Potts mean field equations for combinatorial optimization problems subject to winner-take-all constraints. In the proposed solution method the optimum solution is searched by using gradient descent differential equations whose trajectory is confined within the feasible solution space of optimization problems. This gradient system is proven theoretically to always produce a legal local optimum solution of combinatorial optimization problems. An elementary analog electronic circuit implementing the presented method is designed on the basis of current-mode subthreshold MOS technologies. The core constituent of the circuit is the winner-take-all circuit developed by Lazzaro et al. Correct functioning of the presented circuit is exemplified with simulations of the circuits implementing the scheme for solving the shortest path problems.

CONSTRAINED POTTS MEAN FIELD SYSTEMS AND THEIR ELECTRONIC IMPLEMENTATION

1994 ◽  
Vol 05 (03) ◽  
pp. 229-239 ◽  
Author(s):  
KIICHI URAHAMA ◽  
TADASHI YAMADA
Keyword(s):  
Combinatorial Optimization ◽  
Present Method ◽  
Electronic Circuit ◽  
Optimization Problems ◽  
Mean Field ◽  
Local Optimum ◽  
Combinatorial Optimization Problems ◽  
Maximum Cut ◽  
Cut Problems ◽  
Additional Constraints

The Potts mean field approach for solving combinatorial optimization problems subject to winner-takes-all constraints is extended for problems subject to additional constraints. Extra variables corresponding to the Lagrange multipliers are incorporated into the Potts formulation for the additional constraints to be satisfied. The extended Potts equations are solved by using constrained gradient descent differential systems. This gradient system is proven theoretically to always produce a legal local optimum solution of the constrained combinatorial optimization problems. An analog electronic circuit implementing the present method is designed on the basis of the previous Potts electronic circuit. The performance of the present method is theoretically evaluated for the constrained maximum cut problems. The lower bound of the cut size obtained with the present method is proven to be the same as that of the basic Potts scheme for the unconstrained maximum cut problems.

scholarly journals Optimization of wind solar and battery hybrid renewable system using backtrack search algorithm

2021 ◽  
Vol 24 (3) ◽  
pp. 1269
Author(s):  
Ingudam Chitrasen Meitei ◽  
Rajen Pudur
Keyword(s):  
Power Generation ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cost Optimization ◽  
Combinatorial Optimization Problems ◽  
Hybrid Combination ◽  
The Matrix ◽  
Electrical Engineers ◽  
Backtrack Search ◽  
Efficiency Cost

<p>Penetration of renewable sources to the grid is always a problem for electrical engineers, apart from reliability and efficiency, cost optimization is also a big concern among them. Wind, solar and battery hybrid combinations (WSB-HPS) are also very common among hybrid systems, but this WSBHPS combines wind and solar energy power generation reduces the charge and discharge time of the battery. Therefore, this system improves the reliability of the power supply by fully utilizing the wind and solar power generation and improves the charging and discharging state of the battery and hence reduces the whole cost as the investment in battery is reduced. backtrack search algorithm (BSA) is the highly efficient and powerful algorithm to solve combinatorial optimization problems. In this paper an attempt is made to optimize the hybrid combination using BSA in the matrix laboratory (MATLAB) environment and comparable study is made using HOMER. A complete optimised data is generated for a particular area in Manipur and reduced cost is suggested.</p>

APPLYING TABU SEARCH TO THE TWO-DIMENSIONAL ISING SPIN GLASS

1995 ◽  
Vol 06 (01) ◽  
pp. 11-23 ◽  
Author(s):  
MANUEL LAGUNA ◽  
PABLO LAGUNA
Keyword(s):  
Tabu Search ◽  
Spin Glasses ◽  
Statistical Physics ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Optimization Techniques ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spin Lattice ◽  
Combinatorial Optimization Problems

A variety of problems in statistical physics, such as Ising-like systems, can be modeled as integer programs. Physicists have relied mostly on Monte Carlo methods to find approximate solutions to these computationally difficult problems. In some cases, optimal solutions to relatively small problems have been found using standard optimization techniques, e.g., cutting plane and branch-and-bound algorithms. Motivated by the success of tabu search (TS) in finding optimal or near-optimal solutions to combinatorial optimization problems in a number of different settings, we study the application of this methodology to Ising-like systems. Particularly, we develop a TS method to find ground states of two-dimensional spin glasses. Our method performs a search at different levels of resolution in the spin lattice, and it is designed to obtain optimal or near-optimal solutions to problem instances with several different characteristics. Results are reported for computational experiments with up to 64×64 lattices.

scholarly journals A Non-Volatile All-Spin Analog Matrix Multiplier: An Efficient Hardware Accelerator for Machine Learning

2021 ◽  
Author(s):  
Supriyo Bandyopadhyay ◽  
Rahnuma Rahman
Keyword(s):  
Machine Learning ◽  
Deep Neural Networks ◽  
Tunnel Junctions ◽  
Optimization Problems ◽  
Maximum Energy ◽  
Hardware Accelerator ◽  
Von Neumann ◽  
Combinatorial Optimization Problems ◽  
The Matrix ◽  
Energy Dissipated

We propose and analyze a compact and <i>non-volatile</i> nanomagnetic (all-spin) analog matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions – one activated by strain to act as the multiplier, and the other activated by spin-orbit torque pulses to act as a domain wall synapse that performs the operation of the accumulator. Each MAC operation can be performed in ~1 ns and the maximum energy dissipated per operation is ~100 aJ. This provides a very useful hardware accelerator for machine learning (e.g. training of deep neural networks), solving combinatorial optimization problems with Ising type machines, and other artificial intelligence tasks which often involve the multiplication of large matrices. The non-volatility allows the matrix multiplier to be embedded in powerful non-von-Neumann architectures.

scholarly journals A Non-Volatile All-Spin Analog Matrix Multiplier: An Efficient Hardware Accelerator for Machine Learning

2021 ◽  
Author(s):  
Supriyo Bandyopadhyay ◽  
Rahnuma Rahman
Keyword(s):  
Machine Learning ◽  
Deep Neural Networks ◽  
Tunnel Junctions ◽  
Optimization Problems ◽  
Maximum Energy ◽  
Hardware Accelerator ◽  
Von Neumann ◽  
Combinatorial Optimization Problems ◽  
The Matrix ◽  
Energy Dissipated

We propose and analyze a compact and <i>non-volatile</i> nanomagnetic (all-spin) analog matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions – one activated by strain to act as the multiplier, and the other activated by spin-orbit torque pulses to act as a domain wall synapse that performs the operation of the accumulator. Each MAC operation can be performed in ~1 ns and the maximum energy dissipated per operation is ~100 aJ. This provides a very useful hardware accelerator for machine learning (e.g. training of deep neural networks), solving combinatorial optimization problems with Ising type machines, and other artificial intelligence tasks which often involve the multiplication of large matrices. The non-volatility allows the matrix multiplier to be embedded in powerful non-von-Neumann architectures.

Applications to Other Fields

2013 ◽  
Author(s):  
Daniel L. Stein ◽  
Charles M. Newman
Keyword(s):  
Neural Networks ◽  
Combinatorial Optimization ◽  
Spin Glasses ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Conformational Dynamics ◽  
Prebiotic Evolution ◽  
Combinatorial Optimization Problems ◽  
Protein Conformational Dynamics ◽  
Classic Papers

This chapter explores how spin glass concepts have found use in and, in some cases, further advanced areas such as computational complexity, combinatorial optimization, neural networks, protein conformational dynamics and folding, and computer science (through the introduction of new heuristic algorithms such as simulated annealing and neural-based computation, and through new approaches to analyzing hard combinatorial optimization problems). It also introduces some “short takes” on topics that space constraints prevent covering in detail, but should be at least mentioned: prebiotic evolution, Kauffman's NK model, and the maturation of the immune response. The chapter summarizes the heart of what most people mean when they refer to spin glasses as relevant to complexity. It focuses on the early, classic papers in each subject, giving the reader a flavor of each.

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