158 results on '"Traversa, Fabio L."'
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2. Projective Embedding of Dynamical Systems: uniform mean field equations
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Caravelli, Francesco, Traversa, Fabio L., Bonnin, Michele, and Bonani, Fabrizio
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Mathematics - Dynamical Systems ,Condensed Matter - Disordered Systems and Neural Networks ,Condensed Matter - Mesoscale and Nanoscale Physics ,Computer Science - Neural and Evolutionary Computing ,Mathematical Physics - Abstract
We study embeddings of continuous dynamical systems in larger dimensions via projector operators. We call this technique PEDS, projective embedding of dynamical systems, as the stable fixed point of the dynamics are recovered via projection from the higher dimensional space. In this paper we provide a general definition and prove that for a particular type of projector operator of rank-1, the uniform mean field projector, the equations of motion become a mean field approximation of the dynamical system. While in general the embedding depends on a specified variable ordering, the same is not true for the uniform mean field projector. In addition, we prove that the original stable fixed points remain stable fixed points of the dynamics, saddle points remain saddle, but unstable fixed points become saddles., Comment: 45 pages; one column; 10 figures
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- 2022
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3. Stochastic analysis of a bistable piezoelectric energy harvester with a matched electrical load
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Song, Kailing, Bonnin, Michele, Traversa, Fabio L., and Bonani, Fabrizio
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- 2023
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4. Global minimization via classical tunneling assisted by collective force field formation
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Caravelli, Francesco, Sheldon, Forrest C., and Traversa, Fabio L.
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Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed Matter - Soft Condensed Matter ,Computer Science - Neural and Evolutionary Computing ,Nonlinear Sciences - Chaotic Dynamics ,Physics - Classical Physics - Abstract
Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. The system we study has a simple mapping to a flow network, equivalent to current-driven memristors. The mechanism is appealing for its physical relevance in nanoscale physics, and to possible applications in optimization, novel Monte Carlo schemes and machine learning., Comment: 8 pages double column + 7 supplementary ; 8 figures
- Published
- 2021
5. Memcomputing for Accelerated Optimization
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Aiken, John and Traversa, Fabio L.
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Computer Science - Emerging Technologies ,Computer Science - Hardware Architecture ,Nonlinear Sciences - Adaptation and Self-Organizing Systems - Abstract
In this work, we introduce the concept of an entirely new circuit architecture based on the novel, physics-inspired computing paradigm: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that can be designed leveraging properties of non-linear dynamical systems; ultimate descriptors of electronic circuits. The working principle of these systems relies on the ability of currents and voltages of the circuit to self-organize in order to satisfy mathematical relations. In particular for this work, we discuss self-organizing gates, namely Self-Organizing Algebraic Gates (SOAGs), aimed to solve linear inequalities and therefore used to solve optimization problems in Integer Linear Programming (ILP) format. Unlike conventional I\O gates, SOAGs are terminal-agnostic, meaning each terminal handles a superposition of input and output signals. When appropriately assembled to represent a given ILP problem, the corresponding self-organizing circuit converges to the equilibria that express the solutions to the problem at hand. Because DMM's components are non-quantum, the ordinary differential equations describing it can be efficiently simulated on our modern computers in software, as well as be built in hardware with off-of-the-shelf technology. As an example, we show the performance of this novel approach implemented as Software as a Service (MemCPU XPC) to address an ILP problem. Compared to today's best solution found using a world renowned commercial solver, MemCPU XPC brings the time to solution down from 23 hours to less than 2 minutes.
- Published
- 2020
6. Aircraft Loading Optimization: MemComputing the 5th Airbus Problem
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Traversa, Fabio L.
- Subjects
Computer Science - Emerging Technologies ,Mathematics - Optimization and Control - Abstract
On the January 22nd 2019, Airbus launched a quantum computing challenge to solve a set of problems relevant for the aircraft life cycle (https://www.airbus.com/newsroom/press-releases/en/2019/01/airbus-launches-quantum-computing-challenge-to-transform-the-aircraft-lifecycle.html). The challenge consists of a set of 5 problems that ranges from design to deployment of aircraft. This work addresses the 5th problem. The formulation exploits an Integer programming framework with a linear objective function and the solution relies on the MemComputing paradigm. It is discussed how to use MemCPU$^{\text{TM}}$ software to solve efficiently the proposed problem and assess scaling properties, which turns out to be polynomial for meaningful solutions of the problem at hand. Also discussed are possible formulations of the problem utilizing non-linear objective functions, allowing for different optimization schemes implementable in modified MemCPU software, potentially useful for field operation purposes.
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- 2019
7. Stress-Testing Memcomputing on Hard Combinatorial Optimization Problems
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Sheldon, Forrest, Cicotti, Pietro, Traversa, Fabio L, and Di Ventra, Massimiliano
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Information and Computing Sciences ,Artificial Intelligence ,Dynamical systems ,memcomputing ,optimization problems ,cs.ET ,cs.PF ,math.DS ,math.OC ,Artificial Intelligence & Image Processing ,Artificial intelligence - Abstract
Memcomputing is a novel computing paradigm that employs time non-local dynamical systems to compute with and in memory. The digital version of these machines [digital memcomputing machines or (DMMs)] is scalable, and is particularly suited to solve combinatorial optimization problems. One of its possible realizations is by means of standard electronic circuits, with and without memory. Since these elements are non-quantum, they can be described by ordinary differential equations. Therefore, the circuit representation of DMMs can also be simulated efficiently on our traditional computers. We have indeed previously shown that these simulations only require time and memory resources that scale linearly with the problem size when applied to finding a good approximation to the optimum of hard instances of the maximum-satisfiability problem. The state-of-the-art algorithms, instead, require exponential resources for the same instances. However, in that work, we did not push the simulations to the limit of the processor used. Since linear scalability at smaller problem sizes cannot guarantee linear scalability at much larger sizes, we have extended these results in a stress-test up to 64×106 variables (corresponding to about 1 billion literals), namely the largest case that we could fit on a single core of an Intel Xeon E5-2860 with 128 GB of dynamic random-access memory (DRAM). For this test, we have employed a commercial simulator, Falcon of MemComputing, Inc. We find that the simulations of DMMs still scale linearly in both time and memory up to these very large problem sizes versus the exponential requirements of the state-of-the-art solvers. These results further reinforce the advantages of the physics-based memcomputing approach compared with traditional ones.
- Published
- 2020
8. Taming a non-convex landscape with dynamical long-range order: memcomputing Ising benchmarks
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Sheldon, Forrest, Traversa, Fabio L., and Di Ventra, Massimiliano
- Subjects
Condensed Matter - Disordered Systems and Neural Networks ,Condensed Matter - Statistical Mechanics ,Computer Science - Emerging Technologies ,Nonlinear Sciences - Adaptation and Self-Organizing Systems - Abstract
Recent work on quantum annealing has emphasized the role of collective behavior in solving optimization problems. By enabling transitions of clusters of variables, such solvers are able to navigate their state space and locate solutions more efficiently despite having only local connections between elements. However, collective behavior is not exclusive to quantum annealers, and classical solvers that display collective dynamics should also possess an advantage in navigating a non-convex landscape. Here, we give evidence that a benchmark derived from quantum annealing studies is solvable in polynomial time using digital memcomputing machines, which utilize a collection of dynamical components with memory to represent the structure of the underlying optimization problem. To illustrate the role of memory and clarify the structure of these solvers we propose a simple model of these machines that demonstrates the emergence of long-range order. This model, when applied to finding the ground state of the Ising frustrated-loop benchmarks, undergoes a transient phase of avalanches which can span the entire lattice and demonstrates a connection between long-range behavior and their probability of success. These results establish the advantages of computational approaches based on collective dynamics of continuous dynamical systems.
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- 2018
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9. Taming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks
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Sheldon, Forrest, Traversa, Fabio L, and Di Ventra, Massimiliano
- Subjects
Quantum Physics ,Physical Sciences ,cond-mat.dis-nn ,cond-mat.stat-mech ,cs.ET ,nlin.AO ,Engineering ,Mathematical sciences ,Physical sciences - Abstract
Recent work on quantum annealing has emphasized the role of collective behavior in solving optimization problems. By enabling transitions of clusters of variables, such solvers are able to navigate their state space and locate solutions more efficiently despite having only local connections between elements. However, collective behavior is not exclusive to quantum annealers, and classical solvers that display collective dynamics should also possess an advantage in navigating a nonconvex landscape. Here we give evidence that a benchmark derived from quantum annealing studies is solvable in polynomial time using digital memcomputing machines, which utilize a collection of dynamical components with memory to represent the structure of the underlying optimization problem. To illustrate the role of memory and clarify the structure of these solvers we propose a simple model of these machines that demonstrates the emergence of long-range order. This model, when applied to finding the ground state of the Ising frustrated-loop benchmarks, undergoes a transient phase of avalanches which can span the entire lattice and demonstrates a connection between long-range behavior and their probability of success. These results establish the advantages of computational approaches based on collective dynamics of continuous dynamical systems.
- Published
- 2019
10. MemComputing Integer Linear Programming
- Author
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Traversa, Fabio L. and Di Ventra, Massimiliano
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Computer Science - Emerging Technologies ,Computer Science - Performance ,Mathematics - Optimization and Control ,Nonlinear Sciences - Adaptation and Self-Organizing Systems - Abstract
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class efficiently, while requiring a reasonable compute time. However, although these algorithms have reached various degrees of success over the years, they still face considerable challenges when confronted with particularly hard problem instances, such as those of the MIPLIB 2010 library. In this work we propose a radically different non-algorithmic approach to ILP based on a novel physics-inspired computing paradigm: Memcomputing. This paradigm is based on digital (hence scalable) machines represented by appropriate electrical circuits with memory. These machines can be either built in hardware or, as we do here, their equations of motion can be efficiently simulated on our traditional computers. We first describe a new circuit architecture of memcomputing machines specifically designed to solve for the linear inequalities representing a general ILP problem. We call these self-organizing algebraic circuits, since they self-organize dynamically to satisfy the correct (algebraic) linear inequalities. We then show simulations of these machines using MATLAB running on a single core of a Xeon processor for several ILP benchmark problems taken from the MIPLIB 2010 library, and compare our results against a renowned commercial solver. We show that our approach is very efficient when dealing with these hard problems. In particular, we find within minutes feasible solutions for one of these hard problems (f2000 from MIPLIB 2010) whose feasibility, to the best of our knowledge, has remained unknown for the past eight years.
- Published
- 2018
11. Stress-testing memcomputing on hard combinatorial optimization problems
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Sheldon, Forrest, Cicotti, Pietro, Traversa, Fabio L., and Di Ventra, Massimiliano
- Subjects
Computer Science - Emerging Technologies ,Computer Science - Performance ,Mathematics - Dynamical Systems ,Mathematics - Optimization and Control - Abstract
Memcomputing is a novel paradigm of computation that utilizes dynamical elements with memory to both store and process information on the same physical location. Its building blocks can be fabricated in hardware with standard electronic circuits, thus offering a path to its practical realization. In addition, since memcomputing is based on non-quantum elements, the equations of motion describing these machines can be simulated efficiently on standard computers. In fact, it was recently realized that memcomputing, and in particular its digital (hence scalable) version, when simulated on a classical machine provides a significant speed-up over state-of-the-art algorithms on a variety of non-convex problems. Here, we stress-test the capabilities of this approach on finding approximate solutions to hard combinatorial optimization problems. These fall into a class which is known to require exponentially growing resources in the worst cases, even to generate approximations. We recently showed that in a region where state of the art algorithms demonstrate this exponential growth, simulations of digital memcomputing machines performed using the Falcon$^\copyright$ simulator of MemComputing, Inc. only require time and memory resources that scale linearly. These results are extended in a stress-test up to $64\times10^6$ variables (corresponding to about 1 billion literals), namely the largest case that we could fit on a single node with 128 GB of DRAM. Since memcomputing can be applied to a wide variety of optimization problems, this stress test shows the considerable advantage of non-combinatorial, physics-inspired approaches over standard combinatorial ones.
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- 2018
12. Memcomputing: Leveraging memory and physics to compute efficiently
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Di Ventra, Massimiliano and Traversa, Fabio L.
- Subjects
Computer Science - Emerging Technologies ,Computer Science - Computational Complexity ,Computer Science - Neural and Evolutionary Computing ,Mathematics - Dynamical Systems - Abstract
It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum computer. There are, however, other types of (non-quantum) physical properties that one may leverage to compute efficiently a wide range of hard problems. In this perspective we discuss how to employ one such property, memory (time non-locality), in a novel physics-based approach to computation: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that are scalable. DMMs can be realized with non-linear dynamical systems with memory. The latter property allows the realization of a new type of Boolean logic, one that is self-organizing. Self-organizing logic gates are "terminal-agnostic", namely they do not distinguish between input and output terminals. When appropriately assembled to represent a given combinatorial/optimization problem, the corresponding self-organizing circuit converges to the equilibrium points that express the solutions of the problem at hand. In doing so, DMMs take advantage of the long-range order that develops during the transient dynamics. This collective dynamical behavior, reminiscent of a phase transition, or even the "edge of chaos", is mediated by families of classical trajectories (instantons) that connect critical points of increasing stability in the system's phase space. The topological character of the solution search renders DMMs robust against noise and structural disorder. Since DMMs are non-quantum systems described by ordinary differential equations, not only can they be built in hardware with available technology, they can also be simulated efficiently on modern classical computers. As an example, we will show the polynomial-time solution of the subset-sum problem for the worst...
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- 2018
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13. Accelerating Deep Learning with Memcomputing
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Manukian, Haik, Traversa, Fabio L., and Di Ventra, Massimiliano
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Computer Science - Machine Learning ,Computer Science - Artificial Intelligence ,Computer Science - Emerging Technologies ,Computer Science - Neural and Evolutionary Computing - Abstract
Restricted Boltzmann machines (RBMs) and their extensions, called 'deep-belief networks', are powerful neural networks that have found applications in the fields of machine learning and artificial intelligence. The standard way to training these models resorts to an iterative unsupervised procedure based on Gibbs sampling, called 'contrastive divergence' (CD), and additional supervised tuning via back-propagation. However, this procedure has been shown not to follow any gradient and can lead to suboptimal solutions. In this paper, we show an efficient alternative to CD by means of simulations of digital memcomputing machines (DMMs). We test our approach on pattern recognition using a modified version of the MNIST data set. DMMs sample effectively the vast phase space given by the model distribution of the RBM, and provide a very good approximation close to the optimum. This efficient search significantly reduces the number of pretraining iterations necessary to achieve a given level of accuracy, as well as a total performance gain over CD. In fact, the acceleration of pretraining achieved by simulating DMMs is comparable to, in number of iterations, the recently reported hardware application of the quantum annealing method on the same network and data set. Notably, however, DMMs perform far better than the reported quantum annealing results in terms of quality of the training. We also compare our method to advances in supervised training, like batch-normalization and rectifiers, that work to reduce the advantage of pretraining. We find that the memcomputing method still maintains a quality advantage ($>1\%$ in accuracy, and a $20\%$ reduction in error rate) over these approaches. Furthermore, our method is agnostic about the connectivity of the network. Therefore, it can be extended to train full Boltzmann machines, and even deep networks at once., Comment: 8 pages, 5 figures
- Published
- 2018
14. On the Universality of Memcomputing Machines
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Pei, Yan Ru, Traversa, Fabio L., and Di Ventra, Massimiliano
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Computer Science - Neural and Evolutionary Computing ,Computer Science - Emerging Technologies - Abstract
Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs have been shown to be Turing-complete, namely they can simulate any Turing machine. In this paper, using set theory and cardinality arguments, we compare them with liquid-state machines (or "reservoir computing") and quantum machines ("quantum computing"). We show that UMMs can simulate both types of machines, hence they are both "liquid-" or "reservoir-complete" and "quantum-complete". Of course, these statements pertain only to the type of problems these machines can solve, and not to the amount of resources required for such simulations. Nonetheless, the method presented here provides a general framework in which to describe the relation between UMMs and any other type of computational model., Comment: 10 pages, 2 figures
- Published
- 2017
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15. Evidence of an exponential speed-up in the solution of hard optimization problems
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Traversa, Fabio L., Cicotti, Pietro, Sheldon, Forrest, and Di Ventra, Massimiliano
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Computer Science - Artificial Intelligence ,Computer Science - Computational Complexity ,Nonlinear Sciences - Adaptation and Self-Organizing Systems - Abstract
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve because they belong to the NP-hard class, namely algorithms that always find a solution in polynomial time are not known. Over the past decades, research has focused on developing heuristic approaches that attempt to find an approximation to the solution. However, despite numerous research efforts, in many cases even approximations to the optimal solution are hard to find, as the computational time for further refining a candidate solution grows exponentially with input size. Here, we show a non-combinatorial approach to hard optimization problems that achieves an exponential speed-up and finds better approximations than the current state-of-the-art. First, we map the optimization problem into a boolean circuit made of specially designed, self-organizing logic gates, which can be built with (non-quantum) electronic components; the equilibrium points of the circuit represent the approximation to the problem at hand. Then, we solve its associated non-linear ordinary differential equations numerically, towards the equilibrium points. We demonstrate this exponential gain by comparing a sequential MatLab implementation of our solver with the winners of the 2016 Max-SAT competition on a variety of hard optimization instances. We show empirical evidence that our solver scales linearly with the size of the problem, both in time and memory, and argue that this property derives from the collective behavior of the simulated physical circuit. Our approach can be applied to other types of optimization problems and the results presented here have far-reaching consequences in many fields.
- Published
- 2017
16. Instantons in self-organizing logic gates
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Bearden, Sean R. B., Manukian, Haik, Traversa, Fabio L., and Di Ventra, Massimiliano
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Computer Science - Emerging Technologies ,Condensed Matter - Mesoscale and Nanoscale Physics ,Mathematics - Dynamical Systems - Abstract
Self-organizing logic is a recently-suggested framework that allows the solution of Boolean truth tables "in reverse," i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned ("terminal-agnostic logic"). It can be realized if time non-locality (memory) is present. A practical realization of self-organizing logic gates (SOLGs) can be done by combining circuit elements with and without memory. By employing one such realization, we show, numerically, that SOLGs exploit elementary instantons to reach equilibrium points. Instantons are classical trajectories of the non-linear equations of motion describing SOLGs, and connect topologically distinct critical points in the phase space. By linear analysis at those points, we show that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. We also show that the memory content of these gates only affects the relaxation time to reach the logically consistent solution. Finally, we demonstrate, by solving the corresponding stochastic differential equations, that since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space, but not the initial and final critical points. Therefore, even for extremely large noise levels, the gates self-organize to the correct solution. Our work provides a physical understanding of, and can serve as an inspiration for, new models of bi-directional logic gates that are emerging as important tools in physics-inspired, unconventional computing., Comment: 7 pages, 5 figures
- Published
- 2017
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17. Absence of chaos in Digital Memcomputing Machines with solutions
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Di Ventra, Massimiliano and Traversa, Fabio L.
- Subjects
Nonlinear Sciences - Chaotic Dynamics ,Computer Science - Emerging Technologies ,Nonlinear Sciences - Adaptation and Self-Organizing Systems - Abstract
Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. In particular, we show that both topological transitivity and the strongest property of topological mixing are inconsistent with the point dissipative property of DMMs when equilibrium points are present. This is true for both the whole phase space and the global attractor. Absence of topological transitivity is enough to imply absence of chaotic behavior. In a similar vein, we prove that if DMMs do not have equilibrium points, the only attractors present are invariant tori/periodic orbits with periods that may possibly increase with system size (quasi-attractors).
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- 2017
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18. Memcomputing Numerical Inversion with Self-Organizing Logic Gates
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Manukian, Haik, Traversa, Fabio L., and Di Ventra, Massimiliano
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Computer Science - Emerging Technologies ,Computer Science - Neural and Evolutionary Computing - Abstract
We propose to use Digital Memcomputing Machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion we describe the generalization to solving linear systems and matrix inversion. This method, when realized in hardware, will output the result in only one computational step. As an example, we perform simulations of the scalar case using a 5-bit logic circuit made of SOLGs, and show that the circuit successfully performs the inversion. Our method can be extended efficiently to any level of precision, since we prove that producing n-bit precision in the output requires extending the circuit by at most n bits. This type of numerical inversion can be implemented by DMM units in hardware, it is scalable, and thus of great benefit to any real-time computing application.
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- 2016
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19. Topological field theory and computing with instantons
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Di Ventra, Massimiliano, Traversa, Fabio L., and Ovchinnikov, Igor V.
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Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Computer Science - Emerging Technologies - Abstract
Chern-Simons topological field theories TFTs are the only TFTs that have already found application in the description of some exotic strongly-correlated electron systems and the corresponding concept of topological quantum computing. Here, we show that TFTs of another type, specifically the gauge-field-less Witten-type TFTs known as topological sigma models, describe the recently proposed digital memcomputing machines (DMMs) - engineered dynamical systems with point attractors being the solutions of the corresponding logic circuit that solves a specific task. This result derives from the recent finding that any stochastic differential equation possesses a topological supersymmetry, and the realization that the solution search by a DMM proceeds via an instantonic phase. Certain TFT correlators in DMMs then reveal the presence of a transient long-range order both in space and time, associated with the effective breakdown of the topological supersymmetry by instantons. The ensuing non-locality and the low dimensionality of instantons are the physical reasons why DMMs can solve complex problems efficiently, despite their non-quantum character. We exemplify these results with the solution of prime factorization.
- Published
- 2016
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20. MemComputing Integer Linear Programming
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Traversa, Fabio L and Ventra, Massimiliano Di
- Subjects
cs.ET ,cs.PF ,math.OC ,nlin.AO - Abstract
Integer linear programming (ILP) encompasses a very important class ofoptimization problems that are of great interest to both academia and industry.Several algorithms are available that attempt to explore the solution space ofthis class efficiently, while requiring a reasonable compute time. However,although these algorithms have reached various degrees of success over theyears, they still face considerable challenges when confronted withparticularly hard problem instances, such as those of the MIPLIB 2010 library.In this work we propose a radically different non-algorithmic approach to ILPbased on a novel physics-inspired computing paradigm: Memcomputing. Thisparadigm is based on digital (hence scalable) machines represented byappropriate electrical circuits with memory. These machines can be either builtin hardware or, as we do here, their equations of motion can be efficientlysimulated on our traditional computers. We first describe a new circuitarchitecture of memcomputing machines specifically designed to solve for thelinear inequalities representing a general ILP problem. We call theseself-organizing algebraic circuits, since they self-organize dynamically tosatisfy the correct (algebraic) linear inequalities. We then show simulationsof these machines using MATLAB running on a single core of a Xeon processor forseveral ILP benchmark problems taken from the MIPLIB 2010 library, and compareour results against a renowned commercial solver. We show that our approach isvery efficient when dealing with these hard problems. In particular, we findwithin minutes feasible solutions for one of these hard problems (f2000 fromMIPLIB 2010) whose feasibility, to the best of our knowledge, has remainedunknown for the past eight years.
- Published
- 2018
21. On the Measurement in Quantum Mechanics: the Consistent Measurement Apparatus
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Traversa, Fabio L. and Albareda, Guillermo
- Subjects
Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics - Abstract
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the Copenhagen interpretation (i.e., through the collapse of the wavefunction) compared versus a picture in which the system and the measurement apparatus are considered as a whole. We first consider a projective measurement. In this limiting case, the natural requirements of consistency and equivalence between the two pictures lead to the rigorous definition of consistent measuring apparatus: the orthonormal wavefunctions from the Schmidt decomposition of the system plus apparatus must have non-overlapping supports. This result arises from the comparison of the two pictures (otherwise hidden), and while it seems to be an obvious conclusion in the limit of projective measurements, it has some nontrivial implications as one extends its validity to the domain of weak measurements. In this respect, we argue on the existence of two alternative approaches to mathematically constructing a weak measurement protocol. While the two approaches are equivalent from the system's perspective, they do strongly differ from the apparatus point of view, and hence can be only distinguished one from each other in the picture where system and apparatus are considered as a whole. We show that only one of the two mathematical formulations of the weak measurement fulfills the consistent apparatus condition, while the combination of the two gives rise to a generalized weak measurements framework.
- Published
- 2016
22. Polynomial-time solution of prime factorization and NP-hard problems with digital memcomputing machines
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Traversa, Fabio L. and Di Ventra, Massimiliano
- Subjects
Computer Science - Emerging Technologies ,Condensed Matter - Mesoscale and Nanoscale Physics ,Computer Science - Computational Complexity - Abstract
We introduce a class of digital machines we name Digital Memcomputing Machines (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We initially prove this by introducing the complexity classes for these machines. We then make a connection with dynamical systems theory. This leads to the set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: i) SOLCs possess a global attractor; ii) their only equilibrium points are the solutions of the problems to solve; iii) the system converges exponentially fast to the solutions; iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples we show how to solve the prime factorization and the NP-hard version of the subset-sum problem. Since DMMs map integers into integers they are robust against noise, and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP=P question related to...
- Published
- 2015
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23. Leveraging circuit theory and nonlinear dynamics for the efficiency improvement of energy harvesting
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Bonnin, Michele, Traversa, Fabio L., and Bonani, Fabrizio
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- 2021
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24. Memcomputing NP-complete problems in polynomial time using polynomial resources and collective states
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Traversa, Fabio L., Ramella, Chiara, Bonani, Fabrizio, and Di Ventra, Massimiliano
- Subjects
Computer Science - Emerging Technologies ,Computer Science - Neural and Evolutionary Computing - Abstract
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proved mathematically that memcomputing machines have the same computational power of non-deterministic Turing machines. Therefore, they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size. The reason for this computational power stems from properties inspired by the brain and shared by any universal memcomputing machine, in particular intrinsic parallelism and information overhead, namely the capability of compressing information in the collective state of the memprocessor network. Here, we show an experimental demonstration of an actual memcomputing architecture that solves the NP-complete version of the subset-sum problem in only one step and is composed of a number of memprocessors that scales linearly with the size of the problem. We have fabricated this architecture using standard microelectronic technology so that it can be easily realized in any laboratory setting. Even though the particular machine presented here is eventually limited by noise--and will thus require error-correcting codes to scale to an arbitrary number of memprocessors--it represents the first proof-of-concept of a machine capable of working with the collective state of interacting memory cells, unlike the present-day single-state machines built using the von Neumann architecture., Comment: We have corrected minor typos and improved the presentation
- Published
- 2014
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25. Memcomputing with membrane memcapacitive systems
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Pershin, Yuriy V., Traversa, Fabio L., and Di Ventra, Massimiliano
- Subjects
Computer Science - Emerging Technologies ,Condensed Matter - Mesoscale and Nanoscale Physics ,Computer Science - Neural and Evolutionary Computing - Abstract
We show theoretically that networks of membrane memcapacitive systems -- capacitors with memory made out of membrane materials -- can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network. This polymorphism is an important characteristic of memcomputing (computing with memories) that closely reproduces one of the main features of the brain. A practical realization of these membrane memcapacitive systems, using, e.g., graphene or other 2D materials, would be a step forward towards a solid-state realization of memcomputing with passive devices.
- Published
- 2014
- Full Text
- View/download PDF
26. Noise in oscillators: a review of state space decomposition approaches
- Author
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Traversa, Fabio L., Bonnin, Michele, Corinto, Fernando, and Bonani, Fabrizio
- Subjects
Physics - Data Analysis, Statistics and Probability - Abstract
We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics, to optics, to biology. After presenting a rigorous definition of phase, given in terms of the autonomous system isochrons, we provide a generalized projection technique that allows to decompose the oscillator fluctuations in terms of phase and amplitude noise, pointing out that the very definition of phase (and orbital) deviations depends of the base chosen to define the aforementioned projection. After reviewing the most advanced theories for phase noise, based on the use of the Floquet basis and of the reduction of the projected model by neglecting the orbital fluctuations, we discuss the intricacies of the phase reduction process pointing out the presence of possible variations of the noisy oscillator frequency due to amplitude-related effects.
- Published
- 2014
- Full Text
- View/download PDF
27. Absorption and Injection Models for Open Time-Dependent Quantum Systems
- Author
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Traversa, Fabio L., Zhan, Zhen, and Oriols, Xavier
- Subjects
Quantum Physics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Mathematics - Analysis of PDEs - Abstract
In the time-dependent simulation of pure states dealing with transport in open quantum systems, the initial state is located outside of the active region of interest. Using the superposition principle and the analytical knowledge of the free time-evolution of such state outside the active region, together with absorbing layers and remapping, a model for a very significant reduction of the computational burden associated to the numerical simulation of open time-dependent quantum systems is presented. The model is specially suited to study (many-particle and high-frequency effects) quantum transport, but it can also be applied to any other research field where the initial time-dependent pure state is located outside of the active region. From numerical simulations of open quantum systems described by the (effective mass) Schr\"{o}dinger and (atomistic) tight-binding equations, a reduction of the computational burden of about two orders of magnitude for each spatial dimension of the domain with a negligible error is presented.
- Published
- 2014
- Full Text
- View/download PDF
28. Universal Memcomputing Machines
- Author
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Traversa, Fabio L. and Di Ventra, Massimiliano
- Subjects
Computer Science - Neural and Evolutionary Computing ,Condensed Matter - Mesoscale and Nanoscale Physics ,Computer Science - Emerging Technologies ,Computer Science - Information Theory - Abstract
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location. We analytically prove that the memory properties of UMMs endow them with universal computing power - they are Turing-complete -, intrinsic parallelism, functional polymorphism, and information overhead, namely their collective states can support exponential data compression directly in memory. We also demonstrate that a UMM has the same computational power as a non-deterministic Turing machine, namely it can solve NP--complete problems in polynomial time. However, by virtue of its information overhead, a UMM needs only an amount of memory cells (memprocessors) that grows polynomially with the problem size. As an example we provide the polynomial-time solution of the subset-sum problem and a simple hardware implementation of the same. Even though these results do not prove the statement NP=P within the Turing paradigm, the practical realization of these UMMs would represent a paradigm shift from present von Neumann architectures bringing us closer to brain-like neural computation.
- Published
- 2014
- Full Text
- View/download PDF
29. Analysis of influence of nonlinearities and noise correlation time in a single-DOF energy-harvesting system via power balance description
- Author
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Bonnin, Michele, Traversa, Fabio L., and Bonani, Fabrizio
- Published
- 2020
- Full Text
- View/download PDF
30. Application of Floquet theory to dynamical systems with memory
- Author
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Traversa, Fabio L., Di Ventra, Massimiliano, Cappelluti, Federica, and Bonani, Fabrizio
- Subjects
Mathematical Physics ,Mathematics - Dynamical Systems ,Nonlinear Sciences - Chaotic Dynamics - Abstract
We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.
- Published
- 2013
31. Generalized Floquet theory: application to dynamical systems with memory and Bloch's theorem for nonlocal potentials
- Author
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Traversa, Fabio L., Di Ventra, Massimiliano, and Bonani, Fabrizio
- Subjects
Mathematics - Dynamical Systems ,Mathematical Physics ,Nonlinear Sciences - Chaotic Dynamics - Abstract
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.
- Published
- 2012
- Full Text
- View/download PDF
32. Accelerating deep learning with memcomputing
- Author
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Manukian, Haik, Traversa, Fabio L., and Di Ventra, Massimiliano
- Published
- 2019
- Full Text
- View/download PDF
33. Stochastic description of a matched-load mechanical energy harvester
- Author
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Song, Kailing, primary, Bonnin, Michele, additional, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2023
- Full Text
- View/download PDF
34. Moment-Based Stochastic Analysis of a Bistable Energy Harvester with Matching Network
- Author
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Song, Kailing, primary, Bonnin, Michele, additional, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2023
- Full Text
- View/download PDF
35. A Circuit Theory Perspective on the Modeling and Analysis of Vibration Energy Harvesting Systems: A Review
- Author
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Bonnin, Michele, primary, Song, Kailing, additional, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2023
- Full Text
- View/download PDF
36. Maximizing the Harvested Energy from Mechanical Random Vibrations with a Matching Network: A Stochastic Analysis
- Author
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Song, Kailing, primary, Bonnin, Michele, additional, Bonani, Fabrizio, additional, and Traversa, Fabio L., additional
- Published
- 2022
- Full Text
- View/download PDF
37. Logic gates based on nonlinear oscillators
- Author
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Bonnin, Michele, primary, Bonani, Fabrizio, additional, and Traversa, Fabio L., additional
- Published
- 2022
- Full Text
- View/download PDF
38. Boosting the performance of energy harvesters subject to white Gaussian vibrations through impedance matching solutions
- Author
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Song, Kailing, primary, Bonnin, Michele, additional, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2022
- Full Text
- View/download PDF
39. An Impedance Matching Solution to Increase the Harvested Power and Efficiency of Nonlinear Piezoelectric Energy Harvesters
- Author
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Bonnin, Michele, primary, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2022
- Full Text
- View/download PDF
40. Improved harmonic balance implementation of Floquet analysis for nonlinear circuit simulation
- Author
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Traversa, Fabio L. and Bonani, Fabrizio
- Published
- 2012
- Full Text
- View/download PDF
41. Global minimization via classical tunneling assisted by collective force field formation
- Author
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Caravelli, Francesco, primary, Sheldon, Forrest C., additional, and Traversa, Fabio L., additional
- Published
- 2021
- Full Text
- View/download PDF
42. A cascaded two-port network model for the analysis of harmonic chain-based energy harvesters
- Author
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Bonnin, Michele, primary, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2021
- Full Text
- View/download PDF
43. On the application of circuit theory and nonlinear dynamics to the design of highly efficient energy harvesting systems
- Author
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Bonnin, Michele, primary, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2021
- Full Text
- View/download PDF
44. The Complex World of Oscillator Noise: Modern Approaches to Oscillator (Phase and Amplitude) Noise Analysis
- Author
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Traversa, Fabio L., primary, Bonnin, Michele, additional, and Bonani, Fabrizio, additional
- Published
- 2021
- Full Text
- View/download PDF
45. Application of Floquet theory to dynamical systems with memory
- Author
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Traversa, Fabio L., primary, Di Ventra, Massimiliano, additional, Cappelluti, Federica, additional, and Bonani, Fabrizio, additional
- Published
- 2020
- Full Text
- View/download PDF
46. Colored Noise in Oscillators. Phase-Amplitude Analysis and a Method to Avoid the itô-Stratonovich Dilemma
- Author
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Bonnin, Michele, primary, Traversa, Fabio L., additional, and Bonani, Fabrizio, additional
- Published
- 2019
- Full Text
- View/download PDF
47. On the Universality of Memcomputing Machines
- Author
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Pei, Yan Ru, primary, Traversa, Fabio L., additional, and Di Ventra, Massimiliano, additional
- Published
- 2019
- Full Text
- View/download PDF
48. Logic Gates Implementation with Coupled Oscillators
- Author
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Bonnin, Michele, primary, Bonani, Fabrizio, additional, and Traversa, Fabio L., additional
- Published
- 2018
- Full Text
- View/download PDF
49. Evidence of Exponential Speed-Up in the Solution of Hard Optimization Problems
- Author
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Traversa, Fabio L., primary, Cicotti, Pietro, additional, Sheldon, Forrest, additional, and Di Ventra, Massimiliano, additional
- Published
- 2018
- Full Text
- View/download PDF
50. Memcomputing Numerical Inversion With Self-Organizing Logic Gates
- Author
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Manukian, Haik, primary, Traversa, Fabio L., additional, and Di Ventra, Massimiliano, additional
- Published
- 2018
- Full Text
- View/download PDF
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