The Nature of Computation

Moore, Cristopher; Mertens, Stephan

doi:10.1093/acprof:oso/9780199233212.001.0001

Cited by 328 publications

(331 citation statements)

References 494 publications

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“…Few physical problems fit in the categories of computational complexity theory [1]. An outstanding example for a fruitful interface between physics and computer science is Boson-Sampling [2], the simulation of many indistinguishable bosons that scatter through a randomly chosen linear network with many more modes than particles: As a physical problem [3], it is implemented straightforwardly with single photons [3][4][5], as demonstrated experimentally [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

2015

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The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which interpolates between distinguishable particles and identical bosons, and easily extends to mixed initial states. The permanent of the distinguishability matrix, composed of all mutual scalar products of the single-particle mode-functions, emerges as a natural measure for the degree of interference: It yields a bound on the difference between event probabilities for partially distinguishable bosons and the idealized species, and exactly quantifies the degree of bosonic bunching.

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Section: Introductionmentioning

confidence: 99%

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

2015

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“…The results we have obtained are applicable to many fields. In particular, we note that randomized computer algorithms [54,55] often exhibit heavy tailed run time distributions [56,57] and restart could hence drastically improve performance in these cases and others [58,59].…”

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confidence: 99%

Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem

2015

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. and * T. Rotbart and S. Reuveni had equal contribution to this work.We study the effect of restart, and retry, on the mean completion time of a generic process. The need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of Michaelis & Menten. Stopping a process in its midst-only to start it all over again-may prolong, leave unchanged, or even shorten the time taken for its completion. Here we are interested in the optimal restart problem, i.e., in finding a restart rate which brings the mean completion time of a process to a minimum. We derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest. We then continue to discover regimes at which solutions to the problem take on universal, details independent, forms which further give rise to optimal scaling laws. The formalism we develop, and the results obtained, can be utilized when optimizing stochastic search processes and randomized computer algorithms. An immediate connection with kinetic proofreading is also noted and discussed.When engaged in a specific task for a time period that extends beyond our initial expectations, we are constantly faced with two alternatives-either keep on going or stop everything and start anew. Every now and then we opt for the latter, hoping that a fresh start will break-off an unproductive course of action and expedite the completion of the task at hand. This decision could, however, turn out to be counter-productive-nipping an awaited, but unforeseen, finale in the bud. To restart, or not to restart, that is therefore the question.Not at all unique to our everyday lives, a "dilemma" similar to the one described above is relevant to virtually any physical, chemical, or biological process that can be restarted. Most notably, restart (or unbinding) is an integral part of the renown Michaelis-Menten Reaction Scheme (MMRS) illustrated in Fig. 1 [1]. Originally devised to describe enzymatic catalysis, the MMRS has attracted on-growing scientific interest for more than a century [2]. Indeed, nature is full with an astonishing variety of Michaelian processes. DNA-DNA hybridization, antigen-antibody binding, and various other molecular processes can all be described by the MMRS [3]. That and more, the simplicity and generality of the scheme have rendered it widely applicable and it is now used to describe anything from heterogeneous catalysis [4-6] to in vivo target search kinetics [7]. As a matter of fact, one can easily convince himself that any first passage time (FPT) process [8]-be it the time to target of a simple Brownian particle, or that of more sophisticated stochastic processes [9][10][11][12] and random searchers [13][14][15]-can become subject to restart [16][17][18][19][20][21][22] and is then naturally accommodated by the MMRS. Wishing to acquire a unified view on restart phenomena we identify the MMRS as an ideal object of study.Central to our understanding of the ...

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“…One discipline may, for example, care about the extreme and need input from another to see interesting aspects of the average (cf. phase transitions in the complexity of algorithms [109]). Interdisciplinary information flow could help a discipline overcome technical difficulties.…”

Section: Discussionmentioning

confidence: 99%

Mechanistic models in computational social science

Holme

Liljeros

2015

Front. Phys.

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Quantitative social science is not only about regression analysis or, in general, data inference. Computer simulations of social mechanisms have an over 60 years long history. They have been used for many different purposes-to test scenarios, to test the consistency of descriptive theories (proof-of-concept models), to explore emergent phenomena, for forecasting, etc… In this essay, we sketch these historical developments, the role of mechanistic models in the social sciences and the influences from the natural and formal sciences. We argue that mechanistic computational models form a natural common ground for social and natural sciences, and look forward to possible future information flow across the social-natural divide.

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The Nature of Computation

Cited by 328 publications

References 494 publications

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

Sampling of partially distinguishable bosons and the relation to the multidimensional permanent

Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem

Mechanistic models in computational social science

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