Polynomial time factoring algorithm using Bayesian arithmetic

Feldmann, M.

doi:10.48550/arxiv.1212.4969

Cited by 2 publications

(6 citation statements)

References 4 publications

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“…A continuity equation of a similar nature, and its steady-state solution, were used with a variety of sink terms in several recent studies (Dekel, Sari & Ceverino 2009;Bouché et al 2010;Feldmann 2010). The sink term in eq.…”

Section: Toy Model: Steady Statementioning

confidence: 99%

Toy models for galaxy formation versus simulations

Dekel

Zolotov

Tweed

et al. 2013

Monthly Notices of the Royal Astronomical Society

271

294

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We describe simple useful toy models for key processes of galaxy formation in its most active phase, at z > 1, and test the approximate expressions against the typical behaviour in a suite of high-resolution hydro-cosmological simulations of massive galaxies at z = 4 − 1. We address in particular the evolution of (a) the total mass inflow rate from the cosmic web into galactic haloes based on the EPS approximation, (b) the penetration of baryonic streams into the inner galaxy, (c) the disc size, (d) the implied steady-state gas content and star-formation rate (SFR) in the galaxy subject to mass conservation and a universal star-formation law, (e) the inflow rate within the disc to a central bulge and black hole as derived using energy conservation and self-regulated Q ∼ 1 violent disc instability (VDI), and (f) the implied steady state in the disc and bulge. The toy models provide useful approximations for the behaviour of the simulated galaxies. We find that (a) the inflow rate is proportional to mass and to (1 + z) 5/2 , (b) the penetration to the inner halo is ∼ 50% at z = 4 − 2, (c) the disc radius is ∼ 5% of the virial radius, (d) the galaxies reach a steady state with the SFR following the accretion rate into the galaxy, (e) there is an intense gas inflow through the disc, comparable to the SFR, following the predictions of VDI, and (f) the galaxies approach a steady state with the bulge mass comparable to the disc mass, where the draining of gas by SFR, outflows and disc inflows is replenished by fresh accretion. Given the agreement with simulations, these toy models are useful for understanding the complex phenomena in simple terms and for back-of-the-envelope predictions.

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Section: Toy Model: Steady Statementioning

confidence: 99%

Toy models for galaxy formation versus simulations

Dekel

Zolotov

Tweed

et al. 2013

Monthly Notices of the Royal Astronomical Society

271

294

View full text Add to dashboard Cite

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“…In Ref. [11,12], we have shown that alone, such a change is surprisingly effective in "Bayesian computation".…”

Section: Motivationmentioning

confidence: 97%

“…Given by hypothesis that the prior (Λ) must be satisfied, the probability of any event will be conditional on (Λ). For instance, in the conventional binary addition of two integers U and V [12], the prior (Λ) is the statement that the two integers U and V sum to a third integer S.…”

Section: Bayesian Algebramentioning

confidence: 99%

“…In linear programming, the particular solution is usually selected by maximizing an objective function. Specifically, in Bayesian computation [11,12], we use optimization to select the deterministic distributions when possible. By default, we process on an equal footing all feasible solutions, meaning that we choose the most likely distribution p = g. By Jaynes theory [6], this distribution g is obtained by maximizing the entropy of the classical states.…”

Section: Static Systemsmentioning

confidence: 99%

“…Independently, in a pair of papers [11,12], we have demonstrated that the crucial principle to benefit from the efficiency of Bayesian theory in conventional computation is to regard calculation as a statistical estimation [13] of the involved variables. Technically, this means taking probabilities for the very unknowns of the problem instead of the variables themselves and next equating the calculation to an optimization process.…”

Section: Introductionmentioning

confidence: 99%

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Information-theoretic interpretation of quantum formalism

Feldmann¹

2013

Preprint

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We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and free of any additional axiom or principle. Quantum information is merely construed as a technique of statistical estimation for analyzing a logical system subject to classical constraints, regardless of the specific variables used. The problem is initially formulated in a standard Boolean algebra involving a particular set of working variables. Statistical estimation is to express the truth table in terms of likelihood probability instead of the variables themselves. The constraints are thus converted into a Bayesian prior. This method leads to solving a linear programming problem in a real-valued probability space. The complete set of alternative Boolean variables is introduced afterwards by transcribing the probability space into a Hilbert space, thanks to Gleason's theorem. This allows to completely recover standard quantum information and provides an information-theoretic rationale to its technical rules. The model offers a natural answer to the major puzzles that base quantum mechanics: Why is the theory linear? Why is the theory probabilistic? Where does the Hilbert space come from? Also, most of the paradoxes, such as entanglement, contextuality, nonsignaling correlation, measurement problem, etc., find a quite trivial explanation, while the concept of information conveyed by a wave vector is clarified. We conclude that quantum information, although dramatically expanding the scope of classical information, is not different from the information itself and is therefore a universal tool of reasoning.

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Polynomial time factoring algorithm using Bayesian arithmetic

Cited by 2 publications

References 4 publications

Toy models for galaxy formation versus simulations

Toy models for galaxy formation versus simulations

Information-theoretic interpretation of quantum formalism

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