1,720,983 research outputs found
Improved mean-field dynamical equations are able to detect the two-steps relaxation in glassy dynamics at low temperatures
Full text linkWe study the stochastic relaxation dynamics of the Ising p-spin model on a
random graph, a well-known model with glassy dynamics at low temperatures. We
introduce and discuss a new closure scheme for the master equation governing
the continuous-time relaxation of the system, that translates into a set of
differential equations for the evolution of local probabilities. The solution
to these dynamical mean-field equations describes very well the
out-of-equilibrium dynamics at high temperatures, notwithstanding the key
observation that the off-equilibrium probability measure contains higher-order
interaction terms, not present in the equilibrium measure. In the
low-temperature regime, the solution to the dynamical mean-field equations
shows the correct two-step relaxation (a typical feature of the glassy
dynamics), but with a relaxation timescale too short. We propose a solution to
this problem by identifying the range of energies where entropic barriers play
a key role and defining a renormalized microscopic timescale for the dynamical
mean-field solution. The final result perfectly matches the complex
out-of-equilibrium dynamics computed through extensive Monte Carlo simulations.Comment: 24 pages, 9 figure
A closure for the Master Equation starting from the Dynamic Cavity Method
Full text linkWe consider classical spin systems evolving in continuous time with
interactions given by a locally tree-like graph. Several approximate analysis
methods have earlier been reported based on the idea of Belief Propagation /
cavity method. We introduce a new such method which can be derived in a more
systematic manner, and which performs better on several important classes of
problems.Comment: arXiv admin note: text overlap with arXiv:2205.0075
Theory of Nonequilibrium Local Search on Random Satisfaction Problems
No full textWe study local search algorithms to solve instances of the random k-satisfiability problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that the best such algorithms are akin to nonequilibrium processes in a high-dimensional space. In particular, algorithms known as focused, and which do not obey detailed balance, outperform simulated annealing and related methods in the task of finding the solution to a complex satisfiability problem, that is to find (exactly or approximately) the minimum in a complex energy landscape. A physical question of interest is if the dynamics of these processes can be well predicted by the well-developed theory of equilibrium Gibbs states. While it has been known empirically for some time that this is not the case, an alternative systematic theory that does so has been lacking. In this Letter we introduce such a theory based on the recently developed technique of cavity master equations and test it on the paradigmatic random 3-satisfiability problem. Our theory predicts the qualitative form of the phase boundary between the satisfiable (SAT) and unsatisfiable (UNSAT) region of the phase diagram where the numerics of a focused Metropolis search and cavity master equation cannot be distinguished
Effective noisy dynamics within the phenotypic space of a growth-rate maximizing population
No full textMicrobial systems exhibit marked variability in metabolic phenotypes. A recently-proposed class of models explains this feature within a minimal mathematical setup which assumes that populations evolve towards maximum growth rate in a 'phenotypic space' subject to an intrinsic 'diffusive' stochasticity that causes small random changes in single-cell phenotypes. In such a framework, variability results from the exploration-exploitation balance between hardly accessible fast-growing phenotypes and easily accessible slow-growing ones. Here we extend the above scheme to include a degree of extrinsic noise, showing that the population dynamics over the phenotypic space is captured by an effective process that conflates both sources of randomness. This in turn leads to a simple approximation for the asymptotic distribution of the population over the phenotypic space, highlighting the connection between the strength of the noise that affects the dynamics and the degree of optimization. The theory thus obtained displays an excellent agreement with numerical simulations of low-dimensional systems
Exploring the diluted ferromagnetic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-spin model with a cavity master equation
No full textWe introduce an alternative solution to Glauber multispin dynamics on random graphs. The solution is based on the recently introduced cavity master equation (CME), a time-closure turning the, in principle, exact dynamic cavity method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one Monte Carlo run on the same problem. We show that CME correctly models the ferromagnetic p-spin Glauber dynamics from high temperatures down to and below the spinoidal transition. We also show that CME allows an alternative exploration of the low-temperature spin-glass phase of the model
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Gauge-free cluster variational method by maximal messages and moment matching
Full text linkWe present an implementation of the cluster variational method (CVM) as a message passing algorithm. The kind of message passing algorithm used for CVM, usually named generalized belief propagation (GBP), is a generalization of the belief propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the partition function. However, the connection between fixed points of GBP and the extremal points of the CVM free energy is usually not a one-to-one correspondence because of the existence of a gauge transformation involving the GBP messages. Our contribution is twofold. First, we propose a way of defining messages (fields) in a generic CVM approximation, such that messages arrive on a given region from all its ancestors, and not only from its direct parents, as in the standard parent-to-child GBP. We call this approach maximal messages. Second, we focus on the case of binary variables, reinterpreting the messages as fields enforcing the consistency between the moments of the local (marginal) probability distributions. We provide a precise rule to enforce all consistencies, avoiding any redundancy, that would otherwise lead to a gauge transformation on the messages. This moment matching method is gauge free, i.e., it guarantees that the resulting GBP is not gauge invariant. We apply our maximal messages and moment matching GBP to obtain an analytical expression for the critical temperature of the Ising model in general dimensions at the level of plaquette CVM. The values obtained outperform Bethe estimates, and are comparable with loop corrected belief propagation equations. The method allows for a straightforward generalization to disordered systems
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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