arXiv subjects

Thierry Mora

Publications and source records attributed to Thierry Mora.

119 records · Page 7Linked to original sources

arXiv2009

Steps in the bacterial flagellar motor

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps [Sowa et al. (2005) Nature 437, 916--919]. Here we propose a simple physical model that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties, and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. Our model also predicts a sublinear torque-speed relationship at low torque, and a peak in rotor diffusion as a function of torque.

physics.bio-ph↗

arXiv2008

Thermodynamics of natural images

The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding thermodynamics. We find evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how "surprising" we find individual images, and in the quantitative form of the entropy vs. energy. The energy landscape derived from our thermodynamic framework identifies special image configurations that have intrinsic error correcting properties, and neurons which could detect these features have a strong resemblance to the cells found in primary visual cortex.

q-bio.NC↗

arXiv2008

Constraint satisfaction problems and neural networks: a statistical physics perspective

A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve very large constraint satisfaction problems like random satisfiability, coloring, or error correction. Several aspects of these developments should be relevant for the understanding of functional complexity in neural networks. On the one hand the message passing procedures which are used in these new algorithms are based on local exchange of information, and succeed in solving some of the hardest computational problems. On the other hand some crucial inference problems in neurobiology, like those generated in multi-electrode recordings, naturally translate into hard constraint satisfaction problems. This paper gives a non-technical introduction to this field, emphasizing the main ideas at work in message passing strategies and their possible relevance to neural networks modeling. It also introduces a new message passing algorithm for inferring interactions between variables from correlation data, which could be useful in the analysis of multi-electrode recording data.

q-bio.NC↗

arXiv2008

Random subcubes as a toy model for constraint satisfaction problems

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.

cs.CC↗

arXiv2007

Pairs of SAT Assignment in Random Boolean Formulae

We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp threshold for this property as a function of the clause density. For large enough K, we prove that there exists a region of clause density, below the satisfiability threshold, where the landscape of Hamming distances between SAT assignments experiences a gap: pairs of SAT-assignments exist at small x, and around x=1/2, but they donot exist at intermediate values of x. This result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis (the cavity method), and its algorithmic counterpart (the survey propagation algorithm). The method uses elementary probabilistic arguments (first and second moment methods), and might be useful in other problems of computational and physical interest where similar phenomena appear.

cond-mat.dis-nn↗

arXiv2006

Geometrical organization of solutions to random linear Boolean equations

The random XORSAT problem deals with large random linear systems of Boolean variables. The difficulty of such problems is controlled by the ratio of number of equations to number of variables. It is known that in some range of values of this parameter, the space of solutions breaks into many disconnected clusters. Here we study precisely the corresponding geometrical organization. In particular, the distribution of distances between these clusters is computed by the cavity method. This allows to study the `x-satisfiability' threshold, the critical density of equations where there exist two solutions at a given distance.

cond-mat.dis-nn↗

arXiv2006

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.

cond-mat.dis-nn↗

arXiv2006

Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel

We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding.

cs.IT↗

arXiv2005

A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects

Using equations of motion accurate to the third post-Newtonian (3PN) order (O(v/c)^6 beyond Newtonian gravity), we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulae may be used as an accurate diagnostic of the physical content of quasi-equilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasi-equilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one per cent with a circular orbit and with physically reasonable tidal coefficients.

gr-qc↗

arXiv2005

Buckling of swelling gels

The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a stiff gel, and a thin corona of soft gel clamped to a disk of stiff gel. When the structure is immersed in water, the soft gel swells and bends out of plane leading to a wavy periodic pattern which wavelength is measured. The linear stability of the flat state is studied in the framework of linear elasticity using the equations for thin plates. The flat state is shown to become unstable to oscillations above a critical swelling rate and the computed wavelengths are in quantitative agreement with the experiment.

cond-mat.soft↗

arXiv2002

Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?

We make a comparison between results from numerically generated, quasi-equilibrium configurations of compact binary systems of black holes in close orbits, and results from the post-Newtonian approximation. The post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond Newtonian gravity), and include rotational and spin-orbit effects, but are generalized to permit orbits of non-zero eccentricity. Both treatments ignore gravitational radiation reaction. The energy E and angular momentum J of a given configuration are compared between the two methods as a function of the orbital angular frequency Ω. For small Ω, corresponding to orbital separations a factor of two larger than that of the innermost stable orbit, we find that, if the orbit is permitted to be slightly eccentric, with e ranging from \approx 0.03 to \approx 0.05, and with the two objects initially located at the orbital apocenter (maximum separation), our PN formulae give much better fits to the numerically generated data than do any circular-orbit PN methods, including various ``effective one-body'' resummation techniques. We speculate that the approximations made in solving the initial value equations of general relativity numerically may introduce a spurious eccentricity into the orbits.

gr-qc↗