Matching with shift for one-dimensional Gibbs measures

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The inclusion process: duality and correlation inequalities

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.Comment: This is a new version: correlation inequalities for the Brownian energy process are added, and the part of the asymmetric inclusion process is removed

Efficient and Stable Locomotion for Impulse-Actuated Robots Using Strictly Convex Foot Shapes

Impulsive actuation enables robots to perform agile manoeuvres and surpass difficult terrain, yet its capacity to induce continuous and stable locomotion have not been explored. We claim that strictly convex foot shapes can improve impulse effectiveness (impulse used per travelled distance) and locomotion speed by facilitating periodicity and stability. To test this premise, we introduce a theoretical two-dimensional model based on rigidbody mechanics to prove stability. We then implement a more elaborate model in simulation to study transient behaviour and impulse effectiveness. Finally, we test our findings on a robot platform to prove their physical validity. Our results prove, that continuous and stable locomotion can be achieved in the strictly convex case of a disc with off-centred mass. In keeping with our theory, stable limit cycles of the off-centred disc outperform the theoretical performance of a cube in simulation and experiment, using up to 10 times less impulse per distance to travel at the same locomotion speed

Glassy dynamics, metastability limit and crystal growth in a lattice spin model

We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour typical of fragile glasses. However, the supercooled phase loses stability at an effective spinodal temperature, and thanks to this the Kauzmann paradox is resolved. Below the spinodal the system enters an off-equilibrium regime corresponding to fast crystal nucleation followed by slow activated crystal growth. In this phase and in a time region which is longer the lower the temperature we observe a violation of the fluctuation-dissipation theorem analogous to structural glasses. Moreover, we show that in this system there is no qualitative difference between a locally stable glassy configuration and a highly disordered polycrystal

Optimization Strategies in Complex Systems

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the``greedy'' (quick decrease along the gradient) and the``reluctant'' (slow decrease close to the level curves) as well as those of a``stochastic convex interpolation''of the two. Concepts like the average relaxation time and the wideness of the attraction basin are analyzed and their system size dependence illustrated.Comment: 8 pages, 3 figure