Application of p-adic analysis to models of spontaneous breaking of the replica symmetry

Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page

A note on rattlers in amorphous packings of binary mixtures of hard spheres

It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our theoretical result for the jamming density of a binary mixture of hard spheres (arXiv:0903.5099) apparently violates an upper bound that is obtained by considering the limit where the diameter ratio r = DA/DB goes to infinity. We believe that this apparent contradiction is the consequence of a misunderstanding, which we try to clarify here.Comment: 2 pages, 2 figures; final version published on J.Chem.Phy

Lifelong Learning of Spatiotemporal Representations with Dual-Memory Recurrent Self-Organization

Artificial autonomous agents and robots interacting in complex environments are required to continually acquire and fine-tune knowledge over sustained periods of time. The ability to learn from continuous streams of information is referred to as lifelong learning and represents a long-standing challenge for neural network models due to catastrophic forgetting. Computational models of lifelong learning typically alleviate catastrophic forgetting in experimental scenarios with given datasets of static images and limited complexity, thereby differing significantly from the conditions artificial agents are exposed to. In more natural settings, sequential information may become progressively available over time and access to previous experience may be restricted. In this paper, we propose a dual-memory self-organizing architecture for lifelong learning scenarios. The architecture comprises two growing recurrent networks with the complementary tasks of learning object instances (episodic memory) and categories (semantic memory). Both growing networks can expand in response to novel sensory experience: the episodic memory learns fine-grained spatiotemporal representations of object instances in an unsupervised fashion while the semantic memory uses task-relevant signals to regulate structural plasticity levels and develop more compact representations from episodic experience. For the consolidation of knowledge in the absence of external sensory input, the episodic memory periodically replays trajectories of neural reactivations. We evaluate the proposed model on the CORe50 benchmark dataset for continuous object recognition, showing that we significantly outperform current methods of lifelong learning in three different incremental learning scenario

Jamming Criticality Revealed by Removing Localized Buckling Excitations

Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.Comment: 12 pages, 4 figure

Magnetic field chaos in the SK Model

We study the Sherrington--Kirkpatrick model, both above and below the De Almeida Thouless line, by using a modified version of the Parallel Tempering algorithm in which the system is allowed to move between different values of the magnetic field h. The behavior of the probability distribution of the overlap between two replicas at different values of the magnetic field h_0 and h_1 gives clear evidence for the presence of magnetic field chaos already for moderate system sizes, in contrast to the case of temperature chaos, which is not visible on system sizes that can currently be thermalized.Comment: Latex, 16 pages including 20 postscript figure