3,293 research outputs found
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 -- including the physically relevant
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
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