47 research outputs found
Collective behaviours: from biochemical kinetics to electronic circuits
In this work we aim to highlight a close analogy between cooperative
behaviors in chemical kinetics and cybernetics; this is realized by using a
common language for their description, that is mean-field statistical
mechanics. First, we perform a one-to-one mapping between paradigmatic
behaviors in chemical kinetics (i.e., non-cooperative, cooperative,
ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics
(i.e., paramagnetic, high and low temperature ferromagnetic,
anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a
unified, broad theory for all scenarios and, in particular, Michaelis-Menten,
Hill and Adair equations are consistently recovered. This framework is then
tested against experimental biological data with an overall excellent
agreement. One step forward, we consistently read the whole mapping from a
cybernetic perspective, highlighting deep structural analogies between the
above-mentioned kinetics and fundamental bricks in electronics (i.e.
operational amplifiers, flashes, flip-flops), so to build a clear bridge
linking biochemical kinetics and cybernetics.Comment: 15 pages, 6 figures; to appear on Scientific Reports: Nature
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Notes on the p-spin glass studied via Hamilton-Jacobi and Smooth-Cavity techniques
In these notes, we continue our investigation of classical toy models of
disordered statistical mechanics through various techniques recently developed
and tested mainly on the paradigmatic SK spin glass. Here we consider the
p-spin-glass model with Ising spins and interactions drawn from a normal
distribution N[0,1]. After a general presentation of its properties (e.g.
self-averaging of the free energy, existence of a suitable thermodynamic
limit), we study its equilibrium behavior within the Hamilton-Jacobi framework
and the smooth cavity approach. Through the former we find both the RS and the
1RSB expressions for the free energy, coupled with their self-consistent
relations for the overlaps. Through the latter, we recover these results as
irreducible expression, and we study the generalization of the overlap
polynomial identities suitable for this model; a discussion on their deep
connection with the structure of the internal energy and the entropy closes the
investigation.Comment: To appear on JM
Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique
During the last years, through the combined effort of the insight, coming
from physical intuition and computer simulation, and the exploitation of
rigorous mathematical methods, the main features of the mean field
Sherrington-Kirkpatrick spin glass model have been firmly established. In
particular, it has been possible to prove the existence and uniqueness of the
infinite volume limit for the free energy, and its Parisi expression, in terms
of a variational principle, involving a functional order parameter. Even the
expected property of ultrametricity, for the infinite volume states, seems to
be near to a complete proof. The main structural feature of this model, and
related models, is the deep phenomenon of spontaneous replica symmetry breaking
(RSB), discovered by Parisi many years ago. By expanding on our previous work,
the aim of this paper is to investigate a general frame, where replica symmetry
breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi
type. Here, the analog of the "time" variable is a parameter characterizing the
strength of the interaction, while the "space" variables rule out
quantitatively the broken replica symmetry pattern. Starting from the simple
cases, where annealing is assumed, or replica symmetry, we build up a
progression of dynamical systems, with an increasing number of space variables,
which allow to weaken the effect of the potential in the Hamilton-Jacobi
equation, as the level of symmetry braking is increased. This new machinery
allows to work out mechanically the general K-step RSB solutions, in a
different interpretation with respect to the replica trick, and lightens easily
their properties as existence or uniqueness.Comment: 24 pages, no figure
Mean-field cooperativity in chemical kinetics
We consider cooperative reactions and we study the effects of the interaction
strength among the system components on the reaction rate, hence realizing a
connection between microscopic and macroscopic observables. Our approach is
based on statistical mechanics models and it is developed analytically via
mean-field techniques. First of all, we show that, when the coupling strength
is set positive, the model is able to consistently recover all the various
cooperative measures previously introduced, hence obtaining a single unifying
framework. Furthermore, we introduce a criterion to discriminate between weak
and strong cooperativity, based on a measure of "susceptibility". We also
properly extend the model in order to account for multiple attachments
phenomena: this is realized by incorporating within the model -body
interactions, whose non-trivial cooperative capability is investigated too.Comment: 25 pages, 4 figure
TECNICA TECNOLOGIA E SCIENZA SULLE STRADE NAPOLETANE. LA LARGHEZZA DELLA BANDA DELLE RUOTE E GLI ASSI DELLE VETTURE
IL SAGGIO E' IL TESTO DELLA RELAZIONE AL CONVEGNO "SPAZI DELLA BORGHESIA E GOVERNO DEL TERRITORIO" ORGANIZZATO DAL CENTRO EUROPEO DI STUDI E RICERCHE SUL PERIODO NAPOLEOINICO A ALESSANDRIA NEL 2002. GLI ATTI SONO PUBBLICATI IN UN NUMERO MONOGRAFICO DI "RNR" A CURA DI DI ALDO DI BIASI