66,648 research outputs found
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
In this article the framework for Parisi's spontaneous replica symmetry
breaking is reviewed, and subsequently applied to the example of the
statistical mechanical description of the storage properties of a
McCulloch-Pitts neuron. The technical details are reviewed extensively, with
regard to the wide range of systems where the method may be applied. Parisi's
partial differential equation and related differential equations are discussed,
and a Green function technique introduced for the calculation of replica
averages, the key to determining the averages of physical quantities. The
ensuing graph rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order Ward-Takahashi identity is recovered
analytically and is shown to lead to the Goldstone modes in continuous replica
symmetry breaking phases. The need for a replica symmetry breaking theory in
the storage problem of the neuron has arisen due to the thermodynamical
instability of formerly given solutions. Variational forms for the neuron's
free energy are derived in terms of the order parameter function x(q), for
different prior distribution of synapses. Analytically in the high temperature
limit and numerically in generic cases various phases are identified, among
them one similar to the Parisi phase in the Sherrington-Kirkpatrick model.
Extensive quantities like the error per pattern change slightly with respect to
the known unstable solutions, but there is a significant difference in the
distribution of non-extensive quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation result is also reviewed and
compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi,
eepic), accepted for Physics Report
On the gravitational wave background from compact binary coalescences in the band of ground-based interferometers
This paper reports a comprehensive study on the gravitational wave (GW)
background from compact binary coalescences. We consider in our calculations
newly available observation-based neutron star and black hole mass
distributions and complete analytical waveforms that include post-Newtonian
amplitude corrections. Our results show that: (i) post-Newtonian effects cause
a small reduction in the GW background signal; (ii) below 100 Hz the background
depends primarily on the local coalescence rate and the average chirp
mass and is independent of the chirp mass distribution; (iii) the effects of
cosmic star formation rates and delay times between the formation and merger of
binaries are linear below 100 Hz and can be represented by a single parameter
within a factor of ~ 2; (iv) a simple power law model of the energy density
parameter up to 50-100 Hz is sufficient to be used
as a search template for ground-based interferometers. In terms of the
detection prospects of the background signal, we show that: (i) detection (a
signal-to-noise ratio of 3) within one year of observation by the Advanced LIGO
detectors (H1-L1) requires a coalescence rate of for binary neutron stars (binary black holes); (ii) this limit on
could be reduced 3-fold for two co-located detectors, whereas the
currently proposed worldwide network of advanced instruments gives only ~ 30%
improvement in detectability; (iii) the improved sensitivity of the planned
Einstein Telescope allows not only confident detection of the background but
also the high frequency components of the spectrum to be measured. Finally we
show that sub-threshold binary neutron star merger events produce a strong
foreground, which could be an issue for future terrestrial stochastic searches
of primordial GWs.Comment: A few typos corrected to match the published version in MNRA
Temptation and self-control: some evidence and applications
This paper studies the empirical relevance of temptation and self-control using household-level data from the Consumer Expenditure Survey. We estimate an infinite-horizon consumption-savings model that allows, but does not require, temptation and self-control in preferences. To help identify the presence of temptation, we exploit an implication of the theory that a tempted individual has a preference for commitment. In the presence of temptation, the cross-sectional distribution of the wealth-consumption ratio, in addition to that of consumption growth, becomes a determinant of the asset-pricing kernel, and the importance of this additional pricing factor depends on the strength of temptation. The estimates that we obtain provide statistical evidence supporting the presence of temptation. Based on our estimates, we explore some quantitative implications of this class of preferences on equity premium and on the welfare cost of business cycles.Asset pricing ; Welfare
Continuous quantum phase transition in a Kondo lattice model
We study the magnetic quantum phase transition in an anisotropic Kondo
lattice model. The dynamical competition between the RKKY and Kondo
interactions is treated using an extended dynamic mean field theory (EDMFT)
appropriate for both the antiferromagnetic and paramagnetic phases. A quantum
Monte Carlo approach is used, which is able to reach very low temperatures, of
the order of 1% of the bare Kondo scale. We find that the finite-temperature
magnetic transition, which occurs for sufficiently large RKKY interactions, is
first order. The extrapolated zero-temperature magnetic transition, on the
other hand, is continuous and locally critical.Comment: 4 pages, 4 figures; updated, to appear in PR
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Bioinspired Multifunctional Anti-icing Hydrogel
The recent anti-icing strategies in the state of the art mainly focused on three aspects: inhibiting ice nucleation, preventing ice propagation, and decreasing ice adhesion strength. However, it is has proved difficult to prevent ice nucleation and propagation while decreasing adhesion simultaneously, due to their highly distinct, even contradictory design principles. In nature, anti-freeze proteins (AFPs) offer a prime example of multifunctional integrated anti-icing materials that excel in all three key aspects of the anti-icing process simultaneously by tuning the structures and dynamics of interfacial water. Here, inspired by biological AFPs, we successfully created a multifunctional anti-icing material based on polydimethylsiloxane-grafted polyelectrolyte hydrogel that can tackle all three aspects of the anti-icing process simultaneously. The simplicity, mechanical durability, and versatility of these smooth hydrogel surfaces make it a promising option for a wide range of anti-icing applications
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