3,831 research outputs found
Memory distribution in complex fitness landscapes
In a co-evolutionary context, the survive probability of individual elements
of a system depends on their relation with their neighbors. The natural
selection process depends on the whole population, which is determined by local
events between individuals. Particular characteristics assigned to each
individual, as larger memory, usually improve the individual fitness, but an
agent possess also endogenous characteristics that induce to re-evaluate her
fitness landscape and choose the best-suited kind of interaction, inducing a
non absolute value of the outcomes of the interaction. In this work, a novel
model with agents combining memory and rational choice is introduced, where
individual choices in a complex fitness landscape induce changes in the
distribution of the number of agents as a function of the time. In particular,
the tail of this distribution is fat compared with distributions for agents
interacting only with memory.Comment: 6 pages, 3 figures, submited to Physica
Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD
We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the
collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac
operator. The mechanism, originating from complex Burger's-like equation for
viscid, pressureless, one-dimensional flow of eigenvalues, is similar to
recently observed weak-strong coupling phase transition in large
Yang-Mills theory. The spectral viscosity is proportional to the inverse of the
size of the random matrix that replaces the Dirac operator in the universal
(ergodic) regime. We obtain the exact scaling function and critical exponents
of the chiral phase transition for the averaged characteristic polynomial for
QCD. We reinterpret our results in terms of known properties of
chiral random matrix models and lattice data.Comment: 12 page
Universal shocks in the Wishart random-matrix ensemble - a sequel
We study the diffusion of complex Wishart matrices and derive a partial
differential equation governing the behavior of the associated averaged
characteristic polynomial. In the limit of large size matrices, the inverse
Cole-Hopf transform of this polynomial obeys a nonlinear partial differential
equation whose solutions exhibit shocks at the evolving edges of the eigenvalue
spectrum. In a particular scenario one of those shocks hits the origin that
plays the role of an impassable wall. To investigate the universal behavior in
the vicinity of this wall, a critical point, we derive an integral
representation for the averaged characteristic polynomial and study its
asymptotic behavior. The result is a Bessoid function.Comment: 7 pages, 2 figure
Universal shocks in the Wishart random matrix ensemble - 1
We show that the derivative of the logarithm of the average characteristic
polynomial of a diffusing Wishart matrix obeys an exact partial differential
equation valid for an arbitrary value of N, the size of the matrix. In the
large N limit, this equation generalizes the simple Burgers equation that has
been obtained earlier for Hermitian or unitary matrices. The solution through
the method of characteristics presents singularities that we relate to the
precursors of shock formation in fluid dynamical equations. The 1/N corrections
may be viewed as viscous corrections, with the role of the viscosity being
played by the inverse of the doubled dimension of the matrix. These corrections
are studied through a scaling analysis in the vicinity of the shocks, and one
recovers in a simple way the universal Bessel oscillations (so-called hard edge
singularities) familiar in random matrix theory.Comment: 9 page
M74 Motorway, Glasgow – Geotechnical Aspects of Design and Construction
The 7.8 kilometre long M74 Completion project forms the final part of the motorway box around the city of Glasgow. Construction commenced in May 2008 and was completed in June 2011. The urban route corridor presented many geotechnical challenges to the design and construction teams. It is underlain by Recent, lightly over-consolidated Clyde Alluvium of maximum 35 metres thickness over Glacial Till and Carboniferous Coal Measure Sandstone bedrock. Additionally, it was the location of industries over the 19th and 20th centuries which deposited waste over the natural ground containing chromium, steel works slag and hydrocarbons. The route corridor is also underlain by historical coal mining. This paper details the geotechnical design and construction to overcome the challenges for earthworks and structure foundations posed by th
Large N_c confinement and turbulence
We suggest that the transition that occurs at large in the eigenvalue
distribution of a Wilson loop may have a turbulent origin. We arrived at this
conclusion by studying the complex-valued inviscid Burgers-Hopf equation that
corresponds to the Makeenko-Migdal loop equation, and we demonstrate the
appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This
picture supplements that of the Durhuus-Olesen transition with a particular
realization of disorder. The critical behavior at the formation of the shock
allows us to infer exponents that have been measured recently in lattice
simulations by Narayanan and Neuberger in and . Our analysis leads
us to speculate that the universal behavior observed in these lattice
simulations might be a generic feature of confinement, also in Yang-Mills
theory.Comment: 4 pages, no figures- Some rewriting - Typos corrected - References
completed and some correcte
Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial
We show that the averaged characteristic polynomial and the averaged inverse
characteristic polynomial, associated with Hermitian matrices whose elements
perform a random walk in the space of complex numbers, satisfy certain partial
differential, diffusion-like, equations. These equations are valid for matrices
of arbitrary size. Their solutions can be given an integral representation that
allows for a simple study of their asymptotic behaviors for a broad range of
initial conditions.Comment: 26 pages, 4 figure
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