4,035 research outputs found
Divergent estimation error in portfolio optimization and in linear regression
The problem of estimation error in portfolio optimization is discussed, in
the limit where the portfolio size N and the sample size T go to infinity such
that their ratio is fixed. The estimation error strongly depends on the ratio
N/T and diverges for a critical value of this parameter. This divergence is the
manifestation of an algorithmic phase transition, it is accompanied by a number
of critical phenomena, and displays universality. As the structure of a large
number of multidimensional regression and modelling problems is very similar to
portfolio optimization, the scope of the above observations extends far beyond
finance, and covers a large number of problems in operations research, machine
learning, bioinformatics, medical science, economics, and technology.Comment: 5 pages, 2 figures, Statphys 23 Conference Proceedin
Criticality in inhomogeneous magnetic systems: Application to quantum ferromagnets
We consider a -theory with a position-dependent distance from the
critical point. One realization of this model is a classical ferromagnet
subject to non-uniform mechanical stress. We find a sharp phase transition
where the envelope of the local magnetization vanishes uniformly. The
first-order transition in a quantum ferromagnet also remains sharp. The
universal mechanism leading to a tricritical point in an itinerant quantum
ferromagnet is suppressed, and in principle one can recover a quantum critical
point with mean-field exponents. Observable consequences of these results are
discussed.Comment: 4pp, 4 eps figs, contains additional information compared to PRL
version. PRl, in pres
Direct-write, focused ion beam-deposited,7 K superconducting C-Ga-O nanowire
We have fabricated C-Ga-O nanowires by gallium focused ion beam-induced
deposition from the carbon-based precursor phenanthrene. The electrical
conductivity of the nanowires is weakly temperature dependent below 300 K, and
indicates a transition to a superconducting state below Tc = 7 K. We have
measured the temperature dependence of the upper critical field Hc2(T), and
estimate a zero temperature critical field of 8.8 T. The Tc of this material is
approximately 40% higher than that of any other direct write nanowire, such as
those based on C-W-Ga, expanding the possibility of fabricating direct-write
nanostructures that superconduct above liquid helium temperaturesComment: Accepted for AP
Convergence of simulated annealing by the generalized transition probability
We prove weak ergodicity of the inhomogeneous Markov process generated by the
generalized transition probability of Tsallis and Stariolo under power-law
decay of the temperature. We thus have a mathematical foundation to conjecture
convergence of simulated annealing processes with the generalized transition
probability to the minimum of the cost function. An explicitly solvable example
in one dimension is analyzed in which the generalized transition probability
leads to a fast convergence of the cost function to the optimal value. We also
investigate how far our arguments depend upon the specific form of the
generalized transition probability proposed by Tsallis and Stariolo. It is
shown that a few requirements on analyticity of the transition probability are
sufficient to assure fast convergence in the case of the solvable model in one
dimension.Comment: 11 page
Error threshold in simple landscapes
We consider the quasispecies description of a population evolving in both the
"master sequence" landscape (where a single sequence is evolutionarily
preferred over all others) and the REM landscape (where the fitness of
different sequences is an independent, identically distributed, random
variable). We show that, in both cases, the error threshold is analogous to a
first order thermodynamical transition, where the overlap between the average
genotype and the optimal one drops discontinuously to zero.Comment: 10 pages and 2 figures, Plain LaTe
Signatures of pairing mechanisms and order parameters in ferromagnetic superconductors
Two predictions are made for properties of the ferromagnetic superconductors
discovered recently. The first one is that spin-triplet, p-wave pairing in such
materials will give the magnons a mass inversely proportional to the square of
the magnetization. The second one is based on a specific mechanism for p-wave
pairing, and predicts that the observed broad anomaly in the specific heat of
URhGe will be resolved into a split transition with increasing sample quality.
These predictions will help discriminate between different possible mechanisms
for ferromagnetic superconductivity.Comment: 4 pp., 1 ps fi
Disorder-induced rounding of certain quantum phase transitions
We study the influence of quenched disorder on quantum phase transitions in
systems with over-damped dynamics. For Ising order parameter symmetry disorder
destroys the sharp phase transition by rounding because a static order
parameter can develop on rare spatial regions. This leads to an exponential
dependence of the order parameter on the coupling constant. At finite
temperatures the static order on the rare regions is destroyed. This restores
the phase transition and leads to a double-exponential relation between
critical temperature and coupling strength. We discuss the behavior based on
Lifshitz-tail arguments and illustrate the results by simulations of a model
system.Comment: 4 pages, 3 eps figure
Universal temperature dependence of the conductivity of a strongly disordered granular metal
A disordered array of metal grains with large and random intergrain
conductances is studied within the one-loop accuracy renormalization group
approach. While at low level of disorder the dependence of conductivity on log
T is nonuniversal (it depends on details of the array's geometry), for strong
disorder this dependence is described by a universal nonlinear function, which
depends only on the array's dimensionality. In two dimensions this function is
found numerically. The dimensional crossover in granular films is discussed.Comment: 6 pages, 6 figures, submitted to JETP Letter
Short-wavelength collective modes in a binary hard-sphere mixture
We use hard-sphere generalized hydrodynamic equations to discuss the extended
hydrodynamic modes of a binary mixture. The theory presented here is analytic
and it provides us with a simple description of the collective excitations of a
dense binary mixture at molecular length scales. The behavior we predict is in
qualitative agreement with molecular-dynamics results for soft-sphere mixtures.
This study provides some insight into the role of compositional disorder in
forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive
gives misleading impression of new publicatio
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