3,138 research outputs found
An adaptive Metropolis-Hastings scheme: sampling and optimization
We propose an adaptive Metropolis-Hastings algorithm in which sampled data
are used to update the proposal distribution. We use the samples found by the
algorithm at a particular step to form the information-theoretically optimal
mean-field approximation to the target distribution, and update the proposal
distribution to be that approximatio. We employ our algorithm to sample the
energy distribution for several spin-glasses and we demonstrate the superiority
of our algorithm to the conventional MH algorithm in sampling and in annealing
optimization.Comment: To appear in Europhysics Letter
Analytic Continuation for Asymptotically AdS 3D Gravity
We have previously proposed that asymptotically AdS 3D wormholes and black
holes can be analytically continued to the Euclidean signature. The analytic
continuation procedure was described for non-rotating spacetimes, for which a
plane t=0 of time symmetry exists. The resulting Euclidean manifolds turned out
to be handlebodies whose boundary is the Schottky double of the geometry of the
t=0 plane. In the present paper we generalize this analytic continuation map to
the case of rotating wormholes. The Euclidean manifolds we obtain are quotients
of the hyperbolic space by a certain quasi-Fuchsian group. The group is the
Fenchel-Nielsen deformation of the group of the non-rotating spacetime. The
angular velocity of an asymptotic region is shown to be related to the
Fenchel-Nielsen twist. This solves the problem of classification of rotating
black holes and wormholes in 2+1 dimensions: the spacetimes are parametrized by
the moduli of the boundary of the corresponding Euclidean spaces. We also
comment on the thermodynamics of the wormhole spacetimes.Comment: 28 pages, 14 figure
Geometric Aspects of the Moduli Space of Riemann Surfaces
This is a survey of our recent results on the geometry of moduli spaces and
Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and
math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller
spaces of Riemann surfaces with very good properties, study their curvatures
and boundary behaviors in great detail. Based on the careful analysis of these
new metrics, we have a good understanding of the Kahler-Einstein metric from
which we prove that the logarithmic cotangent bundle of the moduli space is
stable. Another corolary is a proof of the equivalences of all of the known
classical complete metrics to the new metrics, in particular Yau's conjectures
in the early 80s on the equivalences of the Kahler-Einstein metric to the
Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes
corrrecte
Cold acclimation of Concord grapevines III. Relationship between cold hardiness, tissue water content, and shoot maturation
Cold acclimation of Concord grapevines in Michigan begins as early as late August in tissues at the base of current season's growth.Increases in cold hardiness are closely related to decreases in tissue water content as stems achieve vegetative maturity.Greatest differences in hardiness and water content are found in tissues which vary the most in extent of maturation on both primary shoots and summer laterals.Increases in cold resistance are not related to water saturation deficit (WSD) of shoots
Hybrid Local-Order Mechanism for Inversion Symmetry Breaking
Using classical Monte Carlo simulations, we study a simple statistical
mechanical model of relevance to the emergence of polarisation from local
displacements on the square and cubic lattices. Our model contains two key
ingredients: a Kitaev-like orientation-dependent interaction between nearest
neighbours, and a steric term that acts between next-nearest neighbours. Taken
by themselves, each of these two ingredients is incapable of driving long-range
symmetry breaking, despite the presence of a broad feature in the corresponding
heat capacity functions. Instead each component results in a "hidden"
transition on cooling to a manifold of degenerate states, the two manifolds are
different in the sense that they reflect distinct types of local order.
Remarkably, their intersection---\emph{i.e.} the ground state when both
interaction terms are included in the Hamiltonian---supports a spontaneous
polarisation. In this way, our study demonstrates how local ordering mechanisms
might be combined to break global inversion symmetry in a manner conceptually
similar to that operating in the "hybrid" improper ferroelectrics. We discuss
the relevance of our analysis to the emergence of spontaneous polarisation in
well-studied ferroelectrics such as BaTiO and KNbO.Comment: 8 pages, 8 figure
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
The value of the follow-through derives from motor learning depending on future actions.
In ball sports, we are taught to follow through, despite the inability of events after contact or release to influence the outcome [1, 2]. Here we show that the specific motor memory active at any given moment critically depends on the movement that will be made in the near future. We demonstrate that associating a different follow-through movement with two motor skills that normally interfere [3-7] allows them to be learned simultaneously, suggesting that distinct future actions activate separate motor memories. This implies that when learning a skill, a variable follow-through would activate multiple motor memories across practice, whereas a consistent follow-through would activate a single motor memory, resulting in faster learning. We confirm this prediction and show that such follow-through effects influence adaptation over time periods associated with real-world skill learning. Overall, our results indicate that movements made in the immediate future influence the current active motor memory. This suggests that there is a critical time period both before [8] and after the current movement that determines motor memory activation and controls learning.This is the final published version. The article was originally published in Current Biology, Volume 25, Issue 3, p397–401, 2 February 2015, DOI: 10.1016/j.cub.2014.12.03
Black Hole Thermodynamics and Riemann Surfaces
We use the analytic continuation procedure proposed in our earlier works to
study the thermodynamics of black holes in 2+1 dimensions. A general black hole
in 2+1 dimensions has g handles hidden behind h horizons. The result of the
analytic continuation is a hyperbolic 3-manifold having the topology of a
handlebody. The boundary of this handlebody is a compact Riemann surface of
genus G=2g+h-1. Conformal moduli of this surface encode in a simple way the
physical characteristics of the black hole. The moduli space of black holes of
a given type (g,h) is then the Schottky space at genus G. The (logarithm of
the) thermodynamic partition function of the hole is the Kaehler potential for
the Weil-Peterson metric on the Schottky space. Bekenstein bound on the black
hole entropy leads us to conjecture a new strong bound on this Kaehler
potential.Comment: 17+1 pages, 9 figure
Embryonic Pattern Scaling Achieved by Oppositely Directed Morphogen Gradients
Morphogens are proteins, often produced in a localised region, whose
concentrations spatially demarcate regions of differing gene expression in
developing embryos. The boundaries of expression must be set accurately and in
proportion to the size of the one-dimensional developing field; this cannot be
accomplished by a single gradient. Here, we show how a pair of morphogens
produced at opposite ends of a developing field can solve the pattern-scaling
problem. In the most promising scenario, the morphogens effectively interact
according to the annihilation reaction and the switch occurs
according to the absolute concentration of or . In this case embryonic
markers across the entire developing field scale approximately with system
size; this cannot be achieved with a pair of non-interacting gradients that
combinatorially regulate downstream genes. This scaling occurs in a window of
developing-field sizes centred at a few times the morphogen decay length.Comment: 24 pages; 11 figures; uses iopar
Learning, Social Intelligence and the Turing Test - why an "out-of-the-box" Turing Machine will not pass the Turing Test
The Turing Test (TT) checks for human intelligence, rather than any putative
general intelligence. It involves repeated interaction requiring learning in
the form of adaption to the human conversation partner. It is a macro-level
post-hoc test in contrast to the definition of a Turing Machine (TM), which is
a prior micro-level definition. This raises the question of whether learning is
just another computational process, i.e. can be implemented as a TM. Here we
argue that learning or adaption is fundamentally different from computation,
though it does involve processes that can be seen as computations. To
illustrate this difference we compare (a) designing a TM and (b) learning a TM,
defining them for the purpose of the argument. We show that there is a
well-defined sequence of problems which are not effectively designable but are
learnable, in the form of the bounded halting problem. Some characteristics of
human intelligence are reviewed including it's: interactive nature, learning
abilities, imitative tendencies, linguistic ability and context-dependency. A
story that explains some of these is the Social Intelligence Hypothesis. If
this is broadly correct, this points to the necessity of a considerable period
of acculturation (social learning in context) if an artificial intelligence is
to pass the TT. Whilst it is always possible to 'compile' the results of
learning into a TM, this would not be a designed TM and would not be able to
continually adapt (pass future TTs). We conclude three things, namely that: a
purely "designed" TM will never pass the TT; that there is no such thing as a
general intelligence since it necessary involves learning; and that
learning/adaption and computation should be clearly distinguished.Comment: 10 pages, invited talk at Turing Centenary Conference CiE 2012,
special session on "The Turing Test and Thinking Machines
- …