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

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

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

Structure Learning in a Sensorimotor Association Task

Learning is often understood as an organism's gradual acquisition of the association between a given sensory stimulus and the correct motor response. Mathematically, this corresponds to regressing a mapping between the set of observations and the set of actions. Recently, however, it has been shown both in cognitive and motor neuroscience that humans are not only able to learn particular stimulus-response mappings, but are also able to extract abstract structural invariants that facilitate generalization to novel tasks. Here we show how such structure learning can enhance facilitation in a sensorimotor association task performed by human subjects. Using regression and reinforcement learning models we show that the observed facilitation cannot be explained by these basic models of learning stimulus-response associations. We show, however, that the observed data can be explained by a hierarchical Bayesian model that performs structure learning. In line with previous results from cognitive tasks, this suggests that hierarchical Bayesian inference might provide a common framework to explain both the learning of specific stimulus-response associations and the learning of abstract structures that are shared by different task environments

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

Loop Representations for 2+1 Gravity on a Torus

We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this system. In particular, we look at the loop transform in the part of the phase space where the holonomies are boosts and study its kernel. This kernel is dense in the connection representation and the transform is not continuous with respect to the natural topologies, even in its domain of definition. Nonetheless, loop representations isomorphic to the connection representation corresponding to this part of the phase space can still be constructed if due care is taken. We present this construction but note that certain ambiguities remain; in particular, functions of loops cannot be uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

The vein-banding disease syndrome: A synergistic reaction between grapevine viroids and fanleaf virus

Viroid-free Vitis vinifera cultivars Cabernet Sauvignon and Sauvignon blanc were established in controlled field trials in California to evaluate the relationship between grapevine viroids and fanleaf virus for induction of the vein-banding disease. Vein-banding symptoms were observed only on vines which contained the three principal grapevine viroids, grapevine yellow speckle viroids (GYSVd-1, GYSVd-2), and hop stunt viroid (HSVd-g), as well as grapevine fanleaf virus (GFLV). Sauvignon blanc vines which contained the single viroid, HSVd-g, and GFLV were non-symptomatic indicating an absence of a correlation between HSVd-g and the vein-banding disease. The intensity of vein-banding symptoms was directly correlated with an enhanced titer of GYSVd-1 and GYSVd-2. Vein-banding and yellow speckle symptomatic as well as non-symptomatic vines in Italy contained two viroids, GYSVd-1 and HSVd-g. However, symptomatic vines displayed a higher titer of GYSVd-1 than non-symptomatic materials and vein-banding symptomatic vines were GFLV infected. These data experimentally demonstrate that expression of the vein-banding disease is induced by an unique synergistic reaction between a viroid, GYSVd-1 and a virus, GFLV

Forward estimation of movement state in posterior parietal cortex

During goal-directed movements, primates are able to rapidly and accurately control an online trajectory despite substantial delay times incurred in the sensorimotor control loop. To address the problem of large delays, it has been proposed that the brain uses an internal forward model of the arm to estimate current and upcoming states of a movement, which are more useful for rapid online control. To study online control mechanisms in the posterior parietal cortex (PPC), we recorded from single neurons while monkeys performed a joystick task. Neurons encoded the static target direction and the dynamic movement angle of the cursor. The dynamic encoding properties of many movement angle neurons reflected a forward estimate of the state of the cursor that is neither directly available from passive sensory feedback nor compatible with outgoing motor commands and is consistent with PPC serving as a forward model for online sensorimotor control. In addition, we found that the space–time tuning functions of these neurons were largely separable in the angle–time plane, suggesting that they mostly encode straight and approximately instantaneous trajectories