Disentangling the timescales behind the non-perturbative heavy quark potential

The static part of the heavy quark potential has been shown to be closely related to the spectrum of the rectangular Wilson loop. In particular the lowest lying positive frequency peak encodes the late time evolution of the two-body system, characterized by a complex potential. While initial studies assumed a perfect separation of early and late time physics, where a simple Lorentian (Breit-Wigner) shape suffices to describe the spectral peak, we argue that scale decoupling in general is not complete. Thus early time, i.e. non-potential effects, significantly modify the shape of the lowest peak. We derive on general grounds an improved peak distribution that reflects this fact. Application of the improved fit to non-perturbative lattice QCD spectra now yields a potential that is compatible with a transition to a deconfined screening plasma.Comment: 5 pages, 3 figure

Complex Heavy-Quark Potential at Finite Temperature from Lattice QCD

We calculate for the first time the complex potential between a heavy quark and antiquark at finite temperature across the deconfinement transition in lattice QCD. The real and imaginary part of the potential at each separation distance $r$ is obtained from the spectral function of the thermal Wilson loop. We confirm the existence of an imaginary part above the critical temperature $T_C$, which grows as a function of $r$ and underscores the importance of collisions with the gluonic environment for the melting of heavy quarkonia in the quark-gluon-plasma.Comment: 4 pages, 3 figures, to be published in PR

Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.Comment: 20 pages. v2: more elaboration on systematic errors; published versio

Credit assignment in multiple goal embodied visuomotor behavior

The intrinsic complexity of the brain can lead one to set aside issues related to its relationships with the body, but the field of embodied cognition emphasizes that understanding brain function at the system level requires one to address the role of the brain-body interface. It has only recently been appreciated that this interface performs huge amounts of computation that does not have to be repeated by the brain, and thus affords the brain great simplifications in its representations. In effect the brain’s abstract states can refer to coded representations of the world created by the body. But even if the brain can communicate with the world through abstractions, the severe speed limitations in its neural circuitry mean that vast amounts of indexing must be performed during development so that appropriate behavioral responses can be rapidly accessed. One way this could happen would be if the brain used a decomposition whereby behavioral primitives could be quickly accessed and combined. This realization motivates our study of independent sensorimotor task solvers, which we call modules, in directing behavior. The issue we focus on herein is how an embodied agent can learn to calibrate such individual visuomotor modules while pursuing multiple goals. The biologically plausible standard for module programming is that of reinforcement given during exploration of the environment. However this formulation contains a substantial issue when sensorimotor modules are used in combination: The credit for their overall performance must be divided amongst them. We show that this problem can be solved and that diverse task combinations are beneficial in learning and not a complication, as usually assumed. Our simulations show that fast algorithms are available that allot credit correctly and are insensitive to measurement noise

Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop

We propose a non-perturbative and gauge invariant derivation of the static potential between a heavy-quark ($Q$) and an anti-quark ($\bar{Q}$) at finite temperature. This proper potential is defined through the spectral function (SPF) of the thermal Wilson loop and can be shown to satisfy the Schr\"{o}dinger equation for the heavy $Q\bar{Q}$ pair in the thermal medium. In general, the proper potential has a real and an imaginary part,corresponding to the peak position and width of the SPF. The validity of using a Schr\"{o}dinger equation for heavy $Q\bar{Q}$ can also be checked from the structure of the SPF. To test this idea, quenched QCD simulations on anisotropic lattices ($a_\sigma=4a_\tau=0.039\rm fm$, $N^3_\sigma \times N_{\tau} =20^2 \times (96-32)$) are performed. The real part of the proper potential below the deconfinement temperature ($T=0.78T_c$) exhibits the well known Coulombic and confining behavior. At ($T=2.33T_c$) we find that it coincides with the Debye screened potential obtained from Polyakov-line correlations in the color-singlet channel under Coulomb gauge fixing. The physical meaning of the spectral structure of the thermal Wilson loop and the use of the maximum entropy method (MEM) to extract the real and imaginary part of the proper potential are also discussed.Comment: 7 pages, 8 figures, Talk given at the XXVII International Symposium on Lattice Field Theory (LATTICE 2009), July 25-31, 2009, Beijing, Chin

Solving Bongard Problems with a Visual Language and Pragmatic Reasoning

More than 50 years ago Bongard introduced 100 visual concept learning problems as a testbed for intelligent vision systems. These problems are now known as Bongard problems. Although they are well known in the cognitive science and AI communities only moderate progress has been made towards building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a formal language that allows representing complex visual concepts based on this vocabulary. Using this language and Bayesian inference, complex visual concepts can be induced from the examples that are provided in each Bongard problem. Contrary to other concept learning problems the examples from which concepts are induced are not random in Bongard problems, instead they are carefully chosen to communicate the concept, hence requiring pragmatic reasoning. Taking pragmatic reasoning into account we find good agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself. While this approach is far from solving all Bongard problems, it solves the biggest fraction yet

Bayesian Classifier Fusion with an Explicit Model of Correlation

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a hierarchical Bayesian model of probabilistic classifier fusion based on a new correlated Dirichlet distribution. This distribution explicitly models positive correlations between marginally Dirichlet-distributed random vectors thereby allowing explicit modeling of correlations between base classifiers or experts. The proposed model naturally accommodates the classic Independent Opinion Pool and other independent fusion algorithms as special cases. It is evaluated by uncertainty reduction and correctness of fusion on synthetic and real-world data sets. We show that a change in performance of the fused classifier due to uncertainty reduction can be Bayes optimal even for highly correlated base classifiers.Comment: 12 pages, 4 figures, 1 table, revised title and Fig 2, added real data set Bookies

Probabilistic inverse optimal control with local linearization for non-linear partially observable systems

Inverse optimal control methods can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, requires the control signals to be known, or is limited to fully-observable or linear systems. This paper introduces a probabilistic approach to inverse optimal control for stochastic non-linear systems with missing control signals and partial observability that unifies existing approaches. By using an explicit model of the noise characteristics of the sensory and control systems of the agent in conjunction with local linearization techniques, we derive an approximate likelihood for the model parameters, which can be computed within a single forward pass. We evaluate our proposed method on stochastic and partially observable version of classic control tasks, a navigation task, and a manual reaching task. The proposed method has broad applicability, ranging from imitation learning to sensorimotor neuroscience