Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.

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Quasinormal modes of black holes and black branes

The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a 'theorem': assuming 'traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show that the interior of black holes have a 'fuzzball' structure. This nontrivial structure of microstates resolves the information paradox and gives a qualitative picture of how classical intuition can break down in black hole physics.

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The Information paradox: A Pedagogical introduction

Neuronal populations in sensory cortex produce variable responses to sensory stimuli and exhibit intricate spontaneous activity even without external sensory input. Cortical variability and spontaneous activity have been variously proposed to represent random noise, recall of prior experience, or encoding of ongoing behavioral and cognitive variables. Recording more than 10,000 neurons in mouse visual cortex, we observed that spontaneous activity reliably encoded a high-dimensional latent state, which was partially related to the mouse's ongoing behavior and was represented not just in visual cortex but also across the forebrain. Sensory inputs did not interrupt this ongoing signal but added onto it a representation of external stimuli in orthogonal dimensions. Thus, visual cortical population activity, despite its apparently noisy structure, reliably encodes an orthogonal fusion of sensory and multidimensional behavioral information.

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Spontaneous behaviors drive multidimensional, brainwide activity.

1. Opening remarks 2. A heavy ion phenomenology primer 3. Results from lattice QCD at nonzero temperature 4. Introducing the gauge/string duality 5. A duality toolbox 6. Bulk properties of strongly coupled plasma 7. From hydrodynamics for far-from-equilibrium dynamics 8. Probing strongly coupled plasma 9. Quarkonium mesons in strongly coupled plasma 10. Concluding remarks and outlook Appendixes References Index.

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Gauge/String Duality, Hot QCD and Heavy Ion Collisions

Computational strategies used by the brain strongly depend on the amount of information that can be stored in population activity, which in turn strongly depends on the pattern of noise correlations. In vivo, noise correlations tend to be positive and proportional to the similarity in tuning properties. Such correlations are thought to limit information, which has led to the suggestion that decorrelation increases information. In contrast, we found, analytically and numerically, that decorrelation does not imply an increase in information. Instead, the only information-limiting correlations are what we refer to as differential correlations: correlations proportional to the product of the derivatives of the tuning curves. Unfortunately, differential correlations are likely to be very small and buried under correlations that do not limit information, making them particularly difficult to detect. We found, however, that the effect of differential correlations on information can be detected with relatively simple decoders.

Information-limiting correlations

Through multi-agent competition, the simple objective of hide-and-seek, and standard reinforcement learning algorithms at scale, we find that agents create a self-supervised autocurriculum inducing multiple distinct rounds of emergent strategy, many of which require sophisticated tool use and coordination. We find clear evidence of six emergent phases in agent strategy in our environment, each of which creates a new pressure for the opposing team to adapt; for instance, agents learn to build multi-object shelters using moveable boxes which in turn leads to agents discovering that they can overcome obstacles using ramps. We further provide evidence that multi-agent competition may scale better with increasing environment complexity and leads to behavior that centers around far more human-relevant skills than other self-supervised reinforcement learning methods such as intrinsic motivation. Finally, we propose transfer and fine-tuning as a way to quantitatively evaluate targeted capabilities, and we compare hide-and-seek agents to both intrinsic motivation and random initialization baselines in a suite of domain-specific intelligence tests.

Emergent Tool Use From Multi-Agent Autocurricula.

Brain function involves the activity of neuronal populations. Much recent effort has been devoted to measuring the activity of neuronal populations in different parts of the brain under various experimental conditions. Population activity patterns contain rich structure, yet many studies have focused on measuring pairwise relationships between members of a larger population—termed noise correlations. Here we review recent progress in understanding how these correlations affect population information, how information should be quantified, and what mechanisms may give rise to correlations. As population coding theory has improved, it has made clear that some forms of correlation are more important for information than others. We argue that this is a critical lesson for those interested in neuronal population responses more generally: Descriptions of population responses should be motivated by and linked to well-specified function. Within this context, we offer suggestions of where current theoretical framew...

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Correlations and Neuronal Population Information

We set up precision holography for the non-conformal branes preserving 16 supersymmetries. The near-horizon limit of all such p-brane solutions with p ? 4, including the case of fundamental string solutions, is conformal to AdSp+2 ? S8?p with a linear dilaton. We develop holographic renormalization for all these cases. In particular, we obtain the most general asymptotic solutions with appropriate Dirichlet boundary conditions, find the corresponding counterterms and compute the holographic 1-point functions, all in complete generality and at the full non-linear level. The result for the stress energy tensor properly defines the notion of mass for backgrounds with such asymptotics. The analysis is done both in the original formulation of the method and also using a radial Hamiltonian analysis. The latter formulation exhibits most clearly the existence of an underlying generalized conformal structure. In the cases of Dp-branes, the corresponding dual boundary theory, the maximally supersymmetric Yang-Mills theory SYMp+1, indeed exhibits the generalized conformal structure found at strong coupling. We compute the holographic 2-point functions of the stress energy tensor and gluon operator and show they satisfy the expected Ward identities and the constraints of generalized conformal structure. The holographic results are also manifestly compatible with the M-theory uplift, with the asymptotic solutions, counterterms, one and two point functions etc. of the IIA F1 and D4 appropriately descending from those of M2 and M5 branes, respectively. We present a few applications including the computation of condensates in Witten's model of holographic YM{}4 theory.

Precision holography for non-conformal branes

We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-conformal branes is fully determined in terms of conformal hydrodynamics. Using previous results on the latter we predict the form of the non-conformal hydrodynamic stress tensor to second order in derivatives. Furthermore we show that the ratio between bulk and shear viscosity is fixed by the generalized conformal structure to be ζ/η = 2(1/(d−1)−cs2), where cs is the speed of sound in the fluid.

Ingmar Kanitscheider

Papers

Information-limiting correlations

Emergent Tool Use From Multi-Agent Autocurricula.

Correlations and Neuronal Population Information

Precision holography for non-conformal branes

Universal hydrodynamics of non-conformal branes