Distributed representations accelerate evolution of adaptive behaviours

Animals with rudimentary innate abilities require substantial learning to transform those abilities into useful skills, where a skill can be considered as a set of sensory - motor associations. Using linear neural network models, it is proved that if skills are stored as distributed representations, then within- lifetime learning of part of a skill can induce automatic learning of the remaining parts of that skill. More importantly, it is shown that this " free- lunch'' learning ( FLL) is responsible for accelerated evolution of skills, when compared with networks which either 1) cannot benefit from FLL or 2) cannot learn. Specifically, it is shown that FLL accelerates the appearance of adaptive behaviour, both in its innate form and as FLL- induced behaviour, and that FLL can accelerate the rate at which learned behaviours become innate

Recurrent cerebellar architecture solves the motor-error problem

Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences. We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex

Transport of a passive scalar in wide channels with surface topography

We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our theory, valid for small roughness amplitudes of the channel, holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e., the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion tensor.Comment: under consideration for publication in the Journal of Physics: Condensed Matter (JPCM

Using Reaction Times and Binary Responses to Estimate Psychophysical Performance: An Information-Theoretic Analysis

As the strength of a stimulus increases, the proportions of correct binary responses increases, which define the psychometric function. Simultaneously, mean reaction times (RT) decrease, which collectively define the chronometric function. However, RTs are traditionally ignored when estimating psychophysical parameters, even though they may provide additional Shannon information. Here, we extend Palmer et al's (2005) proportional-rate diffusion model (PRD) by: (a) fitting individual RTs to an inverse Gaussian distribution, (b) including lapse rate, (c) point-of-subjective-equality (PSE) parameters, and, (d) using a two-alternative forced choice (2AFC) design based on the proportion of times a variable comparison stimulus is chosen. Maximum likelihood estimates of mean RT values (from fitted inverse Gaussians) and binary responses were fitted both separately and in combination to this extended PRD (EPRD) model, to obtain psychophysical parameter values. Values estimated from binary responses alone (i.e., the psychometric function) were found to be similar to those estimated from RTs alone (i.e., the chronometric function), which provides support for the underlying diffusion model. The EPRD model was then used to estimate the mutual information between binary responses and stimulus strength, and between RTs and stimulus strength. These provide conservative bounds for the average amount of Shannon information the observer gains about stimulus strength on each trial. For the human experiment reported here, the observer gains between 2.68 and 3.55 bits/trial. These bounds are monotonically related to a new measure, the Shannon increment, which is the expected value of the smallest change in stimulus strength detectable by an observer

Spectral Properties of Compressible Magnetohydrodynamic Turbulence from Numerical Simulations

We analyze the spectral properties of driven, supersonic compressible magnetohydrodynamic (MHD) turbulence obtained via high-resolution numerical experiments, for application to understanding the dynamics of giant molecular clouds. Via angle-averaged power spectra, we characterize the transfer of energy from the intermediate, driving scales down to smaller dissipative scales, and also present evidence for inverse cascades that achieve modal-equipartition levels on larger spatial scales. Investigating compressive versus shear modes separately, we evaluate their relative total power, and find that as the magnetic field strength decreases, (1) the shear fraction of the total kinetic power decreases, and (2) slopes of power-law fits over the inertial range steepen. To relate to previous work on incompressible MHD turbulence, we present qualitative and quantitative measures of the scale-dependent spectral anisotropy arising from the shear-Alfv\'{e}n cascade, and show how these vary with changing mean magnetic field strength. Finally, we propose a method for using anisotropy in velocity centroid maps as a diagnostic of the mean magnetic field strength in observed cloud cores.Comment: 22 pages, 11 figures; Ap.J., accepte

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.Comment: 11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theor

Heavy Quark Symmetry Violation in Semileptonic Decays of D Mesons

The decays of $D$ mesons to $K l \nu$ and $K^* l \nu$ final states exhibit significant deviations from the predictions of heavy-quark symmetry, as one might expect since the strange quark's mass is of the same order as the QCD scale. Nonetheless, in order to understand where the most significant effects might lie for heavier systems (such as $B \to D l\nu$ and $B \to D^* l\nu$), the pattern of these deviations is analyzed from the standpoint of perturbative QCD and ${\cal O}(1/m_s)$ corrections. Two main effects are noted. First, the perturbative QCD corrections lead to an overall decrease of predicted rates, which can be understood in terms of production of excited kaonic states. Second, ${\cal O}(1/m_s)$ effects tend to cancel the perturbative QCD corrections in the case of $Kl\nu$ decay, while they have minimal effect in $K^*l\nu$ decay.Comment: 25 pages (LaTeX) + 7 pages of Postscript figures (included at end), EFI-92-3

Perturbations in gut microbiota composition in psychiatric disorders: a review and meta-analysis

Importance: evidence of gut microbiota perturbations has accumulated for multiple psychiatric disorders, with microbiota signatures proposed as potential biomarkers. However, no attempts have been made to evaluate the specificity of these across the range of psychiatric conditions. Objective: to conduct an umbrella and updated meta-analysis of gut microbiota alterations in general adult psychiatric populations and perform a within- and between-diagnostic comparison. Data Sources: Cochrane Library, PubMed, PsycINFO, and Embase were searched up to February 2, 2021, for systematic reviews, meta-analyses, and original evidence. Study Selection: a total of 59 case-control studies evaluating diversity or abundance of gut microbes in adult populations with major depressive disorder, bipolar disorder, psychosis and schizophrenia, anorexia nervosa, anxiety, obsessive compulsive disorder, posttraumatic stress disorder, or attention-deficit/hyperactivity disorder were included. Data Extraction and Synthesis: between-group comparisons of relative abundance of gut microbes and beta diversity indices were extracted and summarized qualitatively. Random-effects meta-analyses on standardized mean difference (SMD) were performed for alpha diversity indices. Main Outcomes and Measures: Alpha and beta diversity and relative abundance of gut microbes. Results: A total of 34 studies provided data and were included in alpha diversity meta-analyses (n = 1519 patients, n = 1429 control participants). Significant decrease in microbial richness in patients compared with control participants were found (observed species SMD = -0.26; 95% CI, -0.47 to -0.06; Chao1 SMD = -0.5; 95% CI, -0.79 to -0.21); however, this was consistently decreased only in bipolar disorder when individual diagnoses were examined. There was a small decrease in phylogenetic diversity (SMD = -0.24; 95% CI, -0.47 to -0.001) and no significant differences in Shannon and Simpson indices. Differences in beta diversity were consistently observed only for major depressive disorder and psychosis and schizophrenia. Regarding relative abundance, little evidence of disorder specificity was found. Instead, a transdiagnostic pattern of microbiota signatures was found. Depleted levels of Faecalibacterium and Coprococcus and enriched levels of Eggerthella were consistently shared between major depressive disorder, bipolar disorder, psychosis and schizophrenia, and anxiety, suggesting these disorders are characterized by a reduction of anti-inflammatory butyrate-producing bacteria, while pro-inflammatory genera are enriched. The confounding associations of region and medication were also evaluated. Conclusions and Relevance: This systematic review and meta-analysis found that gut microbiota perturbations were associated with a transdiagnostic pattern with a depletion of certain anti-inflammatory butyrate-producing bacteria and an enrichment of pro-inflammatory bacteria in patients with depression, bipolar disorder, schizophrenia, and anxiety.