Overlapping Prediction Errors in Dorsal Striatum During Instrumental Learning With Juice and Money Reward in the Human Brain

Prediction error signals have been reported in human imaging studies in target areas of dopamine neurons such as ventral and dorsal striatum during learning with many different types of reinforcers. However, a key question that has yet to be addressed is whether prediction error signals recruit distinct or overlapping regions of striatum and elsewhere during learning with different types of reward. To address this, we scanned 17 healthy subjects with functional magnetic resonance imaging while they chose actions to obtain either a pleasant juice reward (1 ml apple juice), or a monetary gain (5 cents) and applied a computational reinforcement learning model to subjects' behavioral and imaging data. Evidence for an overlapping prediction error signal during learning with juice and money rewards was found in a region of dorsal striatum (caudate nucleus), while prediction error signals in a subregion of ventral striatum were significantly stronger during learning with money but not juice reward. These results provide evidence for partially overlapping reward prediction signals for different types of appetitive reinforcers within the striatum, a finding with important implications for understanding the nature of associative encoding in the striatum as a function of reinforcer type

An edge-weighted hook formula for labelled trees

A number of hook formulas and hook summation formulas have previously appeared, involving various classes of trees. One of these classes of trees is rooted trees with labelled vertices, in which the labels increase along every chain from the root vertex to a leaf. In this paper we give a new hook summation formula for these (unordered increasing) trees, by introducing a new set of indeterminates indexed by pairs of vertices, that we call edge weights. This new result generalizes a previous result by F\'eray and Goulden, that arose in the context of representations of the symmetric group via the study of Kerov's character polynomials. Our proof is by means of a combinatorial bijection that is a generalization of the Pr\"ufer code for labelled trees.Comment: 25 pages, 9 figures. Author-produced copy of the article to appear in Journal of Combinatorics, including referee's suggestion

Light Curve Solutions of Eclipsing Binaries in SMC

We propose a procedure for light-curve solution of eclipsing binary stars in the Small Magellanic Cloud for which photometric data have been obtained in the framework of the OGLE project as well as way of determination of the global stellar parameters on the basis of the obtained solutions, some empirical relations as well as the distance to the SMC. Several examples illustrate this procedure.Comment: 10 pages, 2 figures, accepte

In-ear EEG biometrics for feasible and readily collectable real-world person authentication

The use of EEG as a biometrics modality has been investigated for about a decade, however its feasibility in real-world applications is not yet conclusively established, mainly due to the issues with collectability and reproducibility. To this end, we propose a readily deployable EEG biometrics system based on a `one-fits-all' viscoelastic generic in-ear EEG sensor (collectability), which does not require skilled assistance or cumbersome preparation. Unlike most existing studies, we consider data recorded over multiple recording days and for multiple subjects (reproducibility) while, for rigour, the training and test segments are not taken from the same recording days. A robust approach is considered based on the resting state with eyes closed paradigm, the use of both parametric (autoregressive model) and non-parametric (spectral) features, and supported by simple and fast cosine distance, linear discriminant analysis and support vector machine classifiers. Both the verification and identification forensics scenarios are considered and the achieved results are on par with the studies based on impractical on-scalp recordings. Comprehensive analysis over a number of subjects, setups, and analysis features demonstrates the feasibility of the proposed ear-EEG biometrics, and its potential in resolving the critical collectability, robustness, and reproducibility issues associated with current EEG biometrics

Consistent local projection stabilized finite element methods

This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results

A symmetric nodal conservative finite element method for the Darcy equation

This work introduces and analyzes novel stable Petrov-Galerkin EnrichedMethods (PGEM) for the Darcy problem based on the simplest but unstable continuous P1/P0 pair. Stability is recovered inside a Petrov-Galerkin framework where element-wise dependent residual functions, named multi-scale functions, enrich both velocity and pressure trial spaces. Unlike the velocity test space that is augmented with bubble-like functions, multi-scale functions correct edge residuals as well. The multi-scale functions turn out to be the well-known lowest order Raviart-Thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure. The enrichment strategy suggests the way to recover the local mass conservation property for nodal-based interpolation spaces. We prove that the method and its symmetric version are well-posed and achieve optimal error estimates in natural norms. Numerical validations confirm claimed theoretical results