Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties

A classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n-1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multi-separability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schroedinger operator, deep connections with special functions and with QES systems. Here we announce a complete classification of nondegenerate (i.e., 4-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in 10 variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly 10 nondegenerate potentials.Comment: 35 page

Geometric discretization of the Koenigs nets

We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such transformations, thus proving integrability of the Koenigs lattice. We also investigate the geometry of the discrete Koenigs transformation. In particular we characterize the Koenigs transformation in terms of an involution determined by a congruence conjugate to the lattice.Comment: 17 pages, 2 figures; some spelling and typing errors correcte

The statistical neuroanatomy of frontal networks in the macaque

We were interested in gaining insight into the functional properties of frontal networks based upon their anatomical inputs. We took a neuroinformatics approach, carrying out maximum likelihood hierarchical cluster analysis on 25 frontal cortical areas based upon their anatomical connections, with 68 input areas representing exterosensory, chemosensory, motor, limbic, and other frontal inputs. The analysis revealed a set of statistically robust clusters. We used these clusters to divide the frontal areas into 5 groups, including ventral-lateral, ventral-medial, dorsal-medial, dorsal-lateral, and caudal-orbital groups. Each of these groups was defined by a unique set of inputs. This organization provides insight into the differential roles of each group of areas and suggests a gradient by which orbital and ventral-medial areas may be responsible for decision-making processes based on emotion and primary reinforcers, and lateral frontal areas are more involved in integrating affective and rational information into a common framework

Mathematically Gifted Adolescents Have Deficiencies in Social Valuation and Mentalization

Many mathematically gifted adolescents are characterized as being indolent, underachieving and unsuccessful despite their high cognitive ability. This is often due to difficulties with social and emotional development. However, research on social and emotional interactions in gifted adolescents has been limited. The purpose of this study was to observe differences in complex social strategic behaviors between gifted and average adolescents of the same age using the repeated Ultimatum Game. Twenty-two gifted adolescents and 24 average adolescents participated in the Ultimatum Game. Two adolescents participate in the game, one as a proposer and the other as a responder. Because of its simplicity, the Ultimatum Game is an apt tool for investigating complex human emotional and cognitive decision-making in an empirical setting. We observed strategic but socially impaired offers from gifted proposers and lower acceptance rates from gifted responders, resulting in lower total earnings in the Ultimatum Game. Thus, our results indicate that mathematically gifted adolescents have deficiencies in social valuation and mentalization

Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces \DIII and \DIV five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively

(Super)integrability from coalgebra symmetry: formalism and applications

The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with either undeformed or q-deformed coalgebra symmetry are given, and their Liouville superintegrability is discussed. Among them, (quasi-maximally) superintegrable systems on N-dimensional curved spaces of nonconstant curvature are analysed in detail. Further generalizations of the coalgebra approach that make use of comodule and loop algebras are presented. The generalization of such a coalgebra symmetry framework to quantum mechanical systems is straightforward.Comment: 33 pages. Review-contribution to the "Workshop on higher symmetries in Physics", 6-8 November 2008, Madrid, Spai

Striatal sensitivity to personal responsibility in a regret-based decision-making task

Regret and relief are complex emotional states associated with the counterfactual processing of nonobtained outcomes in a decision-making situation. In the "actor effect," a sense of agency and personal responsibility is thought to heighten these emotions. Using fMRI, we scanned volunteers (n = 22) as they played a task involving choices between two wheel-of-fortune gambles. We examined how neural responses to counterfactual outcomes were modulated by giving subjects the opportunity to change their minds, as a manipulation of personal responsibility. Satisfaction ratings to the outcomes were highly sensitive to the difference between the obtained and nonobtained outcome, and ratings following losses were lower on trials with the opportunity to change one's mind. Outcome-related activity in the striatum and orbitofrontal cortex was positively related to the satisfaction ratings. The striatal response was modulated by the agency manipulation: Following losses, the striatal signal was significantly lower when the subject had the opportunity to change his/her mind. These results support the involvement of frontostriatal mechanisms in counterfactual thinking and highlight the sensitivity of the striatum to the effects of personal responsibility.</p

Identification of Protein Targets of Reactive Metabolites of Tienilic Acid in Human Hepatocytes

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemical Research in Toxicology, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/tx300103jTienilic acid (TA) is a uricosuric diuretic that was withdrawn from the market only months after its introduction because of reports of serious incidents of drug-induced liver injury including some fatalities. Its hepatotoxicity is considered to be primarily immunoallergic in nature. Like other thiophene compounds, TA undergoes biotransformation to a S-oxide metabolite which then reacts covalently with cellular proteins. To identify protein targets of TA metabolites, we incubated [14C]-TA with human hepatocytes, separated cellular proteins by 2D gel electrophoresis, and analyzed proteins in 36 radioactive spots by tryptic digestion followed by LC-MS/MS. Thirty one spots contained at least one identifiable protein. Sixteen spots contained only one of 14 non-redundant proteins which were thus considered to be targets of TA metabolites. Six of the 14 were also found in other radioactive spots that contained from 1 to 3 additional proteins. Eight of the 14 had not been reported to be targets for any reactive metabolite other than TA. The other 15 spots each contained from 2–4 identifiable proteins, many of which are known targets of other chemically reactive metabolites, but since adducted peptides were not observed, the identity of the adducted protein(s) in these spots is ambiguous. Interestingly, all the radioactive spots corresponded to proteins of low abundance, while many highly abundant proteins in the mixture showed no radioactivity. Furthermore, of approximately 16 previously reported protein targets of TA in rat liver (Methogo, R., Dansette, P. and Klarskov, K. (2007) Int. J. Mass Spectrom., 268, 284–295), only one (fumarylacetoacetase) is among the 14 targets identified in this work. One reason for this difference may be statistical, given that each study identified a small number of targets from among thousands present in hepatocytes. Another may be the species difference (i.e. rat vs. human), and still another may be the method of detection of adducted proteins (i.e. Western blot vs. C-14). Knowledge of human target proteins is very limited. Of more than 350 known protein targets of reactive metabolites, only 42 are known from human and only 21 of these are known to be targets for more than one chemical. Nevertheless, the demonstration that human target proteins can be identified using isolated hepatocytes in vitro should enable the question of species differences to be addressed more fully in the future

Moral judgments, gender, and antisocial preferences : an experimental study

Peer reviewedPostprin

Default Network Deactivations Are Correlated with Psychopathic Personality Traits

Background: The posteromedial cortex (PMC) and medial prefrontal cortex (mPFC) are part of a network of brain regions that has been found to exhibit decreased activity during goal-oriented tasks. This network is thought to support a baseline of brain activity, and is commonly referred to as the ‘‘default network’’. Although recent reports suggest that the PMC and mPFC are associated with affective, social, and self-referential processes, the relationship between these default network components and personality traits, especially those pertaining to social context, is poorly understood. Methodology/Principal Findings: In the current investigation, we assessed the relationship between PMC and mPFC deactivations and psychopathic personality traits using fMRI and a self-report measure. We found that PMC deactivations predicted traits related to egocentricity and mPFC deactivations predicted traits related to decision-making. Conclusions/Significance: These results suggest that the PMC and mPFC are associated with processes involving selfrelevancy and affective decision-making, consistent with previous reports. More generally, these findings suggest a link between default network activity and personality traits