Development in a biologically inspired spinal neural network for movement control

In two phases, we develop neural network models of spinal circuitry which self-organises into networks with opponent channels for the control of an antagonistic muscle pair. The self-organisation is enabled by spontaneous activity present in the spinal cord. We show that after the process of self-organisation, the networks have developed the possibility to independently control the length and tension of the innerated muscles. This allows the specification of joint angle independent from the specification of joint stiffness. The first network comprises only motorneurons and inhibitory interneurons through which the two channels interact. The inhibitory interneurons prevent saturation of the motorneuron pools, which is a necessary condition for independent control. In the second network, however, the neurons in the motorneuron pools obey the size-principle, which is a threat to the desired invariance of joint angle for varying joint stiffness, because of the different amplification of inputs in the case these inputs are not equal. To restore the desired invariance the second network ha.s been expanded with Renshaw cells. The manner in which they are included in the circuitry corrects the problem caused by the addition of the size-principle. The results obtained from the two models compare favourably with the FLETE-model for spinal circuitry (Bullock & Grossberg, 1991; Bullock et al., HJ93; Bullock & Contreras-Vidal, 1993) which has been successful in explaining several phenomena related to motor control.Fulbright Scholarship; Office of Naval Research (N00014-92-J-1309, N00014-95-1-0409

The Implications of Galaxy Formation Models for the TeV Observations of Current Detectors

This paper represents a step toward constraining galaxy formation models via TeV gamm a ray observations. We use semi-analytic models of galaxy formation to predict a spectral distribution for the intergalactic infrared photon field, which in turn yields information about the absorption of TeV gamma rays from extra-galactic sources. By making predictions for integral flux observations at >200 GeV for several known EGRE T sources, we directly compare our models with current observational upper limits obtained by Whipple. In addition, our predictions may offer a guide to the observing programs for the current population of TeV gamma ray observatories.Comment: 6 pages, 11 figures, to appear in the proceedings of the 6th TeV Workshop at Snowbird, U

A Vector-Integration-to-Endpoint Model for Performance of Viapoint Movements

Viapoint (VP) movements are movements to a desired point that are constrained to pass through an intermediate point. Studies have shown that VP movements possess properties, such as smooth curvature around the VP, that are not explicable by treating VP movements as strict concatenations of simpler point-to-point (PTP) movements. Such properties have led some theorists to propose whole-trajectory optimization models, which imply that the entire trajectory is pre-computed before movement initiation. This paper reports new experiments conducted to systematically compare VP with PTP trajectories. Analyses revealed a statistically significant early directional deviation in VP movements but no associated curvature change. An explanation of this effect is offered by extending the Vector-Integration-To-Endpoint (VITE) model (Bullock and Grossberg, 1988), which postulates that voluntary movement trajectories emerge as internal gating signals control the integration of continuously computed vector commands based on the evolving, perceptible difference between desired and actual position variables. The model explains the observed trajectories of VP and PTP movements as emergent properties of a dynamical system that does not precompute entire trajectories before movement initiation. The new model includes a working memory and a stage sensitive to time-to-contact information. These cooperate to control serial performance. The structural and functional relationships proposed in the model are consistent with available data on forebrain physiology and anatomy.Office of Naval Research (N00014-92-J-1309, N00014-93-1-1364, N0014-95-1-0409

Asymptotically Optimal Quantum Circuits for d-level Systems

As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit unitary into gates in MATLAB directory of source arxiv format. v2: minor change

Dark Matter from Early Decays

Two leading dark matter candidates from supersymmetry and other theories of physics beyond the standard model are WIMPs and weak scale gravitinos. If the lightest stable particle is a gravitino, then a WIMP will decay into it with a natural lifetime of order a month ~ M_{pl}^2/M_{weak}^3. We show that if the bulk of dark matter today came from decays of neutral particles with lifetimes of order a year or smaller, then it could lead to a reduction in the amount of small scale substructure, less concentrated halos and constant density cores in the smallest mass halos. Such beneficial effects may therefore be realized naturally, as discussed by Cembranos, Feng, Rajaraman, and Takayama, in the case of supersymmetry.Comment: Matches version accepted for publication in PRD. Added a paragraph to Sec V. 9 pages, 3 figure

On the Kauffman bracket skein module of the quaternionic manifold

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A,A^{-1}] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z_2 homology of the manifold, we determine that they are linearly independent.Comment: corrected summation signs in figures 14, 15, 17. Other minor change