A Self-Organizing Neural Model of Motor Equivalent Reaching and Tool Use by a Multijoint Arm

This paper describes a self-organizing neural model for eye-hand coordination. Called the DIRECT model, it embodies a solution of the classical motor equivalence problem. Motor equivalence computations allow humans and other animals to flexibly employ an arm with more degrees of freedom than the space in which it moves to carry out spatially defined tasks under conditions that may require novel joint configurations. During a motor babbling phase, the model endogenously generates movement commands that activate the correlated visual, spatial, and motor information that are used to learn its internal coordinate transformations. After learning occurs, the model is capable of controlling reaching movements of the arm to prescribed spatial targets using many different combinations of joints. When allowed visual feedback, the model can automatically perform, without additional learning, reaches with tools of variable lengths, with clamped joints, with distortions of visual input by a prism, and with unexpected perturbations. These compensatory computations occur within a single accurate reaching movement. No corrective movements are needed. Blind reaches using internal feedback have also been simulated. The model achieves its competence by transforming visual information about target position and end effector position in 3-D space into a body-centered spatial representation of the direction in 3-D space that the end effector must move to contact the target. The spatial direction vector is adaptively transformed into a motor direction vector, which represents the joint rotations that move the end effector in the desired spatial direction from the present arm configuration. Properties of the model are compared with psychophysical data on human reaching movements, neurophysiological data on the tuning curves of neurons in the monkey motor cortex, and alternative models of movement control.National Science Foundation (IRI 90-24877); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0499); National Science Foundation (IRI 90-24877

A Self-Organizing Neural Network for Learning a Body-Centered Invariant Representation of 3-D Target Position

This paper describes a self-organizing neural network that rapidly learns a body-centered representation of 3-D target positions. This representation remains invariant under head and eye movements, and is a key component of sensory-motor systems for producing motor equivalent reaches to targets (Bullock, Grossberg, and Guenther, 1993).National Science Foundation (IRI-87-16960, IRI-90-24877); Air Force Office of Scientific Research (F49620-92-J-0499

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

Time Reversal and n-qubit Canonical Decompositions

For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers' nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians.Comment: 20 pages, 3 figures; v2 (17pp.): major revision, new abstract, introduction, expanded bibliograph

Qudit surface codes and gauge theory with finite cyclic groups

Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group of the surface complex. These code states can be actively stabilized by measurements or, alternatively, can be prepared by cooling to the ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2 (qubit) lattices, such ground states have been proposed as topologically protected memory for qubits. We extend these constructions to lattices or more generally cell complexes with qudits, either of prime level or of level $d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor decomposition, to arbitrary finite levels. The Hamiltonian describes an exact $\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations correspond to abelian anyons. We provide protocols for qudit storage and retrieval and propose an interferometric verification of topological order by measuring quasi-particle statistics.Comment: 26 pages, 5 figure

LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo

Numerical modelling of the transport of trace gases including methane in the subsurface of Mars

We model the transport of gas through the martian subsurface in order to quantify the timescales of release of a trace gas with a source at depth using a Fickian model of diffusion through a putative martian regolith column. The model is then applied to the case of methane previously observed in the martian atmosphere. We investigate which parameters in the model have the greatest effect on transport timescales and find that transport is very sensitive to the pressure profile of the subsurface, but relatively insensitive to the temperature profile. Uncertainties in the composition, structure and physical conditions of the martian subsurface also introduce uncertainties in the timescales calculated. It was found that methane may take several hundred thousand Mars-years to diffuse from a source at depth. Purely diffusive transport cannot explain transient release that varies on timescales of less than one martian year from sources such as serpentinization or methanogenic organisms at depths of more than 2 km. However, diffusion of gas released by the destabilisation of methane clathrate hydrates close to the surface, for example caused by transient mass wasting events or erosion, could produce a rapidly varying flux of methane into the atmosphere of more than 10-3 kg m-2 s-1 over a duration of less than half a martian year, consistent with observations of martian methane variability. Seismic events, magmatic intrusions or impacts could also potentially produce similar patterns of release, but are far more complex to simulate

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

The SOCS-Box of HIV-1 Vif Interacts with ElonginBC by Induced-Folding to Recruit Its Cul5-Containing Ubiquitin Ligase Complex

The HIV-1 viral infectivity factor (Vif) protein recruits an E3 ubiquitin ligase complex, comprising the cellular proteins elongin B and C (EloBC), cullin 5 (Cul5) and RING-box 2 (Rbx2), to the anti-viral proteins APOBEC3G (A3G) and APOBEC3F (A3F) and induces their polyubiquitination and proteasomal degradation. In this study, we used purified proteins and direct in vitro binding assays, isothermal titration calorimetry and NMR spectroscopy to describe the molecular mechanism for assembly of the Vif-EloBC ternary complex. We demonstrate that Vif binds to EloBC in two locations, and that both interactions induce structural changes in the SOCS box of Vif as well as EloBC. In particular, in addition to the previously established binding of Vif's BC box to EloC, we report a novel interaction between the conserved Pro-Pro-Leu-Pro motif of Vif and the C-terminal domain of EloB. Using cell-based assays, we further show that this interaction is necessary for the formation of a functional ligase complex, thus establishing a role of this motif. We conclude that HIV-1 Vif engages EloBC via an induced-folding mechanism that does not require additional co-factors, and speculate that these features distinguish Vif from other EloBC specificity factors such as cellular SOCS proteins, and may enhance the prospects of obtaining therapeutic inhibitors of Vif function

Target 2035-update on the quest for a probe for every protein

Twenty years after the publication of the first draft of the human genome, our knowledge of the human proteome is still fragmented. The challenge of translating the wealth of new knowledge from genomics into new medicines is that proteins, and not genes, are the primary executers of biological function. Therefore, much of how biology works in health and disease must be understood through the lens of protein function. Accordingly, a subset of human proteins has been at the heart of research interests of scientists over the centuries, and we have accumulated varying degrees of knowledge about approximately 65% of the human proteome. Nevertheless, a large proportion of proteins in the human proteome (∼35%) remains uncharacterized, and less than 5% of the human proteome has been successfully targeted for drug discovery. This highlights the profound disconnect between our abilities to obtain genetic information and subsequent development of effective medicines. Target 2035 is an international federation of biomedical scientists from the public and private sectors, which aims to address this gap by developing and applying new technologies to create by year 2035 chemogenomic libraries, chemical probes, and/or biological probes for the entire human proteome