Planning “Discrete” Movements Using a Continuous System: Insights from a Dynamic Field Theory of Movement Preparation

The timed-initiation paradigm developed by Ghez and colleagues (1997) has revealed two modes of motor planning: continuous and discrete. Continuous responding occurs when targets are separated by less than 60° of spatial angle, and discrete responding occurs when targets are separated by greater than 60°. Although these two modes are thought to reflect the operation of separable strategic planning systems, a new theory of movement preparation, the Dynamic Field Theory, suggests that two modes emerge flexibly from the same system. Experiment 1 replicated continuous and discrete performance using a task modified to allow for a critical test of the single system view. In Experiment 2, participants were allowed to correct their movements following movement initiation (the standard task does not allow corrections). Results showed continuous planning performance at large and small target separations. These results are consistent with the proposal that the two modes reflect the time-dependent “preshaping” of a single planning system.

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Two structurally discrete GH7-cellobiohydrolases compete for the same cellulosic substrate fiber

Background: Cellulose consisting of arrays of linear beta-1,4 linked glucans, is the most abundant carbon-containing polymer present in biomass. Recalcitrance of crystalline cellulose towards enzymatic degradation is widely reported and is the result of intra-and inter-molecular hydrogen bonds within and among the linear glucans. Cellobiohydrolases are enzymes that attack crystalline cellulose. Here we report on two forms of glycosyl hydrolase family 7 cellobiohydrolases common to all Aspergillii that attack Avicel, cotton cellulose and other forms of crystalline cellulose. Results: Cellobiohydrolases Cbh1 and CelD have similar catalytic domains but only Cbh1 contains a carbohydrate-binding domain (CBD) that binds to cellulose. Structural superpositioning of Cbh1 and CelD on the Talaromyces emersonii Cel7A 3-dimensional structure, identifies the typical tunnel-like catalytic active site while Cbh1 shows an additional loop that partially obstructs the substrate-fitting channel. CelD does not have a CBD and shows a four amino acid residue deletion on the tunnel-obstructing loop providing a continuous opening in the absence of a CBD. Cbh1 and CelD are catalytically functional and while specific activity against Avicel is 7.7 and 0.5 U. mg prot-1, respectively specific activity on pNPC is virtually identical. Cbh1 is slightly more stable to thermal inactivation compared to CelD and is much less sensitive to glucose inhibition suggesting that an open tunnel configuration, or absence of a CBD, alters the way the catalytic domain interacts with the substrate. Cbh1 and CelD enzyme mixtures on crystalline cellulosic substrates show a strong combinatorial effort response for mixtures where Cbh1 is present in 2: 1 or 4: 1 molar excess. When CelD was overrepresented the combinatorial effort could only be partially overcome. CelD appears to bind and hydrolyze only loose cellulosic chains while Cbh1 is capable of opening new cellulosic substrate molecules away from the cellulosic fiber. Conclusion: Cellobiohydrolases both with and without a CBD occur in most fungal genomes where both enzymes are secreted, and likely participate in cellulose degradation. The fact that only Cbh1 binds to the substrate and in combination with CelD exhibits strong synergy only when Cbh1 is present in excess, suggests that Cbh1 unties enough chains from cellulose fibers, thus enabling processive access of CelD.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal-Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient. (C) 2012 Elsevier B.V. All rights reserved.

A rationale for long-lived quarks and leptons at the LHC: low energy flavour theory

In the framework of gauged flavour symmetries, new fermions in parity symmetric representations of the standard model are generically needed for the compensation of mixed anomalies. The key point is that their masses are also protected by flavour symmetries and some of them are expected to lie way below the flavour symmetry breaking scale(s), which has to occur many orders of magnitude above the electroweak scale to be compatible with the available data from flavour changing neutral currents and CP violation experiments. We argue that, actually, some of these fermions would plausibly get masses within the LHC range. If they are taken to be heavy quarks and leptons, in (bi)-fundamental representations of the standard model symmetries, their mixings with the light ones are strongly constrained to be very small by electroweak precision data. The alternative chosen here is to exactly forbid such mixings by breaking of flavour symmetries into an exact discrete symmetry, the so-called proton-hexality, primarily suggested to avoid proton decay. As a consequence of the large value needed for the flavour breaking scale, those heavy particles are long-lived and rather appropriate for the current and future searches at the LHC for quasi-stable hadrons and leptons. In fact, the LHC experiments have already started to look for them.

Self-similarities of periodic structures for a discrete model of a two-gene system

We report self-similar properties of periodic structures remarkably organized in the two-parameter space for a two-gene system, described by two-dimensional symmetric map. The map consists of difference equations derived from the chemical reactions for gene expression and regulation. We characterize the system by using Lyapunov exponents and isoperiodic diagrams identifying periodic windows, denominated Arnold tongues and shrimp-shaped structures. Period-adding sequences are observed for both periodic windows. We also identify Fibonacci-type series and Golden ratio for Arnold tongues, and period multiple-of-three windows for shrimps. (C) 2012 Elsevier B.V. All rights reserved.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

On the optical properties of copper nanocubes as a function of the edge length as modeled by the discrete dipole approximation

This Letter reports an investigation on the optical properties of copper nanocubes as a function of size as modeled by the discrete dipole approximation. In the far-field, our results showed that the extinction resonances shifted from 595 to 670 nm as the size increased from 20 to 100 nm. Also, the highest optical efficiencies for absorption and scattering were obtained for nanocubes that were 60 and 100 nm in size, respectively. In the near-field, the electric-field amplitudes were investigated considering 514, 633 and 785 nm as the excitation wavelengths. The E-fields increased with size, being the highest at 633 nm. (c) 2012 Elsevier B.V. All rights reserved.

Neural coding tools, based on Information Theory, applied to discrete time series: from electrophysiology to neuroethology

This work is supported by Brazilian agencies Fapesp, CAPES and CNPq

Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik

In den letzten fünf Jahren hat sich mit dem Begriff desspektralen Tripels eine Möglichkeit zur Beschreibungdes an Spinoren gekoppelten Gravitationsfeldes auf(euklidischen) nichtkommutativen Räumen etabliert. Die Dynamik dieses Gravitationsfeldes ist dabei durch diesogenannte spektrale Wirkung, dieSpur einer geeigneten Funktion des Dirac-Operators,bestimmt. Erstaunlicherweise kann man die vollständige Lagrange-Dichtedes (an das Gravitationsfeld gekoppelten) Standardmodellsder Elementarteilchenphysik, also insbesondere auch denmassegebenden Higgs-Sektor, als spektrale Wirkungeines entsprechenden spektralen Tripels ableiten. Diesesspektrale Tripel ist als Produkt des spektralenTripels der (kommutativen) Raumzeit mit einem speziellendiskreten spektralen Tripel gegeben. In der Arbeitwerden solche diskreten spektralen Tripel, die bis vorKurzem neben dem nichtkommutativen Torus die einzigen,bekannten nichtkommutativen Beispiele waren, klassifiziert. Damit kannnun auch untersucht werden, inwiefern sich dasStandardmodell durch diese Eigenschaft gegenüber anderenYang-Mills-Higgs-Theorien auszeichnet. Es zeigt sichallerdings, dasses - trotz mancher Einschränkung - eine sehr große Zahl vonModellen gibt, die mit Hilfe von spektralen Tripelnabgeleitet werden können. Es wäre aber auch denkbar, dass sich das spektrale Tripeldes Standardmodells durch zusätzliche Strukturen,zum Beispiel durch eine darauf ``isometrisch'' wirkendeHopf-Algebra, auszeichnet. In der Arbeit werden, um dieseFrage untersuchen zu können, sogenannte H-symmetrischespektrale Tripel, welche solche Hopf-Isometrien aufweisen,definiert.Dabei ergibt sich auch eine Möglichkeit, neue(H-symmetrische) spektrale Tripel mit Hilfe ihrerzusätzlichen Symmetrienzu konstruieren. Dieser Algorithmus wird an den Beispielender kommutativen Sphäre, deren Spin-Geometrie hier zumersten Mal vollständig in der globalen, algebraischen Sprache der NichtkommutativenGeometrie beschrieben wird, sowie dem nichtkommutativenTorus illustriert.Als Anwendung werden einige neue Beipiele konstruiert. Eswird gezeigt, dass sich für Yang-Mills Higgs-Theorien, diemit Hilfe von H-symmetrischen spektralen Tripeln abgeleitetwerden, aus den zusätzlichen Isometrien Einschränkungen andiefermionischen Massenmatrizen ergeben. Im letzten Abschnitt der Arbeit wird kurz auf dieQuantisierung der spektralen Wirkung für diskrete spektraleTripel eingegangen.Außerdem wird mit dem Begriff des spektralen Quadrupels einKonzept für die nichtkommutative Verallgemeinerungvon lorentzschen Spin-Mannigfaltigkeiten vorgestellt.

From discrete anions to extended solids: new uranium thiophosphates

Die wichtigste Klasse zeotyper Verbindungen sind die Thio- und Selenophosphate der Übergangsmetalle. Ziel dieser Dissertation war die Darstellung und Charakterisierung neuer Uranthiophosphate. Die dargestellten Verbindungen enthalten vierwertige Urankationen, die von acht Schwefelatomen koordiniert sind. Da die enthaltenen Thiophosphatanionen in den meisten Fällen als zweizähnige Liganden fungieren, entstehen dreidimensionale Netzwerke mit pseudotetraedrisch koordinierten Metallzentren. In der Verbindung U(P2S6)2 durchdringen sich drei identische diamantartige Netzwerke, wodurch optimale Raumerfüllung erreicht wird. Die Einführung von Alkalimetallkationen in das System führt zu einer Vielzahl neuer Verbindungen, deren Eigenschaften durch die Stöchiometrie der Edukte und durch die Kationenradien bestimmt werden. Beispielsweise enthält die Kristallstruktur von Na2U(PS4)2 zweidimensionale anionische [U(PS4)2]n-Schichten, während die analoge Verbindung CsLiU(PS4)2 eine poröse dreidimensionale Netzwerkstruktur besitzt. Der Vergleich der untersuchten quaternären und quinären Verbindungen zeigt, dass eine Korrelation zwischen dem Kationenradius und dem Durchmesser der Poren besteht. Dies lässt auf eine Templatfunktion der Alkalimetallkationen beim Aufbau der anionischen Teilstruktur schließen. Die neuen Verbindungen wurden aus reaktiven Polysulfidschmelzflüssen oder durch Auflösen amorpher Vorläufer in Alkalimetallchloridschmelzen synthetisiert. Die Kristallstrukturen wurden durch Einkristall-Röntgenmethoden bestimmt. Ein Vergleich der magnetischen Eigenschaften der Verbindungen beweist, dass in allen untersuchten Fällen U(IV) vorliegt. Die Substanzen zeigen paramagnetisches Verhalten, in UP2S7 und CsLiU(PS4)2 sind außerdem antiferromagnetische Wechselwirkungen zwischen benachbarten Uranatomen nachweisbar.

Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.