Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Supersymmetric Boundaries and Junctions in Four Dimensions

We make a comprehensive study of (rigid) N=1 supersymmetric sigma-models with general K\"ahler potentials K and superpotentials w on four-dimensional space-times with boundaries. We determine the minimal (non-supersymmetric) boundary terms one must add to the standard bulk action to make it off-shell invariant under half the supersymmetries without imposing any boundary conditions. Susy boundary conditions do arise from the variational principle when studying the dynamics. Upon including an additional boundary action that depends on an arbitrary real boundary potential B one can generate very general susy boundary conditions. We show that for any set of susy boundary conditions that define a Lagrangian submanifold of the K\"ahler manifold, an appropriate boundary potential B can be found. Thus the non-linear sigma-model on a manifold with boundary is characterised by the tripel (K,B,w). We also discuss the susy coupling to new boundary superfields and generalize our results to supersymmetric junctions between completely different susy sigma-models, living on adjacent domains and interacting through a "permeable" wall. We obtain the supersymmetric matching conditions that allow us to couple models with different K\"ahler potentials and superpotentials on each side of the wall.Comment: 38 pages, 1 figur

Polarization due to rotational distortion in the bright star Regulus

This is the full published article (retrieved from the 6 months post-publication posting on arXiv) including the Methods and Supplementary Information sections: 33 pages, 10 figures, 8 tablesPolarization in stars was first predicted by Chandrasekhar [1] who calculated a substantial linear polarization at the stellar limb for a pure electron-scattering atmosphere. This polarization will average to zero when integrated over a spherical star but could be detected if the symmetry is broken, for example by the eclipse of a binary companion. Nearly 50 years ago, Harrington and Collins [2] modeled another way of breaking the symmetry and producing net polarization - the distortion of a rapidly rotating hot star. Here we report the first detection of this effect. Observations of the linear polarization of Regulus, with two different high-precision polarimeters, range from +42 parts-per-million (ppm) at a wavelength of 741 nm to -22 ppm at 395 nm. The reversal from red to blue is a distinctive feature of rotation-induced polarization. Using a new set of models for the polarization of rapidly rotating stars we find that Regulus is rotating at 96.5(+0.6/-0.8)% of its critical angular velocity for breakup, and has an inclination greater than 76.5 degrees. The rotation axis of the star is at a position angle of 79.5+/-0.7 degrees. The conclusions are independent of, but in good agreement with, the results of previously published interferometric observations of Regulus [3]. The accurate measurement of rotation in early-type stars is important for understanding their stellar environments [4], and course of their evolution [5].Peer reviewedFinal Accepted Versio

Searching for plasticity in dissociated cortical cultures on multi-electrode arrays

We attempted to induce functional plasticity in dense cultures of cortical cells using stimulation through extracellular electrodes embedded in the culture dish substrate (multi-electrode arrays, or MEAs). We looked for plasticity expressed in changes in spontaneous burst patterns, and in array-wide response patterns to electrical stimuli, following several induction protocols related to those used in the literature, as well as some novel ones. Experiments were performed with spontaneous culture-wide bursting suppressed by either distributed electrical stimulation or by elevated extracellular magnesium concentrations as well as with spontaneous bursting untreated. Changes concomitant with induction were no larger in magnitude than changes that occurred spontaneously, except in one novel protocol in which spontaneous bursts were quieted using distributed electrical stimulation

Efimov effect in quantum magnets

Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. Here we employ an anisotropic Heisenberg model to show that collective excitations in quantum magnets (magnons) also exhibit the Efimov effect. We locate anisotropy-induced two-magnon resonances, compute binding energies of three magnons and find that they fit into the universal scaling law. We propose several approaches to experimentally realize the Efimov effect in quantum magnets, where the emergent Efimov states of magnons can be observed with commonly used spectroscopic measurements. Our study thus opens up new avenues for universal few-body physics in condensed matter systems.Comment: 7 pages, 5 figures; published versio

Topologically protected quantum bits from Josephson junction arrays

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation, while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev, holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Comment: 6 pages, 4 figure

S-duality and 2d Topological QFT

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure

Metabolic analysis of the interaction between plants and herbivores

Insect herbivores by necessity have to deal with a large arsenal of plant defence metabolites. The levels of defence compounds may be increased by insect damage. These induced plant responses may also affect the metabolism and performance of successive insect herbivores. As the chemical nature of induced responses is largely unknown, global metabolomic analyses are a valuable tool to gain more insight into the metabolites possibly involved in such interactions. This study analyzed the interaction between feral cabbage (Brassica oleracea) and small cabbage white caterpillars (Pieris rapae) and how previous attacks to the plant affect the caterpillar metabolism. Because plants may be induced by shoot and root herbivory, we compared shoot and root induction by treating the plants on either plant part with jasmonic acid. Extracts of the plants and the caterpillars were chemically analysed using Ultra Performance Liquid Chromatography/Time of Flight Mass Spectrometry (UPLCT/MS). The study revealed that the levels of three structurally related coumaroylquinic acids were elevated in plants treated on the shoot. The levels of these compounds in plants and caterpillars were highly correlated: these compounds were defined as the ‘metabolic interface’. The role of these metabolites could only be discovered using simultaneous analysis of the plant and caterpillar metabolomes. We conclude that a metabolomics approach is useful in discovering unexpected bioactive compounds involved in ecological interactions between plants and their herbivores and higher trophic levels.

A valley-spin qubit in a carbon nanotube

Although electron spins in III-V semiconductor quantum dots have shown great promise as qubits, a major challenge is the unavoidable hyperfine decoherence in these materials. In group IV semiconductors, the dominant nuclear species are spinless, allowing for qubit coherence times that have been extended up to seconds in diamond and silicon. Carbon nanotubes are a particularly attractive host material, because the spin-orbit interaction with the valley degree of freedom allows for electrical manipulation of the qubit. In this work, we realise such a qubit in a nanotube double quantum dot. The qubit is encoded in two valley-spin states, with coherent manipulation via electrically driven spin resonance (EDSR) mediated by a bend in the nanotube. Readout is performed by measuring the current in Pauli blockade. Arbitrary qubit rotations are demonstrated, and the coherence time is measured via Hahn echo. Although the measured decoherence time is only 65 ns in our current device, this work offers the possibility of creating a qubit for which hyperfine interaction can be virtually eliminated