Tunable transport with broken space-time symmetries

Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drivings, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.Comment: Phys. Rep., in pres

Developing a flexible and expressive realtime polyphonic wave terrain synthesis instrument based on a visual and multidimensional methodology

The Jitter extended library for Max/MSP is distributed with a gamut of tools for the generation, processing, storage, and visual display of multidimensional data structures. With additional support for a wide range of media types, and the interaction between these mediums, the environment presents a perfect working ground for Wave Terrain Synthesis. This research details the practical development of a realtime Wave Terrain Synthesis instrument within the Max/MSP programming environment utilizing the Jitter extended library. Various graphical processing routines are explored in relation to their potential use for Wave Terrain Synthesis

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

Modelling the live-electronics in electroacoustic music using particle systems

Developing the live-electronics for a contemporary electroacoustic piece is a complex process that normally involves the transfer of artistic and aesthetic concepts between the composer and the musical assistant. Translating in technical terms the musical, artistic and aesthetic concepts by means of algorithms and mathematical parameters is seldom an easy and straightforward task. The use of a particle system to describe the dynamics and characteristics of compositional parameters can reveal an effective way for achieving a significant relationship between compositional aspects and their technical implementation. This paper describes a method for creating and modelling a particle system based on compositional parameters and how to map those parameters into digital audio processes. An implementation of this method is described, as well as the use of such a method for the development of the work O Farfalhar das Folhas (The rustling of leaves) (2010), for one flutist, one clarinetist, violin, violoncello, piano and live-electronics, by Flo Menezes.info:eu-repo/semantics/publishedVersio

Machine learning via relativity-inspired quantum dynamics

We present a machine-learning scheme based on the relativistic dynamics of a quantum system, namely a quantum detector inside a cavity resonator. An equivalent analog model can be realized for example in a circuit QED platform subject to properly modulated driving fields. We consider a reservoir-computing scheme where the input data are embedded in the modulation of the system (equivalent to the acceleration of the relativistic object) and the output data are obtained by linear combinations of measured observables. As an illustrative example, we have simulated such a relativistic quantum machine for a challenging classification task, showing a very large enhancement of the accuracy in the relativistic regime. Using kernel-machine theory, we show that in the relativistic regime the task-independent expressivity is dramatically magnified with respect to the Newtonian regime.Comment: Article (2 figures) + Suppl. Mat. (2 figures

Resonance-Assisted Tunneling

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this "resonance-assisted" mechanism is given, which is based on a local perturbative description of the dynamics in the vicinity of the resonances. As underlying picture, we obtain that the quantum state is coupled, via a succession of classically forbidden transitions across nonlinear resonances, to high excitations within the well, from where tunneling occurs with a rather large rate. The connection between this description and the complex classical structure of the underlying integrable dynamics is furthermore studied, giving ground to the general coherence of the description as well as guidelines for the identification of the dominant tunneling paths. The validity of this mechanism is demonstrated within the kicked Harper model, where good agreement between quantum and semiclassical (resonance-assisted) tunneling rates is found.Comment: 52 pages, 16 figures, submitted to Annals of Physic

Odor coding and memory traces in the antennal lobe of honeybee

In dieser Arbeit werden zwei wesentliche neue Ergebnisse vorgestellt. Das erste bezieht sich auf die olfaktorische Kodierung und das zweite auf das sensorische Gedaechtnis. Beide Phaenomene werden am Beispiel des Gehirns der Honigbiene untersucht. In Bezug auf die olfaktorische Kodierung zeige ich, dass die neuronale Dynamik waehrend der Stimulation im Antennallobus duftspezifische Trajektorien beschreibt, die in duftspezifischen Attraktoren enden. Das Zeitinterval, in dem diese Attraktoren erreicht werden, betraegt unabhaengig von der Identitaet und der Konzentration des Duftes ungefaehr 800 ms. Darueber hinaus zeige ich, dass Support-Vektor Maschinen, und insbesondere Perzeptronen, ein realistisches und biologisches Model der Wechselwirkung zwischen dem Antennallobus (dem kodierenden Netwerk) und dem Pilzkoerper (dem dekodierenden Netzwerk) darstellen. Dieses Model kann sowohl Reaktionszeiten von ca. 300 ms als auch die Invarianz der Duftwahrnehmung gegenueber der Duftkonzentration erklaeren. In Bezug auf das sensorische Gedaechtnis zeige ich, dass eine einzige Stimulation ohne Belohnung dem Hebbschen Postulat folgend Veraenderungen der paarweisen Korrelationen zwischen Glomeruli induziert. Ich zeige, dass diese Veranderungen der Korrelationen bei 2/3 der Bienen ausreichen, um den letzten Stimulus zu bestimmen. In der zweiten Minute nach der Stimulation ist eine erfolgreiche Bestimmung des Stimulus nur bei 1/3 der Bienen moeglich. Eine Hauptkomponentenanalyse der spontanen Aktivitaet laesst erkennen, dass das dominante Muster des Netzwerks waehrend der spontanen Aktivitaet nach, aber nicht vor der Stimulation das duftinduzierte Aktivitaetsmuster bei 2/3 der Bienen nachbildet. Man kann deshalb die duftinduzierten (Veraenderungen der) Korrelationen als Spuren eines Kurzzeitgedaechtnisses bzw. als Hebbsche "Reverberationen" betrachtet werden.Two major novel results are reported in this work. The first concerns olfactory coding and the second concerns sensory memory. Both phenomena are investigated in the brain of the honeybee as a model system. Considering olfactory coding I demonstrate that the neural dynamics in the antennal lobe describe odor-specific trajectories during stimulation that converge to odor-specific attractors. The time interval to reach these attractors is, regardless of odor identity and concentration, approximately 800 ms. I show that support-vector machines and, in particular perceptrons provide a realistic and biological model of the interaction between the antennal lobe (coding network) and the mushroom body (decoding network). This model can also account for reaction-times of about 300 ms and for concentration invariance of odor perception. Regarding sensory memory I show that a single stimulation without reward induces changes of pairwise correlation between glomeruli in a Hebbian-like manner. I demonstrate that those changes of correlation suffice to retrieve the last stimulus presented in 2/3 of the bees studied. Succesful retrieval decays to 1/3 of the bees within the second minute after stimulation. In addition, a principal-component analysis of the spontaneous activity reveals that the dominant pattern of the network during the spontaneous activity after, but not before stimulation, reproduces the odor-induced activity pattern in 2/3 of the bees studied. One can therefore consider the odor-induced (changes of) correlation as traces of a short-term memory or as Hebbian reverberations

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA