Invariant submanifold for series arrays of Josephson junctions

We study the nonlinear dynamics of series arrays of Josephson junctions in the large-N limit, where N is the number of junctions in the array. The junctions are assumed to be identical, overdamped, driven by a constant bias current and globally coupled through a common load. Previous simulations of such arrays revealed that their dynamics are remarkably simple, hinting at the presence of some hidden symmetry or other structure. These observations were later explained by the discovery of (N - 3) constants of motion, each choice of which confines the resulting flow in phase space to a low-dimensional invariant manifold. Here we show that the dimensionality can be reduced further by restricting attention to a special family of states recently identified by Ott and Antonsen. In geometric terms, the Ott-Antonsen ansatz corresponds to an invariant submanifold of dimension one less than that found earlier. We derive and analyze the flow on this submanifold for two special cases: an array with purely resistive loading and another with resistive-inductive-capacitive loading. Our results recover (and in some instances improve) earlier findings based on linearization arguments.Comment: 10 pages, 6 figure

Assessing the effect of advertising expenditures upon sales: a Bayesian structural time series model

We propose a robust implementation of the Nerlove--Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a country-wide fast-food franchise network with its weekly sales. Thanks to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating \emph{a priori} information (the manager's views), which can be updated with relevant data. This aspect of the model will be used to present a strategy of budget scheduling across time and channels.Comment: Published at Applied Stochastic Models in Business and Industry, https://onlinelibrary.wiley.com/doi/full/10.1002/asmb.246

Avoiding bias in reconstructing the largest observable scales from partial-sky data

Obscuration due to Galactic emission complicates the extraction of information from cosmological surveys, and requires some combination of the (typically imperfect) modeling and subtraction of foregrounds, or the removal of part of the sky. This particularly affects the extraction of information from the largest observable scales. Maximum-likelihood estimators for reconstructing the full-sky spherical harmonic coefficients from partial-sky maps have recently been shown to be susceptible to contamination from within the sky cut, arising due to the necessity to band-limit the data by smoothing prior to reconstruction. Using the WMAP 7-year data, we investigate modified implementations of such estimators which are robust to the leakage of contaminants from within masked regions. We provide a measure, based on the expected amplitude of residual foregrounds, for selecting the most appropriate estimator for the task at hand. We explain why the related quadratic maximum-likelihood estimator of the angular power spectrum does not suffer from smoothing-induced bias.Comment: 8 pages, 8 figures. v2: replaced with version accepted by PRD (minor amendments to text only

The large core limit of spiral waves in excitable media: A numerical approach

We modify the freezing method introduced by Beyn & Thuemmler, 2004, for analyzing rigidly rotating spiral waves in excitable media. The proposed method is designed to stably determine the rotation frequency and the core radius of rotating spirals, as well as the approximate shape of spiral waves in unbounded domains. In particular, we introduce spiral wave boundary conditions based on geometric approximations of spiral wave solutions by Archimedean spirals and by involutes of circles. We further propose a simple implementation of boundary conditions for the case when the inhibitor is non-diffusive, a case which had previously caused spurious oscillations. We then utilize the method to numerically analyze the large core limit. The proposed method allows us to investigate the case close to criticality where spiral waves acquire infinite core radius and zero rotation frequency, before they begin to develop into retracting fingers. We confirm the linear scaling regime of a drift bifurcation for the rotation frequency and the core radius of spiral wave solutions close to criticality. This regime is unattainable with conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied Dynamical Systems on 20/03/1

Signal processing with Levy information

Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a "message", then under the transformed measure the original Levy process takes on the character of an "information process". In this paper we develop a theory of such Levy information processes. The underlying Levy process, which we call the fiducial process, represents the "noise type". Each such noise type is capable of carrying a message of a certain specification. A number of examples are worked out in detail, including information processes of the Brownian, Poisson, gamma, variance gamma, negative binomial, inverse Gaussian, and normal inverse Gaussian type. Although in general there is no additive decomposition of information into signal and noise, one is led nevertheless for each noise type to a well-defined scheme for signal detection and enhancement relevant to a variety of practical situations.Comment: 27 pages. Version to appear in: Proc. R. Soc. London

Reclaiming human machine nature

Extending and modifying his domain of life by artifact production is one of the main characteristics of humankind. From the first hominid, who used a wood stick or a stone for extending his upper limbs and augmenting his gesture strength, to current systems engineers who used technologies for augmenting human cognition, perception and action, extending human body capabilities remains a big issue. From more than fifty years cybernetics, computer and cognitive sciences have imposed only one reductionist model of human machine systems: cognitive systems. Inspired by philosophy, behaviorist psychology and the information treatment metaphor, the cognitive system paradigm requires a function view and a functional analysis in human systems design process. According that design approach, human have been reduced to his metaphysical and functional properties in a new dualism. Human body requirements have been left to physical ergonomics or "physiology". With multidisciplinary convergence, the issues of "human-machine" systems and "human artifacts" evolve. The loss of biological and social boundaries between human organisms and interactive and informational physical artifact questions the current engineering methods and ergonomic design of cognitive systems. New developpment of human machine systems for intensive care, human space activities or bio-engineering sytems requires grounding human systems design on a renewed epistemological framework for future human systems model and evidence based "bio-engineering". In that context, reclaiming human factors, augmented human and human machine nature is a necessityComment: Published in HCI International 2014, Heraklion : Greece (2014

Spreading dynamics on spatially constrained complex brain networks

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way

Karhunen-Loeve representation of stochastic ocean waves

A new stochastic representation of a seastate is developed based on the Karhunen–Loeve spectral decomposition of stochastic signals and the use of Slepian prolate spheroidal wave functions with a tunable bandwidth parameter. The new representation allows the description of stochastic ocean waves in terms of a few independent sources of uncertainty when the traditional representation of a seastate in terms of Fourier series requires an order of magnitude more independent components. The new representation leads to parsimonious stochastic models of the ambient wave kinematics and of the nonlinear loads and responses of ships and offshore platforms. The use of the new representation is discussed for the derivation of critical wave episodes, the derivation of up-crossing rates of nonlinear loads and responses and the joint stochastic representation of correlated wave and wind profiles for use in the design of fixed or floating offshore wind turbines. The forecasting is also discussed of wave elevation records and vessel responses for use in energy yield enhancement of compliant floating wind turbines.ALSTOM (Firm)Ente nazionale per l'energia elettricab_TE

Bulk spectral function sum rule in QCD-like theories with a holographic dual

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure

Wiener algebra for the quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators