Comment on "Regularizing capacity of metabolic networks"

In a recent paper, Marr, Muller-Linow and Hutt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of reference models. The authors argue that this suggests that metabolic network structure is a major factor behind the stability of biochemical steady states. We reanalyze the same kind of data using a dynamic system modeling actual reaction kinetics. The conclusions about stability, from our analysis, are inconsistent with those of Marr et al. We argue that this issue calls for a more detailed type of modeling

A New View on Worst-Case to Average-Case Reductions for NP Problems

We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that under reasonable assumptions, there is no non-adaptive worst-case to average-case reduction that bases the average-case hardness of an NP-problem on the worst-case complexity of an NP-complete problem. We replace the hiding and the heavy samples protocol in [BT03] by employing the histogram verification protocol of Haitner, Mahmoody and Xiao (CCC, 2010), which proves to be very useful in this context. Once the histogram is verified, our hiding protocol is directly public-coin, whereas the intuition behind the original protocol inherently relies on private coins

Nonuniversal spectral properties of the Luttinger model

The one electron spectral functions for the Luttinger model are discussed for large but finite systems. The methods presented allow a simple interpretation of the results. For finite range interactions interesting nonunivesal spectral features emerge for momenta which differ from the Fermi points by the order of the inverse interaction range or more. For a simplified model with interactions only within the branches of right and left moving electrons analytical expressions for the spectral function are presented which allows to perform the thermodynamic limit. As in the general spinless model and the model including spin for which we present mainly numerical results the spectral functions do not approach the noninteracting limit for large momenta. The implication of our results for recent high resolution photoemission measurements on quasi one-dimensional conductors are discussed.Comment: 19 pages, Revtex 2.0, 5 ps-figures, to be mailed on reques

Measurement of molecular mixing at a conjugated polymer interface by specular and off-specular neutron scattering

Measurements have been performed on thermally equilibrated conjugated-polymer/insulating-polymer bilayers, using specular and off-specular neutron reflectivity. While specular reflectivity is only sensitive to the structure normal to the sample, off-specular measurements can probe the structure of the buried polymer/polymer interface in the plane of the sample. Systematic analysis of the scattering from a set of samples with varying insulating-polymer-thickness, using the distorted-wave Born approximation (DWBA), has allowed a robust determination of the intrinsic width at the buried polymer/polymer interface. The quantification of this width (12 Å ± 4 Å) allows us to examine aspects of the conjugated polymer conformation at the interface, by appealing to self-consistent field theory (SCFT) predictions for equilibrium polymer/polymer interfaces in the cases of flexible and semi-flexible chains. This analysis enables us to infer that mixing at this particular interface cannot be described in terms of polymer chain segments that adopt conformations similar to a random walk. Instead, a more plausible explanation is that the conjugated polymer chain segments become significantly oriented in the plane of the interface. It is important to point out that we are only able to reach this conclusion following the extensive analysis of reflectivity data, followed by comparison with SCFT predictions. It is not simply the case that conjugated polymers would be expected to adopt this kind of oriented conformation at the interface, because of their relatively high chain stiffness. It is the combination of a high stiffness and a relatively narrow intrinsic interfacial width that results in a deviation from flexible chain behaviour

How universal is the one-particle Green's function of a Luttinger liquid?

The one-particle Green's function of the Tomonaga-Luttinger model for one-dimensional interacting Fermions is discussed. Far away from the origin of the plane of space-time coordinates the function falls off like a power law. The exponent depends on the direction within the plane. For a certain form of the interaction potential or within an approximated cut-off procedure the different exponents only depend on the strength of the interaction at zero momentum and can be expressed in terms of the Luttinger liquid parameters $K_{\rho}$ and $K_{\sigma}$ of the model at hand. For a more general interaction and directions which are determined by the charge velocity $v_{\rho}$ and spin velocity $v_{\sigma}$ the exponents also depend on the smoothness of the interaction at zero momentum and the asymptotic behavior of the Green's function is not given by the Luttinger liquid parameters alone. This shows that the physics of large space-time distances in Luttinger liquids is less universal than is widely believed.Comment: 5 pages with 2 figure

Training a perceptron in a discrete weight space

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous perceptron and prediction following the clipped weights. The learning is described by a new set of order parameters, composed of the overlaps between the teacher and the continuous/clipped students. Different scenarios are examined among them on-line learning with discrete/continuous transfer functions and off-line Hebb learning. The generalization error of the clipped weights decays asymptotically as $exp(-K \alpha^2)$/$exp(-e^{|\lambda| \alpha})$ in the case of on-line learning with binary/continuous activation functions, respectively, where $\alpha$ is the number of examples divided by N, the size of the input vector and $K$ is a positive constant that decays linearly with 1/L. For finite $N$ and $L$, a perfect agreement between the discrete student and the teacher is obtained for $\alpha \propto \sqrt{L \ln(NL)}$. A crossover to the generalization error $\propto 1/\alpha$, characterized continuous weights with binary output, is obtained for synaptic depth $L > O(\sqrt{N})$.Comment: 10 pages, 5 figs., submitted to PR

Spin-triplet superconductivity in quasi-one dimension

We consider a system with electron-phonon interaction, antiferromagnetic fluctuations and disconnected open Fermi surfaces. The existence of odd-parity superconductivity in this circumstance is shown for the first time. If it is applied to the quasi-one-dimensional systems like the organic conductors (TMTSF)_2X we obtain spin-triplet superconductivity with nodeless gap. Our result is also valid in higher dimensions(2d and 3d).Comment: 2 page

Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model

We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, at varying the asymmetry parameter, $k$, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to a ``complex'' temporal behaviour. This transition takes place for the same value $k_{\rm c}$ at which one has a change for the mean transient length from a power law in the size of the system ($N$) to an exponential law in $N$. The ``complex'' behaviour during the transient shows strong analogies with the chaotic behaviour: decay of temporal correlations, positive Shannon entropy, non-constant Renyi entropies of different orders. Moreover the transition is very similar to that one for the intermittent transition in chaotic systems: scaling law for the Shannon entropy and strong fluctuations of the ``effective Shannon entropy'' along the transient, for $k > k_{\rm c}$.Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included

Stimulus - response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. On depolarization by an applied current, the model exhibits subthreshold oscillatory activity with occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and their statistics and the mean spike frequency curves. We demonstrate that subthreshold oscillatory neurons in the presence of noise can sensitively and also selectively be tuned by stimulus-dependent variation of model parameters.Comment: 19 pages, 7 figure