A toy model of a fake inflation

Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on Electrodynamics in the cosmic geometry. Such phenomenon of induced metric is rather general and may occurs for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of non linear scalar field. We show that a class of theories that have been analyzed in the literature, having regular configuration in the Minkowski space-time background is such that the field propagates like free waves in an effective deSitter geometry. The observation of these waves would led us to infer, erroneously, that we live in a deSitter universe

Statistical properties of metastable intermediates in DNA unzipping

We unzip DNA molecules using optical tweezers and determine the sizes of the cooperatively unzipping and zipping regions separating consecutive metastable intermediates along the unzipping pathway. Sizes are found to be distributed following a power law, ranging from one base pair up to more than a hundred base pairs. We find that a large fraction of unzipping regions smaller than 10 bp are seldom detected because of the high compliance of the released single stranded DNA. We show how the compliance of a single nucleotide sets a limit value around 0.1 N/m for the stiffness of any local force probe aiming to discriminate one base pair at a time in DNA unzipping experiments.Comment: Main text: 4 pages, 3 figures. Supplementary Information: 18 pages, 15 figure

Single-molecule stochastic resonance

Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively folding/unfolding transitions under the action of an applied oscillating mechanical force with optical tweezers. By varying the frequency of the force oscillation, we investigated the folding/unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measured several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins is a good quantifier of the SR. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance matching condition. Finally, we carried out experiments in short hairpins that show how SR might be useful to enhance the detection of conformational molecular transitions of low SNR.Comment: 11 pages, 7 figures, supplementary material (http://prx.aps.org/epaps/PRX/v2/i3/e031012/prx-supp.pdf

A geometric approach to phase response curves and its numerical computation through the parameterization method

The final publication is available at link.springer.comThe phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new approach to PRCs based on the parameterization method. The underlying idea relies on the construction of a periodic system whose corresponding stroboscopic map has an invariant curve. We demonstrate the relationship between the internal dynamics of this invariant curve and the PRC, which yields a method to numerically compute the PRCs. Moreover, we link the existence properties of this invariant curve as the amplitude of the perturbation is increased with changes in the PRC waveform and with the geometry of isochrons. The invariant curve and its dynamics will be computed by means of the parameterization method consisting of solving an invariance equation. We show that the method to compute the PRC can be extended beyond the breakdown of the curve by means of introducing a modified invariance equation. The method also computes the amplitude response functions (ARCs) which provide information on the displacement away from the oscillator due to the effects of the perturbation. Finally, we apply the method to several classical models in neuroscience to illustrate how the results herein extend the framework of computation and interpretation of the PRC and ARC for perturbations of large amplitude and not necessarily pulsatile.Peer ReviewedPostprint (author's final draft

The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability

We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter $\epsilon$ uncouples the system at $\epsilon=0$. Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down

Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval

We present a quantization scheme of an arbitrary measure space based on overcomplete families of states and generalizing the Klauder and the Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods like geometric quantization are uneasy to implement. The procedure is illustrated by (mostly two-dimensional) elementary examples in which the measure space is a $N$-element set and the unit interval. Spaces of states for the $N$-element set and the unit interval are the 2-dimensional euclidean $\R^2$ and hermitian \C^2 planes