Feedback between node and network dynamics can produce real-world network properties

Real-world networks are characterized by common features, including among others a scale-free degree distribution, a high clustering coefficient and a short typical distance between nodes. These properties are usually explained by the dynamics of edge and node addition and deletion.     

Noise effects in two different biological systems

We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L.) (Heteroptera: Pentatomidae), and (ii) polymer translocation. In the first system we analyze, by directionality tests, the response of N. viridula individuals to subthreshold signals plus noise in their mating behaviour. The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum. Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise. In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source. At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed. At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia. We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport.     

Evolution processes of coupled thermal qubits

We investigate the quantum speed limit time (QSLT) of quantum evolution before thermal equilibrium of two coupled qubits each of which is coupled to a separate thermal bath at the same temperature within the Born-Markov approximation. The evolution process in one particular initial state can change between speed-up and speed-down two times before reaching equilibrium. We call this double cusp behaviour. This behaviour is an anomalous phenomenon in evolution processes in the weak-coupling Markovian regime. We study QSLT corresponding to all pure initial energy eigenstates and categorise them. In addition, we also display the conditions for double cusp behaviour in terms of temperature, qubit interaction and frequency.     

Probabilistic models for stochastic elliptic partial differential equations

Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically.     

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Es wird über eine spezifische Abtrennung des Urans aus Mischungen radioaktiver Spaltprodukte mittels Dünnschichtchromatographie berichtet. Die bei kurz bestrahlten Uranproben am Uranfleck gefundene Radioaktivität kann auf Grund γ-spektrometrischer Messungen dem ²³⁹Np zugeordnet werden.     

Empirical scaling laws and the aggregation of non-stationary data

Widely cited evidence for scaling (self-similarity) of the returns of stocks and other securities is inconsistent with virtually all currently-used models for price movements. In particular, state-of-the-art models provide for ubiquitous, irregular, and oftentimes high-frequency fluctuations in volatility (“stochastic volatility”), both intraday and across the days, weeks, and years over which data is aggregated in demonstrations of self-similarity of returns. Stochastic volatility renders these models, which are based on variants and generalizations of random walks, incompatible with self-similarity. We show here that empirical evidence for self-similarity does not actually contradict the analytic lack of self-similarity in these models. The resolution of the mismatch between models and data can be traced to a statistical consequence of aggregating large amounts of non-stationary data.     

Beyond Black-Scholes: semimartingales and Lévy processes for option pricing

We consider the problem of option pricing when the underlying asset follows a general semimartingale process. After reviewing the foundations of arbitrage pricing theory for semimartingales and the link with Lévy processes, we introduce a general method to price options in this framework based on Fourier and Wavelet analysis. Received 4 September 2000     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

First-Passage and Extreme-Value Statistics of a Particle Subject to a Constant Force Plus a Random Force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point x ₁ of a particle which starts at x ₀ with velocity v ₀. The probability that the particle has not yet arrived at x ₁ after a time t, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement m=max  _t [x(t)].