Search results for "Nonlinear"
showing 10 items of 3684 documents
Bi-squeezed states arising from pseudo-bosons
2018
Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered.
Three-qutrit entanglement and simple singularities
2016
In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety $X$ of separable three-qutrit states within the projective Hilbert space $\mathbb{P}(\mathcal{H}) = \mathbb{P}^{26}$. Given a quantum pure state $|\varphi\rangle\in \mathbb{P}(\mathcal{H})$ we define the $X_\varphi$-hypersuface by cutting $X$ with a hyperplane $H_\varphi$ defined by the linear form $\langle\varphi|$ (the $X_\varphi$-hypersurface of $X$ is $X\cap H_\varphi \subset X$). We prove that when $|\varphi\rangle$ ranges over the SLOCC entanglement classes, the "worst" possible singular $X_\varphi$-hypersuface with isolated singularities, has…
Hydrokinetic simulations of nanoscopic precursor films in rough channels
2009
We report on simulations of capillary filling of high-wetting fluids in nano-channels with and without obstacles. We use atomistic (molecular dynamics) and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence of the formation of thin precursor films, moving ahead of the main capillary front. The dynamics of the precursor films is found to obey a square-root law as the main capillary front, z^2(t) ~ t, although with a larger prefactor, which we find to take the same value for the different geometries (2D-3D) under inspection. The two methods show a quantitative agreement which indicates that the formation and propagation of thin precursors can be handled at a mesoscopic…
Segmented mixed models with random changepoints: a maximum likelihood approach with application to treatment for depression study
2014
We present a simple and effective iterative procedure to estimate segmented mixed models in a likelihood based framework. Random effects and covariates are allowed for each model parameter, including the changepoint. The method is practical and avoids the computational burdens related to estimation of nonlinear mixed effects models. A conventional linear mixed model with proper covariates that account for the changepoints is the key to our estimating algorithm. We illustrate the method via simulations and using data from a randomized clinical trial focused on change in depressive symptoms over time which characteristically show two separate phases of change.
Stepping molecular motor amid Lévy white noise
2015
We consider a model of a stepping molecular motor consisting of two connected heads. Directional motion of the stepper takes place along a one-dimensional track. Each head is subject to a periodic potential without spatial reflection symmetry. When the potential for one head is switched on, it is switched off for the other head. Additionally, the system is subject to the influence of symmetric, white Lévy noise that mimics the action of external random forcing. The stepper exhibits motion with a preferred direction which is examined by analyzing the median of the displacement of a midpoint between the positions of the two heads. We study the modified dynamics of the stepper by numerical sim…
Immune networks: Multi-tasking capabilities at medium load
2013
Associative network models featuring multi-tasking properties have been introduced recently and studied in the low load regime, where the number $P$ of simultaneously retrievable patterns scales with the number $N$ of nodes as $P\sim \log N$. In addition to their relevance in artificial intelligence, these models are increasingly important in immunology, where stored patterns represent strategies to fight pathogens and nodes represent lymphocyte clones. They allow us to understand the crucial ability of the immune system to respond simultaneously to multiple distinct antigen invasions. Here we develop further the statistical mechanical analysis of such systems, by studying the medium load r…
Selfish vs. Unselfish Optimization of Network Creation
2005
We investigate several variants of a network creation model: a group of agents builds up a network between them while trying to keep the costs of this network small. The cost function consists of two addends, namely (i) a constant amount for each edge an agent buys and (ii) the minimum number of hops it takes sending messages to other agents. Despite the simplicity of this model, various complex network structures emerge depending on the weight between the two addends of the cost function and on the selfish or unselfish behaviour of the agents.
Noise-induced resonance-like phenomena in InP crystals embedded in fluctuating electric fields
2016
We explore and discuss the complex electron dynamics inside a low-doped n-type InP bulk embedded in a sub-THz electric field, fluctuating for the superimposition of an external source of Gaussian correlated noise. The results presented in this study derive from numerical simulations obtained by means of a multi-valley Monte Carlo approach to simulate the nonlinear transport of electrons inside the semiconductor crystal. The electronic noise characteristics are statistically investigated by calculating the correlation function of the velocity fluctuations, its spectral density and the integrated spectral density, i.e. the total noise power, for different values of both amplitude and frequenc…
The influence of noise on electron dynamics in semiconductors driven by a periodic electric field
2009
Studies about the constructive aspects of noise and fluctuations in different non-linear systems have shown that the addition of external noise to systems with an intrinsic noise may result in a less noisy response. Recently, the possibility to reduce the diffusion noise in semiconductor bulk materials by adding a random fluctuating contribution to the driving static electric field has been tested. The present work extends the previous theories by considering the noise-induced effects on the electron transport dynamics in low-doped n-type GaAs samples driven by a high-frequency periodic electric field (cyclostationary conditions). By means of Monte Carlo simulations, we calculate the change…
Hybrid recommendation methods in complex networks
2015
We propose here two new recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three relevant data sets, and we compare their performance with several recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow to attain an improvement of performances of up to 20\% with respect to existing non-parametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a …