Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Using dashboards for the business processes status analysis

This paper describes business process status analysis using the dashboards. The dashboards are considered as those, which belong to the most preferred Business Intelligence tools nowadays, which are used by both higher managers and ordinary employees. Existing software tools for dashboard design were reviewed, as well as the most popular visualization charts were outlined. The place and role of analytical dashboards as part of business process management is described

Temporal solitons in optical microresonators

Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance between parametric gain and resonator loss on the one hand and nonlinearity and diffraction or dispersion on the other hand. Mathematically these solitons are solution to the Lugiato-Lefever equation and exist on top of a continuous wave (cw) background. Here we report the observation of temporal dissipative solitons in a high-Q optical microresonator. The solitons are spontaneously generated when the pump laser is tuned through the effective zero detuning point of a high-Q resonance, leading to an effective red-detuned pumping. Red-detuned pumping marks a fundamentally new operating regime in nonlinear microresonators. While usually unstablethis regime acquires unique stability in the presence of solitons without any active feedback on the system. The number of solitons in the resonator can be controlled via the pump laser detuning and transitions to and between soliton states are associated with discontinuous steps in the resonator transmission. Beyond enabling to study soliton physics such as soliton crystals our observations open the route towards compact, high repetition-rate femto-second sources, where the operating wavelength is not bound to the availability of broadband laser gain media. The single soliton states correspond in the frequency domain to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low phase-noise microwave generation.Comment: Includes Supplementary Informatio

Intersection local times of independent fractional Brownian motions as generalized white noise functionals

In this work we present expansions of intersection local times of fractional Brownian motions in $\R^d$, for any dimension $d\geq 1$, with arbitrary Hurst coefficients in $(0,1)^d$. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on $d$ for the existence of intersection local times in $L^2$ is derived, extending the results of D. Nualart and S. Ortiz-Latorre in "Intersection Local Time for Two Independent Fractional Brownian Motions" (J. Theoret. Probab.,20(4)(2007), 759-767) to different and more general Hurst coefficients.Comment: 28 page

Giant Pulses with Nanosecond Time Resolution detected from the Crab Pulsar at 8.5 and 15.1 GHz

We present a study of shape, spectra and polarization properties of giant pulses (GPs) from the Crab pulsar at the very high frequencies of 8.5 and 15.1 GHz. Studies at 15.1 GHz were performed for the first time. Observations were conducted with the 100-m radio telescope in Effelsberg in Oct-Nov 2007 at the frequencies of 8.5 and 15.1 GHz as part of an extensive campaign of multi-station multi-frequency observations of the Crab pulsar. A selection of the strongest pulses was recorded with a new data acquisition system, based on a fast digital oscilloscope, providing nanosecond time resolution in two polarizations in a bandwidth of about 500 MHz. We analyzed the pulse shapes, polarisation and dynamic spectra of GPs as well as the cross-correlations between their LHC and RHC signals. No events were detected outside main pulse and interpulse windows. GP properties were found to be very different for GPs emitted at longitudes of the main pulse and the interpulse. Cross-correlations of the LHC and RHC signals show regular patterns in the frequency domain for the main pulse, but these are missing for the interpulse GPs. We consider consequences of application of the rotating vector model to explain the apparent smooth variation in the position angle of linear polarization for main pulse GPs. We also introduce a new scenario of GP generation as a direct consequence of the polar cap discharge. We find further evidence for strong nano-shot discharges in the magnetosphere of the Crab pulsar. The repetitive frequency spectrum seen in GPs at the main pulse phase is interpreted as a diffraction pattern of regular structures in the emission region. The interpulse GPs however have a spectrum that resembles that of amplitude modulated noise. Propagation effects may be the cause of the differences.Comment: Astronomy & Astrophysics (accepted

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende

Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials

We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for small epsilon the problem admits positive solutions which concentrate as epsilon goes to 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.Comment: 22 page