Optimization in First-Passage Resetting

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability distribution exhibits rich features. In a finite domain, we define a non-trivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.Comment: 4 pages, 3 figures, revtex 4-1 format. Version 1 contains changes in response to referee comments. Version 2: A missing factor of 2 in an inline formula has been correcte

Realistic error estimates on kinematic parameters

Current error estimates on kinematic parameters are based on the assumption that the data points in the spectra follow a Poisson distribution. For realistic data that have undergone several steps in a reduction process, this is generally not the case. Neither is the noise distribution independent in adjacent pixels. Hence, the error estimates on the derived kinematic parameters will (in most cases) be smaller than the real errors. In this paper we propose a method that makes a diagnosis of the characteristics of the observed noise The method also offers the possibility to calculate more realistic error estimates on kinematic parameters. The method was tested on spectroscopic observations of NGC3258. In this particular case, the realistic errors are almost a factor of 2 larger than the errors based on least squares statistics.Comment: 11 pages, 11 figures, accepted for publication by MNRA

Design and characterization of microfabricated on-chip HPLC columns

The analysis of liquid mixtures, as e.g. encountered in environmental monitoring, food safety analysis, the development of novel pharmaceutical compounds, etc... is usually carried out using chromatogaphic separatoin techniques.\ud \ud Theoretical calculations have shown that the efficiency of these techniques can be strongly enhanced if they would be carried out in perfectly ordered chromatographic beds, in stead of the randomly packed tubes filled with spherical particles as used today.\ud \ud In the present work, the various details of the fabrication processes needed to produce such perfectly ordered chromatographic beds (on-chip HPLC columns) have been analyzed and solutions have been proposed. Lithographic etching protocols, based on the use of Bosch-etching process have been optimized to produce ordered arrays of micro-pillars over long column lengths.\ud \ud Optimized turn structures were developed to arrange very long (up to 3m) columns on the surface of a 4 inch wafer. Various coupling techniques, to connect the on-chip HPLC columns with a minimum of coupling losses were developed.\ud \ud In addition, a novel experimental set-up and procedure were developed to study the flow processes, and especially the radial dispersion process in on-chip HPLC-columns in great detail. This work lead to a novel correlation for the velocity dependency of the radial dispersion in ordered and disordered beds of cylindrical micro-pillars

Modelling galactic spectra: I - A dynamical model for NGC3258

In this paper we present a method to analyse absorption line spectra of a galaxy designed to determine the stellar dynamics and the stellar populations by a direct fit to the spectra. This paper is the first one to report on the application of the method to data. The modelling results in the knowledge of distribution functions that are sums of basis functions. The practical implementation of the method is discussed and a new type of basis functions is introduced. With this method, a dynamical model for NGC 3258 is constructed. This galaxy can be successfully modelled with a potential containing 30% dark matter within 1r_e with a mass of 1.6x10^11 M_o. The total mass within 2r_e is estimated as 5x10^11 M_o, containing 63% dark matter. The model is isotropic in the centre, is radially anisotropic between 0.2 and 2 kpc (0.88 r_e) and becomes tangentially anisotropic further on. The photometry reveals the presence of a dust disk near the centre

Phasic pressure measurements for coronary and valvular interventions using fluid-filled catheters: Errors, automated correction, and clinical implications.

We sought to develop an automatic method for correcting common errors in phasic pressure tracings for physiology-guided interventions on coronary and valvular stenosis. Effective coronary and valvular interventions rely on accurate hemodynamic assessment. Phasic (subcycle) indexes remain intrinsic to valvular stenosis and are emerging for coronary stenosis. Errors, corrections, and clinical implications of fluid-filled catheter phasic pressure assessments have not been assessed in the current era of ubiquitous, high-fidelity pressure wire sensors. We recruited patients undergoing invasive coronary physiology assessment. Phasic aortic pressure signals were recorded simultaneously using a fluid-filled guide catheter and 0.014″ pressure wire before and after standard calibration as well as after pullback. We included additional subjects undergoing hemodynamic assessment before and after transcatheter aortic valve implantation. Using the pressure wire as reference standard, we developed an automatic algorithm to match phasic pressures. Removing pressure offset and temporal shift produced the largest improvements in root mean square (RMS) error between catheter and pressure wire signals. However, further optimization <1 mmHg RMS error was possible by accounting for differential gain and the oscillatory behavior of the fluid-filled guide. The impact of correction was larger for subcycle (like systole or diastole) versus whole-cycle metrics, indicating a key role for valvular stenosis and emerging coronary pressure ratios. When calibrating phasic aortic pressure signals using a pressure wire, correction requires these parameters: offset, timing, gain, and oscillations (frequency and damping factor). Automatically eliminating common errors may improve some clinical decisions regarding physiology-based intervention

Wigner function for noninteracting fermions in hard wall potentials

The Wigner function $W_N({\bf x}, {\bf p})$ is a useful quantity to characterize the quantum fluctuations of an $N$-body system in its phase space. Here we study $W_N({\bf x}, {\bf p})$ for $N$ noninteracting spinless fermions in a $d$-dimensional spherical hard box of radius $R$ at temperature $T=0$. In the large $N$ limit, the local density approximation (LDA) predicts that $W_N({\bf x}, {\bf p}) \approx 1/(2 \pi \hbar)^d$ inside a finite region of the $({\bf x}, {\bf p})$ plane, namely for $|{\bf x}| < R$ and $|{\bf p}| < k_F$ where $k_F$ is the Fermi momentum, while $W_N({\bf x}, {\bf p})$ vanishes outside this region, or "droplet", on a scale determined by quantum fluctuations. In this paper we investigate systematically, in this quantum region, the structure of the Wigner function along the edge of this droplet, called the Fermi surf. In one dimension, we find that there are three distinct edge regions along the Fermi surf and we compute exactly the associated nontrivial scaling functions in each regime. We also study the momentum distribution $\hat \rho_N(p)$ and find a striking algebraic tail for very large momenta $\hat \rho_N(p) \propto 1/p^4$, well beyond $k_F$, reminiscent of a similar tail found in interacting quantum systems (discussed in the context of Tan's relation). We then generalize these results to higher $d$ and find, remarkably, that the scaling function close to the edge of the box is universal, i.e., independent of the dimension~$d$.Comment: 31 pages, 14 figure

Exploring the speed limits of liqui chromatography using shear-driven flows through 45 and 85 nm deep nano-channels

We explored the possibility to perform high speed and high efficiency liquid chromatographic separations in channels with a sub-100 nm depth. The mobile phase flow through these nano-channels was generated using the shear-driven flow principle to generate high speed flows which were the equivalent of a 12000 bar pressure-driven flow. It was found that the ultra-fast mass transfer kinetics prevailing in this range of small channel depths allow to drastically reduce the C-term contribution to band broadening, at least up to the upper speed limit of our current set-up (7 mm s−1 mobile phase velocity), leaving the inescapable molecular diffusion (i.e., B-term band broadening) as the sole detectable source of band broadening. Due to the greatly reduced mass transfer limitations, 50000 to 100000 theoretical plates could be generated in the span of 1 to 1.5 seconds. This is nearly two orders of magnitude faster than the best performing commercial pressure-driven UHPLC-systems. With the employed channel depths, we appear to have struck a practical lower limit for the channel miniaturization of shear-driven flows. Despite the use of channel substrates with the highest grades of optical flatness, the overall substrate waviness (on the order of some 5 to 10 nm) can no longer be neglected compared to the etched channel depth, which in turn significantly influenced the local retention factor and band broadening

Compressed-domain shot boundary detection for H.264/AVC using intra partitioning maps

In this paper, a novel technique for shot boundary detection operating on H.264/AVC-compressed sequences is presented. Due to new and improved coding tools in H.264/AVC, the characteristics of the obtained sequences differ from former video coding standards. Although several algorithms working on this new standard are already proposed, the presence of IDR frames can still lead to a low accuracy for abrupt transitions. To solve this issue, we present the motion-compensated intra partitioning map which relies on the intra partitioning modes and the motion vectors present in the compressed video stream. Experimental results show that this motion-compensated map achieves a high accuracy and exceeds related work