Miracle-dz/UniFAR-FTUs huggingface dataset:
Regularity properties and strict complementarity of the output-least-squares approach to parameter estimation in parabolic equations

The problem of determining the diffusion coefficient in a parabolic partial differential equation from data is studied using the regularised output-least-squares formulation. Local and global regularity properties of the minimisers are obtained. Conditions are given which guarantee that certain bounds on the set of admissible parameters are active while the associated Lagrange multipliers are non-trivial.
Reparameterizing, Fitting, and Testing a Simple Growth Model

Abstract If the von Bertalanffy growth model is used to statistically compare the properties of growth in two spatial regions by examination of the estimates of the growth parameter k and the asymptotic length parameter L∞, a possible compound null hypothesis H0, is H0: K1= k2 and L∞1 = L∞ 2 for regions 1 and 2. Since the results of this two-parameter test may be difficult to interpret, an alternative procedure is suggested. In addition, the interpretation of the test must be based upon the nature of the data as well as upon the parameter estimates. A regression fit of the model to real but “inappropriate” data may yield a very “good” statistical fit but unrealistic estimates. The use of a third parameter (for example, t0, the time when length is zero) is necessary to uniquely specify a solution; its inclusion always enhances the statistical fit. Because of the interdependence between parameters k and L∞, we reparameterize the von Bertalanffy model with a new parameter w = k˙L∞. The parameter corresponds .
EFFECTIVE SLIP LENGTH: SOME ANALYTICAL AND NUMERICAL RESULTS

More and more experimental evidence demonstrates that the slip boundary condition plays an important role in the study of nano- or micro-scale fluid. We propose a homogenization approach to study the effective slippage problem. We show that the effective slip length obtained by homogenization agrees with the results obtained by the traditional method in the literature for the simplest Stokes flow; then we use our approach to deal with two examples which seem quite hard by other analytical methods. We also include some numerical results to validate our analytical results.
Estimation in causal graphical models

Pearl (2000), Spirtes et al (1993) and Lauritzen (2001) set up a new framework to encode the causal relationships between the random variables by a causal Bayesian network. The estimation of the conditional probabilities in a Bayesian network has received considerable attention by several investigators (e. g., Jordan (1998), Geiger and Heckerman (1997), Ileckerman et al (1995)), but, this issue has not been studied in a causal Bayesian network. In this thesis, we define the multicausal essential graph on the equivalence class of Bayesian networks in which each member of this class manifests a sort of strong type of invariance under (causal) manipulation called hypercausality. We then characterise the families of prior distributions on the parameters of the Bayesian networks which are consistent with hypercausality and show that their unmanipulated uncertain Bayesian networks must demonstrate the independence assumptions. As a result, such prior distributions satisfy a generalisation of the Geiger and lieckerman condition. In particular, when the corresponding essential graph is undirected, the mentioned class of prior distributions will reduce to the Hyper-Dirichlet family (see Chapter 6). In tile second part of this thesis, we will calculate certain local sensitivity measures and through them we are able to provide the solutions for the following questions: Is the network structure that is learned from data robust with respect to changes of the directionality of some specific arrows? Is the local conditional distributions associated with the specified node robust with respect to the changes to its prior distribution or with respect to the changes to the local conditional distribution of another node? Most importantly, is the posterior distribution associated with the parameters of any node robust with respect to the changes to the prior distribution associated with the parameters of one specific node? Finally, are the quantities mentioned above robust with respect to the changes in the independence assumptions described in Chapter 3? Most of the local sensitivity measures (particularly, local measures of the overall posteriors sensitivity), developed in the last decade, tend to diverge to infinity as the sample size becomes very large (Gustafson (1994) and Gustafson et al (1996)). This is in contrast to our knowledge that, starting from different priors, posteriors tend to agree as the data accumulate. Here we define a now class of metrics with more satisfactory asymptotic behaviour. The advantage of the corresponding local sensitivity measures is boundedness for large sample size.
Fixed points in products of ordered spaces

A topological space is said to have the fixed point property if every map (i.e. continuous function) from the space to itself leaves at least one point fixed. There is a rather well known conjecture (see e.g. [3]) asking if the fact that X and Y have the fixed point property implies that the product space X X Y has the property. This note contains an affirmative answer in the case that X and Y are compact ordered sets (with the order topology, of course). It is perhaps worth noting that there is an analogous result due to Ginsburg [1] for similarity transformations on ordered sets with the product ordered lexicographically. Since a compact ordered space has the fixed point property if and only if it is connected, we may rephrase our result to read as follows. If X and Y are compact connected ordered spaces and Z =X X Y, then Z has the fixed point property. We first establish several auxiliary properties of the space Z.
Relation between universal constants of turbulence

The Yakhot–Orszag relation between the turbulent Prandtl number Pt, the Kolmogorov constant Ko, and the Batchelor constant Ba [Phys. Fluids 30, 3 (1987)] should be revised to be Ba=C Ko Pt, with C=1 or 2 corresponding to two different definitions of Ba, and the experimental data of Ba is 0.5–0.8 for C=1 and 1.0–1.6 for C=2. Hence the Yakhot–Orszag prediction Ba=1.161 for C=1 [Phys. Rev. Lett. 57, 1722 (1986)] is not in agreement with experimental data.
LUCIFER: Neutrinoless Double Beta decay search with scintillating bolometers

One of the fundamental open questions in elementary particle physics is the value of the neutrino mass and its nature of Dirac or Majorana particle. Neutrinoless double beta decay (DBD0ν) is a key tool for investigating these neutrino properties and for finding answers to the open questions concerning mass hierarchy and absolute scale. Experimental techniques based on the calorimetric approach with cryogenic particle detectors are proved to be suitable for the search of this rare decay, thanks to high energy resolution and large mass of the detectors. One of the main issues to access an increase of the experimental sensitivity is strictly related to background reduction, trying to perform possibly a zero background experiment. The LUCIFER (Low-background Underground Cryogenic Installation For Elusive Rates) project, funded by the European Research Council, aims at building a background-free DBD0ν experiment, with a discovery potential comparable with the present generation experiments. The idea of LUCIFER is to measure, simultaneously, heat and scintillation light with ZnSe bolometers. Detector features and operational procedures are reviewed. The expected performances and sensitivity are also discussed.
Irradiated Jets and Outflows in the Pelican Nebula

We report the discovery of new Herbig-Haro objects in the Pelican Nebula (IC 4050). HH 555 is a bipolar jet emerging from the tip of a major elephant trunk protruding into the Pelican Nebula from the adjacent molecular cloud. Both beams of HH 555 bend toward the west, indicating deflection by a side wind. A chain of three nearly equally spaced bow shocks, HH 563, HH 564, and HH 565, trace a bent flow bursting out of the southern rim of the Pelican molecular cloud, possibly driven by the moderate-luminosity Class I protostar IRAS 20489+4406. Object HH 570 is a highly collimated jet emerging from a compact cloud located about 15′ southeast of the Pelican molecular cloud. A parallel outflow, possibly driven by IRAS 20496+4354, powers the bright bow shock HH 569. These observations demonstrate that vigorous star formation is still occurring within the clouds that surround the evolved North America/Pelican Nebula complex.
Lattice vibrations and electron-phonon coupling in superconducting quarternary borocarbides: An inelastic neutron-scattering investigation

The phonon densities of states of the borocarbides ${\mathrm{RNi}}_{2}$${\mathrm{B}}_{2}$C (R=La, Y, and Lu) have been investigated using inelastic neutron-scattering techniques. These vibrational spectra are analyzed with the help of lattice dynamical model calculations. In addition experiments were performed on materials for which superconductivity has been suppressed by substituting 30% Ni by Co. The superconducting compounds display strong anomalous frequency shifts when compared to these Co-doped reference systems. This applies in particular to in-plane boron excitations found between 40 and 60 meV. Furthermore, the low-frequency part of the phonon spectra (up to 38 meV) of the superconducting systems shows a pronounced soft-mode behavior of the Ni-B vibrations and, unexpectedly, also of the heavy R-atoms involved excitations. The latter effect also appears upon cooling ${\mathrm{LuNi}}_{2}$${\mathrm{B}}_{2}$C from room temperature to below 30 K. In contrast to these findings, the high frequency ${\mathrm{A}}_{1\mathrm{g}}$ mode which Mattheiss et al. predicted to couple particularly strongly to the electronic system does not display any unusual frequency shift.
Modeling of the Dissolved Oxygen in a River with Storage Zone on the Banks

The prediction of water quality in terms of variables like dissolved oxygen (DO), biochemical oxygen demand (BOD), pH value, total dissolved solids (TDS) and salinity etc. is useful for evaluating the use of water for various related purposes. The widely used Streeter and Phelps models for computing biochemical oxygen demand and its impact on dissolved oxygen do not account for the settleable component of BOD and related implications. The model also does not account for the impact of storage zone on the stream’s DO. In the present work an attempt is made to develop a model which simultaneously accounts for the settleable component of BOD and the effect of storage zones onriver’s DO. An application of the model to real field data suggests that the cumulative impact of settleable BOD and presence of storage zone in the river is to shift the critical deficit closer to the point source and magnify its amount.
Lung Mechanics: The linear single-compartment model

Establishing the model Model structure The first step in constructing a model of any physiological system is to decide on the structure of the model; how may independent components will it have, what do these components represent, and how are they connected to each other? There is no universally applicable answer to any of these questions, so one must be guided by whatever factors pertain to the situation at hand. In addressing the question of how to model lung mechanics in the simplest possible terms, it is intuitively rather obvious that the lung can be viewed as being like a balloon sealed over the end of a pipe (Fig. 1.4). This model has a clear anatomical analogy to a real lung; the pipe represents the conducting airways and the balloon represents the elastic parenchymal tissue. There is also a functional analogy; the balloon can be inflated and deflated through the pipe in the same way that a lung inspires and expires. It goes without saying, of course, that a real lung is vastly more complicated than this simple construct. On the other hand, it is difficult to see how one could devise a simpler model that has any useful resemblance to the real thing. A tour of the universe of lung models, therefore, starts with the single-compartment model. Although the balloon-on-a-pipe configuration shown in Fig. 1.4 is commonly how the lung is viewed, from now on we will be considering the representation shown in Fig. 3.1.
Entanglement, mesoscopic superpositions and decoherence studies with atoms and photons in a cavity

Experiments involving Rydberg atoms crossing one at a time a superconducting cavity lead to new tests of quantum theory, such as the generation of entangled pairs of atoms of the Einstein-Podolsky-Rosen type, the preparation of mesoscopic superpositions of field states in the cavity ("Schrodinger cats") and the observation of the progressive decoherence of these states. These experiments illustrate basic aspects of the quantum-classical boundary and demonstrate steps of quantum logic operations essential for quantum information processing.
Criterion for the convergence of the solution of the Riccati differential equation

The optimal control problem for a linear system with a quadratic cost function leads to the matrix Riccati differential equation. The convergence of the solution of this equation for increasing time interval is investigated as a function of the final state penalty matrix. A necessary and sufficient condition for convergence is derived for stabilizable systems, even if the output in the cost function is not detectable. An algorithm is developed to determine the limiting value of the solution, which is one of the symmetric positive semidefinite solutions of the algebraic Riccati equation. Examples for convergence and nonconvergence are given. A discussion is also included of the convergence properties of the solution of the Riccati differential equation to any real symmetric (not necessarily positive semidefinite) solution of the algebraic Riccati equation.
Meshless local Petrov-Galerkin method for bioluminescent photon propagation in the biological tissue

As a promising optical molecular imaging modality, bioluminescence tomography (BLT) has attracted remarkable attention for its excellent performance and high cost-effectiveness, which can be employed to specifically and directly reveal physiological and pathological activities in vivo at molecular and cellular levels. The goal of BLT is to reconstruct the internal bioluminescent light source with surface measurements. Therefore, the calculation of surface light exitance plays an important role in the inverse source reconstruction, whereas photon propagation is complicated because of strongly scattering property of the biological tissue. In this contribution, a novel meshless local Petrov-Galerkin (MLPG) method based on diffusion approximation model is developed to avoid the complex and time-consuming mesh division in the conventional finite element method (FEM), and MLPG requires only a series of discretized nodes without consideration of element information and node connectivity. Compared with other meshless methods based on global weak-form, background cells used for Gauss quadrature are also omitted in the proposed method. In addition, the tissue optical parameters are incorporated as a priori knowledge in this algorithm. Finally, the performance of this method is valuated using two- and three-dimensional numerical simulation experiments. The results demonstrate the effectiveness and feasibility of the presented algorithm to predict boundary bioluminescent light power distribution.
Numerical simulation and rational design of optically anisotropic columnar films

Optical anisotropy is an inherent property of columnar dielectric films, such as those fabricated by the glancing angle deposition (GLAD) technique. This process utilizes physical vapor deposition combined with computer-controlled substrate motion to finely tune the direction of column growth and vital morphological parameters such as column cross-section and inter-columnar spacing. Control over the anisotropic properties of the porous film provides an opportunity to design polarization-selective photonic devices and films with improved band gap properties. Anisotropic defects in multilayer films also result in a polarization-sensitive position of resonant transmission modes. We employed the finite-difference time-domain and frequency-domain methods to theoretically analyze and design columnar films with unique band-gap properties. The following morphologies were considered: (i) S-shaped columnar films with polarization-dependent band-gap position and width. Using numerical simulations we have shown that the competitive effect of different sources of anisotropy can be used to engineer photonic band gaps with strong selectivity to linearly-polarized light; (ii) Rugate thin films with an anisotropic defect, which exhibit resonant mode splitting. Optical devices were fabricated using titanium dioxide because it has good transparency in the visible range of the optical spectrum and a large bulk refractive index. Experimental results were compared to simulations to verify the designs and understand the limitations of the fabrication process.
55 MHz ultrasound evaluation of the effects of anti-inflammatory drugs on arthritic cartilage

The current study investigates the ability of 55 MHz ultrasound (US) to detect the effects of two anti-inflammatory drugs, Naproxen (NPX) and Dexamethasone (DEXA), on cartilage and subchondral bone when administrated to relieve rat arthritis. Arthritis was induced in rat knees by intra-articular injection of Zymosan and treated with either NPX or DEXA. Control (n=16), arthritic (n=16), NPX (n=16) and DEXA (n=16) patellae were explored in vitro 5 and 14 days post-injections using a 3D US microscope. US quantitative assessment included the analysis of integrated reflection coefficient (IRC, cartilage surface) and apparent integrated backscatter from cartilage matrix (AIB/sub C/) and cartilage/bone interface (AIB/sub B/). Results were compared to histology. The decrease in IRC (p<0.05) due to Zymosan and related to surface fibrillation was compensated by DEXA-treatment at day 14, whereas NPX had no effect on it. Due to maturation, AIB/sub C/ significantly decreased (p<0.05) with time for all groups except for DEXA rats. Zymosan induced a significant increase (p<0.05) in AIB/sub B/ at day 5 and day 14 due probably to changes in the cartilage/bone interface morphology and/or structure. NPX partially compensated this effect at day 14. For DEXA rats, AIB/sub B/ decreased (p<0.05) at day 5 when compared to Zymosan rats and returned to control level at day 14. Current results show that 55 MHz US is sensitive to changes involving both cartilage and subchondral bone induced by anti-inflammatory treatment of arthritis.
Electron acceleration in impulsive solar flares

Simultaneous observations of the hard X-ray, microwave, and type III and DCIM (decimetric)radio bursts associated with the 1978 December 4 solar flare have been used to study the physical parameters relevant to the acceleration and propagation of energetic electrons during the impulsive phase of a solar flare. The hard X-ray observations were made with the X-ray spectrometer aboard the ISEE 3 spacecraft. The radio spectra in metric and decimetric bands were recorded with the radiospectrograph located at Durnten, near Zurich, Switzerland. The microwave observations were made at the Sagamore Hill and Bern observatories. The three metric type III bursts coincided with the three most prominent hard X-ray peaks. This is the fist time a clear one-to-one association between single type III bursts and hard X-ray peaks has been established. The average delay of the type III bursts with respect to the X-ray peaks was 0.5 s. The harder the X-ray spectrum, the higher was the drift rate of the associated type III burst. The characteristic electron energies inferred from the drift rate are of the order of 70 keV. The observed increase in the high-frequency cutoff of the metric type III bursts during the impulsive phase has been examined inmore » terms of the decreasing altitude of the electron acceleration/injection region, the increasing hardness of the electron spectrum, and the decreasing acceleration time. A pulsating decimetric continuum (DCIM) was also found to be present during and before the impulsive phase. The DCIM source seems to coincide spatially with the electron acceleration region and the (projected) origin of the associated type II shock.ction region. « less
Flow dependence of background errors and their vertical correlations for radiance‐data assimilation

This article examines the dependence of background‐error statistics on synoptic conditions and flow patterns. Error variances and vertical correlations of background temperatures as used for variational radiance‐data assimilation are estimated for two different weather regimes over Europe using the NMC method. The results are validated with real observations, i.e. radiosonde data and microwave satellite radiances and generalised with half a year of global data from the ECMWF forecasting system, where weather conditions are distinguished using model fields of wind speed, mean sea level pressure, and relative vorticity. Strong winds, low pressure, and cyclonic flow generally induce larger background errors of 500 hPa temperature than calm winds, high pressure, and anticyclonic flow, and also broader temperature correlations in the vertical with other tropospheric levels. Copyright © 2010 Royal Meteorological Society
Defect-mode mirrorless lasing in dye-doped organic/inorganic hybrid one-dimensional photonic crystal

We have developed a dye-doped organic/inorganic hybrid one-dimensional (1D) photonic crystal containing a dye-doped defect layer for defect-mode photonic band gap lasing. The multilayer laser structure consists of alternating layers of titania nanoparticles and polymethylmethacrylate (PMMA) with an active emission layer of organic dyes in PMMA. Low threshold lasing has been demonstrated at a single defect-mode wavelength of the 1D photonic band gap structure resulting from the inhibited density of states of photons within the stop band and the enhanced rates of spontaneous emission at the localized resonant defect mode.
Metric properties of measure preserving homeomorphisms

We study "typical" metric (ergodic) properties of measure preserving homeomorphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are "typical" for the metric automorphisms of the Lebesgue spaces are also "typical" for the situation under discussion.