Miracle-dz/UniFAR-FTUs huggingface dataset:
Bahadur Efficiency of Sensitivity Analyses in Observational Studies

An observational study draws inferences about treatment effects when treatments are not randomly assigned, as they would be in a randomized experiment. The naive analysis of an observational study assumes that adjustments for measured covariates suffice to remove bias from nonrandom treatment assignment. A sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of the naive analysis, say leading to the acceptance of a null hypothesis rejected in the naive analysis. Observational studies vary greatly in their sensitivity to unmeasured biases, but a poor choice of test statistic can lead to an exaggerated report of sensitivity to bias. The Bahadur efficiency of a sensitivity analysis is introduced, calculated, and connected to established concepts, such as the power of a sensitivity analysis and the design sensitivity. The Bahadur slope equals zero when the sensitivity parameter equals the design sensitivity, but the Bahadur slope permits more refined distinctions. Specifically, the Bahadur relative efficiency can also compare the relative performance of two test statistics at a value of the sensitivity parameter below the minimum of their design sensitivities. Adaptive procedures that combine several tests can achieve the best design sensitivity and the best Bahadur slope of their component tests. Ultimately, in sufficiently large sample sizes, design sensitivity is more important than efficiency for the power of a sensitivity analysis, and the exponential rate at which rate design sensitivity overtakes efficiency is characterized.
Nonlinear Characteristics of Ensemble Perturbation Evolution and Their Application to Forecasting High-Impact Events

AbstractEnsemble forecasting is becoming an increasingly important aspect of numerical weather prediction. As ensemble perturbation evolution becomes more nonlinear as a forecast evolves, the ensemble mean can diverge from the model attractor on which ensemble members are constrained. In turn, the ensemble mean can become increasingly unrealistic, and although statistically best on average, it can provide poor forecast guidance for specific high-impact events. This study uses an ensemble Kalman filter to investigate this behavior at the synoptic scale for landfalling midlatitude cyclones. This work also aims to understand the best way to select “best members” closest to the mean that both behave realistically and possess the statistically beneficial qualities of the mean. It is found that substantial nonlinearity emerges within forecast times of a day, which roughly agrees with previous research addressing synoptic-scale nonlinearity more generally. The evolving nonlinearity results in unrealistic behavio.
Evolutionary computation applied to combinatorial optimisation problems

This thesis addresses the issues associated with conventional genetic algorithms (GA) when applied to hard optimisation problems. In particular it examines the problem of selecting and implementing appropriate genetic operators in order to meet the validity constraints for constrained optimisation problems. The problem selected is the travelling salesman problem (TSP), a well known NP-hard problem. Following a review of conventional genetic algorithms, this thesis advocates the use of a repair technique for genetic algorithms: GeneRepair. We evaluate the effectiveness of this operator against a wide range of benchmark problems and compare these results with conventional genetic algorithm approaches. A comparison between GeneRepair and the conventional GA approaches is made in two forms: firstly a handcrafted approach compares GAs without repair against those using GeneRepair. A second automated approach is then presented. This meta-genetic algorithm examines different configurations of operators and parameters. Through the use of a cost/benefit (Quality-Time Tradeoff) function, the user can balance the computational effort against the quality of the solution and thus allow the user to specify exactly what the cost benefit point should be for the search. Results have identified the optimal configuration settings for solving selected TSP problems. These results show that GeneRepair when used consistently generates very good TSP solutions for 50, 70 and 100 city problems. GeneRepair assists in finding TSP solutions in an extremely efficient manner, in both time and number of evaluations required.
A Probability Inequality for Linear Combinations of Bounded Random Variables

Let $Y_1, \cdots, Y_n$ be independent random variables with mean zero such that $|Y_i| \leqq i, i = 1, \cdots, n$, and let $\theta_1,\cdots, \theta_n$ be real numbers satisfying $\sum^n_1 \theta_i^2 = 1$. Set $S_n(\theta) = \sum^n_1 \theta_i Y_i$ and let $\varphi(x) = (2\pi)^{-\frac{1}{2}} \exp \lbrack - \frac{1}{2} x^2\rbrack$. THEOREM. For $\alpha > 0$, and for all $\theta_1,\cdots, \theta_n$, \begin{\align*}P\{|S_n(\theta)| \geqq \alpha\} &\leqq 2\inf_{0\leqq u \leqq \alpha} \int^\infty_u \frac{(x - u)^3}{(\alpha - u)^3} \varphi (x) dx \\ &\leqq 12 \frac{\varphi(\alpha)}{\alpha} \inf_{0\leqq \delta \leqq \alpha^2} \frac{\exp\lbrack\delta/2(2 - \delta/\alpha^2)\rbrack}{\delta^3(1 - \delta/\alpha^2)^4}. \\ \end{align*}
Shewhart x-charts with estimated process variance

Properties of the Shewhart X-chart for controlling the mean of a process with a normal distribution are investigated for the situation where the process variance O2must be estimated from initial sample data. The control limits of the X-chart depend on the estimate of O2and thus, unlike the case when O2is known, the X-chart is not equivalent to a sequence of independent tests. When O2is estimated the distribution of the run length is not geometric and cannot be characterized simply in terms of the probability of a signal at a given point. The average run length (ARL) for the X-chart is expressed in terms of an integral involving the normal cdf, and it is shown that the chart signals with probability one, but the ARL may not be finite if the size of the 2 sample used to estimate O2is sufficiently small. In addition, certain bounds for the ARL are also derived. Numerical integration is use to show that the effect of using small sample sizes in estimating O2is to increase the ARL and the variance of the run l.
ROSAT OBSERVATIONS OF AN UMA AND MR SER - THE STATUS OF THE SOFT-X-RAY EXCESS IN AM HER STARS

We present the results of ROSAT pointed observations of the AM Her stars AN UMa and MR Ser. AN UMa was in a high-brightness state. We examine its soft X-ray light curve, and fit its spectrum with a two-component model consisting of an absorbed soft blackbody and a harder thermal bremsstrahlung distribution. MR Ser was found to be in a low-brightness state, and had a spectrum which was well fitted with a single-component, thermal bremsstrahlung model.The question of the energy balance in AM Her stars is reviewed with a view to quantifying the incidence of the 'soft X-ray excess'. The excess has been explained as due to the deposition of energy directly into the white dwarf photosphere by the accretion stream, supplementing the energy of photons from the hot accretion column which irradiate the photosphere. We have calculated the energy balance in AN UMa and 16 other AM Her stars observed with ROSAT. We find that, although the majority of AM Her stars exhibit a soft X-ray excess, a number of objects are consistent with a model which includes radiative heating only. We examine possible factors which could determine the value of the soft X-ray excess. We find a correlation of soft X-ray excess with magnetic field strength or, alternatively, the radius at which material couples on to the magnetic field lines.
Cooperative Versus Competitive Efforts and Problem Solving

The impacts of cooperative and competitive efforts on problem solving were compared. In order to resolve the controversy over whether cooperation promotes higher- or lower-quality individual problem solving than does competition, 46 studies, published between 1929 and 1993, were examined. The findings from these studies were classified in 4 categories according to the type of problem solving measured: linguistic (solved through written and oral language), nonlinguistic (solved through symbols, math, motor activities, actions), well-defined (having clearly defined operations and solutions), and ill-defined (lacking clear definitions, operations, and solutions). The 63 relevant findings that resulted were subjected to a meta-analysis for purposes of integration. Members of cooperative teams outperformed individuals competing with each other on all 4 types of problem solving (effect sizes = 0.37, 0.72, 0.52, 0.60, respectively). These results held for individuals of all ages and for studies of high, medium, and low quality. The superiority of cooperation, however, was greater on nonlinguistic than on linguistic problems.
Conservative numerical methods for nonlinear strings

In this article, a class of numerical schemes for the simulation of nonlinear coupled longitudinal/transverse string vibration is presented. Though there are various ways of arriving at such schemes, special attention is paid here to energy conservation in nonlinear model systems and its transfer to an analogous discrete quantity in a difference scheme. Such exact numerical energy conservation can lead to simple global stability conditions, which can be otherwise difficult to ascertain for nonlinear difference schemes—in particular, such conditions may be arrived at without any reliance on frequency domain concepts (i.e., Fourier or Laplace transforms), which are of only moderate utility in the analysis of nonlinear systems. Implementation details are discussed and numerical results are presented.
Interface effects in highly oriented films of the Heusler alloy Co2MnSi on GaAs(001)

Highly (001) oriented thin films of Co2MnSi have been grown on lattice-matched GaAs(001) without a buffer layer. Stoichiometric films grown at the highest substrate temperature of 689 K showed the lowest resistivity (33μΩcm at 4.2 K) and the lowest coercivity (14 Oe). Twofold in-plane magnetic anisotropy was observed due to the inequivalence of the ⟨110⟩ directions, and this was attributed to the nature of the bonding at the reconstructed GaAs surface. Interfacial reactions resulted in the formation of an epitaxial Mn-As region and a thin interfacial layer that was Co-Ga rich. This prevented the desired lattice matching and resulted in films with a saturation magnetization slightly below the bulk value. In spite of this, the spin polarization of the free surface was measured to be 55%, similar to bulk material.
Boundary layer development after a separated region

Measurements obtained in boundary layers developing downstream of the highly turbulent, separated flow generated at the leading edge of a blunt flat plate are presented. Two cases are considered: first, when there is only very low (wind tunnel) turbulence present in the free-stream flow and, second, when roughly isotropic, homogeneous turbulence is introduced. With conditions adjusted to ensure that the separated region was of the same length in both cases, the flow around reattachment was significantly different and subsequent differences in the development rate of the two boundary layers are identified. The paper complements, but is much more extensive than, the earlier presentation of some of the basic data (Castro & Epik 1996), confirming not only that the development process is very slow, but also that it is non-monotonic. Turbulence stress levels fall below those typical of zero-pressure-gradient boundary layers and, in many ways, the boundary layer has features similar to those found in standard boundary layers perturbed by free-stream turbulence. It is argued that, at least as far as the turbulence structure is concerned, the inner layer region develops no more quickly than does the outer flow and it is the latter which essentially determines the overall rate of development of the whole flow. Some numerical computations are used to assess the extent to which current turbulence models are adequate for such flows.
Markov Decision Processes: Discrete Stochastic Dynamic Programming

From the Publisher: The past decade has seen considerable theoretical and applied research on Markov decision processes, as well as the growing use of these models in ecology, economics, communications engineering, and other fields where outcomes are uncertain and sequential decision-making processes are needed. A timely response to this increased activity, Martin L. Puterman's new work provides a uniquely up-to-date, unified, and rigorous treatment of the theoretical, computational, and applied research on Markov decision process models. It discusses all major research directions in the field, highlights many significant applications of Markov decision processes models, and explores numerous important topics that have previously been neglected or given cursory coverage in the literature. Markov Decision Processes focuses primarily on infinite horizon discrete time models and models with discrete time spaces while also examining models with arbitrary state spaces, finite horizon models, and continuous-time discrete state models. The book is organized around optimality criteria, using a common framework centered on the optimality (Bellman) equation for presenting results. The results are presented in a "theorem-proof" format and elaborated on through both discussion and examples, including results that are not available in any other book. A two-state Markov decision process model, presented in Chapter 3, is analyzed repeatedly throughout the book and demonstrates many results and algorithms. Markov Decision Processes covers recent research advances in such areas as countable state space models with average reward criterion, constrained models, and models with risk sensitive optimality criteria. It also explores several topics that have received little or no attention in other books, including modified policy iteration, multichain models with average reward criterion, and sensitive optimality. In addition, a Bibliographic Remarks section in each chapter comments on relevant historic
On the structure of a Taylor column driven by a buoyant parcel in an unbounded rotating fluid

The velocity and pressure fields produced in a homogeneous rapidly rotating fluid driven by an isolated buoyant parcel are investigated. Gravity and rotation are allowed to have arbitrary orientations and the parcel shape is assumed Gaussian. Inertial forces and time-dependent effects are ignored. The linear problem is easily solved by three-dimensional Fourier transform, and the inversion is facilitated by assuming the Ekman number, E, to be very small. In this limit the fields form a Taylor column extended in the direction of the rotation axis. In the absence of rigid boundaries no boundary layers occur. The velocity and pressure in the vicinity of the parcel are found in closed form while elsewhere (within the Taylor column) they are expressed in terms of relatively simple scalar integrals which are easily evaluated. Within the buoyant parcel, the momentum balance is baroclinic, involving Coriolis, pressure and buoyancy forces. Outside the parcel, the balance is geostrophic at unit order. The viscous force is important at order E and determines the axial structure of the Taylor column. In contrast to the case of flow driven by a rigid body, no ‘Taylor slug’ of recirculating flow occurs. The velocity and pressure decay algebraically with distance from the parcel, with the scale of variation being a/E in the axial direction and a in the radial direction, where a is the parcel radius. In the vicinity of the parcel, the return flow occurs in a broad region surrounding the parcel. The structure of flow in the vicinity of the parcel is independent of the Ekman number. This return flow sweeps the fringes of the parcel backward, making the net rise speed significantly slower than that of a rigid sphere of identical buoyancy. The return flow also acts to deform the parcel; this deformation is quantified.
Algebraic phase unwrapping and zero distribution of polynomial for continuous-time systems

An analytic solution is provided to the symbolic algebra-based computational problem for the unwrapped phase (that can be uniquely expressed as an integral involving itself and its derivative) of a continuous-time linear time-invariant system whose characteristic polynomial has coefficients belonging to the algebraically closed field of complex numbers. This solution is based on the use of the classical Cauchy indices. Application and adaptation of this analytic solution to an arbitrary univariate polynomial, yields its zero distribution with respect to the unbounded imaginary axis in the complex plane. Importantly, the algorithm that yields this zero distribution is designed to enforce the nonoccurrence of singular cases and can be implemented to any desired accuracy by rational operations.
Interferometer-Based Studies of Quantum Hall Phenomena

The fractional quantum Hall (FQH) effect harbors a wealth of unique phenomena, many of which remain mysterious. Of particular interest is the predicted existence of quasi-particles with unusual topological properties, especially in light of recent proposals to observe these properties using electronic interferometers. An introduction to quantum Hall physics and electronic interferometry is given in Chapter 1 of this thesis. The remaining chapters, summarized below, describe a set of experiments in which FQH systems are studied using electronic Fabry-Perot interferometry and related techniques. Since prior studies of electronic Fabry-Perot interferometers revealed unexpected behavior even in the integer quantum Hall (IQH) regime, we began our measurements there. Our initial experiment, presented in Chapter 2, disentangles signatures of Coulomb interaction effects from those of Aharonov-Bohm (AB) interference and provides the first measurement of pure AB interference in these devices. In our next experiment, presented in Chapter 3, we measure AB interference oscillations as a function of an applied dc bias, use their period to study the velocity of the interfering electrons, and study how the oscillations decay as a function of bias and magnetic field. Moving to the FQH regime, applying a similar-sized bias to a quantum point contact leads to long-lasting changes in the strengths and positions of FQH plateaus. The involvement of lattice nuclear spins in this effect, suggested by the long persistence times, is confirmed using NMR-type measurements. Although the exact physical process responsible
Velocity-derivative skewness and two-time velocity correlations of isotropic turbulence as predicted by the LET theory

The local-energy-transfer (LET) theory was used to calculate freely decaying turbulence for arbitrary initial conditions over a range of microscale-based Reynolds numbers 0.5 [les ] Rλ(tf) [les ] 1009, where tf is the final time of computation. The predicted skewness factor S(Rλ) agreed closely with the results of numerical simulations at low-to-moderate Reynolds numbers and followed the same general trend at larger values of Rλ. It was also found that, for Rλ(tf) [les ] 5, the LET calculation was almost indistinguishable from that of the direct-interaction approximation (DIA), with the difference between the two theories tending to zero as Rλ(tf)∞ 0. Two-time correlation and propagator (or response) functions were also obtained. Tests of their scaling behaviour suggest that, contrary to general belief, the convective sweeping of the energy-containing range is much less important than the Kolmogorov timescale in determining inertial-range behaviour. This result raises questions about the accepted explanation for the failure of the direct-interaction approximation, thus motivating a discussion about the relevance of random Galilean invariance (RGI). It is argued that, for a properly constructed ensemble of transformations to inertial frames, invariance in every realization necessarily implies RGI. It is suggested that the defects of the direct-interaction approximation can be understood in terms of a failure to renormalize the stirring forces.
Formation of nanoscale spatially indirect excitons: Evolution of the type-II optical character of CdTe/CdSe heteronanocrystals

In this work, the evolution of the optical properties of nanoscale spatially indirect excitons as a function of the size, shape, and composition of the heteronanostructure is investigated, using colloidal CdTe/CdSe heteronanocrystals (2.6 nm diameter CdTe core and increasing CdSe volume fraction) as a model system. Emphasis is given to quantitative aspects such as the absorption cross section of the lowest-energy exciton transition (μSS), Stokes shift, linewidths, and the exciton radiative lifetime. The hole wave function remains confined to the CdTe core while the electron wave function is initially delocalized over the whole heteronanocrystal (type-I1/2 regime), and gradually localizes in the CdSe segment as the growth proceeds, until the spatially indirect exciton transition becomes the lowest-energy transition (type-II regime). This results in a progressive shift of the optical transitions to lower energies, accompanied by a decrease in the oscillator strengths at emission energies and an increase in the exciton radiative lifetimes. The onset of the type-II regime is characterized by the loss of structure of the lowest-energy absorption band, accompanied by a simultaneous increase in the Stokes shift values and transition linewidths. This can be understood by considering the dispersion of the hole and electron states in k space. The μSS values decrease rapidly in the type-I1/2 regime but only slightly in the type-II regime. This shows that the indirect exciton formation leads primarily to redistribution of the oscillator strength of the lowest-energy transition over a wider frequency range. The total absorption cross section per ion-pair unit (i.e., integrated over all the exciton transitions) remains essentially constant during the heteronanocrystal growth, demonstrating that μSS is redistributed from higher-energy transitions of both the CdTe and the CdSe segments, in response to the reduction in the electron-hole wave-function overlap. Two radiative decay rates are observed and ascribed to exciton states with different degrees of localization of the electron wave function (an upper state with a faster decay rate and a lower state with a slower decay rate). The results presented here provide fundamental insights into nanoscale spatially indirect exciton transitions, highlighting the crucial role of a number of parameters (viz., electron-hole spatial correlation, exciton dispersion and exciton degeneracy, shape effects, and electronic coupling).
Constrained Average Cost Markov Decision Chains

A Markov decision chain with denumerable state space incurs two types of costs — for example, an operating cost and a holding cost. The objective is to minimize the expected average operating cost, subject to a constraint on the expected average holding cost. We prove the existence of an optimal constrained randomized stationary policy, for which the two stationary policies differ on at most one state. The examples treated are a packet communication system with reject option and a single-server queue with service rate control.