Abstract:
Dedicated read-out electronics was developed for low impedance resistive thermometers. Using this high performance temperature controller, the temperature dependence of the excess noise of a YBa2Cu307-d (YBCO) sample in the superconducting transition was monitored as a function of the current bias. The noise could reach 3.10-8 K Hz-1/2 at 1 Hz, 5 mA bias and 90 K.

Abstract:
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating $A\_0$ which does not rely on the knowledge or an estimation of the standard deviation of the noise $\sigma$. Our estimator achieves, up to a logarithmic factor, optimal rates of convergence under the Frobenius risk and, thus, has the same prediction performance as previously proposed estimators which rely on the knowledge of $\sigma$. Our method is based on the solution of a convex optimization problem which makes it computationally attractive.

Abstract:
To treat the difficulties in the design of MIMO fuzzy controller, which arise as high dimensional rule bases and the acquirement of the membership functions and rules, a novel hierarchical fuzzy logical controller (NHFLC) is presented in this paper. Based on the proposed controller, empirical information and expert knowledge about the process are not needed, and the total number of rules is drastically decreased. Genetic algorithm is used to obtain the fuzzy control strategies for the NHFLC. The simulation results show the proposed NHFLC has better dynamic performance and robust stability than the conventional MIMO fuzzy controller.

Abstract:
We discuss the behavior of bounded slope quenched noise invasion models in high dimensions. We first observe that the roughness of such a steady state interface is generated by the combination of the roughness of the invasion process $\chi_c$ and the roughness of the underlying interface dynamics. In high enough dimension we argue that $\chi_c$ decreases to zero. This defines a critical dimension for the problem, over which it reduces to the correlated annealed dynamics, which we show to have the same roughness as the annealed equation at five dimensions. We argue that on the Cayley tree with one additional height coordinate the associated processes are fractal. The critical behavior is anomalous due to strong effects of rare events. Numerical simulations of the model on a Cayley tree and high dimensional lattices support those theoretical predictions.

Abstract:
We consider the simulation of interacting high-dimensional systems using pairwise interacting qubits. The main tool in this context is the generation of effective many-body interactions, and we examine a number of different protocols for obtaining them. These methods include the usage of higher-order processes (commutator method), unitary conjugation or graph state encoding, as well as teleportation based approaches. We illustrate and compare these methods in detail and analyze the time cost for simulation. In the second part of the article, we investigate the influence of noise on the simulation process. We concentrate on errors in the interaction Hamiltonians and consider two generic noise models, (i) timing errors in pairwise interactions and (ii) noisy pairwise interactions described by Master equations of Lindblad form. We analyze and compare the effect of noise for the different simulation methods and propose a way to significantly reduce the influence of noise by making use of entanglement purification together with a teleportation based protocol.

Abstract:
Blue noise refers to sample distributions that are random and well-spaced, with a variety of applications in graphics, geometry, and optimization. However, prior blue noise sampling algorithms typically suffer from the curse-of-dimensionality, especially when striving to cover a domain maximally. This hampers their applicability for high dimensional domains. We present a blue noise sampling method that can achieve high quality and performance across different dimensions. Our key idea is spoke-dart sampling, sampling locally from hyper-annuli centered at prior point samples, using lines, planes, or, more generally, hyperplanes. Spoke-dart sampling is more efficient at high dimensions than the state-of-the-art alternatives: global sampling and advancing front point sampling. Spoke-dart sampling achieves good quality as measured by differential domain spectrum and spatial coverage. In particular, it probabilistically guarantees that each coverage gap is small, whereas global sampling can only guarantee that the sum of gaps is not large. We demonstrate advantages of our method through empirical analysis and applications across dimensions 8 to 23 in Delaunay graphs, global optimization, and motion planning.

Abstract:
Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data into the signal, noise, and indistinguishable subsets. The three-subset categorization is especially relevant under high-dimensionality as a large proportion of signals can be obscured by the large amount of noise. Understanding the three-subset phenomenon is important for the researchers in real applications to design efficient follow-up studies. %For example, candidates belonging to the signal subset may have priority for more focused study, while those in the noise subset can be removed; and, for candidates in the indistinguishable subset, additional data may be collected to further separate weak signals from the noise. We develop an efficient data-driven procedure to identify the three subsets. Theoretical study shows that, under certain conditions, only signals are included in the identified signal subset while the remaining signals are included in the identified indistinguishable subsets with high probability. Moreover, the proposed procedure adapts to the unknown signal intensity, so that the identified indistinguishable subset shrinks with the true indistinguishable subset when signals become stronger. The procedure is examined and compared with methods based on FDR control using Monte Carlo simulation. Further, it is applied successfully in a real-data application to identify genomic variants having different signal intensity.

Abstract:
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional (p > n) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the $\ell_2$-norm of the coefficient vector in high-dimensional linear regression. We derive a novel procedure for this, which is asymptotically correct and produces valid confidence intervals in finite samples as well. The procedure, called EigenPrism, is computationally fast and makes no assumptions on coefficient sparsity or knowledge of the noise level. We investigate the width of the EigenPrism confidence intervals, including a comparison with a Bayesian setting in which our interval is just 5% wider than the Bayes credible interval. We are then able to unify the three aforementioned problems by showing that the EigenPrism procedure with only minor modifications is able to make important contributions to all three. We also investigate the robustness of coverage and find that the method applies in practice and in finite samples much more widely than in the regime covered by the theory. Finally, we apply EigenPrism to a genetic dataset to estimate the genetic signal-to-noise ratio for a number of continuous phenotypes.

Abstract:
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons of a widely observed downward bias of the maximum likelihood estimator of the variance when the data dimension is high. We then propose a bias-corrected estimator using random matrix theory and establish its asymptotic normality. The superiority of the new (bias-corrected) estimator over existing alternatives is first checked by Monte-Carlo experiments with various combinations of $(p, n)$ (dimension and sample size). In order to demonstrate further potential benefits from the results of the paper to general probability PCA analysis, we provide evidence of net improvements in two popular procedures (Ulfarsson and Solo, 2008; Bai and Ng, 2002) for determining the number of principal components when the respective variance estimator proposed by these authors is replaced by the bias-corrected estimator. The new estimator is also used to derive new asymptotics for the related goodness-of-fit statistic under the high-dimensional scheme.

Abstract:
Microscopic current fluctuations are inseparable from conductance. We give an integral account of both quantized conductance and nonequilibrium thermal noise in one-dimensional ballistic wires. Our high-current noise theory opens a very different window on such systems. Central to the role of nonequilibrium ballistic noise is its direct and robust dependence on the statistics of carriers. For, with increasing density, they undergo a marked crossover from classical to strongly degenerate behavior. This is singularly evident where the two-probe conductance shows quantized steps: namely, at the discrete subband-energy thresholds. There the excess thermal noise of field-excited ballistic electrons displays sharp and large peaks, invariably larger than shot noise. Most significant is the nonequilibrium peaks' high sensitivity to inelastic relaxation within the open system. Through that sensitivity, high-current noise provides unique clues to the origin of quantized contact resistance and its evolution towards normal diffusive conduction.