A law of large numbers for finite‐range dependent random matrices

We consider random Hermitian matrices in which distant above‐diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has an algebraic Stieltjes transform by an argument based on dimension theory of Noetherian local rings. © 2008 Wiley Periodicals, Inc.     

Shape-driven segmentation of the arterial wall in intravascular ultrasound images

Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3-D reconstruction, and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior, we utilize an intensity prior through a nonparametric probability-density-based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach.     

Discovering Higher-Order Interactions Through Neural Information Decomposition

If regularity in data takes the form of higher-order functions among groups of variables, models which are biased towards lower-order functions may easily mistake the data for noise. To distinguish whether this is the case, one must be able to quantify the contribution of different orders of dependence to the total information. Recent work in information theory attempts to do this through measures of multivariate mutual information (MMI) and information decomposition (ID). Despite substantial theoretical progress, practical issues related to tractability and learnability of higher-order functions are still largely unaddressed. In this work, we introduce a new approach to information decomposition—termed Neural Information Decomposition (NID)—which is both theoretically grounded, and can be efficiently estimated in practice using neural networks. We show on synthetic data that NID can learn to distinguish higher-order functions from noise, while many unsupervised probability models cannot. Additionally, we demonstrate the usefulness of this framework as a tool for exploring biological and artificial neural networks.     

Linear 6,6'-biazulenyl framework featuring isocyanide termini: synthesis, structure, redox behavior, complexation, and self-assembly on Au(111)

The key step in accessing the title species (5), the first nonbenzenoid diisocyanobiaryl, involved an unexpected homocoupling of a 6-bromoazulene derivative. The reversible 2e(-) reduction of 5 was addressed electrochemically and computationally. The shifts in energies of the S(0)→S(1) and S(0)→S(2) transitions for a series of related 6,6'-biazulenyl derivatives correlate with the e(-)-donating/-withdrawing strength of their 2,2'-substituents but follow opposite trends. Species 5 adsorbs end-on (η(1)) to the Au(111) surface via one of its -NC groups to form a 2-nm-thick film. In addition, bimetallic coordination of 5's -NC termini can be readily achieved.     

Method for the direct determination of available carbohydrates in low-carbohydrate products using high-performance anion exchange chromatography

An improved method for direct determination of available carbohydrates in low-level products has been developed and validated for a low-carbohydrate soy infant formula. The method involves modification of an existing direct determination method to improve specificity, accuracy, detection levels, and run times through a more extensive enzymatic digestion to capture all available (or potentially available) carbohydrates. The digestion hydrolyzes all common sugars, starch, and starch derivatives down to their monosaccharide components, glucose, fructose, and galactose, which are then quantitated by high-performance anion-exchange chromatography with photodiode array detection. Method validation consisted of specificity testing and 10 days of analyzing various spike levels of mixed sugars, maltodextrin, and corn starch. The overall RSD was 4.0% across all sample types, which contained within-day and day-to-day components of 3.6 and 3.4%, respectively. Overall average recovery was 99.4% (n = 10). Average recovery for individual spiked samples ranged from 94.1 to 106% (n = 10). It is expected that the method could be applied to a variety of low-carbohydrate foods and beverages.     

Preparation and evaluation of solid-phase microextraction fibres based on functionalized latex nanoparticle coatings for trace analysis of inorganic anions

The use of a functionalized latex nanoparticle coating as a new sorbent phase for solid-phase microextraction (SPME) was examined. By means of electrostatic absorption onto ionized silanol groups, a fused-silica rod was coated with polymeric nanoparticles functionalized with quaternary ammonium groups. Optimum conditions for the preparation of the coated fibre are presented. The fibre was used for the extraction of a mixture of seven anions from water samples which are analysed by coupling the SPME fibre to an ion chromatographic system via a special interface. The results obtained proved the suitability of this novel coating as a new SPME fibre. A linear calibration for the target analytes was achieved over the concentration range from 5 μg L⁻¹ to 5 mg L⁻¹ (r² > 0.988), while limits of detection for these ions were all below 3.7 μg L⁻¹ (S/N = 3). The reproducibility of a single fibre (n = 4) under similar conditions was between 7 and 12%, while the fibre to fibre reproducibility (n = 5) was between 8.9 and 14%.     

Analysis of Current–Voltage Measurements on Long-Wavelength HgCdTe Photodiodes Fabricated on Si Composite Substrates

We have performed a detailed study of dark current versus voltage to understand existing limitations in dark current and address the nonuniformity of dark current in devices fabricated on HgCdTe grown on silicon substrates. One interesting observation is that trap-assisted tunneling, g-r currents, are not found close to zero bias in certain devices. Devices from the low end of the R ₀ A distribution show heavy shunting paths close to zero bias. We believe that these shunting paths may be the limiting cause of tail distributions in fabricated focal plane array tail distributions. Possible causes for these shunting paths are surface charges associated with dislocation cores and impurity gettering at dislocation cores. The measured non-anti-reflection (AR)-coated quantum efficiency (QE) was 0.576 at 78 K and displays the classical response versus wavelength. The measured QE on isolated single devices is consistent with the 256 × 256 focal-plane array mean QE. Obtained average dark currents are on the order of mid 10⁻⁵ A cm^–2, which is one order of magnitude higher than dark currents obtained from arrays on lattice-matched substrates. On average, arrays on lattice-mismatched substrates show performance characteristics inferior to those of arrays fabricated on lattice-matched substrates. This inferior performance is due to array pixel operability, as can be seen from the tail of the distribution and the average dark currents, which are one order of magnitude higher than those obtained on lattice-matched substrates.     

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (P(fold)=0.5). Using results for the forced unfolding of a RNA hairpin, an exactly soluble model, and an analytic theory, we show that P(fold) is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and a leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.     

On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion

The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen (2005) and subsequently used by others to study the L²$L^2$ and L³$L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional Brownian motion (fBm) was introduced in Yan et al. (2008); however, the definition given there presents difficulties, since it is motivated by an incorrect application of the fractional Itô formula. To rectify this, we introduce a modified DSLT for fBm and prove existence using an explicit Wiener chaos expansion. We will then argue that our modification is the natural version of the DSLT by rigorously proving the corresponding Tanaka formula. This formula corrects a formal identity given in both Rosen (2005) and Yan et al. (2008). In the course of this endeavor we prove a Fubini theorem for integrals with respect to fBm. The Fubini theorem may be of independent interest, as it generalizes (to Hida distributions) similar results previously seen in the literature. As a further byproduct of our investigation, we also provide a small correction to an important technical second-moment bound for fBm which has appeared in the literature many times.