Fast Kalman Filtering and Forward–Backward Smoothing via a Low-Rank Perturbative Approach

Kalman filtering-smoothing is a fundamental tool in statistical time-series analysis. However, standard implementations of the Kalman filter-smoother require O(d³) time and O(d²) space per time step, where d is the dimension of the state variable, and are therefore impractical in high-dimensional problems. In this article we note that if a relatively small number of observations are available per time step, the Kalman equations may be approximated in terms of a low-rank perturbation of the prior state covariance matrix in the absence of any observations. In many cases this approximation may be computed and updated very efficiently (often in just O(k²d) or O(k²d + kdlog?d) time and space per time step, where k is the rank of the perturbation and in general k ? d), using fast methods from numerical linear algebra. We justify our approach and give bounds on the rank of the perturbation as a function of the desired accuracy. For the case of smoothing, we also quantify the error of our algorithm because of the low-rank approximation and show that it can be made arbitrarily low at the expense of a moderate computational cost. We describe applications involving smoothing of spatiotemporal neuroscience data. This article has online supplementary material.     

Room temperature all‐silicon photonic crystal nanocavity light emitting diode at sub‐bandgap wavelengths

Silicon is now firmly established as a high performance photonic material. Its only weakness is the lack of a native electrically driven light emitter that operates CW at room temperature, exhibits a narrow linewidth in the technologically important 1300–1600 nm wavelength window, is small and operates with low power consumption. Here, an electrically pumped all‐silicon nano light source around 1300–1600 nm range is demonstrated at room temperature. Using hydrogen plasma treatment, nano‐scale optically active defects are introduced into silicon, which then feed the photonic crystal nanocavity to enhance the electrically driven emission in a device via Purcell effect. A narrow ( nm) emission line at 1515 nm wavelength with a power density of is observed, which represents the highest spectral power density ever reported from any silicon emitter. A number of possible improvements are also discussed, that make this scheme a very promising light source for optical interconnects and other important silicon photonics applications.     

Cation–Cation Interactions,Magnetic Communication,and Reactivity of the Pentavalent Uranium Ion [U(NtBu)2]+

Communication is important : The dimeric bis(imido) uranium complex [{U(NtBu)₂(I)(tBu₂bpy)}₂] (see picture; U green, N blue, I red) has cation–cation interactions between [U(NR)₂]⁺ ions. This f¹–f¹ system also displays f orbital communication between uranium(V) centers at low temperatures, and can be oxidized to generate uranium(VI) bis(imido) complexes.

     

Generalized degree for classes of finite dimensional upper hemi-continuous mappings in separable Banach spaces

Let E be a real separable Banach space, E^∗ the dual space of E, and Ω⊂E an open bounded subset, and let T:D(T)⊆E→2^E∗ be a finite dimensional upper hemi-continuous mapping with . A generalized degree theory is constructed for such a mapping. This degree is then applied to study the existence of approximate weak solutions to the equation 0∈Tx.     

Multiplicity Results for Second Order Non-Autonomous Singular Dirichlet Systems

In this paper, we establish multiplicity results for second order non-autonomous singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones, and an existence principle proved in Agarwal and O’Regan (J. Differ. Equ. 175:393–414, 2001), which was established using a nonlinear alternative of Leray-Schauder type. Truncation techniques play an important role in the analysis. Some recent results in the literature are generalized and improved.     

Remarkable homology in the electronic spectra of the mixed-valence cation and anion radicals of a conjugated bis(porphyrinyl)butadiyne

The pi-radical cation and anion of the dizinc complex of a bis(triarylporphyrinyl)butadiyne, 1+ and 1-, respectively, display remarkably similar near-IR signatures, with intense bands near 1000 and 2500 nm, as predicted by the appropriate frontier-orbital model for inter-porphyrin coupling across the conjugated bridge.     

Monitoring of headspace total volatile basic nitrogen from selected fish species using reflectance spectroscopic measurements of pH sensitive films

The release of amines from decomposing fish such as trimethylamine (TMA), dimethylamine (DMA) and ammonia, collectively known as total volatile basic nitrogen (TVB-N), are in high enough concentrations in headspace to be monitored by a colour change in a pH-sensitive sensor. A method developed here uses a pH indicator dye physically trapped in a cellulose polymer film to respond to the headspace TVB-N released from selected fish species during spoilage. Two species were selected for analysis on the basis of economic importance and the levels of volatile amines released were followed with time using uv/vis reflectance spectroscopic measurements. The results show that there is a significant increase in the TVB-N content in the headspace of fish samples after an incubation period of 8-12 h for cod and 12-15 h for orange roughy.     

Potential of microemulsion electrokinetic chromatography for the separation of priority endocrine disrupting compounds

This work examines the potential of microemulsion electrokinetic chromatography for the separation of several priority endocrine disrupting compounds (EDCs). The optimised microemulsion system comprised 25 mM phosphate buffer pH 2, 80 mM octane, 900 mM butanol, 200 mM sodium dodecyl sulphate and was further modified with 20% propanol. The use of a low pH buffer resulted in the suppression of electroosmotic flow within the capillary. Reversal of the conventional electrode polarity resulted in faster migration of hydrophobic compounds. Test analytes included the octylphenol, nonylphenol and nonylphenol diethoxylate, which are breakdown products of the alkylphenolic detergents. The synthetic oestrogens diethylstilbestrol and ethynyloestradiol were also included in the separation along with the plastic monomer bisphenol-A. Test analytes were selected due to their reported presence in environmental samples namely industrial and domestic wastewater treatment effluents and sludges. Using the optimised method a separation of six EDCs was achieved within 15 min. The optimised method was then applied to the analysis of a spiked wastewater influent sample with UV detection of all six compounds at 214 nm.