Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.

Estimated detection distance of a baiji's (Chinese river dolphin, Lipotes vexillifer) whistles using a passive acoustic survey method

Source levels and phonation intervals of whistles produced by a free-ranging baiji (Chinese river dolphin) were measured in the seminatural reserve of Shishou in Hubei, China. A total of 43 whistles were recorded over 12 recording sessions. The mean dominant frequency (the frequency at the highest energy) was 5.7 kHz (s.d.=0.67). The calculated source level was 143.2 dB rms re 1 mu Pa (s.d.=5.8). Most phonation intervals were shorter than 460 s, and the average interval was 205 s (s.d. = 254). Theoretical detection range of baiji's whistle was 6600 m at the present study site, but it could reduce a couple of hundred meters in practical noisy situation in the Yangtze River. Sporadic phonation (205 s interval on average) with relatively faint signal of baiji was considered, to be difficult to be detected by a towing hydrophone system. Stationed monitoring or slow speed towing of hydrophones along the river current is recommended. (c) 2006 Acoustical Society of America.

Single-mode behaviour judgment of optical waveguides by imaginary-distance beam propagation method under perfectly matched layer boundary condition

Imaginary-distance beam propagation method under the perfectly matched layer boundary condition is applied to judge single-mode behaviour of optical waveguides, for the first time to our knowledge. A new kind of silicon-on-insulator-based rib structures with half-circle cross-section is presented. The single-mode behaviour of this kind of waveguide with radius 2mum is investigated by this method. It is single-mode when the slab height is not smaller than the radius.

An algorithm of analysis tools on points distribution in high dimension space: The distance of a point and an infinite sub-space

This paper discusses the algorithm on the distance from a point and an infinite sub-space in high dimensional space With the development of Information Geometry([1]), the analysis tools of points distribution in high dimension space, as a measure of calculability, draw more attention of experts of pattern recognition. By the assistance of these tools, Geometrical properties of sets of samples in high-dimensional structures are studied, under guidance of the established properties and theorems in high-dimensional geometry.

Optimal distance from high power laser diode to cylindrical microlens in a coupling system

In a practical coupling system, a cylindrical microlens is used to collimate the emission of a high powerlaser diode (LD) in the dimension perpendicular to the junction plane. Using passive alignment, the LD isplaced in the focus of the cylindrical microlens generally, regardless of the performance of the multimodeoptical fiber and the LD. In this paper, a more complete analysis is arrived at by ray-tracing technique,by which the angle θ of the ray after refraction is computed as a function of the angle θo of the ray beforerefraction. The focus of the cylindrical microlens is not always the optimal position of the LD. In fact, inorder to achieve a higher coupling efficiency, the optimal distance from the LD to the cylindrical microlensis dependent on not only the radius R and the index of refraction n of the cylindrical microlens, but alsothe divergence angle of the LD in the dimension perpendicular to the junction plane and the numericalaperture (NA) of the multimode optical fiber. The results of this discussion are in good agreement withexperimental results.

Real-time far distance micro-vibration measurement using an external cavity semiconductor laser interferometer with a feedback control system

An external cavity semiconductor laser interferometer used to measure far distance micro-vibration in real time is proposed. In the interferometer, a single longitudinal mode and excellent coherent characteristic grating external cavity semiconductor laser is constructed and acted as a light source and a phase compensator. Its coherent length exceeds 200 meters. The angle between normal and incidence beam of the far object is allowed to change in definite range during the measurement with this interferometer, and this makes the far distance interference measurement easier and more convenient. Also, it is not required to keep the amplitudes of the first and second harmonic components equal, and then the dynamic range is increased. A feedback control system is used to compensate the phase disturbance between the two interference beams introduced by environmental vibration.

Drift distance survey in direct plasma injection scheme for high current beam production

In a laser ion source, plasma drift distance is one of the most important design parameters. Ion current density and beam pulse width are defined by plasma drift distance between a laser target and beam extraction position. In direct plasma injection scheme, which uses a laser ion source and a radio frequency quadrupole linac, we can apply relatively higher electric field at beam extraction due to the unique shape of a positively biased electrode. However, when we aim at very high current acceleration such as several tens of milliamperes, we observed mismatched beam extraction conditions. We tested three different ion current at ion extraction region by changing plasma drift distance to study better extraction condition. In this experiment, C6+ beam was accelerated. We confirmed that matching condition can be improved by controlling plasma drift distance.

Dinoflagellate Cysts as Indicators of Cultural Eutrophication in the Oslofjord, Norway

Dinoflagellate cyst records were analysed from four sediment cores from the inner Oslofjord. The cores covered the pre-industrial period, and the most important period of human population growth associated with industrial development of the region, from the mid-1800s to the present, including the reported development of cultural eutrophication. Comparisons between the cyst records and the known history of eutrophication suggest cyst signals that should prove useful for tracing the development of eutrophication. The eutrophication signal consisted of a doubling of total cyst concentration, and a marked increase in one species in particular,Lingulodinium machaerophorum(from <5 to around 50% of the assemblages) with increased eutrophication. In the core considered most representative of general water quality in the inner fjord, these trends reversed back to pre-industrial levels during the 1980s and 1990s when improved sewage treatment took effect.