5,553 research outputs found
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
We study the problem of detecting a structured, low-rank signal matrix
corrupted with additive Gaussian noise. This includes clustering in a Gaussian
mixture model, sparse PCA, and submatrix localization. Each of these problems
is conjectured to exhibit a sharp information-theoretic threshold, below which
the signal is too weak for any algorithm to detect. We derive upper and lower
bounds on these thresholds by applying the first and second moment methods to
the likelihood ratio between these "planted models" and null models where the
signal matrix is zero. Our bounds differ by at most a factor of root two when
the rank is large (in the clustering and submatrix localization problems, when
the number of clusters or blocks is large) or the signal matrix is very sparse.
Moreover, our upper bounds show that for each of these problems there is a
significant regime where reliable detection is information- theoretically
possible but where known algorithms such as PCA fail completely, since the
spectrum of the observed matrix is uninformative. This regime is analogous to
the conjectured 'hard but detectable' regime for community detection in sparse
graphs.Comment: For sparse PCA and submatrix localization, we determine the
information-theoretic threshold exactly in the limit where the number of
blocks is large or the signal matrix is very sparse based on a conditional
second moment method, closing the factor of root two gap in the first versio
Ultra-Compact, High-Resolution LADAR System for 3D Imaging
An eye-safe LADAR system weighs under 500 grams and has range resolution of 1 mm at 10 m. This laser uses an adjustable, tiny microelectromechanical system (MEMS) mirror that was made in SiWave to sweep laser frequency. The size of the laser device is small (70x50x13 mm). The LADAR uses all the mature fiber-optic telecommunication technologies in the system, making this innovation an efficient performer. The tiny size and light weight makes the system useful for commercial and industrial applications including surface damage inspections, range measurements, and 3D imaging
B(C\u3csub\u3e6\u3c/sub\u3eF\u3csub\u3e5\u3c/sub\u3e)\u3csub\u3e3\u3c/sub\u3e-promoted tandem silylation and intramolecular hydrosilylation: diastereoselective synthesis of oxasilinanes and oxasilepanes
B(C6F5)3 promotes regio- and stereoselective cyclizations of unsaturated alkoxysilanes to generate oxasilinanes and oxasilepanes. The same products are available directly from alkenols via tandem silylation and hydrosilylation
Unveiling the Neurotechnology Landscape: Scientific Advancements Innovations and Major Trends
Nanoscaled magnon transistor based on stimulated three-magnon splitting
Magnonics is a rapidly growing field, attracting much attention for its
potential applications in data transport and processing. Many individual
magnonic devices have been proposed and realized in laboratories. However, an
integrated magnonic circuit with several separate magnonic elements has yet not
been reported due to the lack of a magnonic amplifier to compensate for
transport and processing losses. The magnon transistor reported in [Nat.
Commun. 5, 4700, (2014)] could only achieve a gain of 1.8, which is
insufficient in many practical cases. Here, we use the stimulated three-magnon
splitting phenomenon to numerically propose a concept of magnon transistor in
which the energy of the gate magnons at 14.6 GHz is directly pumped into the
energy of the source magnons at 4.2 GHz, thus achieving the gain of 9. The
structure is based on the 100 nm wide YIG nano-waveguides, a directional
coupler is used to mix the source and gate magnons, and a dual-band magnonic
crystal is used to filter out the gate and idler magnons at 10.4 GHz frequency.
The magnon transistor preserves the phase of the signal and the design allows
integration into a magnon circuit.Comment: 8 pages, 3 figure
Moving Domain Computational Fluid Dynamics to Interface with an Embryonic Model of Cardiac Morphogenesis
Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP)y1 transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis. © 2013 Lee et al
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