Empirical Bayes and Full Bayes for Signal Estimation

We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach and a full Bayes (FB) approach. We then apply EB and FB to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian channel within an approximate message passing (AMP) framework. Our numerical results show that FB achieves better performance than EB in scalar channel denoising problems when the signal dimension is small. In the CS setting, the signal dimension must be large enough for AMP to work well; for large signal dimensions, AMP has similar performance with FB and EB.Comment: This work was presented at the Information Theory and Application workshop (ITA), San Diego, CA, Feb. 201

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $\eta=1$ and $\eta=0.5$ are investigated for fixed ratio of roughness height to displacement boundary layer thickness $h/\delta^*=2.86$. Global stability analysis is able to capture the frequency of the primary vortical structures. For $\eta=1$, only varicose instability is seen. For the thinner roughness element ($\eta=0.5$), the varicose instability dominates the sinuous instability, and the sinuous instability becomes more pronounced as $Re_h$ increases, due to increased spanwise shear in the near-wake region. The unstable modes mainly extract energy from the central streak, although the lateral streaks also contribute. The DNS results show that different instability features lead to different behavior and development of vortical structures in the nonlinear transition process. For $\eta=1$, the varicose mode is associated with the shedding of hairpin vortices. As $Re_h$ increases, the breakdown of hairpin vortices occurs closer to the roughness and sinuous breakdown behavior promoting transition to turbulence is seen in the farther wake. A fully-developed turbulent flow is established in both the inner and outer layers farther downstream when $Re_h$ is sufficiently high. For $\eta=0.5$, the sinuous wiggling of hairpin vortices is prominent at higher $Re_h$, leading to stronger interactions in the near wake, as a result of combined varicose and sinuous instabilities. A sinuous mode captured by dynamic mode decomposition (DMD) analysis, and associated with the `wiggling' of streaks persists far downstream

Failure of Aileron Control Cable in Ajeet Aircraft MK-E-2015

The Aileron control cable of an Ajeet aircraft was found snapped . On ootical and scanning electron microscopic examination, it was found that the majority of the strands of the cable had thinned due to excessive contact wear with a oulley and subsequently failed in tension

Recomended for You: The Impact of Profit Incentives on the Relevance of Online Recommendations

Recommender systems are commonly used by Internet firms to improve consumers’ shopping experience and increase firm sales and profits. A large stream of work on recommender design has studied the problem of identifying the most relevant items to recommend to users. In parallel, recent empirical work has started to provide evidence that real-world recommenders contribute to increased sales and profitability for the firms. However, maximizing consumer welfare and firm profit are not the same. Given that recommenders impact sales and profits, a natural question is what is the impact of firm’s profit incentives on recommender design? This paper studies optimal recommender design in a profit-maximizing framework to answer the question and identifies the conditions under which a profit-maximizing recommender recommends the item with highest margins and those under which it recommends the most relevant item. We further elaborate on the social cost of the mismatch between consumer and firm incentives

Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\"acklund transformations of the linear form and some special cases are considered.Comment: 14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the original latex file is not complet

Investigation of aileron control cable failure of a Pushpak aircraft

This is an investigation on the failure of aileron control cable in a Pushpak aircraft carried out at the request of the Deputy Director General of Civil Aviation. The nature of failure is analysed

Catalytic Enantioselective Stereoablative Alkylation of 3-Halooxindoles: Facile Access to Oxindoles with C3 All-Carbon Quaternary Stereocenters

From 2 to 1! Racemic tertiary halooxindoles proceed to enantioenriched oxindoles bearing all-carbon quaternary stereocenters as a result of a catalytic enantioselective stereoablative process (see scheme). The application of this procedure allows for the rapid asymmetric construction of biologically significant alkaloid core motifs

Super-Yang-Mills and M5-branes

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $\eta^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $\eta^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE

Clearer Frames, Anytime: Resolving Velocity Ambiguity in Video Frame Interpolation

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.Comment: Project page: https://zzh-tech.github.io/InterpAny-Clearer/ ; Code: https://github.com/zzh-tech/InterpAny-Cleare

Spin-valley locking for in-gap quantum dots in a MoS2 transistor

Spins confined to atomically-thin semiconductors are being actively explored as quantum information carriers. In transition metal dichalcogenides (TMDCs), the hexagonal crystal lattice gives rise to an additional valley degree of freedom with spin-valley locking and potentially enhanced spin life- and coherence times. However, realizing well-separated single-particle levels, and achieving transparent electrical contact to address them has remained challenging. Here, we report well-defined spin states in a few-layer MoS$_2$ transistor, characterized with a spectral resolution of $\sim{50~\mu}$eV at ${T_\textrm{el} = 150}$~mK. Ground state magnetospectroscopy confirms a finite Berry-curvature induced coupling of spin and valley, reflected in a pronounced Zeeman anisotropy, with a large out-of-plane $g$-factor of ${g_\perp \simeq 8}$. A finite in-plane $g$-factor (${g_\parallel \simeq 0.55-0.8}$) allows us to quantify spin-valley locking and estimate the spin-orbit splitting ${2\Delta_{\rm SO} \sim 100~\mu}$eV. The demonstration of spin-valley locking is an important milestone towards realizing spin-valley quantum bits.Comment: 7 pages, 3 figure