Kernel PCA for multivariate extremes

We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the preimages obtained by kernel PCA, demonstrating that under certain conditions they can effectively identify clusters in the data. We build on these new insights to characterize rigorously the performance of kernel PCA based on an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in extreme value theory and provide a careful analysis in the case where the extremes are generated from a linear factor model. We give theoretical guarantees on the performance of kernel PCA preimages of such extremes by leveraging their asymptotic distribution together with Davis-Kahan perturbation bounds. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods

Two-week joint mobilization intervention improves self-reported function, range of motion, and dynamic balance in those with chronic ankle instability

We examined the effect of a 2-week anterior-to-posterior ankle joint mobilization intervention on weight-bearing dorsiflexion range of motion (ROM), dynamic balance, and self-reported function in subjects with chronic ankle instability (CAI). In this prospective cohort study, subjects received six Maitland Grade III anterior-to-posterior joint mobilization treatments over 2 weeks. Weightbearing dorsiflexion ROM, the anterior, posteromedial, and posterolateral reach directions of the Star Excursion Balance Test (SEBT), and self-reported function on the Foot and Ankle Ability Measure (FAAM) were assessed 1 week before the intervention (baseline), prior to the first treatment (pre-intervention), 24–48 h following the final treatment (post-intervention), and 1 week later (1-week follow-up) in 12 adults (6 males and 6 females) with CAI. The results indicate that dorsiflexion ROM, reach distance in all directions of the SEBT, and the FAAM improved (p < 0.05 for all) in all measures following the intervention compared to those prior to the intervention. No differences were observed in any assessments between the baseline and pre-intervention measures or between the postintervention and 1-week follow-up measures (p > 0.05). These results indicate that the joint mobilization intervention that targeted posterior talar glide was able to improve measures of function in adults with CAI for at least 1 week

Transition states and greedy exploration of the QAOA optimization landscape

The QAOA is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of p layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic intializations were shown to have a good numerical performance, an analytical understanding remains evasive. Inspired by the study of energy landscapes, in this work we focus on so-called transition states (TS) that are saddle points with a unique negative curvature direction that connects to local minima. Starting from a local minimum of QAOA with p layers, we analytically construct 2p + 1 TS for QAOA with p + 1 layers. These TS connect to new local minima, all of which are guaranteed to lower the energy compared to the minimum found for p layers. We introduce a Greedy procedure to effectively maneuver the exponentially increasing number of TS and corresponding local minima. The performance of our procedure matches the best available initialization strategy, and in addition provides a guarantee for the minimal energy to decrease with an increasing number of layers p. Generalization of analytic TS and the Greedy approach to other ans\"atze may provide a universal framework for initialization of variational quantum algorithms.Comment: 5 pages, 4 figures, comments are welcom

Late systolic central hypertension as a predictor of incident heart failure : the Multi-Ethnic Study of Atherosclerosis

Background: Experimental studies demonstrate that high aortic pressure in late systole relative to early systole causes greater myocardial remodeling and dysfunction, for any given absolute peak systolic pressure. Methods and Results: We tested the hypothesis that late systolic hypertension, defined as the ratio of late (last one third of systole) to early (first two thirds of systole) pressure-time integrals (PTI) of the aortic pressure waveform, independently predicts incident heart failure (HF) in the general population. Aortic pressure waveforms were derived from a generalized transfer function applied to the radial pressure waveform recorded noninvasively from 6124 adults. The late/early systolic PTI ratio (L/ESPTI) was assessed as a predictor of incident HF during median 8.5 years of follow-up. The L/ESPTI was predictive of incident HF (hazard ratio per 1% increase= 1.22; 95% CI= 1.15 to 1.29; P58.38%) was more predictive of HF than the presence of hypertension. After adjustment for each other and various predictors of HF, the HR associated with hypertension was 1.39 (95% CI= 0.86 to 2.23; P=0.18), whereas the HR associated with a high L/E was 2.31 (95% CI=1.52 to 3.49; P<0.0001). Conclusions: Independently of the absolute level of peak pressure, late systolic hypertension is strongly associated with incident HF in the general population

Avoiding barren plateaus using classical shadows

Variational quantum algorithms are promising algorithms for achieving quantum advantage on nearterm devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients, which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBPs) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows WBPs to be avoided during the optimization process. This paves the way for efficient barren plateau-free optimization on near-term devices

Electron-Ion Equilibrium and Shock Precursors in the Northeast Limb of the Cygnus Loop

We present an observational study using high-resolution echelle spectroscopy of collisionless shocks in the Cygnus Loop supernova remnant. Measured Hα line profiles constrain pre-shock heating processes, shock speeds, and electron-ion equilibration (Te /Ti ). The shocks produce faint Hα emission line profiles, which are characterized by narrow and broad components. The narrow component is representative of the pre-shock conditions, while the broad component is produced after charge transfer between neutrals entering the shock and protons in the post-shock gas, thus reflecting the properties of the post-shock gas. We observe a diffuse Hα region extending about 25 ahead of the shock with line width ~29 km s–1, while the Hα profile of the shock itself consists of broader than expected narrow (36 km s–1) and broad (250 km s–1) components. The observed diffuse emission arises in a photoionization precursor heated to about 18,000 K by He I and He II emission from the shock, with additional narrow component broadening originating from a thin cosmic-ray precursor. Broad to narrow component intensity ratios of ~1.0 imply full electron-ion temperature equilibration Te Ti in the post-shock region. Broad component line widths indicate shock velocities of about 400 km s–1. Combining the shock velocities with proper motions suggests that the distance to the Cygnus Loop is ~890 pc, significantly greater than the generally accepted upper limit of 637 pc

Increased diversity of libraries from libraries: chemoinformatic analysis of bis-diazacyclic libraries

Combinatorial libraries continue to play a key role in drug discovery. To increase structural diversity, several experimental methods have been developed. However, limited efforts have been performed so far to quantify the diversity of the broadly used diversity-oriented synthetic (DOS) libraries. Herein we report a comprehensive characterization of 15 bis-diazacyclic combinatorial libraries obtained through libraries from libraries, which is a DOS approach. Using MACCS keys, radial and different pharmacophoric fingerprints as well as six molecular properties, it was demonstrated the increased structural and property diversity of the libraries from libraries over the individual libraries. Comparison of the libraries to existing drugs, NCI Diversity and the Molecular Libraries Small Molecule Repository revealed the structural uniqueness of the combinatorial libraries (mean similarity < 0.5 for any fingerprint representation). In particular, bis-cyclic thiourea libraries were the most structurally dissimilar to drugs retaining drug-like character in property space. This study represents the first comprehensive quantification of the diversity of libraries from libraries providing a solid quantitative approach to compare and contrast the diversity of DOS libraries with existing drugs or any other compound collection

Desarrollo experimental de controladores Fuzzy para procesos térmicos y neumáticos

In this project, a Fuzzy control system is proposed in an industrial process training module with two independent systems between them, one thermal and the other pneumatic. The control algorithm is developed in Python language v3.6 executed by a Raspberry Pi B+, both controllers depend on the error and change in error that are updated in times of 2 s and 1 s, for temperature and pressure respectively, communication with the plants uses A/D and D/A converters, the thermal Fuzzy was analyzed with three temperature references [50,100 and 150]°C, with a rise time of 191 s, 360 s and 505 s; steady state error of 5.5%, 0.7% y 0.7%, in the pneumatic system the speed of change between references is evaluated from 10 psi to 15 psi varying the activation of the compressor at the beginning of the&nbsp;experiments, the settling times obtained are 111 s and 106 s, with the compressor off the result is 116 s and 88 s, besides a maximum excess of 13% with inherent oscillations to the type system that are in an acceptable range.&nbsp;En este proyecto, se propone un sistema de control Fuzzy en un módulo de entrenamiento de procesos industriales con dos sistemas independientes entre sí, uno térmico y otro neumático, el algoritmo de control se desarrolla en lenguaje Python v3.6 ejecutado por una Raspberry Pi B+, ambos controladores dependen del error y cambio en el error que se actualizan en tiempos de 2 s y 1 s, para temperatura y presión respectivamente, la comunicación con las plantas emplea conversores A/D y D/A, el Fuzzy térmico se analizo con tres referencias de temperatura [50,100 y 150]°C, con un tiempo de subida de 191 s, 360 s y 505 s; error de estado estacionario de 5.5 %, 0.7% y 0.7 %, en el sistema neumático se evalúo la velocidad de cambio entre referencias de 10 psi a 15 psi variando la activación del compresor al inicio de los experimentos, los tiempos de asentamiento que se obtienen son 111 s y 106 s, con el compresor apagado el resultado es de 116 s y 88 s, además de un sobrepaso máximo de 13% con oscilaciones inherentes al tipo sistema que se encuentran en un rango aceptable.&nbsp