Using an imperfect photonic network to implement random unitaries

We numerically investigate the implementation of Haar-random unitarity transformations and Fourier transformations in photonic devices consisting of beam splitters and phase shifters, which are used for integrated photonics implementations of boson sampling. The distribution of reflectivities required to implement an arbitrary unitary transformation is skewed towards low values, and this skew becomes stronger the larger the number of modes. A realistic implementation using Mach-Zehnder interferometers is incapable of achieving the low values required and thus has limited fidelity. We show that numerical optimisation and adding extra beam splitters to the network can help to restore fidelity

An Exact No Free Lunch Theorem for Community Detection

A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss function and the problem domain. The loss function computes an expectation over only a subset of the universe of possible outputs; thus, it is only asymptotically appropriate with respect to the problem size. By using the correct random model for the problem domain, we provide a stronger, exact No Free Lunch theorem for community detection. The claim generalizes to other set-partitioning tasks including core/periphery separation, $k$-clustering, and graph partitioning. Finally, we review the literature of proposed evaluation functions and identify functions which (perhaps with slight modifications) are compatible with an exact No Free Lunch theorem

Locomotor adaptability in persons with unilateral transtibial amputation

Background Locomotor adaptation enables walkers to modify strategies when faced with challenging walking conditions. While a variety of neurological injuries can impair locomotor adaptability, the effect of a lower extremity amputation on adaptability is poorly understood. Objective Determine if locomotor adaptability is impaired in persons with unilateral transtibial amputation (TTA). Methods The locomotor adaptability of 10 persons with a TTA and 8 persons without an amputation was tested while walking on a split-belt treadmill with the parallel belts running at the same (tied) or different (split) speeds. In the split condition, participants walked for 15 minutes with the respective belts moving at 0.5 m/s and 1.5 m/s. Temporal spatial symmetry measures were used to evaluate reactive accommodations to the perturbation, and the adaptive/de-adaptive response. Results Persons with TTA and the reference group of persons without amputation both demonstrated highly symmetric walking at baseline. During the split adaptation and tied post-adaptation walking both groups responded with the expected reactive accommodations. Likewise, adaptive and de-adaptive responses were observed. The magnitude and rate of change in the adaptive and de-adaptive responses were similar for persons with TTA and those without an amputation. Furthermore, adaptability was no different based on belt assignment for the prosthetic limb during split adaptation walking. Conclusions Reactive changes and locomotor adaptation in response to a challenging and novel walking condition were similar in persons with TTA to those without an amputation. Results suggest persons with TTA have the capacity to modify locomotor strategies to meet the demands of most walking conditions despite challenges imposed by an amputation and use of a prosthetic limb

Isokinetic muscle function comparison of lower limbs among elderly fallers and non-fallers

O objetivo deste estudo foi identificar se há diferenças entre o desempenho muscular de tornozelo, joelho e quadril em idosos com e sem relato de queda nos últimos seis meses. Foram incluídos 81 idosos com 65 anos ou mais: 56 negaram quedas (G1) e 25 relataram quedas (G2). Utilizou-se o questionário perfil de atividade humana para medir o nível de atividade física, e o dinamômetro isocinético para mensurar os parâmetros físicos da função muscular. Os grupos não diferiram entre si em relação à idade (p=0,925), duração (p=0,065) e frequência (p=0,302) da prática do exercício físico, índice de massa corpórea (p=0,995) e nível de atividade física (p=0,561). O G2 apresentou menor desempenho para as variáveis pico de torque de flexão e extensão de joelho esquerdo (p=0,027 e p=0,030, respectivamente) e trabalho por peso corporal (p=0,040) de flexão de joelho esquerdo a 60°/s; pico de torque e trabalho por peso corporal de flexão e extensão de joelho a 180°/s bilateralmente (p<0,050); e potência média de flexão de joelhos direito e esquerdo (p=0,030). A maioria das variáveis do tornozelo e quadril não apresentou diferenças entre os grupos. Apenas a variável pico de torque de extensão de quadril esquerdo foi significativamente maior no G1 (p=0,035). É importante considerar a função muscular do joelho na avaliação clínica de idosos para direcionar a intervenção terapêutica e a prevenção de quedas.The aim of this study was to identify whether there are differences between the performance of muscular groups of ankle, knee and hip among elderly people who didn't have falls and individuals who reported falls in the last six months. The study included 81 elderly aged 65 or older: 56 non-faller subjects (G1) and 25 faaller subjects (G2). To obtain the level of physical activity, the questionnaire Human Activity Profile was used, and the muscle function of the lower limbs was assessed using isokinetic dynamometer. The groups did not differ regarding age (p=0.925), duration (p=0.065) and frequency (p=0.302) of the practice of physical exercise, body mass index (BMI) (p=0.995) and level of physical activity (p=0.561). The G2 showed a lower performance of peak torque of left knee flexion and extension (p=0.027 and p=0.030, respectively) and work proportional to body weight (p=0.040) of left knee flexion at 60°/s; peak torque and work proportional to body weight of bilaterally knee flexion and extension at 180°/s (p<0.05) and average power of right and left knee extension (p=0.03). Most variables of ankle and hip joints did not differ between groups. Only peak torque of left hip extension was significantly higher in the non-faller group (p=0.035). It is important to consider knee muscle function in the clinical evaluation of elderly in order to make the intervention more assertive and thus to prevent falls

Super Weyl invariance: BPS equations from heterotic worldsheets

It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider the RNS-formulation of the heterotic string with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that the cancellation of the Weyl anomaly combined with (2,0) finiteness implies the heterotic BPS conditions: At the one loop level the geometry is required to be conformally balanced and the gauge background has to satisfy the Hermitean Yang-Mills equations.Comment: 1+31 pages LaTeX, 5 figures; final version, discussion relation Weyl invariance and (2,0) finiteness extended, typos correcte

Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking

<p>Abstract</p> <p>Background</p> <p>Motorized treadmills are widely used in research or in clinical therapy. Small kinematics, kinetics and energetics changes induced by Treadmill Walking (TW) as compared to Overground Walking (OW) have been reported in literature. The purpose of the present study was to characterize the differences between OW and TW in terms of stride-to-stride variability. Classical (Standard Deviation, SD) and non-linear (fractal dynamics, local dynamic stability) methods were used. In addition, the correlations between the different variability indexes were analyzed.</p> <p>Methods</p> <p>Twenty healthy subjects performed 10 min TW and OW in a random sequence. A triaxial accelerometer recorded trunk accelerations. Kinematic variability was computed as the average SD (MeanSD) of acceleration patterns among standardized strides. Fractal dynamics (scaling exponent α) was assessed by Detrended Fluctuation Analysis (DFA) of stride intervals. Short-term and long-term dynamic stability were estimated by computing the maximal Lyapunov exponents of acceleration signals.</p> <p>Results</p> <p>TW did not modify kinematic gait variability as compared to OW (multivariate T², p = 0.87). Conversely, TW significantly modified fractal dynamics (t-test, p = 0.01), and both short and long term local dynamic stability (T²p = 0.0002). No relationship was observed between variability indexes with the exception of significant negative correlation between MeanSD and dynamic stability in TW (3 × 6 canonical correlation, r = 0.94).</p> <p>Conclusions</p> <p>Treadmill induced a less correlated pattern in the stride intervals and increased gait stability, but did not modify kinematic variability in healthy subjects. This could be due to changes in perceptual information induced by treadmill walking that would affect locomotor control of the gait and hence specifically alter non-linear dependencies among consecutive strides. Consequently, the type of walking (i.e. treadmill or overground) is important to consider in each protocol design.</p

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability

Metrics matter in community detection

We present a critical evaluation of normalized mutual information (NMI) as an evaluation metric for community detection. NMI exaggerates the leximin method's performance on weak communities: Does leximin, in finding the trivial singletons clustering, truly outperform eight other community detection methods? Three NMI improvements from the literature are AMI, rrNMI, and cNMI. We show equivalences under relevant random models, and for evaluating community detection, we advise one-sided AMI under the $\mathbb{M}_{\mathrm{all}}$ model (all partitions of $n$ nodes). This work seeks (1) to start a conversation on robust measurements, and (2) to advocate evaluations which do not give "free lunch"