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

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

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

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde

Invaders in hot water: a simple decontamination method to prevent the accidental spread of aquatic invasive non-native species.

Watersports equipment can act as a vector for the introduction and spread of invasive non native species (INNS) in freshwater environments. To support advice given to recreational water users under the UK Government’s Check Clean Dry biosecurity campaign and ensure its effectiveness at killing a range of aquatic INNS, we conducted a survival experiment on seven INNS which pose a high risk to UK freshwaters. The efficacy of exposure to hot water (45 °C, 15 min) was tested as a method by which waters users could ‘clean’ their equipment and was compared to drying and a control group (no treatment). Hot water had caused 99 % mortality across all species 1 h after treatment and was more effective than drying at all time points (1 h: χ2 = 117.24, p < 0.001; 1 day χ2 = 95.68, p < 0.001; 8 days χ2 = 12.16, p < 0.001 and 16 days χ2 = 7.58, p < 0.001). Drying caused significantly higher mortality than the control (no action) from day 4 (χ2 = 8.49, p < 0.01) onwards. In the absence of hot water or drying, 6/7 of these species survived for 16 days, highlighting the importance of good biosecurity practice to reduce the risk of accidental spread. In an additional experiment the minimum lethal temperature and exposure time in hot water to cause 100 % mortality in American signal crayfish (Pacifastacus leniusculus), was determined to be 5 min at 40 °C. Hot water provides a simple, rapid and effective method to clean equipment. We recommend that it is advocated in future biosecurity awareness campaigns

The effects of walking speed on minimum toe clearance and on the temporal relationship between minimum clearance and peak swing-foot velocity in unilateral trans-tibial amputees

yesBackground: Minimum toe clearance is a critical gait event because it coincides with peak forward velocity of the swing foot, and thus, there is an increased risk of tripping and falling. Trans-tibial amputees have increased risk of tripping compared to able-bodied individuals. Assessment of toe clearance during gait is thus clinically relevant. In able-bodied gait, minimum toe clearance increases with faster walking speeds, and it is widely reported that there is synchronicity between when peak swing-foot velocity and minimum toe clearance occur. There are no such studies involving lower-limb amputees. Objectives: To determine the effects of walking speed on minimum toe clearance and on the temporal relationship between clearance and peak swing-foot velocity in unilateral trans-tibial amputees. Study design: Cross-sectional. Methods: A total of 10 trans-tibial participants walked at slow, customary and fast speeds. Minimum toe clearance and the timings of minimum toe clearance and peak swing-foot velocity were determined and compared between intact and prosthetic sides. Results: Minimum toe clearance was reduced on the prosthetic side and, unlike on the intact side, did not increase with walking speed increase. Peak swing-foot velocity consistently occurred (~0.014 s) after point of minimum toe clearance on both limbs across all walking speeds, but there was no significant difference in the toe–ground clearance between the two events. Conclusion: The absence of speed related increases in minimum toe clearance on the prosthetic side suggests that speed related modulation of toe clearance for an intact limb typically occurs at the swing-limb ankle. The temporal consistency between peak foot velocity and minimum toe clearance on each limb suggests that swing-phase inter-segmental coordination is unaffected by trans-tibial amputation. Clinical relevance The lack of increase in minimum toe clearance on the prosthetic side at higher walking speeds may potentially increase risk of tripping. Findings indicate that determining the instant of peak swing-foot velocity will also consistently identify when/where minimum toe clearance occurs

Fractal analyses reveal independent complexity and predictability of gait

Locomotion is a natural task that has been assessed for decades and used as a proxy to highlight impairments of various origins. So far, most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent α and the Minkowski fractal dimension D were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. We show that α and D accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity (D) and hence, adaptability. In contrast, walking backward and/or stimulation of the vestibular system decreased D. Furthermore, walking backward increased predictability (α) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures

An evoked potential mapping of transcallosal projections in the cat

In ten adult cats anesthetized with ketamine hydrochloride the neocortex was exposed and rectangular pulses (1msec, 0.5 Hz and variable intensity) were applied to discrete points of one side and transcallosal evoked potentials were recorded from the other. The stimulation and recording positions were determined on a cartesian map of most of the exposable neocortical areas and the potentials were analysed as to their components, voltage and latency. Passive spread and electrotonic potentials and the effects of increasing frequency were also analysed. The results showed large transcallosal potentials in some areas and an increase of potentials in the caudorostral direction, attaining the highest values in anteromedial areas of the suprasylvian gyrus. Confirming anatomical studies, a few silent spots were found in the motor and somesthetic cortex and in restricted posterior regions of the visual cortex, where small or zero voltages occurred. While causing weak contralateral potentials, stimulation of some posterior sites provoked high voltage potentials in anterior regions of the side being stimulated and in the corresponding area of the opposite site. These posterior sites are. poorly interconnected by the corpus callosum. The L-shaped indirect connection described in this work may be involved in some types of epilepsy and may explain the effectiveness of partial callosotomy in their treatment

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