Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz invariant bilinears in the field strength. More generally we prove a theorem regarding certain solutions of unilateral matrix equations of arbitrary order. For solutions which have perturbative expansions in the matrix coefficients, the solution and all its positive powers are sums of terms which are symmetrized in all the matrix coefficients and of terms which are commutators.Comment: 9 pages, LaTeX, no figures, theorem generalized and a new method of proof include

Closed Geodesics on Godel-type Backgrounds

We consider radial oscillations of supertube probes in the Godel-type background which is U-dual to the compactified pp-wave obtained from the Penrose limit of the NS five-brane near horizon geometry. The supertube probe computation can be carried over directly to a string probe calculation on the U-dual background. The classical equations of motion are solved explicitly. In general, the probe is not restricted to travel unidirectionally through any global time coordinate. In particular, we find geodesics that close.Comment: latex, 15 pages, 1 figure. v3: reference added, clarifications added and some discussions expande

Dualities in M-theory and Born-Infeld Theory

We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime

Nonlinear Self-Duality in Even Dimensions

We show that the Born-Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n,n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then introduce a new reality structure leading to a Born-Infeld theory with n real fields and an Sp(2n,R) duality symmetry. The real and complex constructions are extended to arbitrary even dimensions. The maximal noncompact duality group is U(n,n) for complex fields. For real fields the duality group is Sp(2n,R) if half of the dimension of space-time is even and O(n,n) if it is odd. We also discuss duality under the maximal compact subgroup, which is the self-duality group of the theory obtained by fixing the expectation value of a scalar field. Supersymmetric versions of self-dual theories in four dimensions are also discussed.Comment: LaTeX file, 29 pages, expanded discussion in Section

Dualities of the Matrix Model from T-Duality of the Type II String

We investigate in the Matrix theory framework, the subgroup of dualities of the DLCQ of M-theory compactified on three-tori, which corresponds to T-duality in the auxiliary Type II string theory. We show how these dualities are realized in the supersymmetric Yang-Mills gauge theories on dual noncommutative three-tori.Comment: 37 pages, LaTeX, no figures, typos correcte

Using collision cones to assess biological deconfliction methods

Biological systems consistently outperform autonomous systems governed by engineered algorithms in their ability to reactively avoid collisions. To better understand this discrepancy, a collision avoidance algorithm was applied to frames of digitized video trajectory data from bats, swallows and fish (Myotis velifer, Petrochelidon pyrrhonota and Danio aequipinnatus). Information available from visual cues, specifically relative position and velocity, was provided to the algorithm which used this information to define collision cones that allowed the algorithm to find a safe velocity requiring minimal deviation from the original velocity. The subset of obstacles provided to the algorithm was determined by the animal's sensing range in terms of metric and topological distance. The algorithmic calculated velocities showed good agreement with observed biological velocities, indicating that the algorithm was an informative basis for comparison with the three species and could potentially be improved for engineered applications with further study

Sexual Selection, Physical Attractiveness, and Facial Neoteny: Cross-cultural Evidence and Implications [and Comments and Reply]

Physical attractiveness and its relation to the theory of sexual selection deserve renewed attention from cultural and biological anthropologists. This paper focuses on an anomaly associated with physical attractiveness-in our species, in contrast to many others, males seem to be more concerned than females with the attractiveness of potential sexual partners, perhaps because humans show far more age-related variance in female than in male fecundity. The resulting selection for male attraction to markers of female youth may lead incidentally to attraction to females displaying age-related cues in an exaggerated form. This paper reports cross-cultural evidence that males in five populations (Brazilians, U.S. Americans, Russians, Ache, and Hiwi) show an attraction to females with neotenous facial proportions (a combination of large eyes, small noses, and full lips) even after female age is controlled for. Two further studies show that female models have neotenous cephalofacial proportions relative to U.S. undergraduates and that drawings of faces artificially transformed to make them more or less neotenous are perceived as correspondingly more or less attractive. These results suggest several further lines of investigation, including the relationship between facial and bodily cues and the consequences of attraction to neoteny for morphological evolutio

Inspiratory muscle rehabilitation in critically ill adults a systematic review and meta-analysis

Rationale: Respiratory muscle weakness is common in critically ill patients; the role of targeted inspiratory muscle training (IMT) in intensive care unit rehabilitation strategies remains poorly defined. Objectives: The primary objective of the present study was to describe the range and tolerability of published methods for IMT. The secondary objectives were to determine whether IMT improves respiratory muscle strength and clinical outcomes in critically ill patients. Methods: We conducted a systematic review to identify randomized and nonrandomized studies of physical rehabilitation interventions intended to strengthen the respiratory muscles in critically ill adults. We searched the MEDLINE, Embase, HealthSTAR, CINAHL, and CENTRAL databases (inception to September Week 3, 2017) and conference proceedings (2012 to 2017). Data were independently extracted by two authors and collected on a standardized report form. Results: A total of 28 studies (N = 1,185 patients) were included. IMT was initiated during early mechanical ventilation (8 studies), after patients proved difficult to wean (14 studies), or after extubation (3 studies), and 3 other studies did not report exact timing. Threshold loading was the most common technique; 13 studies employed strength training regimens, 11 studies employed endurance training regimens, and 4 could not be classified. IMT was feasible, and there were few adverse events during IMT sessions (nine studies; median, 0%; interquartile range, 0-0%). In randomized trials (n = 20), IMT improved maximal inspiratory pressure compared with control (15 trials; mean increase, 6 cm H2O; 95% confidence interval [CI], 5-8 cm H2O; pooled relative ratio of means, 1.19; 95% CI, 1.14-1.25) and maximal expiratory pressure (4 trials; mean increase, 9 cm H2O; 95% CI, 5-14 cm H2O). IMT was associated with a shorter duration of ventilation (nine trials; mean difference, 4.1 d; 95% CI, 0.8-7.4 d) and a shorter duration of weaning (eight trials; mean difference, 2.3 d; 95% CI, 0.7-4.0 d), but confidence in these pooled estimates was low owing to methodological limitations, including substantial statistical and methodological heterogeneity. Conclusions: Most studies of IMT in critically ill patients have employed inspiratory threshold loading. IMT is feasible and well tolerated in critically ill patients and improves both inspiratory and expiratory muscle strength. The impact of IMT on clinical outcomes requires future confirmation