Length minimizing Hamiltonian paths for symplectically aspherical manifolds

In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our main result determines a natural condition on a fixed global maximum of a Hamiltonian which implies that the corresponding path minimizes the positive Hofer length. We use this to prove that a quasi-autonomous Hamiltonian generates a length minimizing path if it has under-twisted fixed global extrema and no periodic orbits with period one and action greater than the fixed extrema. This, in turn, allows us to produce new examples of autonomous Hamiltonian flows which are length minimizing for all times. These constructions are based on the geometry of coisotropic submanifolds. Finally, we give a new proof of the recent theorem of D. McDuff which states that quasi-autonomous Hamiltonians generate length minimizing paths over short time intervals.Comment: 23 pages, references added and final revisions made for publicatio

A relative Seidel morphism and the Albers map

In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian submanifold L, an element in the Floer homology of L. We show that these elements are related to the absolute Seidel elements by the Albers map. We also study for later use, the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the Floer homologies.Comment: LaTeX 33 pages, 13 figures. Clarified assumptions and reference

DarSwin: Distortion Aware Radial Swin Transformer

Wide-angle lenses are commonly used in perception tasks requiring a large field of view. Unfortunately, these lenses produce significant distortions making conventional models that ignore the distortion effects unable to adapt to wide-angle images. In this paper, we present a novel transformer-based model that automatically adapts to the distortion produced by wide-angle lenses. We leverage the physical characteristics of such lenses, which are analytically defined by the radial distortion profile (assumed to be known), to develop a distortion aware radial swin transformer (DarSwin). In contrast to conventional transformer-based architectures, DarSwin comprises a radial patch partitioning, a distortion-based sampling technique for creating token embeddings, and a polar position encoding for radial patch merging. We validate our method on classification tasks using synthetically distorted ImageNet data and show through extensive experiments that DarSwin can perform zero-shot adaptation to unseen distortions of different wide-angle lenses. Compared to other baselines, DarSwin achieves the best results (in terms of Top-1 and -5 accuracy), when tested on in-distribution data, with almost 2% (6%) gain in Top-1 accuracy under medium (high) distortion levels, and comparable to the state-of-the-art under low and very low distortion levels (perspective-like images).Comment: 8 pages, 8 figure

AdaWCT: Adaptive Whitening and Coloring Style Injection

Adaptive instance normalization (AdaIN) has become the standard method for style injection: by re-normalizing features through scale-and-shift operations, it has found widespread use in style transfer, image generation, and image-to-image translation. In this work, we present a generalization of AdaIN which relies on the whitening and coloring transformation (WCT) which we dub AdaWCT, that we apply for style injection in large GANs. We show, through experiments on the StarGANv2 architecture, that this generalization, albeit conceptually simple, results in significant improvements in the quality of the generated images.Comment: 4 pages + ref

Preparation for an Half-Ironmantm Triathlon amongst Amateur Athlete: Finishing rate and physiological adaptation.

International Journal of Exercise Science 13(6): 766-777, 2020. Long distance triathlon has gained in popularity amongst the general population. Coaches establish training programs based upon their knowledge, personal experience and on current training principles. The goal was to observe the effect of a triathlon training program for a half Ironman event in neophyte amateur athletes. A specific triathlon training program was followed from February to June 2016 by a group preparing for their first half ironman. Out of the 32 participants (19 Males and 13 Females; mean age of 39 ± 9.9 years old; body weight of 72.7 ± 13.4 kg and a height of 171.5 ± 10.2 cm), only one did not complete the event. A mean training volume of 410 ± 201 min per week led to a mean finishing time of 6 hours 28 minutes. The training program significantly increased the maximal oxygen consumption (45.9 ± 8.2 to 48.6 ± 7.5 ml/kg/min, p =0.002) and the maximal power output (293.1 ± 63.7 to 307.8 ± 58.7 W, p \u3c 0.001). The absolute oxygen consumption and power output at both ventilatory thresholds also significantly increased (VT1: 2.2 ± 0.4 to 2.5 ± 0.5 L, p = 0.001; 157.8 ± 41.8 to 176.7 ± 41.1 W p = 0.009 and VT2: 2.9 ± 0.4 to 3.0 ± 0.4 L, p = 0.017; 229.3 ± 62.0 to 244.8± 55.2 W, p = 0.022 ). A significant diminution of waist circumference was observed (83.2 ± 10.0 to 81.8 ± 9.5 cm, p = 0.032) with no significant changes in body weight. Thus, a 24-week specific training program appears to be safe and efficient for amateur athletes aiming to finish their first half- Ironman event