Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Symplectic cohomology and q-intersection numbers

Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the "dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity. Equivariant Lagrangians mirror equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example 7.5, added discussion of sign

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

The Minimal Length of a Lagrangian Cobordism between Legendrians

To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the cobordism. Our primary tool is a set of real-valued capacities for a Legendrian submanifold, which are derived from a filtered version of Legendrian Contact Homology. Relationships between capacities of Legendrians at the ends of a Lagrangian cobordism yield lower bounds on the length of the cobordism. We apply the capacities to Lagrangian cobordisms realizing vertical dilations (which may be arbitrarily short) and contractions (whose lengths are bounded below). We also study the interaction between length and the linking of multiple cobordisms as well as the lengths of cobordisms derived from non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee comments. More general statement in Proposition 3.3 and some reorganization at the end of Section

Life Beyond the Physical Body: The Possibilities of Digital Immortality

We are on the verge of a major shift in the way we perceive digital life, what may cause a significant impact to the real world. Gradually, through increasing knowledge in the areas of artificial intelligence, big data and machine learning, computers have been emulating deceased human beings and, symbolically, with the aid of technology, have been managing to conquer death. This article seeks to understand and problematize the ways in which digital immortality has manifested itself, particularly through digital memorials, chatbots and avatars. Companies like Facebook, Eter9 and Initiative 2045 allow a continuity of life after the death of its users. We analyze, through technical and philosophical questions, imbricated in this discussion, the implications of this digital immortality and how these issues are seen in a differentiated way with the presence of technology.Sociedad Argentina de Informática e Investigación Operativa (SADIO

A High Throughput Configurable SDR Detector for Multi-user MIMO Wireless Systems

Spatial division multiplexing (SDM) in MIMO technology significantly increases the spectral efficiency, and hence capacity, of a wireless communication system: it is a core component of the next generation wireless systems, e.g. WiMAX, 3GPP LTE and other OFDM-based communication schemes. Moreover, spatial division multiple access (SDMA) is one of the widely used techniques for sharing the wireless medium between different mobile devices. Sphere detection is a prominent method of simplifying the detection complexity in both SDM and SDMA systems while maintaining BER performance comparable with the optimum maximum-likelihood (ML) detection. On the other hand, with different standards supporting different system parameters, it is crucial for both base station and handset devices to be configurable and seamlessly switch between different modes without the need for separate dedicated hardware units. This challenge emphasizes the need for SDR designs that target the handset devices. In this paper, we propose the architecture and FPGA realization of a configurable sort-free sphere detector, Flex-Sphere, that supports 4, 16, 64-QAM modulations as well as a combination of 2, 3 and 4 antenna/user configuration for handsets. The detector provides a data rate of up to 857.1 Mbps that fits well within the requirements of any of the next generation wireless standards. The algorithmic optimizations employed to produce an FPGA friendly realization are discussed.Xilinx Inc.National Science Foundatio

Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations

The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather prediction models. However, the validity of this hypothesis under very stable conditions is a subject of on-going debate. In this work, we attempt to address this controversial issue by performing extensive analyses of turbulence data from several field campaigns, wind-tunnel experiments and large-eddy simulations. Wide range of stabilities, diverse field conditions and a comprehensive set of turbulence statistics make this study distinct

The brief international cognitive assessment for multiple sclerosis (BICAMS): Normative values with gender, age and education corrections in the Italian population

Background: BICAMS (Brief International Cognitive Assessment for Multiple Sclerosis) has been recently developed as brief, practical and universal assessment tool for cognitive impairment in MS subjects. It includes the Symbol Digit Modalities Test (SDMT), the California Verbal Learning Test-2 (CVLT2) and the Brief Visuospatial Memory Test-Revised (BVMT-R) . In this study we aimed at gathering regression based normative data for the BICAMS battery in the Italian population.Methods: Healthy subjects were consecutively recruited among patient friends and relatives. Corrections for demographics were calculated using multivariable linear regression models. Test-retest reliability was assessed using the Pearson correlation coefficient.Results: The BICAMS battery was administered to 273 healthy subjects (180 women, mean age 38.9 ± 13.0 years, mean education 14.9 ± 3.0 years). Test-retest reliability was good for all the tests.Conclusions: The study provided normative data of the BICAMS for the Italian population confirming good test-retest reliability which can facilitate the use of the battery in clinical practice, also for longitudinal patient assessments