151,009 research outputs found

    Caustic Skeleton & Cosmic Web

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    We present a general formalism for identifying the caustic structure of an evolving mass distribution in an arbitrary dimensional space. For the class of Hamiltonian fluids the identification corresponds to the classification of singularities in Lagrangian catastrophe theory. Based on this we develop a theoretical framework for the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. The present work represents an extension of the work by Arnol'd et al., who classified the caustics for the 1- and 2-dimensional Zel'dovich approximation. His seminal work established the role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. We introduce an alternative and transparent proof for Lagrangian catastrophe theory, and derive the caustic conditions for general Lagrangian fluids, with arbitrary dynamics, including dissipative terms and vorticity. The new proof allows us to describe the full 3-dimensional complexity of the gravitationally evolving cosmic matter field. One of our key findings is the significance of the eigenvector field of the deformation field for outlining the spatial structure of the caustic skeleton. We consider the caustic conditions for the 3-dimensional Zel'dovich approximation, extending earlier work on those for 1- and 2-dimensional fluids towards the full spatial richness of the cosmic web

    On Lightweight Privacy-Preserving Collaborative Learning for IoT Objects

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    The Internet of Things (IoT) will be a main data generation infrastructure for achieving better system intelligence. This paper considers the design and implementation of a practical privacy-preserving collaborative learning scheme, in which a curious learning coordinator trains a better machine learning model based on the data samples contributed by a number of IoT objects, while the confidentiality of the raw forms of the training data is protected against the coordinator. Existing distributed machine learning and data encryption approaches incur significant computation and communication overhead, rendering them ill-suited for resource-constrained IoT objects. We study an approach that applies independent Gaussian random projection at each IoT object to obfuscate data and trains a deep neural network at the coordinator based on the projected data from the IoT objects. This approach introduces light computation overhead to the IoT objects and moves most workload to the coordinator that can have sufficient computing resources. Although the independent projections performed by the IoT objects address the potential collusion between the curious coordinator and some compromised IoT objects, they significantly increase the complexity of the projected data. In this paper, we leverage the superior learning capability of deep learning in capturing sophisticated patterns to maintain good learning performance. Extensive comparative evaluation shows that this approach outperforms other lightweight approaches that apply additive noisification for differential privacy and/or support vector machines for learning in the applications with light data pattern complexities.Comment: 12 pages,IOTDI 201

    Investability and Firm Value

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    We study how investability, or openness to foreign equity investors, affects firm value in a sample of over 1,400 firms from 26 emerging markets. We find that, on average, investability is associated with a 9% valuation premium (as measured by Tobin's q). However, in firm-fixed effects regressions this valuation premium disappears, suggesting that investability does not have a causal effect on firm value. Analysis of the components of Tobin's q shows that firms that become investable experience significant increases in both market values and physical investment. These effects are strongest for firms that face country-level or firm-level financial constraints prior to becoming investableFinancial liberalization; Investability; Foreign investors; Tobin's q
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