Recursos de colección

Caltech Authors (171.365 recursos)

Repository of works by Caltech published authors.

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Mostrando recursos 1 - 20 de 1.958

  1. Gluing II: Boundary Localization and Gluing Formulas

    Dedushenko, Mykola
    We describe applications of the gluing formalism discussed in the companion paper. When a d-dimensional local theory QFTd is supersymmetric, and if we can find a supersymmetric polarization for QFTd quantized on a (d − 1)-manifold W, gluing along W is described by a non-local QFTd−1 that has an induced supersymmetry. Applying supersymmetric localization to QFTd−1 , which we refer to as the boundary localization, allows in some cases to represent gluing by finite-dimensional integrals over appropriate spaces of supersymmetric boundary conditions. We follow this strategy to derive a number of “gluing formulas” in various dimensions, some of which are new and some of which have been previously conjectured. First we...

  2. Gluing I: Integrals and Symmetries

    Dedushenko, Mykola
    We review some aspects of the cutting and gluing law in local quantum field theory. In particular, we emphasize the description of gluing by a path integral over a space of polarized boundary conditions, which are given by leaves of some Lagrangian foliation in the phase space. We think of this path integral as a non-local $(d-1)$-dimensional gluing theory associated to the parent local $d$-dimensional theory. We describe various properties of this procedure and spell out conditions under which symmetries of the parent theory lead to symmetries of the gluing theory. The purpose of this paper is to set up a playground for the companion paper where these...

  3. Two Deletion Correcting Codes from Indicator Vectors

    Sima, Jin; Raviv, Netanel; Bruck, Jehoshua
    Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek et al., alongside novel applications in DNA storage, have reignited the interest in this longstanding open problem. In spite of recent advances, the amount of redundancy in existing codes is still orders of magnitude away from being optimal. In this paper, a novel approach for constructing binary two-deletion correcting codes is proposed. By this approach, parity symbols are computed from indicator vectors (i.e., vectors that indicate the positions of certain patterns) of the encoded message, rather than from the message itself....

  4. Two Deletion Correcting Codes from Indicator Vectors

    Sima, Jin; Raviv, Netanel; Bruck, Jehoshua
    Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek et al., alongside novel applications in DNA storage, have reignited the interest in this longstanding open problem. In spite of recent advances, the amount of redundancy in existing codes is still orders of magnitude away from being optimal. In this paper, a novel approach for constructing binary two-deletion correcting codes is proposed. By this approach, parity symbols are computed from indicator vectors (i.e., vectors that indicate the positions of certain patterns) of the encoded message, rather than from the message itself....

  5. Secret Sharing with Optimal Decoding and Repair Bandwidth

    Huang, Wentao; Bruck, Jehoshua
    This paper studies the communication efficiency of threshold secret sharing schemes. We construct a family of Shamir’s schemes with asymptotically optimal decoding bandwidth for arbitrary parameters. We also construct a family of secret sharing schemes with both optimal decoding bandwidth and optimal repair bandwidth for arbitrary parameters. The construction also leads to a family of regenerating codes allowing centralized repair of multiple node failures with small sub-packetization.

  6. Secure RAID Schemes from EVENODD and STAR Codes

    Huang, Wentao; Bruck, Jehoshua
    We study secure RAID, i.e., low-complexity schemes to store information in a distributed manner that is resilient to node failures and resistant to node eavesdropping. We describe a technique to shorten the secure EVENODD scheme in [6], which can optimally tolerate 2 node failures and 2 eavesdropping nodes. The shortening technique allows us to obtain secure EVENODD schemes of arbitrary lengths, which is important for practical application. We also construct a new secure RAID scheme from the STAR code. The scheme can tolerate 3 node failures and 3 eavesdropping nodes with optimal encoding/decoding and random access complexity.

  7. Distributed Control Of An Evolving Satellite Assembly During In-Orbit Construction

    Foust, Rebecca C.; Zhao, Michelle; Oliver, Suzanne; Chung, Soon-Jo; Hadaegh, Fred Y.
    This paper presents a method for controlling sets of docked satellites during in-orbit construction of a large-scale satellite assembly from a swarm of heterogeneous satellites. Such a system can be used to enable missions from sparse aperture telescopes to elaborate space stations. Once two or more agents from the swarm are docked, the resulting assembly is an over-actuated system so position and attitude controllers must determine which of the available actuators to use. Typically, control allocation for over-actuated systems is done using a simple linear program, but for this scheme the mass properties and number of control points changes. As...

  8. Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

    Bandyopadhyay, Saptarshi; Chung, Soon-Jo
    The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound...

  9. Robotic Herding of a Flock of Birds Using an Unmanned Aerial Vehicle

    Paranjape, Aditya A.; Chung, Soon-Jo; Kim, Kyunam; Shim, D. Hyunchul
    In this paper, we derive an algorithm for enabling a single robotic unmanned aerial vehicle to herd a flock of birds away from a designated volume of space, such as the air space around an airport. The herding algorithm, referred to as the m-waypoint algorithm, is designed using a dynamic model of bird flocking based on Reynolds’ rules. We derive bounds on its performance using a combination of reduced-order modeling of the flock’s motion, heuristics, and rigorous analysis. A unique contribution of our work is the experimental demonstration of several facets of the herding algorithm on flocks of live birds...

  10. Nonlinear Attitude Control of a Spacecraft with Distributed Actuation of Solar Arrays

    Nakka, Yashwanth Kumar; Chung, Soon-Jo; Allison, James T.; Aldrich, Jack B.; Alvarez-Salazar, Oscar S.
    This article presents a novel control architecture and algorithm for precision attitude control of a one-degree-of-freedom dynamic model of a spacecraft. To achieve a parametric model-based control design approach for this new spacecraft actuation and control architecture, the nonlinear dynamics of the open-loop plant are modeled as an Ordinary Differential Equation (ODE)-Partial Differential Equation (PDE) system. The ODE describes the spacecraft single-axis rigid-body rotation, and the PDE describes the spatially continuous flexible dynamics of the solar array including an allocation for a multi-input distributed piezoelectric actuation system bonded on the solar array. This distributed actuation system is called strain-actuated solar...

  11. Temperature Dependent Electron-Phonon Scattering and Electron Mobility in SrTiO_3 Perovskite from First Principles

    Zhou, Jin-Jian; Hellman, Olle; Bernardi, Marco
    Structural phase transitions and soft phonon modes pose a longstanding challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO_3 is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200~K. Our calculations can accurately predict the temperature dependence of...

  12. Regularity in time along the coarse scale flow for the incompressible Euler equations

    Isett, Philip
    One of the most remarkable features of known nonstationary solutions to the incompressible Euler equations is the phenomenon that coarse scale averages of the velocity carry the fine scale features of the flow. In this paper, we study time-regularity properties of Euler flows which are connected to this phenomenon and the observation that each frequency level has a natural time scale when it is viewed along the coarse scale flow. We assume only that our velocity field is Hölder continuous in the spatial variables, which is well-motivated by problems related to turbulence. We show that any periodic Euler flow in...

  13. Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

    Isett, Philip
    Building on the recent work of C. De Lellis and L. Székelyhidi, we construct global weak solutions to the three-dimensional incompressible Euler equations which are zero outside of a finite time interval and have velocity in the Hölder class C^(1/(5−ϵ))_(t,x). By slightly modifying the proof, we show that every smooth solution to incompressible Euler on (−2,2) ×

  14. Terahertz Waveguiding in Silicon-Core Fibers

    Bas, Derek A.; Cushing, Scott K.; Ballato, John; Bristow, Alan D.
    We propose the use of a silicon-core optical fiber for terahertz (THz) waveguide applications. Finite-difference time-domain simulations have been performed based on a cylindrical waveguide with a silicon core and silica cladding. High-resistivity silicon has a flat dispersion over a 0.1 - 3 THz range, making it viable for propagation of tunable narrowband CW THz and possibly broadband picosecond pules of THz radiation. Simulations show the propagation dynamics and the integrated intensity, from which transverse mode profiles and absorption lengths are extraced. It is found that for 140 - 250 micron core diameters the mode is primarily confined to the...

  15. Valley-Specific Hot Phonon and Carrier Relaxation Pathways in Si(100) Determined by Transient Extreme Ultraviolet Spectroscopy

    Cushing, Scott K.; Zürch, Michael; Kraus, Peter M.; Carneiro, Lucas M.; Lee, Angela; Chang, Hung-Tzu; Kaplan, Christopher J.; Leone, Stephen R.
    The valley-specific thermalization of hot carriers and phonons gives direct insight into the scattering processes that mediate electrical and thermal transport. Obtaining the scattering rates for both hot carriers and phonons currently requires multiple measurements with incommensurate timescales. Here, transient extreme-ultraviolet (XUV) spectroscopy on the silicon 2p core level at 100 eV is used to measure hot carrier and phonon thermalization pathways in Si(100) from tens of femtoseconds to 200 ps for the Δ, L, and Γ valleys. The ground state XUV spectrum is first theoretically predicted using a combination of a single plasmon pole model and the Bethe-Salpeter equation...

  16. Banjo Drum Physics — sound experiments and simple acoustics demos

    Politzer, David
    11" D mylar heads over a normal range of tensions (DrumDial 85 to 91) and “open-back” backed pots of depths 2", 2 3/4", and 5 5/8" are studied over the range 100 to 2000 Hz. Normal modes and resonant frequencies of the heads and of the pot air separately are easily identified and agree with simple expectations. The present focus is the head ↔ pot air interaction. There is no "gold-plated" example of a pair of head–air interacting modes that are distant in frequency from all others. (Had there been such a pair, their interaction could have been isolated and...

  17. Context Embedding Networks

    Kim, Kun Ho; Mac Aodha, Oisin; Perona, Pietro
    Low dimensional embeddings that capture the main variations of interest in collections of data are important for many applications. One way to construct these embeddings is to acquire estimates of similarity from the crowd. However, similarity is a multi-dimensional concept that varies from individual to individual. Existing models for learning embeddings from the crowd typically make simplifying assumptions such as all individuals estimate similarity using the same criteria, the list of criteria is known in advance, or that the crowd workers are not influenced by the data that they see. To overcome these limitations we introduce Context Embedding Networks (CENs). In...

  18. Approximate Expected Utility Rationalization

    Echenique, Federico; Imai, Taisuke; Saito, Kota
    We propose a new measure of deviations from expected utility, given data on economic choices under risk and uncertainty. In a revealed preference setup, and given a positive number e, we provide a characterization of the datasets whose deviation (in beliefs, utility, or perceived prices) is within e of expected utility theory. The number e can then be used as a distance to the theory. We apply our methodology to three recent large-scale experiments. Many subjects in those experiments are consistent with utility aximization, but not expected utility maximization. The correlation of our measure with demographics is also interesting, and...

  19. Resting-state functional brain connectivity best predicts the personality dimension of openness to experience

    Dubois, Julien; Galdi, Paola; Han, Yanting; Paul, Lynn K.; Adolphs, Ralph
    Personality neuroscience aims to find associations between brain measures and personality traits. Findings to date have been severely limited by a number of factors, including small sample size and omission of out-of-sample prediction. We capitalized on the recent availability of a large database, together with the emergence of specific criteria for best practices in neuroimaging studies of individual differences. We analyzed resting-state functional magnetic resonance imaging data from 884 young healthy adults in the Human Connectome Project (HCP) database. We attempted to predict personality traits from the "Big Five", as assessed with the NEO-FFI test, using individual functional connectivity matrices....

  20. A distributed brain network predicts general intelligence from resting-state human neuroimaging data

    Dubois, Julien; Galdi, Paola; Paul, Lynn K.; Adolphs, Ralph
    Individual people differ in their ability to reason, solve problems, think abstractly, plan and learn. A reliable measure of this general ability, also known as intelligence, can be derived from scores across a diverse set of cognitive tasks. There is great interest in understanding the neural underpinnings of individual differences in intelligence, since it is the single best predictor of long-term life success, and since individual differences in a similar broad ability are found across animal species. The most replicated neural correlate of human intelligence to date is total brain volume. However, this coarse morphometric correlate gives no insights into...

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