16,537 research outputs found
A Lower Bound for Sampling Disjoint Sets
Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x subseteq[n] and Bob ends up with a set y subseteq[n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant beta0 of the uniform distribution over all pairs of disjoint sets of size sqrt{n}
Black holes as random particles: entanglement dynamics in infinite range and matrix models
We first propose and study a quantum toy model of black hole dynamics. The
model is unitary, displays quantum thermalization, and the Hamiltonian couples
every oscillator with every other, a feature intended to emulate the color
sector physics of large- matrix models. Considering out of
equilibrium initial states, we analytically compute the time evolution of every
correlator of the theory and of the entanglement entropies, allowing a proper
discussion of global thermalization/scrambling of information through the
entire system. Microscopic non-locality causes factorization of reduced density
matrices, and entanglement just depends on the time evolution of occupation
densities. In the second part of the article, we show how the gained intuition
extends to large- matrix models, where we provide a gauge
invariant entanglement entropy for `generalized free fields', again depending
solely on the quasinormal frequencies. The results challenge the fast
scrambling conjecture and point to a natural scenario for the emergence of the
so-called brick wall or stretched horizon. Finally, peculiarities of these
models in regards to the thermodynamic limit and the information paradox are
highlighted.Comment: Journal versio
PF-OLA: A High-Performance Framework for Parallel On-Line Aggregation
Online aggregation provides estimates to the final result of a computation
during the actual processing. The user can stop the computation as soon as the
estimate is accurate enough, typically early in the execution. This allows for
the interactive data exploration of the largest datasets. In this paper we
introduce the first framework for parallel online aggregation in which the
estimation virtually does not incur any overhead on top of the actual
execution. We define a generic interface to express any estimation model that
abstracts completely the execution details. We design a novel estimator
specifically targeted at parallel online aggregation. When executed by the
framework over a massive TPC-H instance, the estimator provides
accurate confidence bounds early in the execution even when the cardinality of
the final result is seven orders of magnitude smaller than the dataset size and
without incurring overhead.Comment: 36 page
Secure and Efficient RNS Approach for Elliptic Curve Cryptography
Scalar multiplication, the main operation in elliptic
curve cryptographic protocols, is vulnerable to side-channel
(SCA) and fault injection (FA) attacks. An efficient countermeasure
for scalar multiplication can be provided by using alternative
number systems like the Residue Number System (RNS). In RNS,
a number is represented as a set of smaller numbers, where each
one is the result of the modular reduction with a given moduli
basis. Under certain requirements, a number can be uniquely
transformed from the integers to the RNS domain (and vice
versa) and all arithmetic operations can be performed in RNS.
This representation provides an inherent SCA and FA resistance
to many attacks and can be further enhanced by RNS arithmetic
manipulation or more traditional algorithmic countermeasures.
In this paper, extending our previous work, we explore the
potentials of RNS as an SCA and FA countermeasure and provide
an description of RNS based SCA and FA resistance means. We
propose a secure and efficient Montgomery Power Ladder based
scalar multiplication algorithm on RNS and discuss its SCAFA
resistance. The proposed algorithm is implemented on an
ARM Cortex A7 processor and its SCA-FA resistance is evaluated
by collecting preliminary leakage trace results that validate our
initial assumptions
Multivariate sparse interpolation using randomized Kronecker substitutions
We present new techniques for reducing a multivariate sparse polynomial to a
univariate polynomial. The reduction works similarly to the classical and
widely-used Kronecker substitution, except that we choose the degrees randomly
based on the number of nonzero terms in the multivariate polynomial, that is,
its sparsity. The resulting univariate polynomial often has a significantly
lower degree than the Kronecker substitution polynomial, at the expense of a
small number of term collisions. As an application, we give a new algorithm for
multivariate interpolation which uses these new techniques along with any
existing univariate interpolation algorithm.Comment: 21 pages, 2 tables, 1 procedure. Accepted to ISSAC 201
ENSO dynamics: low-dimensional-chaotic or stochastic?
We apply a test for low-dimensional, deterministic dynamics to the Nino 3
time series for the El Nino Southern Oscillation (ENSO). The test is negative,
indicating that the dynamics is high-dimensional/stochastic. However,
application of stochastic forcing to a time-delay equation for equatorial-wave
dynamics can reproduce this stochastic dynamics and other important aspects of
ENSO. Without such stochastic forcing this model yields low-dimensional,
deterministic dynamics, hence these results emphasize the importance of the
stochastic nature of the atmosphere-ocean interaction in low-dimensional models
of ENSO
How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation
The feasibility of computationally superior quantum computers is one of the
most exciting and clear-cut scientific questions of our time. The question
touches on fundamental issues regarding probability, physics, and
computability, as well as on exciting problems in experimental physics,
engineering, computer science, and mathematics. We propose three related
directions towards a negative answer. The first is a conjecture about physical
realizations of quantum codes, the second has to do with correlations in
stochastic physical systems, and the third proposes a model for quantum
evolutions when noise accumulates. The paper is dedicated to the memory of
Itamar Pitowsky.Comment: 16 page
Online Computation with Untrusted Advice
The advice model of online computation captures the setting in which the online algorithm is given some partial information concerning the request sequence. This paradigm allows to establish tradeoffs between the amount of this additional information and the performance of the online algorithm. However, unlike real life in which advice is a recommendation that we can choose to follow or to ignore based on trustworthiness, in the current advice model, the online algorithm treats it as infallible. This means that if the advice is corrupt or, worse, if it comes from a malicious source, the algorithm may perform poorly. In this work, we study online computation in a setting in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms that are robust and perform well even when the advice is generated in a malicious, adversarial manner. To this end, we focus on well- studied online problems such as ski rental, online bidding, bin packing, and list update. For ski-rental and online bidding, we show how to obtain algorithms that are Pareto-optimal with respect to the competitive ratios achieved; this improves upon the framework of Purohit et al. [NeurIPS 2018] in which Pareto-optimality is not necessarily guaranteed. For bin packing and list update, we give online algorithms with worst-case tradeoffs in their competitiveness, depending on whether the advice is trusted or not; this is motivated by work of Lykouris and Vassilvitskii [ICML 2018] on the paging problem, but in which the competitiveness depends on the reliability of the advice. Furthermore, we demonstrate how to prove lower bounds, within this model, on the tradeoff between the number of advice bits and the competitiveness of any online algorithm. Last, we study the effect of randomization: here we show that for ski-rental there is a randomized algorithm that Pareto-dominates any deterministic algorithm with advice of any size. We also show that a single random bit is not always inferior to a single advice bit, as it happens in the standard model
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