254 research outputs found
Quantum random walks without walking
Quantum random walks have received much interest due to their non-intuitive
dynamics, which may hold the key to a new generation of quantum algorithms.
What remains a major challenge is a physical realization that is experimentally
viable and not limited to special connectivity criteria. We present a scheme
for walking on arbitrarily complex graphs, which can be realized using a
variety of quantum systems such as a BEC trapped inside an optical lattice.
This scheme is particularly elegant since the walker is not required to
physically step between the nodes; only flipping coins is sufficient.Comment: 12 manuscript pages, 3 figure
Lower bounds in differential privacy
This is a paper about private data analysis, in which a trusted curator
holding a confidential database responds to real vector-valued queries. A
common approach to ensuring privacy for the database elements is to add
appropriately generated random noise to the answers, releasing only these {\em
noisy} responses. In this paper, we investigate various lower bounds on the
noise required to maintain different kind of privacy guarantees.Comment: Corrected some minor errors and typos. To appear in Theory of
Cryptography Conference (TCC) 201
The Evolution of Secularization: Cultural Transmission, Religion and Fertility Theory, Simulations and Evidence
This study presents an evolutionary process of secularization that integrates a theoretical model, simulations, and an empirical estimation that employs data from 32 countries (included in the International Social Survey Program: Religion II – ISSP, 1998). Following Bisin and Verdier (2000, 2001a), it is assumed that cultural/social norms are transmitted from one generation to the next one via two venues: (i) direct socialization – across generations, by parents; and (ii) oblique socialization – within generations, by the community and cultural environment. This paper focuses on the transmission of religious norms and in particular on the 'religious taste for children'. The theoretical framework describes the setting and the process leading to secularization of the population; the simulations give more insight into the process; and 'secularization regressions' estimate the effects of the various explanatory variables on secularization (that is measured by rare mass-attendance and by rare-prayer), lending support to corollaries derived from the theory and simulations. The main conclusions/findings are that (i) direct religious socialization efforts of one generation have a negative effect on secularization within the next generation; (ii) oblique socialization by the community has a parabolic effect on secularization; and (iii) the two types of socialization are complements in 'producing' religiosity of the next generation.cultural transmission, religion, fertility, secularization, ISSP
The Evolution of Secularization: Cultural Transmission, Religion and Fertility Theory, Simulations and Evidence
This study presents an evolutionary process of secularization that integrates a theoretical model, simulations, and an empirical estimation that employs data from 32 countries (included in the International Social Survey Program: Religion II – ISSP, 1998). Following Bisin and Verdier (2000, 2001a), it is assumed that cultural/social norms are transmitted from one generation to the next one via two venues: (i) direct socialization – across generations, by parents; and (ii) oblique socialization – within generations, by the community and cultural environment. This paper focuses on the transmission of religious norms and in particular on the 'religious taste for children'. The theoretical framework describes the setting and the process leading to secularization of the population; the simulations give more insight into the process; and 'secularization regressions' estimate the effects of the various explanatory variables on secularization (that is measured by rare mass-attendance and by rare-prayer), lending support to corollaries derived from the theory and simulations. The main conclusions/findings are that (i) direct religious socialization efforts of one generation have a negative effect on secularization within the next generation; (ii) oblique socialization by the community has a parabolic effect on secularization; and (iii) the two types of socialization are complements in 'producing' religiosity of the next generation.cultural transmission, religion, fertility, secularization, ISSP
Sampling Triples from Restricted Networks Using MCMC Strategy
In large networks, the connected triples are useful for solving various tasks including link prediction, community detection, and spam filtering. Existing works in this direction concern mostly with the exact or approximate counting of connected triples that are closed (aka, triangles). Evidently, the task of triple sampling has not been explored in depth, although sampling is a more fundamental task than counting, and the former is useful for solving various other tasks, including counting. In recent years, some works on triple sampling have been proposed that are based on direct sampling, solely for the purpose of triangle count approximation. They sample only from a uniform distribution, and are not effective for sampling triples from an arbitrary user-defined distribution. In this work we present two indirect triple sampling methods that are based on Markov Chain Monte Carlo (MCMC) sampling strategy. Both of the above methods are highly efficient compared to a direct sampling-based method, specifically for the task of sampling from a non-uniform probability distribution. Another significant advantage of the proposed methods is that they can sample triples from networks that have restricted access, on which a direct sampling based method is simply not applicable
Quantified Derandomization of Linear Threshold Circuits
One of the prominent current challenges in complexity theory is the attempt
to prove lower bounds for , the class of constant-depth, polynomial-size
circuits with majority gates. Relying on the results of Williams (2013), an
appealing approach to prove such lower bounds is to construct a non-trivial
derandomization algorithm for . In this work we take a first step towards
the latter goal, by proving the first positive results regarding the
derandomization of circuits of depth .
Our first main result is a quantified derandomization algorithm for
circuits with a super-linear number of wires. Specifically, we construct an
algorithm that gets as input a circuit over input bits with
depth and wires, runs in almost-polynomial-time, and
distinguishes between the case that rejects at most inputs
and the case that accepts at most inputs. In fact, our
algorithm works even when the circuit is a linear threshold circuit, rather
than just a circuit (i.e., is a circuit with linear threshold gates,
which are stronger than majority gates).
Our second main result is that even a modest improvement of our quantified
derandomization algorithm would yield a non-trivial algorithm for standard
derandomization of all of , and would consequently imply that
. Specifically, if there exists a quantified
derandomization algorithm that gets as input a circuit with depth
and wires (rather than wires), runs in time at
most , and distinguishes between the case that rejects at
most inputs and the case that accepts at most
inputs, then there exists an algorithm with running time
for standard derandomization of .Comment: Changes in this revision: An additional result (a PRG for quantified
derandomization of depth-2 LTF circuits); rewrite of some of the exposition;
minor correction
Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost
In a two-player game, two cooperating but non communicating players, Alice
and Bob, receive inputs taken from a probability distribution. Each of them
produces an output and they win the game if they satisfy some predicate on
their inputs/outputs. The entangled value of a game is the
maximum probability that Alice and Bob can win the game if they are allowed to
share an entangled state prior to receiving their inputs.
The -fold parallel repetition of consists of instances of
where the players receive all the inputs at the same time and produce all
the outputs at the same time. They win if they win each instance of .
In this paper we show that for any game such that , decreases exponentially in . First, for
any game on the uniform distribution, we show that , where and are the sizes of the input
and output sets. From this result, we show that for any entangled game ,
where is the input distribution of and
. This implies parallel
repetition with exponential decay as long as for
general games. To prove this parallel repetition, we introduce the concept of
\emph{Superposed Information Cost} for entangled games which is inspired from
the information cost used in communication complexity.Comment: In the first version of this paper we presented a different, stronger
Corollary 1 but due to an error in the proof we had to modify it in the
second version. This third version is a minor update. We correct some typos
and re-introduce a proof accidentally commented out in the second versio
EquiX---A Search and Query Language for XML
EquiX is a search language for XML that combines the power of querying with
the simplicity of searching. Requirements for such languages are discussed and
it is shown that EquiX meets the necessary criteria. Both a graphical abstract
syntax and a formal concrete syntax are presented for EquiX queries. In
addition, the semantics is defined and an evaluation algorithm is presented.
The evaluation algorithm is polynomial under combined complexity.
EquiX combines pattern matching, quantification and logical expressions to
query both the data and meta-data of XML documents. The result of a query in
EquiX is a set of XML documents. A DTD describing the result documents is
derived automatically from the query.Comment: technical report of Hebrew University Jerusalem Israe
The Communication Complexity of the Hamming Distance Problem
We investigate the randomized and quantum communication complexity of the
Hamming Distance problem, which is to determine if the Hamming distance between
two n-bit strings is no less than a threshold d. We prove a quantum lower bound
of \Omega(d) qubits in the general interactive model with shared prior
entanglement. We also construct a classical protocol of O(d \log d) bits in the
restricted Simultaneous Message Passing model, improving previous protocols of
O(d^2) bits (A. C.-C. Yao, Proceedings of the Thirty-Fifth Annual ACM Symposium
on Theory of Computing, pp. 77-81, 2003), and O(d\log n) bits (D. Gavinsky, J.
Kempe, and R. de Wolf, quant-ph/0411051, 2004).Comment: 8 pages, v3, updated reference. to appear in Information Processing
Letters, 200
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