3,240 research outputs found
Concurrent Knowledge-Extraction in the Public-Key Model
Knowledge extraction is a fundamental notion, modelling machine possession of
values (witnesses) in a computational complexity sense. The notion provides an
essential tool for cryptographic protocol design and analysis, enabling one to
argue about the internal state of protocol players without ever looking at this
supposedly secret state. However, when transactions are concurrent (e.g., over
the Internet) with players possessing public-keys (as is common in
cryptography), assuring that entities ``know'' what they claim to know, where
adversaries may be well coordinated across different transactions, turns out to
be much more subtle and in need of re-examination. Here, we investigate how to
formally treat knowledge possession by parties (with registered public-keys)
interacting over the Internet. Stated more technically, we look into the
relative power of the notion of ``concurrent knowledge-extraction'' (CKE) in
the concurrent zero-knowledge (CZK) bare public-key (BPK) model.Comment: 38 pages, 4 figure
Rearrangeable Networks with Limited Depth
Rearrangeable networks are switching systems capable of establishing simultaneous independent communication paths in accordance with any one-to-one correspondence between their n inputs and n outputs. Classical results show that Ξ©( n log n ) switches are necessary and that O( n log n ) switches are sufficient for such networks. We are interested in the minimum possible number of switches in rearrangeable networks in which the depth (the length of the longest path from an input to an output) is at most k, where k is fixed as n increases. We show that Ξ©( n1 + 1/k ) switches are necessary and that O( n1 + 1/k ( log n )1/k ) switches are sufficient for such networks
Brightest galaxies as halo centre tracers in SDSS DR7
Determining the positions of halo centres in large-scale structure surveys is
crucial for many cosmological studies. A common assumption is that halo centres
correspond to the location of their brightest member galaxies. In this paper,
we study the dynamics of brightest galaxies with respect to other halo members
in the Sloan Digital Sky Survey DR7. Specifically, we look at the line-of-sight
velocity and spatial offsets between brightest galaxies and their neighbours.
We compare those to detailed mock catalogues, constructed from high-resolution,
dark-matter-only -body simulations, in which it is assumed that satellite
galaxies trace dark matter subhaloes. This allows us to place constraints on
the fraction of haloes in which the brightest galaxy is not the
central. Compared to previous studies we explicitly take into account the
unrelaxed state of the host haloes, velocity offsets of halo cores and
correlations between and the satellite occupation. We find that
strongly decreases with the luminosity of the brightest galaxy
and increases with the mass of the host halo. Overall, in the halo mass range
we find , in good
agreement with a previous study by Skibba et al. We discuss the implications of
these findings for studies inferring the galaxy--halo connection from satellite
kinematics, models of the conditional luminosity function and galaxy formation
in general.Comment: 24 pages, 15 figures. Accepted for publication in MNRA
How to Optimally Constrain Galaxy Assembly Bias: Supplement Projected Correlation Functions with Count-in-cells Statistics
Most models for the connection between galaxies and their haloes ignore the
possibility that galaxy properties may be correlated with halo properties other
than mass, a phenomenon known as galaxy assembly bias. Yet, it is known that
such correlations can lead to systematic errors in the interpretation of survey
data. At present, the degree to which galaxy assembly bias may be present in
the real Universe, and the best strategies for constraining it remain
uncertain. We study the ability of several observables to constrain galaxy
assembly bias from redshift survey data using the decorated halo occupation
distribution (dHOD), an empirical model of the galaxy--halo connection that
incorporates assembly bias. We cover an expansive set of observables, including
the projected two-point correlation function ,
the galaxy--galaxy lensing signal , the void
probability function , the distributions of
counts-in-cylinders , and counts-in-annuli
, and the distribution of the ratio of counts in cylinders
of different sizes . We find that despite the frequent use of the
combination in
interpreting galaxy data, the count statistics, and
, are generally more efficient in constraining galaxy
assembly bias when combined with . Constraints
based upon and
share common degeneracy directions in the parameter space, while combinations
of with the count statistics are more
complementary. Therefore, we strongly suggest that count statistics should be
used to complement the canonical observables in future studies of the
galaxy--halo connection.Comment: Figures 3 and 4 show the main results. Published in Monthly Notices
of the Royal Astronomical Societ
Generalized Tsirelson Inequalities, Commuting-Operator Provers, and Multi-Prover Interactive Proof Systems
A central question in quantum information theory and computational complexity
is how powerful nonlocal strategies are in cooperative games with imperfect
information, such as multi-prover interactive proof systems. This paper
develops a new method for proving limits of nonlocal strategies that make use
of prior entanglement among players (or, provers, in the terminology of
multi-prover interactive proofs). Instead of proving the limits for usual
isolated provers who initially share entanglement, this paper proves the limits
for "commuting-operator provers", who share private space, but can apply only
such operators that are commutative with any operator applied by other provers.
Commuting-operator provers are at least as powerful as usual isolated but
prior-entangled provers, and thus, limits for commuting-operator provers
immediately give limits for usual entangled provers. Using this method, we
obtain an n-party generalization of the Tsirelson bound for the Clauser-Horne-
Shimony-Holt inequality for every n. Our bounds are tight in the sense that, in
every n-party case, the equality is achievable by a usual nonlocal strategy
with prior entanglement. We also apply our method to a 3-prover 1-round binary
interactive proof for NEXP. Combined with the technique developed by Kempe,
Kobayashi, Matsumoto, Toner and Vidick to analyze the soundness of the proof
system, it is proved to be NP-hard to distinguish whether the entangled value
of a 3-prover 1-round binary-answer game is equal to 1 or at most 1-1/p(n) for
some polynomial p, where n is the number of questions. This is in contrast to
the 2-prover 1-round binary-answer case, where the corresponding problem is
efficiently decidable. Alternatively, NEXP has a 3-prover 1-round binary
interactive proof system with perfect completeness and soundness 1-2^{-poly}.Comment: 20 pages. v2: An incorrect statement in the abstract about the
two-party case is corrected. Relation between this work and a preliminary
work by Sun, Yao and Preda is clarifie
The Galaxy Clustering Crisis in Abundance Matching
Galaxy clustering on small scales is significantly under-predicted by
sub-halo abundance matching (SHAM) models that populate (sub-)haloes with
galaxies based on peak halo mass, . SHAM models based on the peak
maximum circular velocity, , have had much better success. The
primary reason based models fail is the relatively low abundance
of satellite galaxies produced in these models compared to those based on
. Despite success in predicting clustering, a simple based SHAM model results in predictions for galaxy growth that are at
odds with observations. We evaluate three possible remedies that could "save"
mass-based SHAM: (1) SHAM models require a significant population of "orphan"
galaxies as a result of artificial disruption/merging of sub-haloes in modern
high resolution dark matter simulations; (2) satellites must grow significantly
after their accretion; and (3) stellar mass is significantly affected by halo
assembly history. No solution is entirely satisfactory. However, regardless of
the particulars, we show that popular SHAM models based on
cannot be complete physical models as presented. Either truly is
a better predictor of stellar mass at and it remains to be seen how
the correlation between stellar mass and comes about, or SHAM
models are missing vital component(s) that significantly affect galaxy
clustering.Comment: 25 pages, 22 figures, submitted to MNRAS, comments welcom
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