6,928 research outputs found
CFT Duals for Extreme Black Holes
It is argued that the general four-dimensional extremal Kerr-Newman-AdS-dS
black hole is holographically dual to a (chiral half of a) two-dimensional CFT,
generalizing an argument given recently for the special case of extremal Kerr.
Specifically, the asymptotic symmetries of the near-horizon region of the
general extremal black hole are shown to be generated by a Virasoro algebra.
Semiclassical formulae are derived for the central charge and temperature of
the dual CFT as functions of the cosmological constant, Newton's constant and
the black hole charges and spin. We then show, assuming the Cardy formula, that
the microscopic entropy of the dual CFT precisely reproduces the macroscopic
Bekenstein-Hawking area law. This CFT description becomes singular in the
extreme Reissner-Nordstrom limit where the black hole has no spin. At this
point a second dual CFT description is proposed in which the global part of the
U(1) gauge symmetry is promoted to a Virasoro algebra. This second description
is also found to reproduce the area law. Various further generalizations
including higher dimensions are discussed.Comment: 18 pages; v2 minor change
Offline to Online Conversion
We consider the problem of converting offline estimators into an online
predictor or estimator with small extra regret. Formally this is the problem of
merging a collection of probability measures over strings of length 1,2,3,...
into a single probability measure over infinite sequences. We describe various
approaches and their pros and cons on various examples. As a side-result we
give an elementary non-heuristic purely combinatoric derivation of Turing's
famous estimator. Our main technical contribution is to determine the
computational complexity of online estimators with good guarantees in general.Comment: 20 LaTeX page
MDL Convergence Speed for Bernoulli Sequences
The Minimum Description Length principle for online sequence
estimation/prediction in a proper learning setup is studied. If the underlying
model class is discrete, then the total expected square loss is a particularly
interesting performance measure: (a) this quantity is finitely bounded,
implying convergence with probability one, and (b) it additionally specifies
the convergence speed. For MDL, in general one can only have loss bounds which
are finite but exponentially larger than those for Bayes mixtures. We show that
this is even the case if the model class contains only Bernoulli distributions.
We derive a new upper bound on the prediction error for countable Bernoulli
classes. This implies a small bound (comparable to the one for Bayes mixtures)
for certain important model classes. We discuss the application to Machine
Learning tasks such as classification and hypothesis testing, and
generalization to countable classes of i.i.d. models.Comment: 28 page
Solomonoff Induction Violates Nicod's Criterion
Nicod's criterion states that observing a black raven is evidence for the
hypothesis H that all ravens are black. We show that Solomonoff induction does
not satisfy Nicod's criterion: there are time steps in which observing black
ravens decreases the belief in H. Moreover, while observing any computable
infinite string compatible with H, the belief in H decreases infinitely often
when using the unnormalized Solomonoff prior, but only finitely often when
using the normalized Solomonoff prior. We argue that the fault is not with
Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201
An Enhanced Features Extractor for a Portfolio of Constraint Solvers
Recent research has shown that a single arbitrarily efficient solver can be
significantly outperformed by a portfolio of possibly slower on-average
solvers. The solver selection is usually done by means of (un)supervised
learning techniques which exploit features extracted from the problem
specification. In this paper we present an useful and flexible framework that
is able to extract an extensive set of features from a Constraint
(Satisfaction/Optimization) Problem defined in possibly different modeling
languages: MiniZinc, FlatZinc or XCSP. We also report some empirical results
showing that the performances that can be obtained using these features are
effective and competitive with state of the art CSP portfolio techniques
Bayesian DNA copy number analysis
BACKGROUND: Some diseases, like tumors, can be related to chromosomal aberrations, leading to
changes of DNA copy number. The copy number of an aberrant genome can be represented as a
piecewise constant function, since it can exhibit regions of deletions or gains. Instead, in a healthy
cell the copy number is two because we inherit one copy of each chromosome from each our
parents.
Bayesian Piecewise Constant Regression (BPCR) is a Bayesian regression method for data that are
noisy observations of a piecewise constant function. The method estimates the unknown segment
number, the endpoints of the segments and the value of the segment levels of the underlying
piecewise constant function. The Bayesian Regression Curve (BRC) estimates the same data with
a smoothing curve. However, in the original formulation, some estimators failed to properly
determine the corresponding parameters. For example, the boundary estimator did not take into
account the dependency among the boundaries and succeeded in estimating more than one
breakpoint at the same position, losing segments.
RESULTS: We derived an improved version of the BPCR (called mBPCR) and BRC, changing the
segment number estimator and the boundary estimator to enhance the fitting procedure. We also
proposed an alternative estimator of the variance of the segment levels, which is useful in case of
data with high noise. Using artificial data, we compared the original and the modified version of
BPCR and BRC with other regression methods, showing that our improved version of BPCR
generally outperformed all the others. Similar results were also observed on real data.
CONCLUSION: We propose an improved method for DNA copy number estimation, mBPCR, which
performed very well compared to previously published algorithms. In particular, mBPCR was more
powerful in the detection of the true position of the breakpoints and of small aberrations in very
noisy data. Hence, from a biological point of view, our method can be very useful, for example, to
find targets of genomic aberrations in clinical cancer samples
An integrated Bayesian analysis of LOH and copy number data
BACKGROUND Cancer and other disorders are due to genomic lesions. SNP-microarrays are able to measure simultaneously both genotype and copy number (CN) at several Single Nucleotide Polymorphisms (SNPs) along the genome. CN is defined as the number of DNA copies, and the normal is two, since we have two copies of each chromosome. The genotype of a SNP is the status given by the nucleotides (alleles) which are present on the two copies of DNA. It is defined homozygous or heterozygous if the two alleles are the same or if they differ, respectively. Loss of heterozygosity (LOH) is the loss of the heterozygous status due to genomic events. Combining CN and LOH data, it is possible to better identify different types of genomic aberrations. For example, a long sequence of homozygous SNPs might be caused by either the physical loss of one copy or a uniparental disomy event (UPD), i.e. each SNP has two identical nucleotides both derived from only one parent. In this situation, the knowledge of the CN can help in distinguishing between these two events. RESULTS To better identify genomic aberrations, we propose a method (called gBPCR) which infers the type of aberration occurred, taking into account all the possible influence in the microarray detection of the homozygosity status of the SNPs, resulting from an altered CN level. Namely, we model the distributions of the detected genotype, given a specific genomic alteration and we estimate the parameters involved on public reference datasets. The estimation is performed similarly to the modified Bayesian Piecewise Constant Regression, but with improved estimators for the detection of the breakpoints.Using artificial and real data, we evaluate the quality of the estimation of gBPCR and we also show that it outperforms other well-known methods for LOH estimation. CONCLUSIONS We propose a method (gBPCR) for the estimation of both LOH and CN aberrations, improving their estimation by integrating both types of data and accounting for their relationships. Moreover, gBPCR performed very well in comparison with other methods for LOH estimation and the estimated CN lesions on real data have been validated with another technique.This work was supported by Swiss National Science Foundation (grants
205321-112430, 205320-121886/1); Oncosuisse grants OCS-1939-8-2006 and
OCS - 02296-08-2008; Cantone Ticino ("Computational life science/Ticino in
reteâ program); Fondazione per la Ricerca e la Cura sui Linfomi (Lugano,
Switzerland)
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