5,417 research outputs found
A notion of graph likelihood and an infinite monkey theorem
We play with a graph-theoretic analogue of the folklore infinite monkey
theorem. We define a notion of graph likelihood as the probability that a given
graph is constructed by a monkey in a number of time steps equal to the number
of vertices. We present an algorithm to compute this graph invariant and closed
formulas for some infinite classes. We have to leave the computational
complexity of the likelihood as an open problem.Comment: 6 pages, 1 EPS figur
A matrix representation of graphs and its spectrum as a graph invariant
We use the line digraph construction to associate an orthogonal matrix with
each graph. From this orthogonal matrix, we derive two further matrices. The
spectrum of each of these three matrices is considered as a graph invariant.
For the first two cases, we compute the spectrum explicitly and show that it is
determined by the spectrum of the adjacency matrix of the original graph. We
then show by computation that the isomorphism classes of many known families of
strongly regular graphs (up to 64 vertices) are characterized by the spectrum
of this matrix. We conjecture that this is always the case for strongly regular
graphs and we show that the conjecture is not valid for general graphs. We
verify that the smallest regular graphs which are not distinguished with our
method are on 14 vertices.Comment: 14 page
Increased signaling entropy in cancer requires the scale-free property of protein interaction networks
One of the key characteristics of cancer cells is an increased phenotypic
plasticity, driven by underlying genetic and epigenetic perturbations. However,
at a systems-level it is unclear how these perturbations give rise to the
observed increased plasticity. Elucidating such systems-level principles is key
for an improved understanding of cancer. Recently, it has been shown that
signaling entropy, an overall measure of signaling pathway promiscuity, and
computable from integrating a sample's gene expression profile with a protein
interaction network, correlates with phenotypic plasticity and is increased in
cancer compared to normal tissue. Here we develop a computational framework for
studying the effects of network perturbations on signaling entropy. We
demonstrate that the increased signaling entropy of cancer is driven by two
factors: (i) the scale-free (or near scale-free) topology of the interaction
network, and (ii) a subtle positive correlation between differential gene
expression and node connectivity. Indeed, we show that if protein interaction
networks were random graphs, described by Poisson degree distributions, that
cancer would generally not exhibit an increased signaling entropy. In summary,
this work exposes a deep connection between cancer, signaling entropy and
interaction network topology.Comment: 20 pages, 5 figures. In Press in Sci Rep 201
On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback
© 1963-2012 IEEE. We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions
Frictional dissipation at the interface of a two-layer quasi-geostrophic flow
In two-layer ocean circulation models the possible dissipation mechanism arising at the interface between the layers is parameterised in terms of the difference between the horizontal velocities of the flow in each layer. We explain and derive such parameterisation by extending the classical Ekman theory, which originally refers to the surface and to the benthic boundary layers, to the interface
of a quasi-geostrophic, two-layered flow
Multi-core job submission and grid resource scheduling for ATLAS AthenaMP
AthenaMP is the multi-core implementation of the ATLAS software framework and allows the efficient sharing of memory pages between multiple threads of execution. This has now been validated for production and delivers a significant reduction on the overall application memory footprint with negligible CPU overhead. Before AthenaMP can be routinely run on the LHC Computing Grid it must be determined how the computing resources available to ATLAS can best exploit the notable improvements delivered by switching to this multi-process model. A study into the effectiveness and scalability of AthenaMP in a production environment will be presented. Best practices for configuring the main LRMS implementations currently used by grid sites will be identified in the context of multi-core scheduling optimisation
Longitudinal LASSO: Jointly Learning Features and Temporal Contingency for Outcome Prediction
Longitudinal analysis is important in many disciplines, such as the study of
behavioral transitions in social science. Only very recently, feature selection
has drawn adequate attention in the context of longitudinal modeling. Standard
techniques, such as generalized estimating equations, have been modified to
select features by imposing sparsity-inducing regularizers. However, they do
not explicitly model how a dependent variable relies on features measured at
proximal time points. Recent graphical Granger modeling can select features in
lagged time points but ignores the temporal correlations within an individual's
repeated measurements. We propose an approach to automatically and
simultaneously determine both the relevant features and the relevant temporal
points that impact the current outcome of the dependent variable. Meanwhile,
the proposed model takes into account the non-{\em i.i.d} nature of the data by
estimating the within-individual correlations. This approach decomposes model
parameters into a summation of two components and imposes separate block-wise
LASSO penalties to each component when building a linear model in terms of the
past measurements of features. One component is used to select features
whereas the other is used to select temporal contingent points. An accelerated
gradient descent algorithm is developed to efficiently solve the related
optimization problem with detailed convergence analysis and asymptotic
analysis. Computational results on both synthetic and real world problems
demonstrate the superior performance of the proposed approach over existing
techniques.Comment: Proceedings of the 21th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining. ACM, 201
Lorentz Beams
A new kind of tridimensional scalar optical beams is introduced. These beams
are called Lorentz beams because the form of their transverse pattern in the
source plane is the product of two independent Lorentz functions. Closed-form
expression of free-space propagation under paraxial limit is derived and pseudo
non-diffracting features pointed out. Moreover, as the slowly varying part of
these fields fulfils the scalar paraxial wave equation, it follows that there
exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original
Lorentz beam to a Gaussian apodization function. Although the existence of
Lorentz-Gauss beams can be shown by using two different and independent ways
obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega
et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different
approach, which makes use of Lie's group theory, and which possesses the merit
to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics
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