On the exact learnability of graph parameters: The case of partition functions

We study the exact learnability of real valued graph parameters $f$ which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph $H$ with vertex weights $\alpha$ and edge weights $\beta$. M. Freedman, L. Lov\'asz and A. Schrijver have given a characterization of these graph parameters in terms of the $k$-connection matrices $C(f,k)$ of $f$. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter $f$, the learner can ask for the values of $f$ for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices $C(f,k)$ of $f$. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions, the rigid partition functions, can be learned in time polynomial in the size of $H$ and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.Comment: 14 pages, full version of the MFCS 2016 conference pape

Finiteness conditions for graph algebras over tropical semirings

Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lov{\'a}sz and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical rings (max-plus algebras) over the real numbers. We show that rank-finiteness of join matrices implies that these graph parameters can be computed in polynomial time on graph classes of bounded clique-width. In the case of graph parameters with values in arbitrary commutative semirings, this remains true for graph classes of bounded linear clique-width. B. Godlin, T. Kotek and J.A. Makowsky (2008) showed that definability of a graph parameter in Monadic Second Order Logic implies rank finiteness. We also show that there are uncountably many integer valued graph parameters with connection matrices or join matrices of fixed finite rank. This shows that rank finiteness is a much weaker assumption than any definability assumption.Comment: 12 pages, accepted for presentation at FPSAC 2014 (Chicago, June 29 -July 3, 2014), to appear in Discrete Mathematics and Theoretical Computer Scienc

Weighted Automata and Monadic Second Order Logic

Let S be a commutative semiring. M. Droste and P. Gastin have introduced in 2005 weighted monadic second order logic WMSOL with weights in S. They use a syntactic fragment RMSOL of WMSOL to characterize word functions (power series) recognizable by weighted automata, where the semantics of quantifiers is used both as arithmetical operations and, in the boolean case, as quantification. Already in 2001, B. Courcelle, J.Makowsky and U. Rotics have introduced a formalism for graph parameters definable in Monadic Second order Logic, here called MSOLEVAL with values in a ring R. Their framework can be easily adapted to semirings S. This formalism clearly separates the logical part from the arithmetical part and also applies to word functions. In this paper we give two proofs that RMSOL and MSOLEVAL with values in S have the same expressive power over words. One proof shows directly that MSOLEVAL captures the functions recognizable by weighted automata. The other proof shows how to translate the formalisms from one into the other.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Spatiotemporal Properties of Sub‐Rayleigh and Supershear Ruptures Inferred From Full‐Field Dynamic Imaging of Laboratory Experiments

Many earthquakes propagate at sub‐Rayleigh speeds. Earthquakes propagating at supershear speeds, though less common, are by far more destructive. Hence, it is important to quantify the motion characteristics associated with both types of earthquake ruptures. Here we report on the spatiotemporal properties of dynamic ruptures measured in our laboratory experiments using the dynamic digital image correlation technique. Earthquakes are mimicked by the frictional rupture propagating along the interface of two Homalite plates. Digital images of the propagating ruptures are captured by an ultrahigh‐speed camera and processed with digital image correlation in order to produce sequences of evolving displacement and velocity maps. Our measurements reveal the full‐field structure of the velocity components, bridge the gap between previous spatially sparse velocimeter measurements available only at two to three locations, and enable us to quantify the attenuation patterns away from the interface

Colored filters improve exclusion of perceptual noise in visually symptomatic dyslexics

Dyslexic individuals have deficits in detecting visual stimuli embedded in high levels of perceptual noise. Here we show that visually symptomatic dyslexics, who otherwise had elevated contrast thresholds for discriminating symbols in visual noise, had thresholds similar to non-dyslexics when wearing colored filters. These findings provide evidence that colored filters, which minimize the visual distortions and discomfort of dyslexics when reading, improve dyslexics' noise exclusion to normal levels

Spectroscopic Identification of Type 2 Quasars at Z < 1 in SDSS-III/BOSS

The physics and demographics of type 2 quasars remain poorly understood, and new samples of such objects selected in a variety of ways can give insight into their physical properties, evolution, and relationship to their host galaxies. We present a sample of 2758 type 2 quasars at z $\leq$ 1 from the SDSS-III/BOSS spectroscopic database, selected on the basis of their emission-line properties. We probe the luminous end of the population by requiring the rest-frame equivalent width of [OIII] to be > 100 {\AA}. We distinguish our objects from star-forming galaxies and type 1 quasars using line widths, standard emission line ratio diagnostic diagrams at z < 0.52 and detection of [Ne V]{\lambda}3426{\AA} at z > 0.52. The majority of our objects have [OIII] luminosities in the range 10^8.5-10^10 L$_{\odot}$ and redshifts between 0.4 and 0.65. Our sample includes over 400 type 2 quasars with incorrectly measured redshifts in the BOSS database; such objects often show kinematic substructure or outflows in the [OIII] line. The majority of the sample has counterparts in the WISE survey, with median infrared luminosity {\nu}L{\nu}[12{\mu}m] = 4.2 x 10^44 erg/sec. Only 34 per cent of the newly identified type 2 quasars would be selected by infrared color cuts designed to identify obscured active nuclei, highlighting the difficulty of identifying complete samples of type 2 quasars. We make public the multi-Gaussian decompositions of all [OIII] profiles for the new sample and for 568 type 2 quasars from SDSS I/II, together with non-parametric measures of line profile shapes and identify over 600 candidate double-peaked [OIII] profiles.Comment: 15 pages, 15 figures, 2 tables. Online tables: http://zakamska.johnshopkins.edu/data.ht

Evaluation of the Theoretical Uncertainties in the W to Lepton and Neutrino Cross Sections at the LHC

We study the sources of systematic errors in the measurement of the W to lepton and neutrino cross-sections at the LHC. We consider the systematic errors in both the total cross-section and acceptance for anticipated experimental cuts. We include the best available analysis of QCD effects at NNLO in assessing the effect of higher order corrections and PDF and scale uncertainties on the theoretical acceptance. In addition, we evaluate the error due to missing NLO electroweak corrections and propose which MC generators and computational schemes should be implemented to best simulate the events.Comment: 33 pages, 109 eps figures, uses JHEP3.cls, rotating.sty Version 2 corrects an error in Table 1, adds some references, and updates an author addres

Models of Galaxy Clusters with Thermal Conduction

We present a simple model of hot gas in galaxy clusters, assuming hydrostatic equilibrium and energy balance between radiative cooling and thermal conduction. For five clusters, A1795, A1835, A2199, A2390 and RXJ1347.5-1145, the model gives a good description of the observed radial profiles of electron density and temperature, provided we take the thermal conductivity $\kappa$ to be about 30% of the Spitzer conductivity. Since the required $\kappa$ is consistent with the recent theoretical estimate of Narayan & Medvedev (2001) for a turbulent magnetized plasma, we consider a conduction-based equilibrium model to be viable for these clusters. We further show that the hot gas is thermally stable because of the presence of conduction. For five other clusters, A2052, A2597, Hydra A, Ser 159-03 and 3C295, the model requires unphysically large values of $\kappa$ to fit the data. These clusters must have some additional source of heat, most likely an active galactic nucleus since all the clusters have strong radio galaxies at their centers. We suggest that thermal conduction, though not dominant in these clusters, may nevertheless play a significant role by preventing the gas from becoming thermally unstable.Comment: Published in ApJ; 22 pages, including 2 tables, 4 figures; typos corrected to match the published versio

Ancient properties of spider silks revealed by the complete gene sequence of the prey-wrapping silk protein (AcSp1).

Spider silk fibers have impressive mechanical properties and are primarily composed of highly repetitive structural proteins (termed spidroins) encoded by a single gene family. Most characterized spidroin genes are incompletely known because of their extreme size (typically &gt;9 kb) and repetitiveness, limiting understanding of the evolutionary processes that gave rise to their unusual gene architectures. The only complete spidroin genes characterized thus far form the dragline in the Western black widow, Latrodectus hesperus. Here, we describe the first complete gene sequence encoding the aciniform spidroin AcSp1, the primary component of spider prey-wrapping fibers. L. hesperus AcSp1 contains a single enormous (∼19 kb) exon. The AcSp1 repeat sequence is exceptionally conserved between two widow species (∼94% identity) and between widows and distantly related orb-weavers (∼30% identity), consistent with a history of strong purifying selection on its amino acid sequence. Furthermore, the 16 repeats (each 371-375 amino acids long) found in black widow AcSp1 are, on average, &gt;99% identical at the nucleotide level. A combination of stabilizing selection on amino acid sequence, selection on silent sites, and intragenic recombination likely explains the extreme homogenization of AcSp1 repeats. In addition, phylogenetic analyses of spidroin paralogs support a gene duplication event occurring concomitantly with specialization of the aciniform glands and the tubuliform glands, which synthesize egg-case silk. With repeats that are dramatically different in length and amino acid composition from dragline spidroins, our L. hesperus AcSp1 expands the knowledge base for developing silk-based biomimetic technologies