New Query Lower Bounds for Submodular Function Minimization

We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as possible. State-of-the-art algorithms succeed with $\tilde{O}(n^2)$ queries [LeeSW15], yet the best-known lower bound has never been improved beyond $n$ [Harvey08]. We provide a query lower bound of $2n$ for submodular function minimization, a $3n/2-2$ query lower bound for the non-trivial minimizer of a symmetric submodular function, and a $\binom{n}{2}$ query lower bound for the non-trivial minimizer of an asymmetric submodular function. Our $3n/2-2$ lower bound results from a connection between SFM lower bounds and a novel concept we term the cut dimension of a graph. Interestingly, this yields a $3n/2-2$ cut-query lower bound for finding the global mincut in an undirected, weighted graph, but we also prove it cannot yield a lower bound better than $n+1$ for $s$-$t$ mincut, even in a directed, weighted graph

Universality of Long-Range Correlations in Expansion-Randomization Systems

We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent $\chi$ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of $\chi$, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.Comment: 23 pages, 15 figure

Is there a twelfth protein-coding gene in the genome of influenza A? A selection-based approach to the detection of overlapping genes in closely related sequences

Protein-coding genes often contain long overlapping open-reading frames (ORFs), which may or may not be functional. Current methods that utilize the signature of purifying selection to detect functional overlapping genes are limited to the analysis of sequences from divergent species, thus rendering them inapplicable to genes found only in closely related sequences. Here, we present a method for the detection of selection signatures on overlapping reading frames by using closely related sequences, and apply the method to several known overlapping genes, and to an overlapping ORF on the negative strand of segment 8 of influenza A virus (NEG8), for which the suggestion has been made that it is functional. We find no evidence that NEG8 is under selection, suggesting that the intact reading frame might be non-functional, although we cannot fully exclude the possibility that the method is not sensitive enough to detect the signature of selection acting on this gene. We present the limitations of the method using known overlapping genes and suggest several approaches to improve it in future studies. Finally, we examine alternative explanations for the sequence conservation of NEG8 in the absence of selection. We show that overlap type and genomic context affect the conservation of intact overlapping ORFs and should therefore be considered in any attempt of estimating the signature of selection in overlapping gene

Is There a Twelfth Protein-Coding Gene in the Genome of Influenza A? A Selection-Based Approach to the Detection of Overlapping Genes in Closely Related Sequences

Abstract Protein-coding genes often contain long overlapping open-reading frames (ORFs), which may or may not be functional. Current methods that utilize the signature of purifying selection to detect functional overlapping genes are limited to the analysis of sequences from divergent species, thus rendering them inapplicable to genes found only in closely related sequences. Here, we present a method for the detection of selection signatures on overlapping reading frames by using closely related sequences, and apply the method to several known overlapping genes, and to an overlapping ORF on the negative strand of segment 8 of influenza A virus (NEG8), for which the suggestion has been made that it is functional. We find no evidence that NEG8 is under selection, suggesting that the intact reading frame might be non-functional, although we cannot fully exclude the possibility that the method is not sensitive enough to detect the signature of selection acting on this gene. We present the limitations of the method using known overlapping genes and suggest several approaches to improve it in future studies. Finally, we examine alternative explanations for the sequence conservation of NEG8 in the absence of selection. We show that overlap type and genomic context affect the conservation of intact overlapping ORFs and should therefore be considered in any attempt of estimating the signature of selection in overlapping genes

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network’s evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective

SN Refsdal: Classification as a Luminous and Blue SN 1987A-like Type II Supernova

We have acquired Hubble Space Telescope (HST) and Very Large Telescope near-infrared spectra and images of supernova (SN) Refsdal after its discovery as an Einstein cross in Fall 2014. The HST light curve of SN Refsdal matches the distinctive, slowly rising light curves of SN 1987A-like supernovae (SNe), and we find strong evidence for a broad H-alpha P-Cygni profile in the HST grism spectrum at the redshift (z = 1.49) of the spiral host galaxy. SNe IIn, powered by circumstellar interaction, could provide a good match to the light curve of SN Refsdal, but the spectrum of a SN IIn would not show broad and strong H-alpha absorption. From the grism spectrum, we measure an H-alpha expansion velocity consistent with those of SN 1987A-like SNe at a similar phase. The luminosity, evolution, and Gaussian profile of the H-alpha emission of the WFC3 and X-shooter spectra, separated by ~2.5 months in the rest frame, provide additional evidence that supports the SN 1987A-like classification. In comparison with other examples of SN 1987A-like SNe, SN Refsdal has a blue B-V color and a high luminosity for the assumed range of potential magnifications. If SN Refsdal can be modeled as a scaled version of SN 1987A, we estimate it would have an ejecta mass of 20+-5 solar masses. The evolution of the light curve at late times will provide additional evidence about the potential existence of any substantial circumstellar material (CSM). Using MOSFIRE and X-shooter spectra, we estimate a subsolar host-galaxy metallicity (8.3+-0.1 dex and <8.4 dex, respectively) near the explosion site.Comment: Submitted to ApJ; 26 page

CLASH: New Multiple-Images Constraining the Inner Mass Profile of MACS J1206.2-0847

We present a strong-lensing analysis of the galaxy cluster MACS J1206.2-0847 ($z$=0.44) using UV, Optical, and IR, HST/ACS/WFC3 data taken as part of the CLASH multi-cycle treasury program, with VLT/VIMOS spectroscopy for some of the multiply-lensed arcs. The CLASH observations, combined with our mass-model, allow us to identify 47 new multiply-lensed images of 12 distant sources. These images, along with the previously known arc, span the redshift range 1\la z\la5.5, and thus enable us to derive a detailed mass distribution and to accurately constrain, for the first time, the inner mass-profile of this cluster. We find an inner profile slope of $d\log \Sigma/d\log \theta\simeq -0.55\pm 0.1$ (in the range [1\arcsec, 53\arcsec], or 5\la r \la300 kpc), as commonly found for relaxed and well-concentrated clusters. Using the many systems uncovered here we derive credible critical curves and Einstein radii for different source redshifts. For a source at $z_{s}\simeq2.5$, the critical curve encloses a large area with an effective Einstein radius of \theta_{E}=28\pm3\arcsec, and a projected mass of $1.34\pm0.15\times10^{14} M_{\odot}$. From the current understanding of structure formation in concordance cosmology, these values are relatively high for clusters at $z\sim0.5$, so that detailed studies of the inner mass distribution of clusters such as MACS J1206.2-0847 can provide stringent tests of the $\Lambda$CDM paradigm.Comment: 7 pages, 1 table, 4 figures; submitted to ApJ Letters; V3: minor correction

Type Ia Supernova Rate Measurements To Redshift 2.5 From CANDELS: Searching For Prompt Explosions In The Early Universe

dThe Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) was a multi-cycle treasury program on the Hubble Space Telescope (HST) that surveyed a total area of -0.25 deg2 with -900 HST orbits spread across five fields over three years. Within these survey images we discovered 65 supernovae (SNe) of all types, out to z 2.5. We classify -24 of these as Type Ia SNe (SNe Ia) based on host galaxy redshifts and SN photometry (supplemented by grism spectroscopy of six SNe). Here we present a measurement of the volumetric SN Ia rate as a function of redshift, reaching for the first time beyond z =- 2 and putting new constraints on SN Ia progenitor models. Our highest redshift bin includes detections of SNe that exploded when the universe was only -3 Gyr old and near the peak of the cosmic star formation history. This gives the CANDELS high redshift sample unique leverage for evaluating the fraction of SNe Ia that explode promptly after formation ( 40 Myr. However, mild tension is apparent between ground-based low-z surveys and space-based high-z surveys. In both CANDELS and the sister HST program CLASH (Cluster Lensing And Supernova Survey with Hubble), we find a low rate of SNe Ia at z > 1. This could be a hint that prompt progenitors are in fact relatively rare, accounting for only 20% of all SN Ia explosions-though further analysis and larger samples will be needed to examine that suggestion. Key words: infrared: general - supernovae:Astronom

The Cluster Lensing and Supernova Survey with Hubble (CLASH): Strong Lensing Analysis of Abell 383 from 16-Band HST WFC3/ACS Imaging

We examine the inner mass distribution of the relaxed galaxy cluster Abell 383 in deep 16-band HST/ACS+WFC3 imaging taken as part of the CLASH multi-cycle treasury program. Our program is designed to study the dark matter distribution in 25 massive clusters, and balances depth with a wide wavelength coverage to better identify lensed systems and generate precise photometric redshifts. This information together with the predictive strength of our strong-lensing analysis method identifies 13 new multiply-lensed images and candidates, so that a total of 27 multiple-images of 9 systems are used to tightly constrain the inner mass profile, $d\log \Sigma/d\log r\simeq -0.6\pm 0.1$ (r<160 kpc). We find consistency with the standard distance-redshift relation for the full range spanned by the lensed images, 1.01<z<6.03, with the higher redshift sources deflected through larger angles as expected. The inner mass profile derived here is consistent with the results of our independent weak-lensing analysis of wide-field Subaru images, with good agreement in the region of overlap. The overall mass profile is well fitted by an NFW profile with M_{vir}=(5.37^{+0.70}_{-0.63}\pm 0.26) x 10^{14}M_{\odot}/h and a relatively high concentration, c_{vir}=8.77^{+0.44}_{-0.42}\pm 0.23, which lies above the standard c-M relation similar to other well-studied clusters. The critical radius of Abell 383 is modest by the standards of other lensing clusters, r_{E}\simeq16\pm2\arcsec (for z_s=2.55), so the relatively large number of lensed images uncovered here with precise photometric redshifts validates our imaging strategy for the CLASH survey. In total we aim to provide similarly high-quality lensing data for 25 clusters, 20 of which are X-ray selected relaxed clusters, enabling a precise determination of the representative mass profile free from lensing bias. (ABRIDGED)Comment: 15 pages, 14 figures, 2 tabels; V3 matches the submitted version later published in Ap