Bayesian Reconstruction Method Research Articles

Imprints of the large-scale structure on AGN formation and evolution

Black hole masses are found to correlate with several global properties of their host galaxies, suggesting that black holes and galaxies have an intertwined evolution and that active galactic nuclei (AGN) have a significant impact on galaxy evolution. Since the large-scale environment can also affect AGN, this work studies how their formation and properties depend on the environment. We have used a reconstructed three-dimensional high-resolution density field obtained from a Bayesian large-scale structure reconstruction method applied to the 2M++ galaxy sample. A web-type classification relying on the shear tensor is used to identify different structures on the cosmic web, defining voids, sheets, filaments, and clusters. We confirm that the environmental density affects the AGN formation and their properties. We found that the AGN abundance is equivalent to the galaxy abundance, indicating that active and inactive galaxies reside in similar dark matter halos. However, occurrence rates are different for each spectral type and accretion rate. These differences are consistent with the AGN evolutionary sequence suggested by previous authors, Seyferts and Transition objects transforming into low-ionization nuclear emission line regions (LINERs), the weaker counterpart of Seyferts. We conclude that AGN properties depend on the environmental density more than on the web-type. More powerful starbursts and younger stellar populations are found in high densities, where interactions and mergers are more likely. AGN hosts show smaller masses in clusters for Seyferts and Transition objects, which might be due to gas stripping. In voids, the AGN population is dominated by the most massive galaxy hosts.

ABayesQR: A Bayesian Method for Reconstruction of Viral Populations Characterized by Low Diversity.

RNA viruses replicate with high mutation rates, creating closely related viral populations. The heterogeneous virus populations, referred to as viral quasispecies, rapidly adapt to environmental changes thus adversely affecting efficiency of antiviral drugs and vaccines. Therefore, studying the underlying genetic heterogeneity of viral populations plays a significant role in the development of effective therapeutic treatments. Recent high-throughput sequencing technologies have provided invaluable opportunity for uncovering the structure of quasispecies populations. However, accurate reconstruction of viral quasispecies remains difficult due to limited read lengths and presence of sequencing errors. The problem is particularly challenging when the strains in a population are highly similar, that is, the sequences are characterized by low mutual genetic distances, and further exacerbated if some of those strains are relatively rare; this is the setting where state-of-the-art methods struggle. In this article, we present a novel viral quasispecies reconstruction algorithm, aBayesQR, that uses a maximum-likelihood framework to infer individual sequences in a mixture from high-throughput sequencing data. The search for the most likely quasispecies is conducted on long contigs that our method constructs from the set of short reads via agglomerative hierarchical clustering; operating on contigs rather than short reads enables identification of close strains in a population and provides computational tractability of the Bayesian method. Results on both simulated and real HIV-1 data demonstrate that the proposed algorithm generally outperforms state-of-the-art methods; aBayesQR particularly stands out when reconstructing a set of closely related viral strains (e.g., quasispecies characterized by low diversity).

A bayesian method for accelerated magnetic resonance elastography of the liver.

PurposeMagnetic resonance elastography is a noninvasive tool for quantifying soft tissue stiffness. Magnetic resonance elastography has been adopted as a clinical method for staging liver fibrosis. However, the application of liver magnetic resonance elastography requires multiple lengthy breath‐holds. We propose a new data acquisition and processing method to reduce magnetic resonance elastography scan time.MethodsA Bayesian image reconstruction method that uses transform sparsity and magnitude consistency across different phase offsets to recover images from highly undersampled data is proposed. The method is validated using retrospectively down‐sampled phantom data and prospectively down‐sampled in vivo data (N = 86).ResultsThe proposed technique allows accurate quantification of mean liver stiffness up to an acceleration factor of R = 6, enabling acquisition of a slice in 4.3 s. Bland‐Altman analysis indicates that the proposed technique (R = 6) has a bias of −0.04 kPa and limits of agreement of −0.36 to + 0.28 kPa when compared with traditional generalized autocalibrating partial parallel acquisition reconstruction (R = 1.4).ConclusionBy exploiting transform sparsity and magnitude consistency, accurate quantification of mean stiffness in the liver can be obtained at an acceleration rate of up to R = 6. This potentially enables the collection of three to four liver slices, as per clinical protocol, within a single breath‐hold. Magn Reson Med 80:1178–1188, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

A Phylogenetic Overview of the GenusVertigoO. F. Müller, 1773 (Gastropoda: Pulmonata: Pupillidae: Vertigininae)

We document global phylogenetic pattern in the pupillid land snail genus Vertigo by analyses of nDNA (ITS1 and ITS2) and mtDNA (CytB and 16S) sequence from 424 individuals representing 91 putative specific and subspecific Vertigo taxa. nDNA and mtDNA data were separately subjected to neighbor-joining, minimum evolution, maximum likelihood and Bayesian reconstruction methods, with conclusions being drawn from shared topological structures. Six highly supported, reciprocally monophyletic subgeneric level clades were identified: Vertigo, Alaea, Boreovertigo new subgenus, Isthmia, Staurodon and Vertilla. 88 species or subspecies were also confirmed, nine of which are new and formally described herein: V. beringiana, V. chiricahuensis, V. chytryi, V. genesioides, V. kodamai, V. kurilensis, V. lilljeborgi vinlandica, V. pimuensis and V. pisewensis. Thirteen taxa were synonymized: V. arthuri basidens, V. arthuri hubrichti, V. arthuri paradoxa (= V. arthuri); V. allyniana (= V. modesta); V. andrusiana (= V. columbiana); V. conecuhensis (= V. alabamensis); V. dedecora tamagonari (= V. dedecora); V. elatior, V. idahoensis (= V. ventricosa); V. eogea (= V. ovata); V. modesta insculpta (= V. modesta concinnula), V. modesta microphasma, V. modesta sculptilis (= V. modesta castanea). Qualitative observations of conchological features, ecological preferences and geographic coverage were conducted for each subgenus and genetically supported species or subspecies-level taxon. These demonstrated that: (1) a suite of diagnostic shell features usually exists to demarcate each species-level taxon; (2) shell features were incapable of defining genetically validated subgenera; (3) all subgenera had transcontinental ranges; (4) ⅓ of all species possess continental or trans-continental ranges, with very few having range extents < 1,000 km; (5) all subgenera and fully ⅔ of global Vertigo species and subspecies are found in North America, more than 2.5 times the number found in central and eastern Asia, the second most diverse region. This is similar to several other molluscan groups, such as the polygyrid land snails and unionid bivalves for which North America is the global biodiversity hotspot.

Attention training modulates resting-state neurophysiological abnormalities in posttraumatic stress disorder

Recent research indicates the relative benefits of computerized attention control treatment (ACT) and attention bias modification treatment (ABMT) for posttraumatic stress disorder (PTSD); however, neural changes underlying these therapeutic effects remain unknown. This study examines how these two types of attention training modulate neurological dysfunction in veterans with PTSD. A community sample of 46 combat veterans with PTSD participated in a randomized double-blinded clinical trial of ACT versus ABMT and 32 of those veterans also agreed to undergo resting-state magnetoencephalography (MEG) recordings. Twenty-four veterans completed psychological and MEG assessments at pre- and post-training to evaluate treatment effects. MEG data were imaged using an advanced Bayesian reconstruction method and examined using statistical parametric mapping. In this report, we focus on the neural correlates and the differential treatment effects observed using MEG; the results of the full clinical trial have been described elsewhere. Our results indicated that ACT modulated occipital and ABMT modulated medial temporal activity more strongly than the comparative treatment. PTSD symptoms decreased significantly from pre- to post-test. These initial neurophysiological outcome data suggest that ACT modulates visual pathways, while ABMT modulates threat-processing regions, but that both are associated with normalizing aberrant neural activity in veterans with PTSD.

Holographic SAR Tomography Image Reconstruction by Combination of Adaptive Imaging and Sparse Bayesian Inference

In this letter, we propose an imaging algorithm for the holographic synthetic aperture radar tomography in the circumstance of sparse and nonuniform elevation circular passes. Considering the anisotropic behavior of scatterers and the off-grid effect of sparse signal recovery, the algorithm combines the 2-D adaptive imaging method for circular SAR and the sparse Bayesian inference-based method for elevation reconstruction. For each circular pass, the azimuth-range 2-D image can be formed by the adaptive imaging method, which depends on the preretrieved maximum azimuth response angle and the azimuth persistence width. To deal with the off-grid effect in elevation reconstruction, which is caused by the deviation between the true scatterers and the discretized imaging grids, the off-grid sparse Bayesian inference method jointly estimates the scatterers and elevation off-grid error by applying their hierarchical priors. Compared with the conventional compressive sensing method that does not concern the off-grid effect, the proposed algorithm can provide more accurate 3-D reconstruction for pointlike targets, which is verified by the real-data experiments.

Bayesian compressive sensing using wavelet based Markov random fields

Compressive sensing (CS) is a novel method for acquisition of signals below the Nyquist sampling rate. Many signals and images are sparse in the wavelet domain. Therefore, in CS reconstruction algorithms, in addition to the sparsity, tree-structure of wavelet coefficients can be used as a knowledge of the signal. Also, the probability of each element of the sparse vector to be negligible depends on the value of its neighbors. So in this paper, we propose a model which exploits both the tree structure and the neighborhood relation of the coefficients, named wavelet-based Markov random fields (WMRF), and we use Bayesian method for signal reconstruction. Variational Bayesian expectation maximization (VBEM) inference procedure is used to acquire posterior distributions of the model. Also, SESOP algorithm, which is based on MPL estimation, is employed to estimate model parameters. Simulation results demonstrate that the reconstruction error of the proposed algorithm is lower than that of the state-of-the-art algorithms.

Disentangling Timing of Admixture, Patterns of Introgression, and Phenotypic Indicators in a Hybridizing Wolf Population.

Hybridization is a natural or anthropogenic process that can deeply affect the genetic make-up of populations, possibly decreasing individual fitness but sometimes favoring local adaptations. The population of Italian wolves (Canis lupus), after protracted demographic declines and isolation, is currently expanding in anthropic areas, with documented cases of hybridization with stray domestic dogs. However, identifying admixture patterns in deeply introgressed populations is far from trivial. In this study, we used a panel of 170,000 SNPs analyzed with multivariate, Bayesian and local ancestry reconstruction methods to identify hybrids, estimate their ancestry proportions and timing since admixture. Moreover, we carried out preliminary genotype–phenotype association analyses to identify the genetic bases of three phenotypic traits (black coat, white claws, and spur on the hind legs) putative indicators of hybridization. Results showed no sharp subdivisions between nonadmixed wolves and hybrids, indicating that recurrent hybridization and deep introgression might have started mostly at the beginning of the population reexpansion. In hybrids, we identified a number of genomic regions with excess of ancestry in one of the parental populations, and regions with excess or resistance to introgression compared with neutral expectations. The three morphological traits showed significant genotype–phenotype associations, with a single genomic region for black coats and white claws, and with multiple genomic regions for the spur. In all cases the associated haplotypes were likely derived from dogs. In conclusion, we show that the use of multiple genome-wide ancestry reconstructions allows clarifying the admixture dynamics even in highly introgressed populations, and supports their conservation management.

Resting-State Neurophysiological Abnormalities in Posttraumatic Stress Disorder: A Magnetoencephalography Study.

Posttraumatic stress disorder (PTSD) is a debilitating psychiatric condition that is common in veterans returning from combat operations. While the symptoms of PTSD have been extensively characterized, the neural mechanisms that underlie PTSD are only vaguely understood. In this study, we examined the neurophysiology of PTSD using magnetoencephalography (MEG) in a sample of veterans with and without PTSD. Our primary hypothesis was that veterans with PTSD would exhibit aberrant activity across multiple brain networks, especially those involving medial temporal and frontal regions. To this end, we examined a total of 51 USA combat veterans with a battery of clinical interviews and tests. Thirty-one of the combat veterans met diagnostic criteria for PTSD and the remaining 20 did not have PTSD. All participants then underwent high-density MEG during an eyes-closed resting-state task, and the resulting data were analyzed using a Bayesian image reconstruction method. Our results indicated that veterans with PTSD had significantly stronger neural activity in prefrontal, sensorimotor and temporal areas compared to those without PTSD. Veterans with PTSD also exhibited significantly stronger activity in the bilateral amygdalae, parahippocampal and hippocampal regions. Conversely, healthy veterans had stronger neural activity in the bilateral occipital cortices relative to veterans with PTSD. In conclusion, these data suggest that veterans with PTSD exhibit aberrant neural activation in multiple cortical areas, as well as medial temporal structures implicated in affective processing.

DETECTING RELATIVISTIC X-RAY JETS IN HIGH-REDSHIFT QUASARS

ABSTRACT We analyze Chandra X-ray images of a sample of 11 quasars that are known to contain kiloparsec scale radio jets. The sample consists of five high-redshift (z ≥ 3.6) flat-spectrum radio quasars, and six intermediate redshift (2.1 &lt; z &lt; 2.9) quasars. The data set includes four sources with integrated steep radio spectra and seven with flat radio spectra. A total of 25 radio jet features are present in this sample. We apply a Bayesian multi-scale image reconstruction method to detect and measure the X-ray emission from the jets. We compute deviations from a baseline model that does not include the jet, and compare observed X-ray images with those computed with simulated images where no jet features exist. This allows us to compute p-value upper bounds on the significance that an X-ray jet is detected in a pre-determined region of interest. We detected 12 of the features unambiguously, and an additional six marginally. We also find residual emission in the cores of three quasars and in the background of one quasar that suggest the existence of unresolved X-ray jets. The dependence of the X-ray to radio luminosity ratio on redshift is a potential diagnostic of the emission mechanism, since the inverse Compton scattering of cosmic microwave background photons (IC/CMB) is thought to be redshift dependent, whereas in synchrotron models no clear redshift dependence is expected. We find that the high-redshift jets have X-ray to radio flux ratios that are marginally inconsistent with those from lower redshifts, suggesting that either the X-ray emissions are due to the IC/CMB rather than the synchrotron process, or that high-redshift jets are qualitatively different.

Multiple transisthmian divergences, extensive cryptic diversity, occasional long-distance dispersal, and biogeographic patterns in a marine coastal isopod with an amphi-American distribution.

Excirolana braziliensis is a coastal intertidal isopod with a broad distribution spanning the Atlantic and Pacific tropical and temperate coasts of the American continent. Two separate regional studies (one in Panama and one in Chile) revealed the presence of highly genetically divergent lineages, implying that this taxon constitutes a cryptic species complex. The relationships among the lineages found in these two different regions and in the rest of the distribution, however, remain unknown. To better understand the phylogeographic patterns of E. braziliensis, we conducted phylogenetic analyses of specimens from much of its entire range. We obtained DNA sequences for fragments of four mitochondrial genes (16S rDNA, 12S rDNA, COI, and Cytb) and also used publicly available sequences. We conducted maximum likelihood and Bayesian phylogenetic reconstruction methods. Phylogeographic patterns revealed the following: (1) new highly divergent lineages of E. braziliensis; (2) three instances of Atlantic–Pacific divergences, some of which appear to predate the closure of the Isthmus of Panama; (3) the distributional limit of highly divergent lineages found in Brazil coincides with the boundary between two major marine coastal provinces; (4) evidence of recent long‐distance dispersal in the Caribbean; and (5) populations in the Gulf of California have closer affinities with lineages further south in the Pacific, which contrasts with the closer affinity with the Caribbean reported for other intertidal organisms. The high levels of cryptic diversity detected also bring about challenges for the conservation of this isopod and its fragile environment, the sandy shores. Our findings underscore the importance of comprehensive geographic sampling for phylogeographic and taxonomical studies of broadly distributed putative species harboring extensive cryptic diversity.

Phylogeny of Mental Glands, Revisited.

Mental glands and their associated delivery behaviors during courtship are unique to the plethodontid salamanders. Because previous interpretations of the evolution of these features were conducted using older phylogenetic hypotheses, we reanalyzed these traits with newer courtship descriptions and contemporary phylogenetic methods. Using Bayesian ancestral state reconstruction methods that have been developed since the first phylogenetic analyses were conducted in the mid-1990s, we reconstructed mental gland and courtship behavior evolution on a Bayesian phylogeny of the nuclear gene Rag1. The most probable ancestral condition for plethodontids was resolved as presence of a mental gland. Loss of a mental gland occurred in each subfamily and was recovered as the most probable ancestral condition for the Spelerpinae. In contrast, parsimony reconstruction recovered the presence of a mental gland in the ancestor to Spelerpinae with multiple secondary losses. We hypothesize that that absence of a mental gland is possibly ancestral in some clades (i.e., Spelerpinae) and secondary in others (e.g., paedomorphic Eurycea). The most probable ancestral form of the mental gland is likely to be the large pad-type distributed extensively in Plethodontinae and Bolitoglossinae. Desmognathans have the most unique mental glands, occurring in an anterior protrusion or bifurcated form (in Desmognathus wrighti). Fan-shaped mental glands evolved independently in Eurycea and Oedipina. Small pads arose independently in Bolitoglossinae, Plethodontinae, and Spelerpinae. Head-rubbing behavior for mental gland delivery mode was recovered as the most probable and parsimonious ancestral state for the Plethodontidae, with independent losses of this behavior in Plethodontinae and Spelerpinae. Because head-rubbing was observed in outgroups, we hypothesize that head-rubbing behavior predated mental gland evolution. Pulling, snapping, slapping, and biting behaviors evolved independently in the Plethodontinae and Spelerpinae and are not homologous with head-rubbing. All hypotheses of mental gland and courtship evolution invoke homoplasy.

Bayesian redshift-space distortions correction from galaxy redshift surveys

AbstractWe present a Bayesian reconstruction method which maps a galaxy distribution from redshift- to real-space inferring the distances of the individual galaxies. The method is based on sampling density fields assuming a lognormal prior with a likelihood modelling non-linear stochastic bias. Coherent redshift-space distortions are corrected in a Gibbs-sampling procedure by moving the galaxies from redshift- to real-space according to the peculiar motions derived from the recovered density field using linear theory. The virialized distortions are corrected by sampling candidate real-space positions along the line of sight, which are compatible with the bulk flow corrected redshift-space position adding a random dispersion term in high-density collapsed regions (defined by the eigenvalues of the Hessian). This approach presents an alternative method to estimate the distances to galaxies using the three-dimensional spatial information, and assuming isotropy. Hence the number of applications is very broad. In this work, we show the potential of this method to constrain the growth rate up to k ∼ 0.3 h Mpc−1. Furthermore it could be useful to correct for photometric redshift errors, and to obtain improved baryon acoustic oscillations (BAO) reconstructions.

Detecting reticulate relationships among diploid Leucanthemum Mill. (Compositae, Anthemideae) taxa using multilocus species tree reconstruction methods and AFLP fingerprinting

We examined the evolutionary history of the diploid representatives of the genus Leucanthemum Mill. (Compositae, Anthemideae), which constitutes an extensive polyploid complex comprising around 41 species with ploidy levels ranging from 2x to 22x. The inference of phylogenetic relationships even on the diploid level is complicated in this genus due to the overlay of hybridisation and incomplete lineage sorting processes leading to incongruence among gene trees based on nuclear and plastid sequence information. Species tree and network reconstructions were based on gene trees from nine low-copy nuclear markers and the concatenated sequence information for five intergenic spacer regions of the chloroplast genome, either sequenced by Roche 454 pyrosequencing techniques or traditional Sanger sequencing techniques. Additional phylogenetic information came from multi-locus AFLP-fingerprinting of representative individuals of all diploid taxa under study and the subsequent analysis of AFLP patterns with Bayesian clustering and network reconstruction methods. To distinguish between hybridisation and incomplete lineage sorting, we developed and utilized a new ‘hybrid index’ calculation for individual taxa of the data set, which was compared to a simulated null-distribution assuming the occurrence of incomplete lineage sorting alone for pinpointing taxa with a significant hybrid signal. As a result, two species groups with contrasting patterns of gene flow and/or hybrid speciation signals could be identified in the diploids of Leucanthemum: (a) an early-diverging stock of allopatrically distributed diploid species with a lack of evidence for recent hybridisation events among its members and (b) a more recently radiated taxon assemblage with morphologically less clearly circumscribed taxa and a pronounced signal of gene flow among lineages and several candidate taxa, for which a homoploid hybrid origin may be considered.

A Bayesian sparse reconstruction method for fault detection and isolation

This article develops a Bayesian method for fault detection and isolation using a sparse reconstruction framework. The normal/training data is assumed to follow a signal‐plus‐noise model, and an indicator matrix is used to show whether the test data is from a faulty process. The distribution of the indicator matrix is modeled by a Laplacian distribution, which forces the indicator matrix to be a sparse one, and a Gibbs sampler is derived to obtain the estimation/reconstruction of the indicator matrix, the unobserved signals, and other parameters like signal mean, covariance, and noise variance. The faulty variables can then be detected and isolated by inspecting whether corresponding rows of the indicator matrix are zero. The proposed Bayesian approach is data driven; it allows for simultaneous fault detection and isolation. A simulation study and an industrial case study are used to test the performance of the proposed method. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Bayesian Method for Shape Reconstruction in the Inverse Interior Scattering Problem

The inverse scattering problem of an interior cavity with three different boundary conditions is considered. Bayesian method is used to reconstruct the shape of the cavity from scattered fields incited by point source(s) and measured on a closed curve inside the cavity. We prove the well-posedness in Bayesian perspective and present numerical examples to show the viability of the method.

Surveillance of Echinococcus isolates from Qinghai, China

Echinococcosis is highly endemic over large parts of the Qinghai–Tibet Plateau (QTP), China. Based on a large number of samples, we present data on the current presence, host distribution, and genetic diversity of Echinococcus in the Qinghai Province, located in the northeastern corner of the QTP and constituting >25% of the area of the plateau. We used 521 samples (including 451 newly collected samples and 70 samples from our previous study) from humans, yaks, sheep, goats, dogs, fox, plateau pikas, and voles in 36 counties, and genotyped them using the mitochondrial DNA marker cytochrome oxidase subunit I (cox1) gene and the maximum parsimony and Bayesian reconstruction methods. Based on the 792bp sequence matrix, we recorded 177 variable sites; 157 were parsimony-informative. A total of 105 haplotypes (H1–H105) were detected, of which H1–H15 and H90–H104, H16–H17, H18–H89, and H105 belonged to Echinococcus shiquicus, Echinococcus multilocularis, Echinococcus granulosus, and Echinococcus canadensis, respectively. Our results showed that, (i) the Qinghai Province was under a high burden of Echinococcus epidemiology; (ii) E. granulosus was the main echinococcosis threat to the local people, and the followed is E. multilocularis; (iii) there are a considerable number of haplotypes shared by domestic animals (sheep, yaks, and dogs) and humans, demonstrating the close relationship between human and domestic animals epidemiology; (iv) the threat of E. shiquicus on humans and livestock can be mostly ignored, while the infection risk of E. canadensis echinococcosis should not be neglected.

An evolutionary analysis of the Secoviridae family of viruses.

The plant-infecting Secoviridae family of viruses forms part of the Picornavirales order, an important group of non-enveloped viruses that infect vertebrates, arthropods, plants and algae. The impact of the secovirids on cultivated crops is significant, infecting a wide range of plants from grapevine to rice. The overwhelming majority are transmitted by ecdysozoan vectors such as nematodes, beetles and aphids. In this study, we have applied a variety of computational methods to examine the evolutionary traits of these viruses. Strong purifying selection pressures were calculated for the coat protein (CP) sequences of nine species, although for two species evidence of both codon specific and episodic diversifying selection were found. By using Bayesian phylogenetic reconstruction methods CP nucleotide substitution rates for four species were estimated to range from between 9.29×10−3 to 2.74×10−3 (subs/site/year), values which are comparable with the short-term estimates of other related plant- and animal-infecting virus species. From these data, we were able to construct a time-measured phylogeny of the subfamily Comovirinae that estimated divergence of ninety-four extant sequences occurred less than 1,000 years ago with present virus species diversifying between 50 and 250 years ago; a period coinciding with the intensification of agricultural practices in industrial societies. Although recombination (modularity) was limited to closely related taxa, significant and often unique similarities in the protein domains between secovirid and animal infecting picorna-like viruses, especially for the protease and coat protein, suggested a shared ancestry. We discuss our results in a wider context and find tentative evidence to indicate that some members of the Secoviridae might have their origins in insects, possibly colonizing plants in a number of founding events that have led to speciation. Such a scenario; virus infection between species of different taxonomic kingdoms, has significant implications for virus emergence.

A non-stationary image prior combination in super-resolution

A new Bayesian Super-Resolution (SR) image registration and reconstruction method is proposed. The new method utilizes a prior distribution based on a general combination of spatially adaptive, or non-stationary, image filters, which includes an adaptive local strength parameter able to preserve both image edges and textures. With the application of variational techniques, the proposed method allows for the automatic estimation of all problem unknowns. An experimental comparison between state of the art methods and the proposed SR approach has been performed on both synthetic and real images.

Phylogenetic Systematics of the Mesa Mints: &lt;I&gt;Pogogyne&lt;/I&gt; (Lamiaceae)

Abstract Pogogyne (Lamiaceae) is a small genus of annual plants, occurring almost entirely in vernal pool habitats. To infer the phylogenetic relationships of this group, DNA sequence data from the trnQ-rps16 chloroplast spacer and both ETS and ITS nuclear regions were obtained from all seven extant species and several outgroups and analyzed using both parsimony and Bayesian phylogeny reconstruction methods. Ancestral state reconstructions were performed for morphological characters that have been used to separate groups within Pogogyne. This study indicates that subgenus Hedeomoides is monophyletic with good support and can be diagnosed by two apomorphies: a reduction in stamen number and a reduced corolla size. Subgenus Pogogyne is paraphyletic, but with poor support. Several clades within the genus Pogogyne have discrete biogeographic distributions. The Pogogyne genus clade has a relatively long stem lineage, but its crown clade has quite short branches. Our estimate for the mean divergence time of the...