Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

Observations on some large mammals of the Transaltai, Djungarian and Shargin Gobi, Mongolia

Résultats des missions préliminaires à l’établissement d’un Parc National de 3 800 000 ha et d’une Réserve de 900 000 ha en République Populaire de Mongolie. La faune des grands mammi fères de la région est encore riche et des renseignements biolo giques sont donnés sur plusieurs espèces. Le cheval de Przewalski est malheureusement disparu à l’état sauvage.This paper describes the efforts being made by the Mongolian authorities to protect the Fauna and Flora of the Gobi region and records significant observations made during a series of expedi tions to this region organized from 1972 to 1976, particularly on Panther a unicaf Canis lupus , Ursus pruinosus , Equus przewalskii, Equus hemionus, Camelus bactrianus, Capra sibirica, Ovis ammon, Gazella subgutturosa and Saiga tatarica mongolica

HIV-1 Accessory Proteins Impart a Modest Interferon Response and Upregulate Cell Cycle-Related Genes in Macrophages

HIV-1 infection of myeloid cells is associated with the induction of an IFN response. How HIV-1 manipulates and subverts the IFN response is of key interest for the design of therapeutics to improve immune function and mitigate immune dysregulation in people living with HIV. HIV-1 accessory genes function to improve viral fitness by altering host pathways in ways that enable transmission to occur without interference from the immune response. We previously described changes in transcriptomes from HIV-1 infected and from IFN-stimulated macrophages and noted that transcription of IFN-regulated genes and genes related to cell cycle processes were upregulated during HIV-1 infection. In the present study, we sought to define the roles of individual viral accessory genes in upregulation of IFN-regulated and cell cycle-related genes using RNA sequencing. We observed that Vif induces a set of genes involved in mitotic processes and that these genes are potently downregulated upon stimulation with type-I and -II IFNs. Vpr also upregulated cell cycle-related genes and was largely responsible for inducing an attenuated IFN response. We note that the induced IFN response most closely resembled a type-III IFN response. Vpu and Nef-regulated smaller sets of genes whose transcriptomic signatures upon infection related to cytokine and chemokine processes. This work provides more insight regarding processes that are manipulated by HIV-1 accessory proteins at the transcriptional level.This research was partially funded by the National Institutes of Health, grants AI143567-02 (V.P. and M.C.) and AI122377-05 (V.P.) and by startup funds from the Department of Pathology, University of Utah School of Medicine (T.M.H.).S

SAMHD1 Phosphorylation Coordinates the Anti-HIV-1 Response by Diverse Interferons and Tyrosine Kinase Inhibition.

Macrophages are susceptible to human immunodeficiency virus type 1 (HIV-1) infection despite abundant expression of antiviral proteins. Perhaps the most important antiviral protein is the restriction factor sterile alpha motif domain and histidine/aspartic acid domain-containing protein 1 (SAMHD1). We investigated the role of SAMHD1 and its phospho-dependent regulation in the context of HIV-1 infection in primary human monocyte-derived macrophages and the ability of various interferons (IFNs) and pharmacologic agents to modulate SAMHD1. Here we show that stimulation by type I, type II, and to a lesser degree, type III interferons share activation of SAMHD1 via dephosphorylation at threonine-592 as a consequence of signaling. Cyclin-dependent kinase 1 (CDK1), a known effector kinase for SAMHD1, was downregulated at the protein level by all IFN types tested. Pharmacologic inhibition or small interfering RNA (siRNA)-mediated knockdown of CDK1 phenocopied the effects of IFN on SAMHD1. A panel of FDA-approved tyrosine kinase inhibitors potently induced activation of SAMHD1 and subsequent HIV-1 inhibition. The viral restriction imposed via IFNs or dasatinib could be overcome through depletion of SAMHD1, indicating that their effects are exerted primarily through this pathway. Our results demonstrate that SAMHD1 activation, but not transcriptional upregulation or protein induction, is the predominant mechanism of HIV-1 restriction induced by type I, type II, and type III IFN signaling in macrophages. Furthermore, SAMHD1 activation presents a pharmacologically actionable target through which HIV-1 infection can be subverted

Sequence stratigraphy, basin morphology and sea-level history for the Permian Kapp Starostin Formation of Svalbard, Norway

Based on seven measured sections from Svalbard, the marine strata of the Permian Kapp Starostin Formation are arranged into seven transgressive–regressive sequences (TR1–TR7) of c. 4–5 Ma average duration, each bound by a maximum regressive surface. Facies, including heterozoan-dominated limestones, spiculitic cherts, sandstones, siltstones and shales, record deposition within inner, middle and outer shelf areas. The lowermost sequence, TR1, comprises most of the basal Vøringen Member, which records a transgression across the Gipshuken Formation following a hiatus of unknown duration. Temperate to cold, storm-dominated facies established in inner to middle shelf areas between the latest Artinskian and Kungurian. Prolonged deepening during sequences TR2 and TR3 was succeeded by a long-term shallowing-upward trend that lasted until the latest Permian (TR4–TR7). A major depocentre existed in central and western Spitsbergen while to the north, Dickson Land remained a shallow platform, leading to a shallow homoclinal ramp in NE Spitsbergen and Nordaustlandet. The Middle Permian extinction (late Capitanian) is recorded near the base of TR6 in deeper parts of the basin only; elsewhere this sequence is not recorded. Likewise the youngest sequence, TR7, extending to the upper formational contact of latest Permian age, is found only in the basin depocentre. Comparison with age-equivalent strata in the Sverdrup Basin of Canada reveals a remarkably similar depositional history, with, for example, two (third-order) sea-level cycles recorded in the Late Permian of both regions, in keeping with the global record. Sequence stratigraphy may therefore be a powerful correlative tool for onshore and offshore Permian deposits across NW Pangaea

A process-based model of conifer forest structure and function with special emphasis on leaf lifespan

We describe the University of Sheffield Conifer Model (USCM), a process-based approach for simulating conifer forest carbon, nitrogen, and water fluxes by up-scaling widely applicable relationships between leaf lifespan and function. The USCM is designed to predict and analyze the biogeochemistry and biophysics of conifer forests that dominated the ice-free high-latitude regions under the high pCO2 “greenhouse” world 290–50 Myr ago. It will be of use in future research investigating controls on the contrasting distribution of ancient evergreen and deciduous forests between hemispheres, and their differential feedbacks on polar climate through the exchange of energy and materials with the atmosphere. Emphasis is placed on leaf lifespan because this trait can be determined from the anatomical characteristics of fossil conifer woods and influences a range of ecosystem processes. Extensive testing of simulated net primary production and partitioning, leaf area index, evapotranspiration, nitrogen uptake, and land surface energy partitioning showed close agreement with observations from sites across a wide climatic gradient. This indicates the generic utility of our model, and adequate representation of the key processes involved in forest function using only information on leaf lifespan, climate, and soils

Carboniferous and Permian Rugosochonetidae (Brachiopoda) from West Spitsbergen

The rugosochonetid brachiopod species Lissochonetes geinitzianus from the Kazimovian of the Nordenskioldbreen Formation, and Dyoros (Dyoros) mucronata sp. nov., Dyoros (Dyoros) spitzbergianus and Lissochonetes superba from the Artinskian to latest Permian Kapp Starostin Formation in West Spitsbergen are described and figured. Dyoros is generally restricted to the Boreal Realm, whereas Lissochonetes is mostly distributed in the Boreal Realm, but occasionally present in the Palaeoequatorial and Gondwanan Realms<br /

Palaeomagnetic age constraints on folding and faulting events in Devonian carbonates of the Kielce Fold Zone (southern Holy Cross Mountains, Central Poland)

The results of numerous palaeomagnetic studies performed in the last three decades in Devonian carbonates of the Holy Cross Mountains (HCM) have documented the occurrence of several episodes of remagnetisation. This knowledge was applied in this study to determine the temporal relationships between the acquisition of particular secondary palaeomagnetic components and the formation of tectonic structures. This made it possible to estimate the timing of several episodes in the multistage tectonic evolution of particular folds and faults. We show that the westernmost part of the southern HCM was rotated clockwise after the early Permian. Detailed palaeomagnetic analysis documented also shape modifications in some map-scale and minor folds. This tectonic overprinting of originally Carboniferous folds postdated the early Permian. It was furthermore shown that the N-S trending dextral strike-slip faults studied were active between the early Permian and the Permo/Triassic. Our recent data show also the post-early Permian age of breccia that covers the deformed Devonian strata