Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

SLAM using an Imaging Sonar for Partially Structured Underwater Environments

In this paper we describe a system for underwater navigation with AUVs in partially structured environments, such as dams, ports or marine platforms. An imaging sonar is used to obtain information about the location of planar structures present in such environments. This information is incorporated into a feature-based SLAM algorithm in a two step process: (I) the full 360deg sonar scan is undistorted (to compensate for vehicle motion), thresholded and segmented to determine which measurements correspond to planar environment features and which should be ignored; and (2) SLAM proceeds once the data association is obtained: both the vehicle motion and the measurements whose correct association has been previously determined are incorporated in the SLAM algorithm. This two step delayed SLAM process allows to robustly determine the feature and vehicle locations in the presence of large amounts of spurious or unrelated measurements that might correspond to boats, rocks, etc. Preliminary experiments show the viability of the proposed approach

Activity of the δ-Opioid Receptor Is Partially Reduced, Whereas Activity of the κ-Receptor Is Maintained in Mice Lacking the μ-Receptor

Previous pharmacological studies have indicated the possible existence of functional interactions between μ-, δ- and κ-opioid receptors in the CNS. We have investigated this issue using a genetic approach. Here we describe in vitro and in vivo functional activity of δ- and κ-opioid receptors in mice lacking the μ-opioid receptor (MOR). Measurements of agonist-induced [35S]GTPγS binding and adenylyl cyclase inhibition showed that functional coupling of δ- and κ-receptors to G-proteins is preserved in the brain of mutant mice. In the mouse vas deferens bioassay, deltorphin II and cyclic[d-penicillamine2,d-penicillamine5] enkephalin exhibited similar potency to inhibit smooth muscle contraction in both wild-type and MOR −/− mice. δ-Analgesia induced by deltorphin II was slightly diminished in mutant mice, when the tail flick test was used. Deltorphin II strongly reduced the respiratory frequency in wild-type mice but not in MOR −/− mice. Analgesic and respiratory responses produced by the selective κ-agonist U-50,488H were unchanged in MOR-deficient mice. In conclusion, the preservation of δ- and κ-receptor signaling properties in mice lacking μ-receptors provides no evidence for opioid receptor cross-talk at the cellular level. Intact antinociceptive and respiratory responses to the κ-agonist further suggest that the κ-receptor mainly acts independently from the μ-receptor in vivo. Reduced δ-analgesia and the absence of δ-respiratory depression in MOR-deficient mice together indicate that functional interactions may take place between μ-receptors and central δ-receptors in specific neuronal pathways.

On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Generalized canonical correlation analysis of matrices with different row and column orders

A Method is offered that makes it possible to apply generalized canonicalcorrelations analysis (CANCOR) to two or more matrices of different row and column order. The new method optimizes the generalized canonical correlationanalysis objective by considering only the observed values. This is achieved byemploying selection matrices. We present and discuss fit measures to assessthe quality of the solutions. In a simulation study we assess the performance of our new method and compare it to an existing procedure called GENCOM,proposed by Green and Carroll. We find that our new method outperforms the GENCOM algorithm both with respect to model fit and recovery of the truestructure. Moreover, as our new method does not require any type of iteration itis easier to implement and requires less computation. We illustrate the methodby means of an example concerning the relative positions of the political parties inthe Netherlands based on provincial data.

Diagenetic processes in a partially dolomitized carbonate reservoir: Casablanca oil field, Valencia Trough, offshore Spain.

Mesozoic and Neogene carbonates located in the Valencia Trough (offshore Spain, western Mediterranean Sea)are oil reservoirs. This paper investigates the diagenetic evolution of the Upper Jurassic limestones, currently dolomitized, that constitute the main reservoir of the Casablanca oil field. Core samples from Casablanca-1A well have been studied to determine the diagenetic products and their relation with porosity evolution, and to reconstruct the fluid flow history prior to and during oil emplacement. On the basis of petrological observations and geochemical analyses (major, minor and trace element composition and oxygen, carbon and strontium isotope composition), a major dolomitization event is recognized postdating subaerial exposure, erosion and karstification. The dolomitization event originated two replacive dolomites (RD1 and RD2) and two dolomite cements (saddle dolomite cement, SDC, and milky-white dolomite cement, MDC)which are partially cogenetic. RD1, RD2 and SDC precipitated at increasing temperatures (over 60ºC and below 110ºC), probably from meteoric water mixed with marine water. The last dolomite type milky-white dolomite cement) precipitated with increasing burial conditions and by arrival of hydrothermal fluids during the Miocene. The post-dolomitization sequence comprises precipitation of calcite cement and partial calcitization of all previous dolomites. The oxygen, carbon and strontium isotope compositions suggest that this calcite cementation occurred from meteoric waters mixed with Burdigalian - Langhian marine waters trapped in the sediments and expelled by compaction in the moderate to deep burial realm. Normal faults were the conduits for upward migration of these fluids as well as for later oil expulsion from the Burdigalian - Langhian source rocks. Late corrosion associated with organic acid-enriched fluids took place prior or simultaneously to oil migration during the Pliocene, enhancing porosity and increasing eservoir quality.

Evidence for the influence of the North Atlantic Oscillation on the total ozone column at northern low latitudes and midlatitudes during winter and summer seasons.

The strong influence of the winter North Atlantic Oscillation (NAO) on the total ozone column (TOC) in the Northern Hemisphere has been reported in a number of previous studies. In this study we show that this influence is not restricted to the winter season but is also significant in summer. Especially interesting effects of the summer NAO (SNAO) on the TOC are observed over the eastern Mediterranean region, where a strongly positive SNAO index is related to the creation of a geopotential height-negative anomaly over Greece with maximum amplitude at 200 hPa. Another anomaly was observed west of the Iberian Peninsula with similar effects on the TOC. Analyzing 26 years of Total Ozone Mapping Spectrometer (TOMS) and Ozone Monitoring Instrument (OMI) data from the equator to midlatitudes (60°) in the Northern Hemisphere, we demonstrate that the SNAO accounts for up to 30% of the TOC variability with a strong latitudinal and longitudinal dependence. Additionally, we obtain significant correlations between the NAO index and the thermal tropopause pressure and also with the geopotential heights at 200 and 500 hPa. Finally, some indirect connections between NAO and the TOC through teleconnections are also discussed.

Finding and characterizing Partially Methylated Domains in human haematopoietic cells

DNA cytosine methylation has been demonstrated to be a central epigenetic modification that has essential roles in a myriad of cellular processes. Some examples of these include gene regulation, DNA-protein interactions, cellular differentiation, X-inactivation, maintenance of genome integrity by suppressing transposable elements and viruses, embryogenesis, genomic imprinting and tumourigenesis. This list is increasingly growing thanks to recent advances in genome-wide technologies, like Whole Genome Bisulfite Sequencing (WGBS-Seq). The development of this technology in research has allowed the identification of new features of the DNA methylation landscape that was not possible using previous technologies, like Partially Methylated Domains (PMDs). PMDs have been found in several cell lines, as well as in both healthy and cancer primary samples. They have been described as regions with high variability in methylation levels across individual CpG sites and intermediate methylation levels on average with respect to the genome. Here, we performed an extensive search of PMDs in a big dataset of different haematopoietic primary cells from both myeloid and lymphoid lineages. We found and characterized significant PMDs in plasma B cells, confirming that PMDs are a phenomenon that is restricted to certain differentiated cells. Additionally, we found loci aberrantly hypomethylated in a myeloma sample which overlapped with plasma B cell PMDs. Genome-wide comparison of the myeloma and plasma B cell sample revealed that this is probably also the case for other loci.