Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Monads in double categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and dene what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.

Estudi de la reformació amb vapor de biocombustibles per a l'obtenció d'hidrogen utilitzant suports estructurats ceràmics funcionalitzats

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Aspectes geomètrics i dinàmics de transformacions racionals planes

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Strong isomorphism reductions in complexity theory

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

Consistency and optimality

Assume that the problem Qo is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T U {ConT} as the minimal extension of T proving for some algorithm that it decides Qo as fast as any algorithm B with the property that T proves that B decides Qo. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Protein-binding site at the immunoglobulin mu membrane polyadenylylation signal: possible role in transcription termination.

mRNAs specifying immunoglobulin mu and delta heavy chains are encoded by a single large, complex transcription unit (mu + delta gene). The transcriptional activity of delta gene segments in terminally differentiated, IgM-secreting B lymphocytes is 10-20 times lower than in earlier B-lineage cells expressing delta mRNA. We find that transcription of the mu + delta gene in IgM-secreting murine myeloma cells terminates within a region of 500-1000 nucleotides immediately following the mu membrane (mu m) polyadenylylation site. Transcription decreases only minimally through this region in murine cell lines representative of earlier stages in B-cell development. A DNA fragment containing the mu m polyadenylylation signal gives protein-DNA complexes with different mobilities in gel retardation assays with nuclear extracts from myeloma cells than with nuclear extracts from earlier B-lineage cells. However, using a recently developed "footprinting" procedure in which protein-DNA complexes resolved in gel retardation assays are subjected to nucleolytic cleavage while still in the polyacrylamide gel, we find that the DNA sequences protected by factors from the two cell types are indistinguishable. The factor-binding site on the DNA is located 5' of the mu m polyadenylylation signal AATAAA and includes the 15-nucleotide-long A + T-rich palindrome CTGTAAACAAATGTC. This type of palindromic binding site exhibits orientation-dependent activity consistent with the reported properties of polymerase II termination signals. This binding site is followed by two sets of directly repeated DNA sequences with different helical conformation as revealed by their reactivity with the chemical nuclease 1,10-phenanthroline-copper. The close proximity of these features to the signals for mu m mRNA processing may reflect a linkage of the processes of developmentally regulated mu m polyadenylylation and transcription termination.

Cooperative binding of estrogen receptor to imperfect estrogen-responsive DNA elements correlates with their synergistic hormone-dependent enhancer activity.

The Xenopus vitellogenin (vit) gene B1 estrogen-inducible enhancer is formed by two closely adjacent 13 bp imperfect palindromic estrogen-responsive elements (EREs), i.e. ERE-2 and ERE-1, having one and two base substitutions respectively, when compared to the perfect palindromic consensus ERE (GGTCANNNTGACC). Gene transfer experiments indicate that these degenerated elements, on their own, have a low or no regulatory capacity at all, but in vivo act together synergistically to confer high receptor- and hormone-dependent transcription activation to the heterologous HSV thymidine kinase promoter. Thus, the DNA region upstream of the vitB1 gene comprising these two imperfect EREs separated by 7 bp, was called the vitB1 estrogen-responsive unit (vitB1 ERU). Using in vitro protein-DNA interaction techniques, we demonstrate that estrogen receptor dimers bind cooperatively to the imperfect EREs of the vitB1 ERU. Binding of a first receptor dimer to the more conserved ERE-2 increases approximately 4- to 8-fold the binding affinity of the receptor to the adjacent less conserved ERE-1. Thus, we suggest that the observed synergistic estrogen-dependent transcription activation conferred by the pair of hormone-responsive DNA elements of the vit B1 ERU is the result of cooperative binding of two estrogen receptor dimers to these two adjacent imperfect EREs.

Publication trends of shared decision making in 15 high impact medical journals: a full-text review with bibliometric analysis.

BACKGROUND: Shared Decision Making (SDM) is increasingly advocated as a model for medical decision making. However, there is still low use of SDM in clinical practice. High impact factor journals might represent an efficient way for its dissemination. We aimed to identify and characterize publication trends of SDM in 15 high impact medical journals. METHODS: We selected the 15 general and internal medicine journals with the highest impact factor publishing original articles, letters and editorials. We retrieved publications from 1996 to 2011 through the full-text search function on each journal website and abstracted bibliometric data. We included publications of any type containing the phrase "shared decision making" or five other variants in their abstract or full text. These were referred to as SDM publications. A polynomial Poisson regression model with logarithmic link function was used to assess the evolution across the period of the number of SDM publications according to publication characteristics. RESULTS: We identified 1285 SDM publications out of 229,179 publications in 15 journals from 1996 to 2011. The absolute number of SDM publications by journal ranged from 2 to 273 over 16 years. SDM publications increased both in absolute and relative numbers per year, from 46 (0.32% relative to all publications from the 15 journals) in 1996 to 165 (1.17%) in 2011. This growth was exponential (P < 0.01). We found fewer research publications (465, 36.2% of all SDM publications) than non-research publications, which included non-systematic reviews, letters, and editorials. The increase of research publications across time was linear. Full-text search retrieved ten times more SDM publications than a similar PubMed search (1285 vs. 119 respectively). CONCLUSION: This review in full-text showed that SDM publications increased exponentially in major medical journals from 1996 to 2011. This growth might reflect an increased dissemination of the SDM concept to the medical community.

Clinical and molecular epidemiology of extended-spectrum beta-lactamase-producing Escherichia coli as a cause of nosocomial infection or colonization: implications for control.

BACKGROUND: Extended-spectrum beta-lactamase (ESBL)-producing members of the Enterobacteriaceae family are important nosocomial pathogens. Escherichia coli producing a specific family of ESBL (the CTX-M enzymes) are emerging worldwide. The epidemiology of these organisms as causes of nosocomial infection is poorly understood. The aims of this study were to investigate the clinical and molecular epidemiology of nosocomial infection or colonization due to ESBL-producing E. coli in hospitalized patients, consider the specific types of ESBLs produced, and identify the risk factors for infection and colonization with these organisms. METHODS: All patients with nosocomial colonization and/or infection due to ESBL-producing E. coli in 2 centers (a tertiary care hospital and a geriatric care center) identified between January 2001 and May 2002 were included. A double case-control study was performed. The clonal relatedness of the isolates was studied by repetitive extragenic palindromic-polymerase chain reaction and pulsed-field gel electrophoresis. ESBLs were characterized by isoelectric focusing, polymerase chain reaction, and sequencing. RESULTS: Forty-seven case patients were included. CTX-M-producing E. coli were clonally unrelated and more frequently susceptible to nonoxyimino-beta-lactams. Alternately, isolates producing SHV- and TEM-type ESBL were epidemic and multidrug resistant. Urinary catheterization was a risk factor for both CTX-M-producing and SHV-TEM-producing isolates. Previous oxyimino-beta-lactam use, diabetes, and ultimately fatal or nonfatal underlying diseases were independent risk factors for infection or colonization with CTX-M-producing isolates, whereas previous fluoroquinolone use was associated with infection or colonization with SHV-TEM-producing isolates. CONCLUSIONS: The epidemiology of ESBL-producing E. coli as a cause of nosocomial infection is complex. Sporadic CTX-M-producing isolates coexisted with epidemic multidrug-resistant SHV-TEM-producing isolates. These data should be taken into account for the design of control measures.

On optimal computation of MPLS label binding for multipoint-to-point connections

Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in Multiprotocol Label Switched (MPLS) networks using label merging - better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have tree- shapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS - the Merging Problem - cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a hard- decision problem. However, in this letter, the Merging Problem is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the Merging Problem as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced