The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme. DOI: 10.1103/PhysRevB.86.214204

A Mutational Hotspot and Strong Selection Contribute to the Order of Mutations Selected for during Escherichia coli Adaptation to the Gut

The relative role of drift versus selection underlying the evolution of bacterial species within the gut microbiota remains poorly understood. The large sizes of bacterial populations in this environment suggest that even adaptive mutations with weak effects, thought to be the most frequently occurring, could substantially contribute to a rapid pace of evolutionary change in the gut. We followed the emergence of intra-species diversity in a commensal Escherichia coli strain that previously acquired an adaptive mutation with strong effect during one week of colonization of the mouse gut. Following this first step, which consisted of inactivating a metabolic operon, one third of the subsequent adaptive mutations were found to have a selective effect as high as the first. Nevertheless, the order of the adaptive steps was strongly affected by a mutational hotspot with an exceptionally high mutation rate of 10-5. The pattern of polymorphism emerging in the populations evolving within different hosts was characterized by periodic selection, which reduced diversity, but also frequency-dependent selection, actively maintaining genetic diversity. Furthermore, the continuous emergence of similar phenotypes due to distinct mutations, known as clonal interference, was pervasive. Evolutionary change within the gut is therefore highly repeatable within and across hosts, with adaptive mutations of selection coefficients as strong as 12% accumulating without strong constraints on genetic background. In vivo competitive assays showed that one of the second steps (focA) exhibited positive epistasis with the first, while another (dcuB) exhibited negative epistasis. The data shows that strong effect adaptive mutations continuously recur in gut commensal bacterial species.

Emergent Antiferromagnetism Out Of The Hidden-order" State In Uru2si2: High Magnetic Field Nuclear Magnetic Resonance To 40 T."

Very high field (29)Si-NMR measurements using a fully (29)Si-enriched URu(2)Si(2) single crystal were carried out in order to microscopically investigate the hidden order (HO) state and adjacent magnetic phases in the high field limit. At the lowest measured temperature of 0.4 K, a clear anomaly reflecting a Fermi surface instability near 22 T inside the HO state is detected by the (29)Si shift, (29)K(c). Moreover, a strong enhancement of (29)K(c) develops near a critical field H(c) ≃ 35.6 T, and the ^{29}Si-NMR signal disappears suddenly at H(c), indicating the total suppression of the HO state. Nevertheless, a weak and shifted (29)Si-NMR signal reappears for fields higher than H(c) at 4.2 K, providing evidence for a magnetic structure within the magnetic phase caused by the Ising-type anisotropy of the uranium ordered moments.

Exotic phases induced by strong spin-orbit coupling in ordered double perovskites

We construct and analyze a microscopic model for insulating rocksalt ordered double perovskites, with the chemical formula A(2)BB'O(6), where the B' atom has a 4d(1) or 5d(1) electronic configuration and forms a face-centered-cubic lattice. The combination of the triply degenerate t(2g) orbital and strong spin-orbit coupling forms local quadruplets with an effective spin moment j=3/2. Moreover, due to strongly orbital-dependent exchange, the effective spins have substantial biquadratic and bicubic interactions (fourth and sixth order in the spins, respectively). This leads, at the mean-field level, to three main phases: an unusual antiferromagnet with dominant octupolar order, a ferromagnetic phase with magnetization along the [110] direction, and a nonmagnetic but quadrupolar ordered phase, which is stabilized by thermal fluctuations and intermediate temperatures. All these phases have a two-sublattice structure described by the ordering wave vector Q=2 pi(001). We consider quantum fluctuations and argue that in the regime of dominant antiferromagnetic exchange, a nonmagnetic valence-bond solid or quantum-spin-liquid state may be favored instead. Candidate quantum-spin-liquid states and their basic properties are described. We also address the effect of single-site anisotropy driven by lattice distortions. Existing and possible future experiments are discussed in light of these results.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Reshaping European Union development policy: collective choices and the new global order

Abstract The European Union (EU) is one of the world´s leading donors in official development assistance (ODA) to give a strong weight in the relationship with recipient partner countries, in particular with those that are more dependent on it. Besides the material weight of its funding, the EU has retained historical ties and influence in diplomatic, political and economic terms in many of its ODA recipient partner countries (particular in Sub-Saharan Africa). Since the 2000s, the EU development policy has not only undergone major structural changes in its institutional framework but also has started to face a new international aid scenario. This paper explores why a normative-based EU development policy is being challenged by reformed EU institutions and a new global order, and how the EU is attempting to respond to this context in face of the deepest recession since the end of the Second World War.

Ferromagnetic order in aged Co-doped TiO2 anatase nanopowders

Oxide based diluted magnetic semiconductor (DMS) materials have been a subject of increasing interest due to reports of room temperature ferromagnetism in several systems and their potential use in the development of spintronic devices. However, concerns on the stability of the magnetic properties of different DMS systems have been raised. Their magnetic moment is often unstable, vanishing with a characteristic decay time of weeks or months, which precludes the development of real applications. This paper reports on the ferromagnetic properties of two-year-aged Ti1-xCoxO2-δ reduced anatase nanopowders with different Co contents (0.03≤x≤0.10). Aged samples retain rather high values of magnetization, remanence and coercivity which provide strong evidence for a quite preserved long-range ferromagnetic order. In what concern Co segregation, some degree of metastability of the diluted Co doped anatase structure could be inferred in the case of the sample with the higher Co content.

Measurement of transverse energy-energy correlations in multi-jet events in pp collisions at s√=7 TeV using the ATLAS detector and determination of the strong coupling constant αs(mZ)

High transverse momentum jets produced in pp collisions at a centre of mass energy of 7 TeV are used to measure the transverse energy--energy correlation function and its associated azimuthal asymmetry. The data were recorded with the ATLAS detector at the LHC in the year 2011 and correspond to an integrated luminosity of 158 pb−1. The selection criteria demand the average transverse momentum of the two leading jets in an event to be larger than 250 GeV. The data at detector level are well described by Monte Carlo event generators. They are unfolded to the particle level and compared with theoretical calculations at next-to-leading-order accuracy. The agreement between data and theory is good and provides a precision test of perturbative Quantum Chromodynamics at large momentum transfers. From this comparison, the strong coupling constant given at the Z boson mass is determined to be αs(mZ)=0.1173±0.0010 (exp.) +0.0065−0.0026 (theo.).

Orthogonal higher order structure and confirmatory factor analysis of the French Wechsler Adult Intelligence Scale (WAIS-III).

According to the most widely accepted Cattell-Horn-Carroll (CHC) model of intelligence measurement, each subtest score of the Wechsler Intelligence Scale for Adults (3rd ed.; WAIS-III) should reflect both 1st- and 2nd-order factors (i.e., 4 or 5 broad abilities and 1 general factor). To disentangle the contribution of each factor, we applied a Schmid-Leiman orthogonalization transformation (SLT) to the standardization data published in the French technical manual for the WAIS-III. Results showed that the general factor accounted for 63% of the common variance and that the specific contributions of the 1st-order factors were weak (4.7%-15.9%). We also addressed this issue by using confirmatory factor analysis. Results indicated that the bifactor model (with 1st-order group and general factors) better fit the data than did the traditional higher order structure. Models based on the CHC framework were also tested. Results indicated that a higher order CHC model showed a better fit than did the classical 4-factor model; however, the WAIS bifactor structure was the most adequate. We recommend that users do not discount the Full Scale IQ when interpreting the index scores of the WAIS-III because the general factor accounts for the bulk of the common variance in the French WAIS-III. The 4 index scores cannot be considered to reflect only broad ability because they include a strong contribution of the general factor.

Rapid and strong human CD8+ T cell responses to vaccination with peptide, IFA, and CpG oligodeoxynucleotide 7909.

The induction of potent CD8+ T cell responses by vaccines to fight microbes or tumors remains a major challenge, as many candidates for human vaccines have proved to be poorly immunogenic. Deoxycytidyl-deoxyguanosin oligodeoxynucleotides (CpG ODNs) trigger Toll-like receptor 9, resulting in dendritic cell maturation that can enhance immunogenicity of peptide-based vaccines in mice. We tested whether a synthetic ODN, CpG 7909, could improve human tumor antigen-specific CD8+ T cell responses. Eight HLA-A2+ melanoma patients received 4 monthly vaccinations of low-dose CpG 7909 mixed with melanoma antigen A (Melan-A; identical to MART-1) analog peptide and incomplete Freund's adjuvant. All patients exhibited rapid and strong antigen-specific T cell responses: the frequency of Melan-A-specific T cells reached over 3% of circulating CD8+ T cells. This was one order of magnitude higher than the frequency seen in 8 control patients treated similarly but without CpG and 1-3 orders of magnitude higher than that seen in previous studies with synthetic vaccines. The enhanced T cell populations consisted primarily of effector memory cells, which in part secreted IFN- and expressed granzyme B and perforin ex vivo. In vitro, T cell clones recognized and killed melanoma cells in an antigen-specific manner. Thus, CpG 7909 is an efficient vaccine adjuvant that promotes strong antigen-specific CD8+ T cell responses in humans.

An axiomatic characterization of the strong constrained egalitarian solution

In this paper we axiomatize the strong constrained egalitarian solution (Dutta and Ray, 1991) over the class of weak superadditive games using constrained egalitarianism, order-consistency, and converse order-consistency. JEL classification: C71, C78. Keywords: Cooperative TU-game, strong constrained egalitarian solution, axiomatization.