A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.

Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

New constraints on muon-neutrino to electron-neutrino transitions in MINOS

This paper reports results from a search for nu(mu) -> nu(e) transitions by the MINOS experiment based on a 7 x 10(20) protons-on-target exposure. Our observation of 54 candidate nu(e) events in the far detector with a background of 49.1 +/- 7.0(stat) +/- 2.7(syst) events predicted by the measurements in the near detector requires 2sin(2)(2 theta(13))sin(2)theta(23) < 0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at delta(CP) = 0. The experiment sets the tightest limits to date on the value of theta(13) for nearly all values of delta(CP) for the normal neutrino mass hierarchy and maximal sin(2)(2 theta(23)).

Search for Muon-Neutrino to Electron-Neutrino Transitions in MINOS

This Letter reports on a search for nu(mu)->nu(e) transitions by the MINOS experiment based on a 3.14x10(20) protons-on-target exposure in the Fermilab NuMI beam. We observe 35 events in the Far Detector with a background of 27 +/- 5(stat)+/- 2(syst) events predicted by the measurements in the Near Detector. If interpreted in terms of nu(mu)->nu(e) oscillations, this 1.5 sigma excess of events is consistent with sin(2)(2 theta(13)) comparable to the CHOOZ limit when |Delta m(2)|=2.43x10(-3) eV(2) and sin(2)(2 theta(23))=1.0 are assumed.

Search for Active Neutrino Disappearance Using Neutral-Current Interactions in the MINOS Long-Baseline Experiment

We report the first detailed comparisons of the rates and spectra of neutral-current neutrino interactions at two widely separated locations. A depletion in the rate at the far site would indicate mixing between nu(mu) and a sterile particle. No anomalous depletion in the reconstructed energy spectrum is observed. Assuming oscillations occur at a single mass-squared splitting, a fit to the neutral- and charged-current energy spectra limits the fraction of nu(mu) oscillating to a sterile neutrino to be below 0.68 at 90% confidence level. A less stringent limit due to a possible contribution to the measured neutral-current event rate at the far site from nu(e) appearance at the current experimental limit is also presented.

Testing Lorentz Invariance and CPT Conservation with NuMI Neutrinos in the MINOS Near Detector

A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).

Measurement of neutrino oscillations with the MINOS detectors in the NuMI beam

This Letter reports new results from the MINOS experiment based on a two-year exposure to muon neutrinos from the Fermilab NuMI beam. Our data are consistent with quantum-mechanical oscillations of neutrino flavor with mass splitting vertical bar Delta m(2)vertical bar = (2.43 +/- 0.13) x 10(-3) eV(2) (68% C.L.) and mixing angle sin(2)(2 theta) > 0.90 (90% C.L.). Our data disfavor two alternative explanations for the disappearance of neutrinos in flight: namely, neutrino decays into lighter particles and quantum decoherence of neutrinos, at the 3.7 and 5.7 standard-deviation levels, respectively.

New Measurement of the pi(0) Radiative Decay Width

High precision measurements of the differential cross sections for pi(0) photoproduction at forward angles for two nuclei, (12)C and (208)Pb, have been performed for incident photon energies of 4.9-5.5 GeV to extract the pi(0) -> gamma gamma decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The pi(0) -> gamma gamma decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is Gamma(pi(0) -> gamma gamma) = 7.82 +/- 0.14(stat) +/- 0.17(syst) eV. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current Particle Data Group average of this fundamental quantity, and it is consistent with current theoretical predictions.

Spatial portability of numerical models of leaf wetness duration based on empirical approaches

Leaf wetness duration (LWD) models based on empirical approaches offer practical advantages over physically based models in agricultural applications, but their spatial portability is questionable because they may be biased to the climatic conditions under which they were developed. In our study, spatial portability of three LWD models with empirical characteristics - a RH threshold model, a decision tree model with wind speed correction, and a fuzzy logic model - was evaluated using weather data collected in Brazil, Canada, Costa Rica, Italy and the USA. The fuzzy logic model was more accurate than the other models in estimating LWD measured by painted leaf wetness sensors. The fraction of correct estimates for the fuzzy logic model was greater (0.87) than for the other models (0.85-0.86) across 28 sites where painted sensors were installed, and the degree of agreement k statistic between the model and painted sensors was greater for the fuzzy logic model (0.71) than that for the other models (0.64-0.66). Values of the k statistic for the fuzzy logic model were also less variable across sites than those of the other models. When model estimates were compared with measurements from unpainted leaf wetness sensors, the fuzzy logic model had less mean absolute error (2.5 h day(-1)) than other models (2.6-2.7 h day(-1)) after the model was calibrated for the unpainted sensors. The results suggest that the fuzzy logic model has greater spatial portability than the other models evaluated and merits further validation in comparison with physical models under a wider range of climate conditions. (C) 2010 Elsevier B.V. All rights reserved.

Effect of bacterial inoculation, plant genotype and developmental stage on root-associated and endophytic bacterial communities in potato (Solanum tuberosum)

Beneficial bacteria interact with plants by colonizing the rhizosphere and roots followed by further spread through the inner tissues, resulting in endophytic colonization. The major factors contributing to these interactions are not always well understood for most bacterial and plant species. It is believed that specific bacterial functions are required for plant colonization, but also from the plant side specific features are needed, such as plant genotype (cultivar) and developmental stage. Via multivariate analysis we present a quantification of the roles of these components on the composition of root-associated and endophytic bacterial communities in potato plants, by weighing the effects of bacterial inoculation, plant genotype and developmental stage. Spontaneous rifampicin resistant mutants of two bacterial endophytes, Paenibacillus sp. strain E119 and Methylobacterium mesophilicum strain SR1.6/6, were introduced into potato plants of three different cultivars (Eersteling, Robijn and Karnico). Densities of both strains in, or attached to potato plants were measured by selective plating, while the effects of bacterial inoculation, plant genotype and developmental stage on the composition of bacterial, Alphaproteobacterial and Paenibacillus species were determined by PCR-denaturing gradient gel-electrophoresis (DGGE). Multivariate analyses revealed that the composition of bacterial communities was mainly driven by cultivar type and plant developmental stage, while Alphaproteobacterial and Paenibacillus communities were mainly influenced by bacterial inoculation. These results are important for better understanding the effects of bacterial inoculations to plants and their possible effects on the indigenous bacterial communities in relation with other plant factors such as genotype and growth stage.

Endophytic Colonization of Potato (Solanum tuberosum L.) by a Novel Competent Bacterial Endophyte, Pseudomonas putida Strain P9, and Its Effect on Associated Bacterial Communities

Pseudomonas putida strain P9 is a novel competent endophyte from potato. P9 causes cultivar-dependent suppression of Phytophthora infestans. Colonization of the rhizoplane and endosphere of potato plants by P9 and its rifampin-resistant derivative P9R was studied. The purposes of this work were to follow the fate of P9 inside growing potato plants and to establish its effect on associated microbial communities. The effects of P9 and P9R inoculation were studied in two separate experiments. The roots of transplants of three different cultivars of potato were dipped in suspensions of P9 or P9R cells, and the plants were planted in soil. The fate of both strains was followed by examining colony growth and by performing PCR-denaturing gradient gel electrophoresis (PCR-DGGE). Colonies of both strains were recovered from rhizoplane and endosphere samples of all three cultivars at two growth stages. A conspicuous band, representing P9 and P9R, was found in all Pseudomonas PCR-DGGE fingerprints for treated plants. The numbers of P9R CFU and the P9R-specific band intensities for the different replicate samples were positively correlated, as determined by linear regression analysis. The effects of plant growth stage, genotype, and the presence of P9R on associated microbial communities were examined by multivariate and unweighted-pair group method with arithmetic mean cluster analyses of PCR-DGGE fingerprints. The presence of strain P9R had an effect on bacterial groups identified as Pseudomonas azotoformans, Pseudomonas veronii, and Pseudomonas syringae. In conclusion, strain P9 is an avid colonizer of potato plants, competing with microbial populations indigenous to the potato phytosphere. Bacterization with a biocontrol agent has an important and previously unexplored effect on plant-associated communities.

Two physically, functionally, and developmentally distinct peritoneal macrophage subsets

The peritoneal cavity (PerC) is a unique compartment within which a variety of immune cells reside, and from which macrophages (Mempty set) are commonly drawn for functional studies. Here we define two Mempty set subsets that coexist in PerC in adult mice. One, provisionally called the large peritoneal Mempty set (LPM), contains approximately 90% of the PerC Mempty set in unstimulated animals but disappears rapidly from PerC following lipopolysaccharide (LPS) or thioglycolate stimulation. These cells express high levels of the canonical Mempty set surface markers, CD11b and F4/80. The second subset, referred to as small peritoneal Mempty set (SPM), expresses substantially lower levels of CD11b and F4/80 but expresses high levels of MHC-II, which is not expressed on LPM. SPM, which predominates in PerC after LPS or thioglycolate stimulation, does not derive from LPM. Instead, it derives from blood monocytes that rapidly enter the PerC after stimulation and differentiate to mature SPM within 2 to 4 d. Both subsets show clear phagocytic activity and both produce nitric oxide (NO) in response to LPS stimulation in vivo. However, their responses to LPS show key differences: in vitro, LPS stimulates LPM, but not SPM, to produce NO; in vivo, LPS stimulates both subsets to produce NO, albeit with different response patterns. These findings extend current models of Mempty set heterogeneity and shed new light on PerC Mempty set diversity, development, and function. Thus, they introduce a new context for interpreting (and reinterpreting) data from ex vivo studies with PerC Mempty set.

THE POLICY AGENDA OF ISPRM

This paper suggests a comprehensive policy agenda and first steps to be undertaken by the International Society of Physical and Rehabilitation Medicine (ISPRM) in order to realize its humanitarian, professional and scientific mandates. The general aims of ISPRM, as formulated in its guiding documents, the relations with the World Health Organization (WHO) and the United Nations system, and demands of ISPRM`s constituency herein form the basis of this policy agenda Agenda items encompass contributions to the establishment of rehabilitation services worldwide and the development of PRM societies ISPRM`s possible input in general curricula in disability and rehabilitation, and in fighting discrimination against people experiencing disability are discuss. Moreover, the implementation of the International Classification of Functioning. Disability and Health (ICF) in medicine, contributions to WHO guidelines relevant to disability and rehabilitation the provision of a conceptual description of the rehabilitation strategy and the outline of a rehabilitation services matrix are seen as important agenda items of ISPRM`s external policy. With regard to its constituency and internal policy, a definition of the field of competence and a conceptual description of PRM, as well as the development of a consistent and comprehensive congress topic list and congress structure appear to be crucial items. The proposed agenda items serve as a basis for future discussions.

Abatacept in children with juvenile idiopathic arthritis: a randomised, double-blind, placebo-controlled withdrawal trial

Background Some children with juvenile idiopathic arthritis either do not respond, or are intolerant to, treatment with disease-modifying antirheumatic drugs, including anti-tumour necrosis factor (TNF) drugs. We aimed to assess the safety and efficacy of abatacept, a selective T-cell costimulation modulator, in children with juvenile idiopathic arthritis who had failed previous treatments. Methods We did a double-blind, randomised controlled withdrawal trial between February, 2004, and June, 2006. We enrolled 190 patients aged 6-17 years, from 45 centres, who had a history of active juvenile idiopathic arthritis; at least five active joints; and an inadequate response to, or intolerance to, at least one disease-modifying antirheumatic drug. All 190 patients were given 10 mg/kg of abatacept intravenously in the open-label period of 4 months. Of the 170 patients who completed this lead-in course, 47 did not respond to the treatment according to predefined American College of Rheumatology (ACR) paediatric criteria and were excluded. Of the patients who did respond to abatacept, arthritis, and 62 were randomly assigned to receive placebo at the same dose and timing. The primary endpoint was time to flare of arthritis. Flare was defined as worsening of 30% or more in at least three of six core variables, with at least 30% improvement in no more than one variable. We analysed all patients who were treated as per protocol. This trial is registered, number NCT00095173. Findings Flares of arthritis occurred in 33 of 62 (53%) patients who were given placebo and 12 of 60 (20%) abatacept patients during the double-blind treatment (p=0.0003). Median time to flare of arthritis was 6 months for patients given placebo (insufficient events to calculate IQR); insufficient events had occurred in the abatacept group for median time to flare to be assessed (p=0.0002). The risk of flare in patients who contined abatacept was less than a third of that for controls during that double-blind period (hazard ratio 0.31, 95% CI 0.16-0.95). During the double-blind period, the frequency of adverse events did not differ in the two treatment groups, Adverse events were recorded in 37 abatacept recipients (62%) and 34 (55%) placebo recipients (p=0.47); only two serious adverse events were reported, bouth in controls (p=0.50). Interpretation Selective modulation of T-cell costimulation with abatacept is a rational alternative treatment for children with juvenile idiopathic arthritis. Funding Bristol-Myers Squibb.