Rational matrix pseudodifferential operators

The skewfield K(d) of rational pseudodifferential operators over a differential field K is the skewfield of fractions of the algebra of differential operators K[d]. In our previous paper we showed that any H from K(d) has a minimal fractional decomposition H=AB^(-1), where A,B are elements of K[d], B is non-zero, and any common right divisor of A and B is a non-zero element of K. Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-zero element of K[d]. In the present paper we study the ring M_n(K(d)) of nxn matrices over the skewfield K(d). We show that similarly, any H from M_n(K(d)) has a minimal fractional decomposition H=AB^(-1), where A,B are elements of M_n(K[d]), B is non-degenerate, and any common right divisor of A and B is an invertible element of the ring M_n(K[d]). Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-degenerate element of M_n(K [d]). We give several equivalent definitions of the minimal fractional decomposition. These results are applied to the study of maximal isotropicity property, used in the theory of Dirac structures.Comment: 20 page

Some algebraic properties of differential operators

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that the Dieudonne' determinant of a matrix pseudodifferential operator with coefficients in a differential subring A of K lies in the integral closure of A in K, and we give an example of a 2x2 matrix differential operator with coefficients in A whose Dieudonne' determiant does not lie in A.Comment: 15 page

p̲ -reduced Multicomponent KP Hierarchy and Classical W -algebras W(glN,p̲)

For each partition p̲ of an integer N≥ 2 , consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p̲-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction of the generators of the corresponding classical W-algebra W(glN,p̲), and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows

Interference and zero-bias anomaly in tunneling between Luttinger-liquid wires

We present theoretical calculations and experimental measurements which reveal the Luttinger-liquid (LL) nature of elementary excitations in a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can be accounted for by spin-charge separation of the elementary excitations in the interacting wires. Furthermore, boundaries affect the LL exponents of the voltage and temperature dependence of the tunneling conductance at low energies. We show that the measured temperature dependence of the conductance zero-bias dip as well as the voltage modulation of the conductance oscillation pattern can be used to extract the electron interaction parameters in the wires.Comment: 17 pages, 12 figure

Enhanced osteoclast development in collagen-induced arthritis in interferon-γ receptor knock-out mice as related to increased splenic CD11b(+ )myelopoiesis

Collagen-induced arthritis (CIA) in mice is accompanied by splenomegaly due to the selective expansion of immature CD11b(+ )myeloblasts. Both disease manifestations are more pronounced in interferon-γ receptor knock-out (IFN-γR KO) mice. We have taken advantage of this difference to test the hypothesis that the expanding CD11b(+ )splenic cell population constitutes a source from which osteoclast precursors are recruited to the joint synovia. We found larger numbers of osteoclasts and more severe bone destruction in joints of IFN-γR KO mice than in joints of wild-type mice. Osteoclast-like multinucleated cells appeared in splenocyte cultures established in the presence of macrophage colony-stimulating factor (M-CSF) and stimulated with the osteoclast-differentiating factor receptor activator of NF-κB ligand (RANKL) or with tumour necrosis factor-α (TNF-α). Significantly larger numbers of such cells could be generated from splenocytes of IFN-γR KO mice than from those of wild-type mice. This was not accompanied, as might have been expected, by increased concentrations of the intracellular adaptor protein TRAF6, known to be involved in signalling of RANKL- and TNF-α-induced osteoclast formation. Splenocyte cultures of IFN-γR KO mice also produced more TNF-α and more RANKL than those of wild-type mice. Finally, splenocytes isolated from immunised IFN-γR KO mice contained comparatively low levels of pro-interleukin-1β (pro-IL-1β) and pro-caspase-1, indicating more extensive conversion of pro-IL-1β into secreted active IL-1β. These observations provide evidence that all conditions are fulfilled for the expanding CD11b(+ )splenocytes to act as a source of osteoclasts and to be indirectly responsible for bone destruction in CIA. They also provide a plausible explanation for the higher susceptibility of IFN-γR KO mice to CIA

Inter edge Tunneling in Quantum Hall Line Junctions

We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors $\nu\sim1$ the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter $K$, leading to the appearance of a zero-bias differential conductance peak of magnitude $G_t=Ke^2/h$ at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value $\nu^* \gtrsim 1$, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage $V$, the crossover scale $T_K$, and the temperature $T$. The low height of the zero bias peak $\sim 0.1e^2/h$ observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for $\nu \gtrsim 2$ can be explained as an effect caused by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a small polarization near $\nu\sim2$. We also predict that as the temperature is lowered $\nu^*$ should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for $\nu \gtrsim 2$.Comment: 17 pages, 8 figure

Horizontal and vertical diversity jointly shape food web stability against small and large perturbations

The biodiversity of food webs is composed of horizontal (i.e. within trophic levels) and vertical diversity (i.e. the number of trophic levels). Understanding their joint effect on stability is a key challenge. Theory mostly considers their individual effects and focuses on small perturbations near equilibrium in hypothetical food webs. Here, we study the joint effects of horizontal and vertical diversity on the stability of hypothetical (modelled) and empirical food webs. In modelled food webs, horizontal and vertical diversity increased and decreased stability, respectively, with a stronger positive effect of producer diversity on stability at higher consumer diversity. Experiments with an empirical plankton food-web, where we manipulated horizontal and vertical diversity and measured stability from species interactions and from resilience against large perturbations, confirmed these predictions. Taken together, our findings highlight the need to conserve horizontal biodiversity at different trophic levels to ensure stability

Relevant factors for the optimal duration of extended endocrine therapy in early breast cancer

Purpose: For postmenopausal patients with hormone receptor-positive early breast cancer, the optimal subgroup and duration of extended endocrine therapy is not clear yet. The aim of this study using the IDEAL patient cohort was to identify a subgroup for which longer (5 years) extended therapy is beneficial over shorter (2.5 years) extended endocrine therapy. Methods: In the IDEAL trial, 1824 patients who completed 5 years of adjuvant endocrine therapy (either 5 years of tamoxifen (12%), 5 years of an AI (29%), or a sequential strategy of both (59%)) were randomized between either 2.5 or 5 years of extended letrozole. For each prior therapy subgroup, the value of longer therapy was assessed for both node-negative and node-positive patients using Kaplan Meier and Cox regression survival analyses. Results: In node-positive patients, there was a significant benefit of 5 years (over 2.5 years) of extended therapy (disease-free survival (DFS) HR 0.67, p = 0.03, 95% CI 0.47–0.96). This effect was only observed in patients who were treated initially with a sequential scheme (DFS HR 0.60, p = 0.03, 95% CI 0.38–0.95). In all other subgroups, there was no significant benefit of longer extended therapy. Similar results were found in patients who were randomized for their initial adjuvant therapy in the TEAM trial (DFS HR 0.37, p = 0.07, 95% CI 0.13–1.06), although this additional analysis was underpowered for definite conclusions. Conclusions: This study suggests that node-positive patients could benefit from longer extended endocrine therapy, although this effect appears isol

European Organization for Research and Treatment of Cancer (EORTC) open label phase II study on glufosfamide administered as a 60-minute infusion every 3 weeks in recurrent glioblastoma multiforme

Background: Glufosfamide is a new alkylating agent in which the active metabolite of isophosphoramide mustard is covalently linked to β-d-glucose to target the glucose transporter system and increase intracellular uptake in tumor cells. We investigated this drug in a multicenter prospective phase II trial in recurrent glioblastoma multiforme (GBM). Patients and methods: Eligible patients had recurrent GBM following surgery, radiotherapy and no more than one prior line of chemotherapy. Patients were treated with glufosfamide 5000 mg/m2 administered as a 1-h intravenous infusion. Treatment success was defined as patients with either an objective response according to Macdonald's criteria or 6 months progression-free survival. Toxicity was assessed with the Common Toxicity Criteria (CTC) version 2.0. Results: Thirty-one eligible patients were included. Toxicity was modest, the main clinically relevant toxicities being leukopenia (CTC grade >3 in five patients) and hepatotoxicity (in three patients). No responses were observed; one patient (3%; 95% confidence interval 0 to 17%) was free from progression at 6 months. Pharmacokinetic analysis showed a 15% decrease in area under the curve and glufosfamide clearance in patients treated with enzyme-inducing antiepileptic drugs, but no effect of these drugs on maximum concentration and plasma half-life. Conclusion: Glufosfamide did not show significant clinical antitumor activity in patients with recurrent GB

The skeletons of free distributive lattices

AbstractThe skeletons of free distributive lattices are studied by methods of formal concept analysis; in particular, a specific closure system of sublattices is elaborated to clarify the structure of the skeletons. Up to five generators, the skeletons are completely described