Darboux Transformations for a Lax Integrable System in 2n2n-Dimensions

A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.Comment: Latex, 14 pages, to be published in Lett. Math. Phy

The Minimum Backlog Problem

We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP. The discrete MBP is a 2-person game played on a graph $G=(V,E)$. The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time. The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog. We show that the competitive ratio of any algorithm for the MBP has a lower bound of $\Omega(D)$, where $D$ is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog. For the absolute value of the backlog there is a trivial lower bound of $\Omega(D)$, and the deamortization analysis of Dietz and Sleator gives an upper bound of $O(D\log N)$ for $N$ cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of $O(D)$, independently of the number of cups.Comment: 1+16 pages, 3 figure

Coherent X-ray Scattering from Manganite Charge and Orbital Domains

We report coherent x-ray scattering studies of charge and orbital domains in manganite systems. The experiments were carried out on LaMnO_3 and Pr_{0.6}Ca_{0.4}MnO_3, with the incident photon energy tuned near the Mn K edge. At room temperature, the orbital speckle pattern of LaMnO_3 was observed to be constant over a timescale of at least minutes, which is indicative of static orbital domains on this timescale. For Pr_{0.6}Ca_{0.4}MnO_3, both charge and orbital speckle patterns were observed. The observation of the latter rules out the presence of fast orbital fluctuations, while long time series data-- on the order of several minutes-- were suggestive of slow dynamic behavior. In contrast, the charge order speckle patterns were static.Comment: 6 pages, 4 figure

Manganites at Quarter Filling: Role of Jahn-Teller Interactions

We have analyzed different correlation functions in a realistic spin-orbital model for half-doped manganites. Using a finite-temperature diagonalization technique the CE phase was found in the charge-ordered phase in the case of small antiferromagnetic interactions between $t_{2g}$ electrons. It is shown that a key ingredient responsible for stabilization of the CE-type spin and orbital-ordered state is the cooperative Jahn-Teller (JT) interaction between next-nearest Mn$^{+3}$ neighbors mediated by the breathing mode distortion of Mn$^{+4}$ octahedra and displacements of Mn$^{+4}$ ions. The topological phase factor in the Mn-Mn hopping leading to gap formation in one-dimensional models for the CE phase as well as the nearest neighbor JT coupling are not able to produce the zigzag chains typical for the CE phase in our model.Comment: 16 pages with 16 figures, contains a more detailed parameter estimate based on the structural data by Radaelli et al. (accepted for publication in Phys. Rev. B

Origin of defect-related green emission from ZnO nanoparticles: effect of surface modification

We investigated the optical properties of colloidal-synthesized ZnO spherical nanoparticles prepared from 1-octadecene (OD), a mixture of trioctylamine (TOA) and OD (1:10), and a mixture of trioctylphosphine oxide (TOPO) and OD (1:12). It is found that the green photoluminescence (PL) of samples from the mixture of TOA/OD and TOPO/OD is largely suppressed compared with that from pure OD. Moreover, it is found that all spherical nanoparticles have positive zeta potential, and spherical nanoparticles from TOA/OD and TOPO/OD have a smaller zeta potential than those from OD. A plausible explanation is that oxygen vacancies, presumably located near the surface, contribute to the green PL, and the introduction of TOA and TOPO will reduce the density of oxygen vacancies near the surfaces. Assuming that the green emission arises due to radiative recombination between deep levels formed by oxygen vacancies and free holes, we estimate the size of optically active spherical nanoparticles from the spectral energy of the green luminescence. The results are in good agreement with results from TEM. Since this method is independent of the degree of confinement, it has a great advantage in providing a simple and practical way to estimate the size of spherical nanoparticles of any size. We would like to point out that this method is only applicable for samples with a small size distribution

Adalimumab medium-term dosing strategy in moderate-to-severe hidradenitis suppurativa: integrated results from the phase III randomized placebo-controlled PIONEER trials

Background: Weekly adalimumab (Humira®) is approved for the treatment of hidradenitis suppurativa (HS) based on the 12-week placebo-controlled periods of the two phase III PIONEER trials. Objectives: Using PIONEER integrated trial results, we aimed to evaluate the optimal medium-term adalimumab maintenance dosing strategy for moderate-to-severe HS. Methods: Each trial had two double-blind periods; 12-week Period A and 24-week Period B. Patients randomized to adalimumab 40 mg every week (ADAew) (Period A), were rerandomized in Period B to ADAew (ADAew/ew), ADA every other week (ADAew/eow), or placebo (ADAew/pbo). Placebo-randomized patients were reassigned in Period B to ADAew (PIONEER I) or placebo (PIONEER II). The primary outcome was HS Clinical Response (HiSCR). Patients who lost response during Period B were discontinued from the study and offered an option to enter the open-label extension (OLE) to receive ADAew. Results are reported across the two study periods, and data were combined from the two study periods and the OLE. Results: For week-12 HiSCR achievers, the HiSCR week-36 rate was 48·1% (ADAew/ew) vs. 46·2% (ADAew/eow) and 32·1% (ADAew/pbo). Combining (post hoc) these patients with week-12 partial responders further differentiated outcomes in Period B (ADAew/ew 55·7% vs. ADAew/eow 40·0% and ADAew/pbo 30·1%). Period-B adverse-event rates were ADAew/ew 59·6% vs. ADAew/eow 57·4% and ADAew/pbo 65·0%. One patient (ADAew/ew) reported a serious infection. Conclusions: Weekly adalimumab treatment, effective throughout 36 weeks, was the optimal maintenance medium-term dosing regimen for this population. At least partial response after 12 weeks with continued weekly dosing had better outcomes than dose reduction or interruption. Patients who do not show at least a partial response to weekly adalimumab by week 12 are unlikely to benefit from continued therapy. No new safety risks were identified. What's already known about this topic?. Hidradenitis suppurativa (HS) is a chronic inflammatory disease, commonly misinterpreted as an infection and treated with long-term antibiotic regimens or surgical incisions. Based on the chronicity of HS and the lack of evidence for efficacious and safe long-term HS treatments, it is important to evaluate medium- to long-term therapies for HS. Weekly adalimumab (Humira®) is approved for the treatment of moderate-to-severe HS based on the two phase III PIONEER trials. What does this study add?. This study pooled data from the two PIONEER trials, providing a more robust assessment of outcomes. After at least partial treatment success with weekly adalimumab short-term therapy (12 weeks), continuing weekly dosing during the subsequent 24 weeks had better outcomes than dose reduction or treatment interruption. Patients who do not show at least a partial response to weekly adalimumab by week 12 are unlikely to benefit from continued therapy