Kato square root problem with unbounded leading coefficients

We prove the Kato conjecture for elliptic operators, $L=-\nabla\cdot\left((\mathbf A+\mathbf D)\nabla\ \right)$, with $\mathbf A$ a complex measurable bounded coercive matrix and $\mathbf D$ a measurable real-valued skew-symmetric matrix in $\mathbb{R}^n$ with entries in $BMO(\mathbb{R}^n)$;\, i.e., the domain of $\sqrt{L}\,$ is the Sobolev space $\dot H^1(\mathbb{R}^n)$ in any dimension, with the estimate $\|\sqrt{L}\, f\|_2\lesssim \| \nabla f\|_2$

Cisplatin and fluorouracil with or without panitumumab in patients with recurrent or metastatic squamous-cell carcinoma of the head and neck (SPECTRUM): an open-label phase 3 randomised trial

Background: Previous trials have shown that anti-EGFR monoclonal antibodies can improve clinical outcomes of patients with recurrent or metastatic squamous-cell carcinoma of the head and neck (SCCHN). We assessed the efficacy and safety of panitumumab combined with cisplatin and fluorouracil as first-line treatment for these patients. Methods: This open-label phase 3 randomised trial was done at 126 sites in 26 countries. Eligible patients were aged at least 18 years; had histologically or cytologically confi rmed SCCHN; had distant metastatic or locoregionally recurrent disease, or both, that was deemed to be incurable by surgery or radiotherapy; had an Eastern Cooperative Oncology Group performance status of 1 or less; and had adequate haematological, renal, hepatic, and cardiac function. Patients were randomly assigned according to a computer-generated randomisation sequence (1:1; stratifi ed by previous treatment, primary tumour site, and performance status) to one of two groups. Patients in both groups received up to six 3-week cycles of intravenous cisplatin (100 mg/m(2) on day 1 of each cycle) and fl uorouracil (1000 mg/m(2) on days 1-4 of each cycle); those in the experimental group also received intravenous panitumumab (9 mg/kg on day 1 of each cycle). Patients in the experimental group could choose to continue maintenance panitumumab every 3 weeks. The primary endpoint was overall survival and was analysed by intention to treat. In a prospectively defi ned retrospective analysis, we assessed tumour human papillomavirus (HPV) status as a potential predictive biomarker of outcomes with a validated p16-INK4A (henceforth, p16) immunohistochemical assay. Patients and investigators were aware of group assignment; study statisticians were masked until primary analysis; and the central laboratory assessing p16 status was masked to identifi cation of patients and treatment. This trial is registered with ClinicalTrials. gov, number NCT00460265. Findings: Between May 15, 2007, and March 10, 2009, we randomly assigned 657 patients: 327 to the panitumumab group and 330 to the control group. Median overall survival was 11.1 months (95% CI 9.8-12.2) in the panitumumab group and 9.0 months (8.1-11.2) in the control group (hazard ratio [HR] 0.873, 95% CI 0.729-1.046; p = 0.1403). Median progression-free survival was 5.8 months (95% CI 5.6-6.6) in the panitumumab group and 4.6 months (4.1-5.4) in the control group (HR 0.780, 95% CI 0.659-0.922; p = 0.0036). Several grade 3 or 4 adverse events were more frequent in the panitumumab group than in the control group: skin or eye toxicity (62 [19%] of 325 included in safety analyses vs six [2%] of 325), diarrhoea (15 [5%] vs four [1%]), hypomagnesaemia (40 [12%] vs 12 [4%]), hypokalaemia (33 [10%] vs 23 [7%]), and dehydration (16 [5%] vs seven [2%]). Treatment-related deaths occurred in 14 patients (4%) in the panitumumab group and eight (2%) in the control group. Five (2%) of the fatal adverse events in the panitumumab group were attributed to the experimental agent. We had appropriate samples to assess p16 status for 443 (67%) patients, of whom 99 (22%) were p16 positive. Median overall survival in patients with p16-negative tumours was longer in the panitumumab group than in the control group (11.7 months [95% CI 9.7-13.7] vs 8.6 months [6.9-11.1]; HR 0.73 [95% CI 0.58-0.93]; p = 0.0115), but this difference was not shown for p16-positive patients (11.0 months [7.3-12.9] vs 12.6 months [7.7-17.4]; 1.00 [0.62-1.61]; p = 0.998). In the control group, p16-positive patients had numerically, but not statistically, longer overall survival than did p16-negative patients (HR 0.70 [95% CI 0.47-1.04]). Interpretation: Although the addition of panitumumab to chemotherapy did not improve overall survival in an unselected population of patients with recurrent or metastatic SCCHN, it improved progression-free survival and had an acceptable toxicity profile. p16 status could be a prognostic and predictive marker in patients treated with panitumumab and chemotherapy. Prospective assessment will be necessary to validate our biomarker findings

Ultrahigh Surface Area Three-Dimensional Porous Graphitic Carbon from Conjugated Polymeric Molecular Framework

Porous graphitic carbon is essential for many applications such as energy storage devices, catalysts, and sorbents. However, current graphitic carbons are limited by low conductivity, low surface area, and ineffective pore structure. Here we report a scalable synthesis of porous graphitic carbons using a conjugated polymeric molecular framework as precursor. The multivalent cross-linker and rigid conjugated framework help to maintain micro- and mesoporous structures, while promoting graphitization during carbonization and chemical activation. The above unique design results in a class of highly graphitic carbons at temperature as low as 800 ??C with record-high surface area (4073 m2 g-1), large pore volume (2.26 cm-3), and hierarchical pore architecture. Such carbons simultaneously exhibit electrical conductivity >3 times more than activated carbons, very high electrochemical activity at high mass loading, and high stability, as demonstrated by supercapacitors and lithium-sulfur batteries with excellent performance. Moreover, the synthesis can be readily tuned to make a broad range of graphitic carbons with desired structures and compositions for many applications.clos

Search for gravitational wave bursts in LIGO's third science run

We report on a search for gravitational wave bursts in data from the three LIGO interferometric detectors during their third science run. The search targets subsecond bursts in the frequency range 100-1100 Hz for which no waveform model is assumed, and has a sensitivity in terms of the root-sum-square (rss) strain amplitude of hrss ~ 10^{-20} / sqrt(Hz). No gravitational wave signals were detected in the 8 days of analyzed data.Comment: 12 pages, 6 figures. Amaldi-6 conference proceedings to be published in Classical and Quantum Gravit

A New Method for the Characterization of Strain-Specific Conformational Stability of Protease-Sensitive and Protease-Resistant PrPSc

Although proteinacious in nature, prions exist as strains with specific self-perpetuating biological properties. Prion strains are thought to be associated with different conformers of PrPSc, a disease-associated isoform of the host-encoded cellular protein (PrPC). Molecular strain typing approaches have been developed which rely on the characterization of protease-resistant PrPSc. However, PrPSc is composed not only of protease-resistant but also of protease-sensitive isoforms. The aim of this work was to develop a protocol for the molecular characterization of both, protease-resistant and protease-sensitive PrPSc aggregates. We first set up experimental conditions which allowed the most advantageous separation of PrPC and PrPSc by means of differential centrifugation. The conformational solubility and stability assay (CSSA) was then developed by measuring PrPSc solubility as a function of increased exposure to GdnHCl. Brain homogenates from voles infected with human and sheep prion isolates were analysed by CSSA and showed strain-specific conformational stabilities, with mean [GdnHCl]1/2 values ranging from 1.6 M for MM2 sCJD to 2.1 for scrapie and to 2.8 M for MM1/MV1 sCJD and E200K gCJD. Interestingly, the rank order of [GdnHCl]1/2 values observed in the human and sheep isolates used as inocula closely matched those found following transmission in voles, being MM1 sCJD the most resistant (3.3 M), followed by sheep scrapie (2.2 M) and by MM2 sCJD (1.6 M). In order to test the ability of CSSA to characterise protease-sensitive PrPSc, we analysed sheep isolates of Nor98 and compared them to classical scrapie isolates. In Nor98, insoluble PrPSc aggregates were mainly protease-sensitive and showed a conformational stability much lower than in classical scrapie. Our results show that CSSA is able to reveal strain-specified PrPSc conformational stabilities of protease-resistant and protease-sensitive PrPSc and that it is a valuable tool for strain typing in natural hosts, such as humans and sheep

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer's classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation