Heat kernel estimates for general boundary problems

We show that not feeling the boundary estimates for heat kernels hold for any non-negative self-adjoint extension of the Laplace operator acting on vector-valued compactly supported functions on a domain in R d Rd . They are therefore valid for any choice of boundary condition and we show that the implied constants can be chosen independent of the self-adjoint extension. The method of proof is very general and is based on fi nite propagation speed estimates and explicit Fourier Tauberian theorems obtained by Y. Safarov

End User Perception and Software Quality Assessment

The topic of software quality assessment is at the forefront of the software engineering movement. Many models of organization and quality control exist which serve to foster software quality and reliability (Bloom, McPheters & Tsiang, 1973; Brandl, 1990; Comer, 1988; Dunn, 1990; Kaplan, Clark & Tang, 1994; Livson, 1988; Musa, lannino & Okumoto, 1987). Some models now consider the software engineering project team and end users, but most still treat them as static contributors to the system. Major factors often ignored in most conventional models include the cybernetics of the process, and human factors which have a significant impact on the assessment of the quality of the software. Software environment, adaptability, and motivation have all been discussed as essential in creating a superior product. Yet, the factor of human perception has been either overlooked or avoided in the ensuing discussions. In software development the software engineers\u27 perceptions as well as those of all potential end users, must be considered in order to ensure software quality and reliability.End User Perception and Software Quality Assessmen

Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

Responder analysis of a randomized comparison of the 13.3 mg/24 h and 9.5 mg/24 h rivastigmine patch

INTRODUCTION: OPtimizing Transdermal Exelon In Mild-to-moderate Alzheimer’s disease (OPTIMA) was a randomized, double-blind comparison of 13.3 mg/24 h versus 9.5 mg/24 h rivastigmine patch in patients with mild-to-moderate Alzheimer’s disease who declined despite open-label treatment with 9.5 mg/24 h patch. Over 48 weeks of double-blind treatment, high-dose patch produced greater functional and cognitive benefits compared with 9.5 mg/24 h patch. METHODS: Using OPTIMA data, a post-hoc responder analysis was performed to firstly, compare the proportion of patients demonstrating improvement or absence of decline with 13.3 mg/24 h versus 9.5 mg/24 h patch; and secondly, identify predictors of improvement or absence of decline. ‘Improvers’ were patients who improved on the Alzheimer’s Disease Assessment Scale–cognitive subscale (ADAS-cog) by ≥4 points from baseline, and did not decline on the instrumental domain of the Alzheimer’s Disease Cooperative Study–Activities of Daily Living scale (ADCS-IADL). ‘Non-decliners’ were patients who did not decline on either scale. RESULTS: Overall, 265 patients randomized to 13.3 mg/24 h and 271 to 9.5 mg/24 h patch met the criteria for inclusion in the intention-to-treat population and were included in the analyses. Significantly more patients were ‘improvers’ with 13.3 mg/24 h compared with 9.5 mg/24 h patch at Weeks 24 (44 (16.6%) versus 19 (7.0%); P < 0.001) and 48 (21 (7.9%) versus 10 (3.7%); P = 0.023). A significantly greater proportion of patients were ‘non-decliners’ with 13.3 mg/24 h compared with 9.5 mg/24 h patch at Week 24 (71 (26.8%) versus 44 (16.2%); P = 0.002). At Week 48, there was a trend in favor of 13.3 mg/24 h patch. Functional and cognitive assessment scores at double-blind baseline did not consistently predict effects at Weeks 24 or 48. CONCLUSION: More patients with mild-to-moderate Alzheimer’s disease who are titrated to 13.3 mg/24 h rivastigmine patch at time of decline are ‘improvers’ or ‘non-decliners’ i.e. show responses on cognition and activities of daily living compared with patients remaining on 9.5 mg/24 h patch. TRIAL REGISTRATION: Clinicaltrials.gov identifier: NCT00506415; registered July 20, 2007. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13195-014-0088-8) contains supplementary material, which is available to authorized users

Anomalous Expansion of Attractively Interacting Fermionic Atoms in an Optical Lattice

Strong correlations can dramatically modify the thermodynamics of a quantum many-particle system. Especially intriguing behaviour can appear when the system adiabatically enters a strongly correlated regime, for the interplay between entropy and strong interactions can lead to counterintuitive effects. A well known example is the so-called Pomeranchuk effect, occurring when liquid 3He is adiabatically compressed towards its crystalline phase. Here, we report on a novel anomalous, isentropic effect in a spin mixture of attractively interacting fermionic atoms in an optical lattice. As we adiabatically increase the attraction between the atoms we observe that the gas, instead of contracting, anomalously expands. This expansion results from the combination of two effects induced by pair formation in a lattice potential: the suppression of quantum fluctuations as the attraction increases, which leads to a dominant role of entropy, and the progressive loss of the spin degree of freedom, which forces the gas to excite additional orbital degrees of freedom and expand to outer regions of the trap in order to maintain the entropy. The unexpected thermodynamics we observe reveal fundamentally distinctive features of pairing in the fermionic Hubbard model.Comment: 6 pages (plus appendix), 6 figure

Efficacy of Higher Dose 13.3 mg/24 h Rivastigmine Patch on Instrumental Activities of Daily Living in Patients with Mild-to-Moderate Alzheimer's Disease

Background: Stabilizing/reducing decline in the ability to perform activities of daily living (ADLs) is important in management of Alzheimer's disease (AD). Methods: Post hoc analysis of OPtimizing Transdermal Exelon In Mild-to-moderate Alzheimer's disease (OPTIMA), a double-blind trial comparing 13.3 and 9.5 mg/24 h rivastigmine patch in patients with AD demonstrating functional and cognitive decline with 9.5 mg/24 h patch. Efficacy on Alzheimer's disease Cooperative Study-instrumental ADL (ADCS-IADL) items, higher level function (HLF), and autonomy factors was assessed. Results: The ADCS-IADL, HLF, and autonomy factors favored 13.3 mg/24 h patch at all time points, reaching significance from weeks 16 to 48, 24 to 48, and 32 to 48, respectively. Higher dose patch demonstrated significantly greater efficacy on 10 of 17 ADCS-IADL items at 1 or more time points ( P < .05 vs 9.5 mg/24 h patch). More adverse events were observed with higher dose patch; study discontinuations were similar between the doses. Conclusions: Greater efficacy of 13.3 versus 9.5 mg/24 h patch on ADL, including autonomy and HLF factors, supports this additional dosing option to prolong patients' independence

Crown-of-thorns sea star Acanthaster cf. solaris has tissue-characteristic microbiomes with potential roles in health and reproduction

© 2018 American Society for Microbiology. Outbreaks of coral-eating crown-of-thorns sea stars (CoTS; Acanthaster species complex) cause substantial coral loss; hence, there is considerable interest in developing prevention and control strategies. We characterized the microbiome of captive CoTS and assessed whether dysbiosis was evident in sea stars during a disease event. Most tissue types had a distinct microbiome. The exception was female gonads, in which the microbiomes were highly variable among individuals. Male gonads were dominated (> 97% of reads) by a single Mollicutes-related operational taxonomic unit (OTU). Detailed phylogenetic and microscopy analysis demonstrated the presence of a novel Spiroplasma-related bacterium in the spermatogenic layer. Body wall samples had high relative abundance (43 to 64% of reads) of spirochetes, likely corresponding to subcuticular symbionts reported from many echinoderms. Tube feet were characterized by Hyphomonadaceae (24 to 55% of reads). Pyloric cecal microbiomes had high alpha diversity, comprising many taxa commonly found in gastrointestinal systems. The order Oceanospirillales (genera Endozoicomonas and Kistimonas) was detected in all tissues. A microbiome shift occurred in diseased individuals although differences between tissue types were retained. The relative abundance of spirochetes was significantly reduced in diseased individuals. Kistimonas was present in all diseased individuals and significantly associated with diseased tube feet, but its role in disease causation is unknown. While Arcobacter was significantly associated with diseased tissues and Vibrionaceae increased in diversity, no single OTU was detected in all diseased individuals, suggesting opportunistic proliferation of these taxa in this case. This study shows that CoTS have tissuecharacteristic bacterial communities and identifies taxa that could play a role in reproduction and host health

Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime

We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the real free scalar field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same argument also works for anti-commutation relations and it can be generalised to vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a very weak form of the Jost-Schroer theorem. The original proofs of these results in the Wightman framework make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.Comment: 18 page

Quantum Energy Inequalities in Pre-Metric Electrodynamics

Pre-metric electrodynamics is a covariant framework for electromagnetism with a general constitutive law. Its lightcone structure can be more complicated than that of Maxwell theory as is shown by the phenomenon of birefringence. We study the energy density of quantized pre-metric electrodynamics theories with linear constitutive laws admitting a single hyperbolicity double-cone and show that averages of the energy density along the worldlines of suitable observers obey a Quantum Energy Inequality (QEI) in states that satisfy a microlocal spectrum condition. The worldlines must meet two conditions: (a) the classical weak energy condition must hold along them, and (b) their velocity vectors have positive contractions with all positive frequency null covectors (we call such trajectories `subluminal'). After stating our general results, we explicitly quantize the electromagnetic potential in a translationally invariant uniaxial birefringent crystal. Since the propagation of light in such a crystal is governed by two nested lightcones, the theory shows features absent in ordinary (quantized) Maxwell electrodynamics. We then compute a QEI bound for worldlines of inertial `subluminal' observers, which generalizes known results from the Maxwell theory. Finally, it is shown that the QEIs fail along trajectories that have velocity vectors which are timelike with respect to only one of the lightcones