Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

Agreement between methods of measurement with multiple observations per individual

Limits of agreement provide a straightforward and intuitive approach to agreement between different methods for measuring the same quantity. When pairs of observations using the two methods are independent, i.e., on different subjects, the calculations are very simple and straightforward. Some authors collect repeated data, either as repeated pairs of measurements on the same subject, whose true value of the measured quantity may be changing, or more than one measurement by one or both methods of an unchanging underlying quantity. In this paper we describe methods for analysing such clustered observations, both when the underlying quantity is assumed to be changing and when it is not

Dynamical properties of ultracold bosons in an optical lattice

We study the excitation spectrum of strongly correlated lattice bosons for the Mott-insulating phase and for the superfluid phase close to localization. Within a Schwinger-boson mean-field approach we find two gapped modes in the Mott insulator and the combination of a sound mode (Goldstone) and a gapped (Higgs) mode in the superfluid. To make our findings comparable with experimental results, we calculate the dynamic structure factor as well as the linear response to the optical lattice modulation introduced by Stoeferle et al. [Phys. Rev. Lett. 92, 130403 (2004)]. We find that the puzzling finite frequency absorption observed in the superfluid phase could be explained via the excitation of the gapped (Higgs) mode. We check the consistency of our results with an adapted f-sum-rule and propose an extension of the experimental technique by Stoeferle et al. to further verify our findings.Comment: 13 pages, 5 figure

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Comment: 34 pages; exposition of Hochschild homology expanded; references added; introduction re-written; some imrecisions, typos and the orbit diagram in the last section correcte

Stress engineering at the nanometer scale: Two-component adlayer stripes

Spontaneously formed equilibrium nanopatterns with long-range order are widely observed in a variety of systems, but their pronounced temperature dependence remains an impediment to maintain such patterns away from the temperature of formation. Here, we report on a highly ordered stress-induced stripe pattern in a two-component, Pd-O, adsorbate monolayer on W(110), produced at high temperature and identically preserved at lower temperatures. The pattern shows a tunable period (down to 16 nm) and orientation, as predicted by a continuum model theory along with the surface stress and its anisotropy found in our DFT calculations. The control over thermal fluctuations in the stripe formation process is based on the breaking/restoring of ergodicity in a high-density lattice gas with long-range interactions upon turning off/on particle exchange with a heat bath.Comment: 6 pages, 4 figure

Survey of the quality of experimental design, statistical analysis and reporting of research using animals

For scientific, ethical and economic reasons, experiments involving animals should be appropriately designed, correctly analysed and transparently reported. This increases the scientific validity of the results, and maximises the knowledge gained from each experiment. A minimum amount of relevant information must be included in scientific publications to ensure that the methods and results of a study can be reviewed, analysed and repeated. Omitting essential information can raise scientific and ethical concerns. We report the findings of a systematic survey of reporting, experimental design and statistical analysis in published biomedical research using laboratory animals. Medline and EMBASE were searched for studies reporting research on live rats, mice and non-human primates carried out in UK and US publicly funded research establishments. Detailed information was collected from 271 publications, about the objective or hypothesis of the study, the number, sex, age and/or weight of animals used, and experimental and statistical methods. Only 59% of the studies stated the hypothesis or objective of the study and the number and characteristics of the animals used. Appropriate and efficient experimental design is a critical component of high-quality science. Most of the papers surveyed did not use randomisation (87%) or blinding (86%), to reduce bias in animal selection and outcome assessment. Only 70% of the publications that used statistical methods described their methods and presented the results with a measure of error or variability. This survey has identified a number of issues that need to be addressed in order to improve experimental design and reporting in publications describing research using animals. Scientific publication is a powerful and important source of information; the authors of scientific publications therefore have a responsibility to describe their methods and results comprehensively, accurately and transparently, and peer reviewers and journal editors share the responsibility to ensure that published studies fulfil these criteria

Extending Hybrid CSP with Probability and Stochasticity

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly intertwining discrete, continuous and stochastic dynamics complicates modelling, analysis and verification of stochastic hybrid systems (SHSs). In the literature, this issue has been extensively investigated, but unfortunately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which is called stochastic HCSP (SHCSP). To this end, ordinary differential equations (ODEs) are generalized by stochastic differential equations (SDEs) and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to specify and reason about SHCSP processes. We demonstrate our approach by an example from real-world.Comment: The conference version of this paper is accepted by SETTA 201

Fe on W(001) from continuous films to nanoparticles: Growth and magnetic domain structure

The evolution of the structural and magnetic properties of Fe films during growth on the W(001) surface have been studied with low energy electron diffraction, real-time low energy electron microscopy, and quasi-real-time, spin-polarized low energy electron microscopy in the absence of a magnetic field (virgin state). Depending on the growth temperature, different growth modes are observed: growth of atomically rough and highly strained (10.4% tensile) pseudomorphic films at room temperature, kinetically limited layer-by-layer growth (quasi–Frank-van der Merwe growth mode) of smooth pseudomorphic films up to 4 monolayers at around 500 K and growth of fully relaxed three-dimensional Fe islands on top of a thermodynamically stable 2-monolayer-thick wetting layer (Stranski-Krastanov growth mode) at and above 700 K. Around 500 K, layered growth is terminated by partial (2 monolayers) dewetting of the metastable Fe film and formation of thin, partially relaxed, elongated islands on a thermodynamically stable 2 monolayer film. Ferromagnetic order is first detected during growth at room temperature at 2.35 monolayer Fe film thickness. The magnetization is in-plane with a thickness-dependent direction, rotating from the substrate ⟨110⟩ directions at 3 monolayers toward the ⟨100⟩ directions at 4 monolayers and back again toward the ⟨110⟩ directions at about 8 monolayers. The in-plane spin reorientation that occurs at room temperature is accompanied by significant changes of the magnetic domain structure. In the Frank-van der Merwe growth regime, large magnetic domains are observed in metastable 3 and 4 monolayer films. The isolated three-dimensional Fe islands that form in the Stranski-Krastanov regime have vortex, quasi-single domain (C state), or single magnetic domain structures, depending on their size and shape. The detailed results that are obtained with high thickness, lateral and azimuthal angular resolution with spin-polarized low energy electron microscopy are compared with earlier laterally averaging and laterally resolving magnetic studies, and discrepancies are explained