Large deviations for many Brownian bridges with symmetrised initial-terminal condition

Consider a large system of $N$ Brownian motions in $\mathbb{R}^d$ with some non-degenerate initial measure on some fixed time interval $[0,\beta]$ with symmetrised initial-terminal condition. That is, for any $i$, the terminal location of the $i$-th motion is affixed to the initial point of the $\sigma(i)$-th motion, where $\sigma$ is a uniformly distributed random permutation of $1,...,N$. Such systems play an important role in quantum physics in the description of Boson systems at positive temperature $1/\beta$. In this paper, we describe the large-N behaviour of the empirical path measure (the mean of the Dirac measures in the $N$ paths) and of the mean of the normalised occupation measures of the $N$ motions in terms of large deviations principles. The rate functions are given as variational formulas involving certain entropies and Fenchel-Legendre transforms. Consequences are drawn for asymptotic independence statements and laws of large numbers. In the special case related to quantum physics, our rate function for the occupation measures turns out to be equal to the well-known Donsker-Varadhan rate function for the occupation measures of one motion in the limit of diverging time. This enables us to prove a simple formula for the large-N asymptotic of the symmetrised trace of ${\rm e}^{-\beta \mathcal{H}_N}$, where $\mathcal{H}_N$ is an $N$-particle Hamilton operator in a trap

Reply to N.M. Vegter ‘Discussion on the kinetics of the elution of gold from activated carbon’

Mr Vetger has analysed, in some depth, the approximations made in the treatment of the kinetic data presented in the original by ourselves..

Estimates of scale and scope economies in the New Zealand life insurance industry

Recent multi-product statistical studies of life insurance industries in North America and the United Kingdom have produced mixed findings with regard to economies of scale and scope. This study presents results for the insurance industry in a small economy where the industry is comparatively unregulated. 135 pooled observations for the population of non-bank insurance companies in New Zealand for the period 1988-1992 are used in a two input/three output translog model. We find that while small companies enjoy economies of scale, the optimum plant size is modest, and medium-and large-sized companies experience a significant scale disadvantage. In contrast, all sizes of company benefit from scope economies, but such economies tend to be much greater for the larger companies

Genetic characterization of flea-derived Bartonella species from native animals in Australia suggests host-parasite co-evolution

Fleas are important arthropod vectors for a variety of diseases in veterinary and human medicine, and bacteria belonging to the genus Bartonella are among the organisms most commonly transmitted by these ectoparasites. Recently, a number of novel Bartonella species and novel species candidates have been reported in marsupial fleas in Australia. In the present study the genetic diversity of marsupial fleas was investigated; 10 species of fleas were collected from seven different marsupial and placental mammal hosts in Western Australia including woylies (Bettongia penicillata), western barred bandicoots (Perameles bougainville), mardos (Antechinus flavipes), bush rats (Rattus fuscipes), red foxes (Vulpes vulpes), feral cats (Felis catus) and rabbits (Oryctolagus cuniculus). PCR and sequence analysis of the cytochrome oxidase subunit I (COI) and the 18S rRNA genes from these fleas was performed. Concatenated phylogenetic analysis of the COI and 18S rRNA genes revealed a close genetic relationship between marsupial fleas, with Pygiopsylla hilli from woylies, Pygiopsylla tunneyi from western barred bandicoots and Acanthopsylla jordani from mardos, forming a separate cluster from fleas collected from the placental mammals in the same geographical area. The clustering of Bartonella species with their marsupial flea hosts suggests co-evolution of marsupial hosts, marsupial fleas and Bartonella species in Australia

Acute Lower Extremity Posterior Compartment Syndrome: A Rare Complication of Apixaban Use

Apixaban is an oral anticoagulant that directly inhibits Factor Xa and is indicated for the prophylaxis and treatment of deep venous thrombosis and stroke prevention in non-valvular atrial fibrillation. Acute lower extremity Posterior Compartment Syndrome is a rare complication of Apixaban use. We present a 78-year-old male with significant medical morbidities taking Apixaban for Atrial Fibrillation presenting with post-traumatic extensive hemorrhagic bullae on the left proximal pretibial region secondary to anticoagulation. We recommend that clinicians develop awareness of the potential for serious bleeding complications of anticoagulants and devise strategies to identify the need for early recognition and prompt management

Advancing current approaches to disease management evaluation:Capitalizing on heterogeneity to understand what works and for whom

BACKGROUND: Evaluating large-scale disease management interventions implemented in actual health care settings is a complex undertaking for which universally accepted methods do not exist. Fundamental issues, such as a lack of control patients and limited generalizability, hamper the use of the ‘gold-standard’ randomized controlled trial, while methodological shortcomings restrict the value of observational designs. Advancing methods for disease management evaluation in practice is pivotal to learn more about the impact of population-wide approaches. Methods must account for the presence of heterogeneity in effects, which necessitates a more granular assessment of outcomes. METHODS: This paper introduces multilevel regression methods as valuable techniques to evaluate ‘real-world’ disease management approaches in a manner that produces meaningful findings for everyday practice. In a worked example, these methods are applied to retrospectively gathered routine health care data covering a cohort of 105,056 diabetes patients who receive disease management for type 2 diabetes mellitus in the Netherlands. Multivariable, multilevel regression models are fitted to identify trends in clinical outcomes and correct for differences in characteristics of patients (age, disease duration, health status, diabetes complications, smoking status) and the intervention (measurement frequency and range, length of follow-up). RESULTS: After a median one year follow-up, the Dutch disease management approach was associated with small average improvements in systolic blood pressure and low-density lipoprotein, while a slight deterioration occurred in glycated hemoglobin. Differential findings suggest that patients with poorly controlled diabetes tend to benefit most from disease management in terms of improved clinical measures. Additionally, a greater measurement frequency was associated with better outcomes, while longer length of follow-up was accompanied by less positive results. CONCLUSIONS: Despite concerted efforts to adjust for potential sources of confounding and bias, there ultimately are limits to the validity and reliability of findings from uncontrolled research based on routine intervention data. While our findings are supported by previous randomized research in other settings, the trends in outcome measures presented here may have alternative explanations. Further practice-based research, perhaps using historical data to retrospectively construct a control group, is necessary to confirm results and learn more about the impact of population-wide disease management

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Cooling atoms in an optical trap by selective parametric excitation

We demonstrate the possibility of energy-selective removal of cold atoms from a tight optical trap by means of parametric excitation of the trap vibrational modes. Taking advantage of the anharmonicity of the trap potential, we selectively remove the most energetic trapped atoms or excite those at the bottom of the trap by tuning the parametric modulation frequency. This process, which had been previously identified as a possible source of heating, also appears to be a robust way for forcing evaporative cooling in anharmonic traps.Comment: 5 pages, 5 figure

Towards the deconstruction of M-theory

We argue that there is an equivalence of M-theory on T^3 \times A_{N-1} with a four-dimensional non-supersymmetric quiver gauge theory on the Higgs branch. The quiver theory in question has gauge group SU(N)^{N_4N_6N_8} and is considered in a strong coupling and large N_{4,6,8} limit. We provide field- and string-theoretical evidence for the equivalence making use of the deconstruction technique. In particular, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies.Comment: LaTeX, 15 pages, 4 figures, added reference

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set of minimisers as a whole. `Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.Comment: 83 pages, 1 figur