Quasi-invariance of countable products of Cauchy measures under non-unitary dilations

Consider an infinite sequence (Un)n∈N of independent Cauchy random variables, defined by a sequence (δn)n∈N of location parameters and a sequence (γn)n∈N of scale parameters. Let (Wn)n∈N be another infinite sequence of independent Cauchy random variables defined by the same sequence of location parameters and the sequence (σnγn)n∈N of scale parameters, with σn≠0 for all n∈N. Using a result of Kakutani on equivalence of countably infinite product measures, we show that the laws of (Un)n∈N and (Wn)n∈N are equivalent if and only if the sequence (|σn|−1)n∈N is square-summable

Equivalence of weak and strong modes of measures on topological vector spaces

A strong mode of a probability measure on a normed space $X$ can be defined as a point $u$ such that the mass of the ball centred at $u$ uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened this definition by considering only pairwise comparisons with balls whose centres differ by vectors in a dense, proper linear subspace $E$ of $X$, and posed the question of when these two types of modes coincide. We show that, in a more general setting of metrisable vector spaces equipped with measures that are finite on bounded sets, the density of $E$ and a uniformity condition suffice for the equivalence of these two types of modes. We accomplish this by introducing a new, intermediate type of mode. We also show that these modes can be inequivalent if the uniformity condition fails. Our results shed light on the relationships between among various notions of maximum a posteriori estimator in non-parametric Bayesian inference.Comment: 22 pages, 3 figure

Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

Recurrence of Preeclampsia in Northern Tanzania: A Registry-based Cohort Study.

Preeclampsia occurs in about 4 per cent of pregnancies worldwide, and may have particularly serious consequences for women in Africa. Studies in western countries have shown that women with preeclampsia in one pregnancy have a substantially increased risk of preeclampsia in subsequent pregnancies. We estimate the recurrence risks of preeclampsia in data from Northern Tanzania. A prospective cohort study was designed using 19,811 women who delivered singleton infants at a hospital in Northern Tanzania between 2000 and 2008. A total of 3,909 women were recorded with subsequent deliveries in the hospital with follow up through 2010. Adjusted recurrence risks of preeclampsia were computed using regression models. The absolute recurrence risk of preeclampsia was 25%, which was 9.2-fold (95% CI: 6.4 - 13.2) compared with the risk for women without prior preeclampsia. When there were signs that the preeclampsia in a previous pregnancy had been serious either because the baby was delivered preterm or had died in the perinatal period, the recurrence risk of preeclampsia was even higher. Women who had preeclampsia had increased risk of a series of adverse pregnancy outcomes in future pregnancies. These include perinatal death (RR= 4.3), a baby with low birth weight (RR= 3.5), or a preterm birth (RR= 2.5). These risks were only partly explained by recurrence of preeclampsia. Preeclampsia in one pregnancy is a strong predictor for preeclampsia and other adverse pregnancy outcomes in subsequent pregnancies in Tanzania. Women with previous preeclampsia may benefit from close follow-up during their pregnancies

An event-based resource management framework for distributed decision-making in decentralized virtual power plants

The Smart Grid incorporates advanced information and communication technologies (ICTs) in power systems, and is characterized by high penetration of distributed energy resources (DERs). Whether it is the nation-wide power grid or a single residential building, the energy management involves different types of resources that often depend on and influence each other. The concept of virtual power plant (VPP) has been proposed to represent the aggregation of energy resources in the electricity market, and distributed decision-making (DDM) plays a vital role in VPP due to its complex nature. This paper proposes a framework for managing different resource types of relevance to energy management for decentralized VPP. The framework views VPP as a hierarchical structure and abstracts energy consumption/generation as contractual resources, i.e., contractual offerings to curtail load/supply energy, from third party VPP participants for DDM. The proposed resource models, event-based approach to decision making, multi-agent system and ontology implementation of the framework are presented in detail. The effectiveness of the proposed framework is then demonstrated through an application to a simulated campus VPP with real building energy data

AC and DC House Wiring Efficiency Estimations Using a Fast Extensive Measurements Approach

DC-based appliances are exponentially increasing in the present market. This scenario opens the opportunity to utilize the DC electricity produced by the PV panels directly without going through the conversion stages. Due to high penetration of DC electricity sources, it is timely to utilize DC electricity directly. Several research works have been reported in the literature to experimentally test and compare AC and DC wiring options. Accurate and precise experimental measurements are vital to establish a sound theoretical basis. However, this is difficult due to cost and time constraints. Therefore, to avoid costly measurements, this paper develops a mathematical model based on measurements on selected AC and DC wiring at four voltage levels (12 V DC, 24 V DC, 48 V DC, and 230 V AC). A digital simulation calibration using DigSilent is conducted to validate the proposed mathematical model. This paper proposed to utilize the simulation calibration approach that is a cost-effective and timesaving option to perform extensive measurements accurately

Морфологические изменения в нижнеальвеолярном нерве на экспериментальной модели его травмы разной степени тяжести

У роботі на 40 лабораторних щурах досліджено закономірності та патоморфологічні зміни у нижньоальвеолярному нерві й параневральных тканинах у різний термін після операції, що викликані різним ступенем дії травмуючого фактору.During the experiments on 40 laboratory rodents we have studied the regularities and pathomorphological changes in lower dental nerve and paraneural tissues induced by disturbing factor of varying influence intensity observed at different postoperative periods

The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures

Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.Comment: 29 pages. Plain TeX. Phyzzx needed. An example and some references added. To appear in J. Phys.