Rough differential equations driven by signals in Besov spaces

Rough differential equations are solved for signals in general Besov spaces unifying in particular the known results in H\"older and p-variation topology. To this end the paracontrolled distribution approach, which has been introduced by Gubinelli, Imkeller and Perkowski ["Paracontrolled distribution and singular PDEs", Forum of Mathematics, Pi (2015)] to analyze singular stochastic PDEs, is extended from H\"older to Besov spaces. As an application we solve stochastic differential equations driven by random functions in Besov spaces and Gaussian processes in a pathwise sense.Comment: Former title: "Rough differential equations on Besov spaces", 37 page

Fragmentation in Jets at NNLO

Beam and jet functions in Soft-Collinear Effective Theory describe collinear initial- and final-state radiation (jets), and enter in factorization theorems for N-jet production, the Higgs pT spectrum, etc. We show that they may directly be calculated as phase-space integrals of QCD splitting functions. At NLO all computations are trivial, as we demonstrate explicitly for the beam function, the transverse-momentum-dependent beam function, the jet function and the fragmenting jet function. This approach also highlights the role of crossing symmetry in these calculations. At NNLO we reproduce the quark jet function and calculate the fragmenting quark jet function for the first time. Here we use two methods: a direct phase-space integration and a reduction to master integrals which are computed using differential equations.Comment: 25 pages + Mathematica files with expressions, v2: introduction expanded, errors fixed in NNLO fragmenting jet matching coefficients (Sec. IV F), v3: journal versio

Information and participation in decision-making about treatment: a qualitative study of the perceptions and preferences of patients with rheumatoid arthritis.

Objectives: To elicit the perceptions and preferences of patients with rheumatoid arthritis regarding information and participation in treatment decision-making. To analyse the patients’ narratives on the background of the ethical discourse on various approaches to treatment decisionmaking. Design: In-depth interviews with themes identified using principles of grounded theory. Participants: 22 patients with long-standing rheumatoid arthritis. Main outcome measures: Qualitative data on patients’ perceptions and preferences regarding information and participation in decision-making about treatment. Results: Decision-making about treatment has been described by the patients as a process consisting of different stages with shifting loci of control and responsibility. Patients initially received one treatment recommendation and were not aware of alternative treatment options. Those participants in this study who wanted information about negative effects of a treatment cited ‘‘interest in one’s own health’’ and the potential ‘‘use of information’’ as reasons for their preference. The physicians’ expert knowledge and clinical experience regarding the effects of medication were cited as arguments by patients for a treatment recommendation. Conclusions: The patients’ accounts of decision-making about treatment differ from models of physician–patient relationship that have been put forward in ethical discourse. These differences may be relevant with respect to the starting point of an ethical analysis of treatment decision-making. Patients’ accounts with respect to a lack of information on treatment alternatives point to ethically relevant challenges regarding treatment decision-making in clinical practice

On the relative strengths of fragments of collection

Let $\mathbf{M}$ be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, $\Delta_0$-separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set-theoretic collection scheme to $\mathbf{M}$. We focus on two common parameterisations of collection: $\Pi_n$-collection, which is the usual collection scheme restricted to $\Pi_n$-formulae, and strong $\Pi_n$-collection, which is equivalent to $\Pi_n$-collection plus $\Sigma_{n+1}$-separation. The main result of this paper shows that for all $n \geq 1$, (1) $\mathbf{M}+\Pi_{n+1}\textrm{-collection}+\Sigma_{n+2}\textrm{-induction on } \omega$ proves the consistency of Zermelo Set Theory plus $\Pi_{n}$-collection, (2) the theory $\mathbf{M}+\Pi_{n+1}\textrm{-collection}$ is $\Pi_{n+3}$-conservative over the theory $\mathbf{M}+\textrm{strong }\Pi_n \textrm{-collection}$. It is also shown that (2) holds for $n=0$ when the Axiom of Choice is included in the base theory. The final section indicates how the proofs of (1) and (2) can be modified to obtain analogues of these results for theories obtained by adding fragments of collection to a base theory (Kripke-Platek Set Theory with Infinity and $V=L$) that does not include the powerset axiom.Comment: 22 page

On the causal interpretation of acyclic mixed graphs under multivariate normality

In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed, under multivariate normality, every mixed graph corresponds to a set of covariance matrices that contains as a full-dimensional subset the covariance matrices associated with a causally interpretable acyclic digraph. This digraph generally has some of its nodes corresponding to hidden variables. We seek to clarify for which mixed graphs there exists an acyclic digraph whose hidden variable model coincides with the mixed graph model. Restricting to the tractable setting of chain graphs and multivariate normality, we show that decomposability of the bidirected part of the chain graph is necessary and sufficient for equality between the mixed graph model and some hidden variable model given by an acyclic digraph

The Home Bias and Capital Income Flows between Countries and Regions

This paper documents a marked increase in international consumption risk sharing throughout the recent globalization period. Unlike earlier studies that have found it difficult to document a consistent effect of financial globalization on international consumption comovements, we make use of the information implicit in the relative levels of consumption and output to measure long-run risk sharing among OECD countries and US federal states. We derive our empirical setup from a deliberately simplistic model in which countries can trade perpetual claims to each other?s output (Shiller securities). This model allows us to identify the channels through which improvements in international risk sharing have come about. The model predicts crosscountry and cross-regional income flows with considerable precision. Both international income flows as well as consumption risk sharing have increased since 1990, in line with the gradual removal of country portfolio home bias documented elsewhere. Still, the increase in international income flows falls short of explaining all of the consumption risk sharing we see in international data. We show that heterogeneity in countries? gross foreign asset positions is important in explaining this result. While countries with less portfolio home bias enjoy better consumption risk sharing, our findings also suggest that heterogeneity in country portfolios opens an separate channel for consumption risk sharing, possibly through asymmetric valuation effects that have been emphasized in the recent literature. --Consumption Risk Sharing,International and regional business cycles,Capital flows,Home Bias,Non-stationary panel data

On Understanding Sources of Growth and Output Gaps for Switzerland

In this paper, we measure the main factors explaining nominal output growth and deviations from trend output in Switzerland over the period 1980 to 2001. The decompositions are based on the GDP function and its dual, the national income function. The results indicate that whereas nominal output growth frequently reflects movements in domestic prices, it is capital formation that makes the largest contribution to real output growth, followed by gains in total factor productivity and improvements in the terms of trade. Deviations of real output from trend appear to have been driven by deviations of labour utilization, of productivity and, during the first decade, of the terms of trade from their respective long-run trends. The important role attributed to productivity and the terms of trade support the view that the customary measures of the output gap should be used with caution when formulating monetary policy.GDP growth, output gap, index numbers, welfare