On Hausdorff dimension of the set of closed orbits for a cylindrical transformation

We deal with Besicovitch's problem of existence of discrete orbits for transitive cylindrical transformations $T_\varphi:(x,t)\mapsto(x+\alpha,t+\varphi(x))$ where $Tx=x+\alpha$ is an irrational rotation on the circle \T and \varphi:\T\to\R is continuous, i.e.\ we try to estimate how big can be the set D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}. We show that for almost every $\alpha$ there exists $\varphi$ such that the Hausdorff dimension of $D(\alpha,\varphi)$ is at least $1/2$. We also provide a Diophantine condition on $\alpha$ that guarantees the existence of $\varphi$ such that the dimension of $D(\alpha,\varphi)$ is positive. Finally, for some multidimensional rotations $T$ on \T^d, $d\geq3$, we construct smooth $\varphi$ so that the Hausdorff dimension of $D(\alpha,\varphi)$ is positive.Comment: 32 pages, 1 figur

"It ain't over till the fat lady sings" : A response to Cameron N. McIntosh, improving the evaluation of model fit in confirmatory factor analysis

Peer reviewedPublisher PD

Effects of mode of administration (MOA) on the measurement properties of the EORTC QLQ-C30: a randomized study

<p>Abstract</p> <p>Background</p> <p>While modern electronic data collection methods (e.g., computer touch-screen or web-based) hold much promise, most current studies continue to make use of more traditional data collection techniques, including paper-and-pencil administration and telephone interviews. The present randomized trial investigated the measurement properties of the EORTC QLQ-C30 under three different modes of administration (MOA's).</p> <p>Methods</p> <p>A heterogeneous sample of 314 cancer patients undergoing treatment at a specialized treatment center in Amsterdam were randomized to one of three MOA's for the QLQ-C30: paper-and-pencil at home via the mail, telephone interview, and paper-and-pencil at the hospital clinic. Group differences in internal consistency reliabilities (Cronbach's alpha coefficient) for the scale scores were compared. Differences in mean scale scores were also compared by means of ANOVA, with adjustment for potential confounders.</p> <p>Results</p> <p>Only one statistically significant, yet minor, difference in Cronbach's alpha between the MOA groups was observed for the Role Functioning scale (all 3 alphas >0.80). Significant differences in group means -after adjustment- were found for the Emotional Functioning (EF) scale. Patients completing the written questionnaire at home had significantly lower levels of EF as compared to those interviewed via the telephone; EF scores of those completing the questionnaire at the clinic fell in-between those of the other two groups. These differences, however, were small in magnitude.</p> <p>Conclusions</p> <p>MOA had little effect on the reliability or the mean scores of the EORTC QLQ-C30, with the possible exception of the EF scale.</p

Observation of quantum interference as a function of Berry's phase in a complex Hadamard optical network

Emerging models of quantum computation driven by multi-photon quantum interference, while not universal, may offer an exponential advantage over classical computers for certain problems. Implementing these circuits via geometric phase gates could mitigate requirements for error correction to achieve fault tolerance while retaining their relative physical simplicity. We report an experiment in which a geometric phase is embedded in an optical network with no closed-loops, enabling quantum interference between two photons as a function of the phase.Comment: Comments welcom

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio

Quantum Commuting Circuits and Complexity of Ising Partition Functions

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy (PH) collapses at the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of the partition functions of Ising models. We apply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable in the strong sense, by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising models with imaginary coupling constants. Specifically, we show that there is no fully polynomial randomized approximation scheme (FPRAS) for Ising models with almost all imaginary coupling constants even on a planar graph of a bounded degree, unless the PH collapses at the third level. Furthermore, we also show a multiplicative approximation of such a class of Ising partition functions is at least as hard as a multiplicative approximation for the output distribution of an arbitrary quantum circuit.Comment: 36 pages, 5 figure

Approximate locality for quantum systems on graphs

In this Letter we make progress on a longstanding open problem of Aaronson and Ambainis [Theory of Computing 1, 47 (2005)]: we show that if A is the adjacency matrix of a sufficiently sparse low-dimensional graph then the unitary operator e^{itA} can be approximated by a unitary operator U(t) whose sparsity pattern is exactly that of a low-dimensional graph which gets more dense as |t| increases. Secondly, we show that if U is a sparse unitary operator with a gap \Delta in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/\Delta increases. These two results can be interpreted as a way to convert between local continuous-time and local discrete-time processes. As an example we show that the discrete-time coined quantum walk can be realised as an approximately local continuous-time quantum walk. Finally, we use our construction to provide a definition for a fractional quantum fourier transform.Comment: 5 pages, 2 figures, corrected typ

Exceptions to the rule of informed consent for research with an intervention

Background In specific situations it may be necessary to make an exception to the general rule of informed consent for scientific research with an intervention. Earlier reviews only described subsets of arguments for exceptions to waive consent. Methods Here, we provide a more extensive literature review of possible exceptions to the rule of informed consent and the accompanying arguments based on literature from 1997 onwards, using both Pubmed and PsycINFO in our search strategy. Results We identified three main categories of arguments for the acceptability of a consent waiver: data validity and quality, major practical problems, and distress or confusion of participants. Approval by a medical ethical review board always needs to be obtained. Further, we provide examples of specific conditions under which consent waiving might be allowed, such as additional privacy protection measures. Conclusions The reasons legitimized by the authors of the papers in this overview can be used by researchers to form their own opinion about requesting an exception to the rule of informed consent for their own study. Importantly, rules and guidelines applicable in their country, institute and research field should be followed. Moreover, researchers should also take the conditions under which they feel an exception is legitimized under consideration. After discussions with relevant stakeholders, a formal request should be sent to an IRB

Feasibility of a home-based exercise intervention with remote guidance for patients with stable grade II and III gliomas:A pilot randomized controlled trial

Objective: In this pilot study, we investigated the feasibility of a home-based, remotely guided exercise intervention for patients with gliomas. Design: Pilot randomized controlled trial (RCT) with randomization (2:1) to exercise or control group. Subjects: Patients with stable grade II and III gliomas. Intervention: The six-month intervention included three home-based exercise sessions per week at 60%–85% of maximum heart rate. Participants wore heart rate monitors connected to an online platform to record activities that were monitored weekly by the physiotherapist. Main measures: Accrual, attrition, adherence, safety, satisfaction, patient-reported physical activity, VO2 peak (by maximal cardiopulmonary exercise testing) and body mass index (BMI) at baseline and at six-month follow-up. Results: In all, 34 of 136 eligible patients (25%) were randomized to exercise training (N = 23) or the control group (N = 11), of whom 19 and 9, respectively, underwent follow-up. Mean adherence to prescribed sessions was 79%. Patients’ experiences were positive. There were no adverse events. Compared to the control group, the exercise group showed larger improvements in absolute VO2 peak (+158.9 mL/min; 95% CI: −44.8 to 362.5) and BMI (−0.3 kg/m²; 95% CI: −0.9 to 0.2). The median increase in physical activity was 1489 metabolic equivalent of task (MET) minutes higher in the exercise group. The most reported reasons for non-participation were lack of motivation or time. Conclusion: This innovative and intensive home-based exercise intervention was feasible in a small subset of patients with stable gliomas who were interested in exercising. The observed effects suggest that the programme may improve cardiorespiratory fitness. These results support the need for large-scale trials of exercise interventions in brain tumour patients. Keywords: Glioma, brain tumour, exercise, physical training, physical fitnes