How large can the first eigenvalue be on a surface of genus two?

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture.Comment: 20 pages; 4 figure

Folklore as a Special Form of Creation

Papers. With an introduction by Felix J. Oinas

Linguistics

Contains research objectives and reports on one research project.National Science Foundation (Grant G-7364)National Science Foundation (Grant G-13903

Multiple mechanisms repress N-Bak mRNA translation in the healthy and apoptotic neurons

Peer reviewe

Spectral statistics of random geometric graphs

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the spectrum via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Delta_3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio

High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows

We relate high-energy limits of Laplace-type and Dirac-type operators to frame flows on the corresponding manifolds, and show that the ergodicity of frame flows implies quantum ergodicity in an appropriate sense for those operators. Observables for the corresponding quantum systems are matrix-valued pseudodifferential operators and therefore the system remains non-commutative in the high-energy limit. We discuss to what extent the space of stationary high-energy states behaves classically.Comment: 26 pages, latex2

Transverse instability for non-normal parameters

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as ``non-normal''. If there is chaos in the invariant subspace that is not structurally stable, this has the effect of ``blurring out'' blowout bifurcations over a range of parameter values that we show can have positive measure in parameter space. Associated with such blowout bifurcations are bifurcations to attractors displaying a new type of intermittency that is phenomenologically similar to on-off intermittency, but where the intersection of the attractor by the invariant subspace is larger than a minimal attractor. The presence of distinct repelling and attracting invariant sets leads us to refer to this as ``in-out'' intermittency. Such behaviour cannot appear in systems where the transverse dynamics is a skew product over the system on the invariant subspace. We characterise in-out intermittency in terms of its structure in phase space and in terms of invariants of the dynamics obtained from a Markov model of the attractor. This model predicts a scaling of the length of laminar phases that is similar to that for on-off intermittency but which has some differences.Comment: 15 figures, submitted to Nonlinearity, the full paper available at http://www.maths.qmw.ac.uk/~eo

Affective iconic words benefit from additional sound–meaning integration in the left amygdala

Recent studies have shown that a similarity between sound and meaning of a word (i.e., iconicity) can help more readily access the meaning of that word, but the neural mechanisms underlying this beneficial role of iconicity in semantic processing remain largely unknown. In an fMRI study, we focused on the affective domain and examined whether affective iconic words (e.g., high arousal in both sound and meaning) activate additional brain regions that integrate emotional information from different domains (i.e., sound and meaning). In line with our hypothesis, affective iconic words, compared to their non‐iconic counterparts, elicited additional BOLD responses in the left amygdala known for its role in multimodal representation of emotions. Functional connectivity analyses revealed that the observed amygdalar activity was modulated by an interaction of iconic condition and activations in two hubs representative for processing sound (left superior temporal gyrus) and meaning (left inferior frontal gyrus) of words. These results provide a neural explanation for the facilitative role of iconicity in language processing and indicate that language users are sensitive to the interaction between sound and meaning aspect of words, suggesting the existence of iconicity as a general property of human language

Isospectral domains with mixed boundary conditions

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.Comment: 9 figures. Statement of Theorem 5.1 correcte

Trial of Remote Continuous versus Intermittent NEWS monitoring after major surgery (TRaCINg): protocol for a feasibility randomised controlled trial

Background: Despite medical advances, major surgery remains high risk. Up to 44% of patients experience postoperative complications, which can have huge impacts for patients and the healthcare system. Early recognition of postoperative complications is crucial in reducing morbidity and preventing long-term disability. The current standard of care is intermittent manual vital signs monitoring, but new wearable remote monitors offer the benefits of continuous vital signs monitoring without limiting the patient’s mobility. The aim of this study is to evaluate the feasibility, acceptability and clinical impacts of continuous remote monitoring after major surgery. Methods: The study is a randomised, controlled, unblinded, parallel group, feasibility trial. Adult patients undergoing elective major surgery will be invited to participate if they have the capacity to provided informed, written consent and do not have a cardiac pacemaker or an allergy to adhesives. Participants will be randomly assigned to receive continuous remote monitoring and normal National Early Warning Score (NEWS) monitoring (intervention group) or normal NEWS monitoring alone (control group). Continuous remote monitoring will be achieved using the SensiumVitals® wireless patch which is worn on the patient’s chest and monitors heart rate, respiratory rate and temperature continuously and alerts the nurse when there is deviation from pre-set physiological norms. Participants will be followed up throughout their hospital admission and for 30 days after discharge. Feasibility will be assessed by evaluating recruitment rate, adherence to protocol and randomisation, and the amount of missing data. The acceptability of the patch to nursing staff and patients will be assessed using questionnaires and interviews. Clinical outcomes will include time to antibiotics in cases of sepsis, length of hospital stay, number of critical care admissions and rate of readmission within 30 days of discharge. Discussion: Early detection and treatment of complications minimises the need for critical care, improves patient outcomes, and produces significant cost savings for the healthcare system. Remote continuous monitoring systems have the potential to allow earlier detection of complications, but evidence from the literature is mixed. Demonstrating significant benefit over intermittent monitoring to offset the practical and economic implications of continuous monitoring requires well-controlled studies in high-risk populations to demonstrate significant differences in clinical outcomes; this feasibility trial seeks to provide evidence of how best to conduct such a confirmatory trial. Trial registration: This study is listed on the ISRCTN registry with study ID ISRCTN16601772