1,400 research outputs found
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
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
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
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
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
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
- …