K3-fibered Calabi-Yau threefolds I, the twist map

A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in particular one case has K3 surfaces as fibers. These Calabi-Yaus are of some interest in connection with Type II -heterotic string dualities in dimension 4. A section at the end of the paper summarises this for the non-expert mathematician.Comment: 31 pages LaTeX, 11pt, 2 figures. To appear in International Journal of Mathematics. On the web at http://personal-homepages.mis.mpg.de/bhunt/preprints.html , #

Generalised dimensions of measures on almost self-affine sets

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

Thermal conductivity of lightly Sr- and Zn-doped La2_2CuO4_4 single crystals

Both ab-plane and c-axis thermal conductivities ($\kappa_{ab}$ and $\kappa_c$) of lightly doped La$_{2-x}$Sr$_x$CuO$_4$ and La$_2$Cu$_{1-y}$Zn$_y$O$_4$ single crystals ($x$ or $y$ = 0 -- 0.04) are measured from 2 to 300 K. It is found that the low-temperature phonon peak (at 20 -- 25 K) is significantly suppressed upon Sr or Zn doping even at very low doping, though its precise doping dependences show interesting differences between the Sr and Zn dopants, or between the $ab$ plane and the c axis. Most notably, the phonon peak in $\kappa_c$ decreases much more quickly with Sr doping than with Zn doping, while the phonon-peak suppression in $\kappa_{ab}$ shows an opposite trend. It is discussed that the scattering of phonons by stripes is playing an important role in the damping of the phonon heat transport in lightly doped LSCO, in which static spin stripes has been observed by neutron scattering. We also show $\kappa_{ab}$ and $\kappa_c$ data of La$_{1.28}$Nd$_{0.6}$Sr$_{0.12}$CuO$_4$ and La$_{1.68}$Eu$_{0.2}$Sr$_{0.12}$CuO$_4$ single crystals to compare with the data of the lightly doped crystals for the discussion of the role of stripes. At high temperature, the magnon peak (i.e., the peak caused by the spin heat transport near the N\'{e}el temperature) in $\kappa_{ab}(T)$ is found to be rather robust against Zn doping, while it completely disappears with only 1% of Sr doping.Comment: 7 pages, 4 figures, accepted for publication in Phys. Rev.

Readmission to intensive care: development of a nomogram for individualising risk

Background: Readmission to intensive care during the same hospital stay has been associated with a greater risk of in-hospital mortality and has been suggested as a marker ofquality of care. There is lack of published research attempting to develop clinical prediction tools that individualise the risk of readmission to the intensive care unit during the same hospital stay. Objective: To develop a prediction model using an inception cohort of patients surviving an initial ICU stay. Design, setting and participants: The study was conducted at Liverpool Hospital, Sydney. An inception cohort of 14 952 patients aged 15 years or more surviving an initial ICU stay and transferred to general wards in the study hospital between 1 January 1997 and 31 December 2007 was used to develop the model. Binary logistic regression was used to develop the prediction model and anomogram was derived to individualise the risk of readmission to the ICU during the same hospital stay. Main outcome measure: Readmission to the ICU during the same hospital stay.Results: Among members of the study cohort there were 987 readmissions to ICU during the study period. Compared with patients not readmitted to the ICU, patients who were readmitted were more likely to have had ICU stays of at least 7 days (odds ratio [OR], 2.2 [95% CI, 1.85-2.56]); non-elective initial admission to the ICU (OR, 1.7[95% CI, 1.44-2.08]); and acute renal failure (OR, 1.6 [95%CI, 0.97-2.47]). Patients admitted to the ICU from the operating theatre or recovery ward had a lower risk of readmission to ICU than those admitted from general wards, the emergency department or other hospitals. The maximum error between observed frequencies and predicted probabilities of readmission to ICU was estimatedto be 3%. The area under the receiver operating characteristic curve of the final model was 0.66.Conclusion: We have developed a practical clinical tool toindividualise the risk of readmission to the ICU during the same hospital stay in patients who survive an initial episodeof intensive care

Manifestation of Chaos in Real Complex Systems: Case of Parkinson's Disease

In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve as a reliable quantitative estimation of the state of a complex system and help to estimate the deviation of this state from its normal condition. As the IMC we suggest the statistical spectrum of the non-Markovity parameter (NMP) and its frequency behavior. Our preliminary studies of real complex systems in cardiology, neurophysiology and seismology have shown that the NMP has diverse frequency dependence. It testifies to the competition between Markovian and non-Markovian, random and regular processes and makes a crossover from one relaxation scenario to the other possible. On this basis we can formulate the new concept in the study of the manifestation of chaoticity. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of the IMC in real complex systems. With the help of the IMC we have found out the evident manifestation of chaosity in a normal (healthy) state of the studied system, its sharp reduction in the period of crises, catastrophes and various human diseases. It means that one can appreciably improve the state of a patient (of any system) by increasing the IMC of the studied live system. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson's disease in particular.Comment: 20 pages, 8 figures, 3 tables. To be published in "The Logistic Map and the Route to Chaos: From the Beginnings to the Modern Applications", eds. by M. Ausloos, M. Dirickx, pp. 175-196, Springer-Verlag, Berlin (2006

First time determination of the microscopic structure of a stripe phase: Low temperature NMR in La2NiO4.17

The experimental observations of stripes in superconducting cuprates and insulating nickelates clearly show the modulation in charge and spin density. However, these have proven to be rather insensitive to the harmonic structure and (site or bond) ordering. Using 139La NMR in La2NiO4.17, we show that in the 1/3 hole doped nickelate below the freezing temperature the stripes are strongly solitonic and site ordered with Ni3+ ions carrying S=1/2 in the domain walls and Ni2+ ions with S=1 in the domains.Comment: 4 pages including 4 figure

Linear-T resistivity and change in Fermi surface at the pseudogap critical point of a high-Tc superconductor

A fundamental question of high-temperature superconductors is the nature of the pseudogap phase which lies between the Mott insulator at zero doping and the Fermi liquid at high doping p. Here we report on the behaviour of charge carriers near the zero-temperature onset of that phase, namely at the critical doping p* where the pseudogap temperature T* goes to zero, accessed by investigating a material in which superconductivity can be fully suppressed by a steady magnetic field. Just below p*, the normal-state resistivity and Hall coefficient of La1.6-xNd0.4SrxCuO4 are found to rise simultaneously as the temperature drops below T*, revealing a change in the Fermi surface with a large associated drop in conductivity. At p*, the resistivity shows a linear temperature dependence as T goes to zero, a typical signature of a quantum critical point. These findings impose new constraints on the mechanisms responsible for inelastic scattering and Fermi surface transformation in theories of the pseudogap phase.Comment: 24 pages, 6 figures. Published in Nature Physics. Online at http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys1109.htm

Stochastic stability versus localization in chaotic dynamical systems

We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's conjecture about the approximation of the dynamics of a chaotic system by a finite state Markov chain. Conditions under which the localization phenomenon (i.e. stabilization of singular invariant measures) takes place are also considered. Our main tools are the so called bounded variation approach combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random walk argument that we apply to prove the absence of ``traps'' under the action of random perturbations.Comment: 27 pages, LaTe