On the Arnold Conjecture and the Atiyah-Patodi-Singer Index Theorem

The Arnold conjecture yields a lower bound to the number of periodic classical trajectories in a Hamiltonian system. Here we count these trajectories with the help of a path integral, which we inspect using properties of the spectral flow of a Dirac operator in the background of a \Sp(2N) valued gauge field. We compute the spectral flow from the Atiyah-Patodi-Singer index theorem, and apply the results to evaluate the path integral using localization methods. In this manner we find a lower bound to the number of periodic classical trajectories which is consistent with the Arnold conjecture.Comment: 12 pages, references correcte

Radio continuum imaging of the R CrA star-forming region with the ATCA

The aim of this study is to investigate the nature of radio sources associated with young stellar objects (YSOs) belonging to the R CrA cluster. By combining the centimetre radio data with the wealth of shorter wavelength data accumulated recently we wish to refine estimates of the evolutionary stages of the YSOs. Fluxes and spectral indices for the brightest radio sources were derived from the observations at 3, 6, and 20 cm using the ATCA. Seven of detected sources can be assigned to YSOs, which have counterparts in the X-rays, infrared or submm. One of the YSOs, Radio Source 9, is a Class 0 candidate, and another, IRS 7B, is suggested to be in the Class 0/I transition stage. IRS 7B is associated with extended radio lobes at 6 and 20 cm. The lobes may have a gyrosynchrotron emission component, which could be understood in terms of Fermi accleration in shocks. The Class I objects detected here seem to be a mixed lot. One of these, the wide binary IRS 5, shows a negative spectral index, rapid variability, and a high degree of circular polarisation with $V/I\approx33$ % on one of the days of observation. These signs of magnetic activity suggest that at least one of the binary components has advanced beyond the Class I stage. The radio source without YSO assigment, Radio Source 5, has been suggested to be a brown dwarf. The radio properties, in particular its persistent strong emission, do not support this classification. The radio characteristics of the detected YSOs roughly agree with the scheme where the dominant emission mechanism changes with age. The heterogeneity of the Class I group can possibly be explained by a drastic decline in the jet activity during this stage, which also changes the efficiency of free-free absorption around the protostar.Comment: Accepted for publication in A&A (8 pages, 4 figures, 4 tables

{MDL4BMF}: Minimum Description Length for Boolean Matrix Factorization

Matrix factorizations—where a given data matrix is approximated by a prod- uct of two or more factor matrices—are powerful data mining tools. Among other tasks, matrix factorizations are often used to separate global structure from noise. This, however, requires solving the ‘model order selection problem’ of determining where fine-grained structure stops, and noise starts, i.e., what is the proper size of the factor matrices. Boolean matrix factorization (BMF)—where data, factors, and matrix product are Boolean—has received increased attention from the data mining community in recent years. The technique has desirable properties, such as high interpretability and natural sparsity. However, so far no method for selecting the correct model order for BMF has been available. In this paper we propose to use the Minimum Description Length (MDL) principle for this task. Besides solving the problem, this well-founded approach has numerous benefits, e.g., it is automatic, does not require a likelihood function, is fast, and, as experiments show, is highly accurate. We formulate the description length function for BMF in general—making it applicable for any BMF algorithm. We discuss how to construct an appropriate encoding, starting from a simple and intuitive approach, we arrive at a highly efficient data-to-model based encoding for BMF. We extend an existing algorithm for BMF to use MDL to identify the best Boolean matrix factorization, analyze the complexity of the problem, and perform an extensive experimental evaluation to study its behavior

Aspects of Duality and Confining Strings

We inspect the excitation energy spectrum of a confining string in terms of solitons in an effective field theory model. The spectrum can be characterized by a spectral function, and twisting and bending of the string is manifested by the invariance of this function under a duality transformation. Both general considerations and numerical simulations reveal that the spectral function can be approximated by a simple rational form, which we propose becomes exact in the Yang-Mills theory.Comment: refinement of certain argument

On the number of signals in multivariate time series

We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we extract the non-noise latent components using some standard method, allowing the modelling of the extracted univariate time series individually. An important question is the determination of which of the latent components are of interest in modelling and which can be considered as noise. Bootstrap-based methods have recently been used in determining the latent dimension in various methods of unsupervised and supervised dimension reduction and we propose a set of similar estimation strategies for second-order stationary time series. Simulation studies and a sound wave example are used to show the method's effectiveness

Identification of transcriptional and metabolic programs related to mammalian cell size

SummaryBackgroundRegulation of cell size requires coordination of growth and proliferation. Conditional loss of cyclin-dependent kinase 1 in mice permits hepatocyte growth without cell division, allowing us to study cell size in vivo using transcriptomics and metabolomics.ResultsLarger cells displayed increased expression of cytoskeletal genes but unexpectedly repressed expression of many genes involved in mitochondrial functions. This effect appears to be cell autonomous because cultured Drosophila cells induced to increase cell size displayed a similar gene-expression pattern. Larger hepatocytes also displayed a reduction in the expression of lipogenic transcription factors, especially sterol-regulatory element binding proteins. Inhibition of mitochondrial functions and lipid biosynthesis, which is dependent on mitochondrial metabolism, increased the cell size with reciprocal effects on cell proliferation in several cell lines.ConclusionsWe uncover that large cell-size increase is accompanied by downregulation of mitochondrial gene expression, similar to that observed in diabetic individuals. Mitochondrial metabolism and lipid synthesis are used to couple cell size and cell proliferation. This regulatory mechanism may provide a possible mechanism for sensing metazoan cell size

Magnetic Geometry and the Confinement of Electrically Conducting Plasmas

We develop an effective field theory approach to inspect the electromagnetic interactions in an electrically neutral plasma, with an equal number of negative and positive charge carriers. We argue that the static equilibrium configurations within the plasma are topologically stable solitons, that describe knotted and linked fluxtubes of helical magnetic fields.Comment: 9 pages 1 ps-figur

Predictors and Consequences of Anaemia Among Antiretroviral-Naïve HIV-Infected and HIV-Uninfected Children in Tanzania.

Predictors and consequences of childhood anaemia in settings with high HIV prevalence are not well known. The aims of the present study were to identify maternal and child predictors of anaemia among children born to HIV-infected women and to study the association between childhood anaemia and mortality. Prospective cohort study. Maternal characteristics during pregnancy and Hb measurements at 3-month intervals from birth were available for children. Information was also collected on malaria and HIV infection in the children, who were followed up for survival status until 24 months after birth. Dar es Salaam, Tanzania. The study sample consisted of 829 children born to HIV-positive women. Advanced maternal clinical HIV disease (relative risk (RR) for stage > or =2 v. stage 1: 1.31, 95 % CI 1.14, 1.51) and low CD4 cell counts during pregnancy (RR for <350 cells/mm3 v. > or =350 cells/mm3: 1.58, 95 % CI 1.05, 2.37) were associated with increased risk of anaemia among children. Birth weight <2500 g, preterm birth (<34 weeks), malaria parasitaemia and HIV infection in the children also increased the risk of anaemia. Fe-deficiency anaemia in children was an independent predictor of mortality in the first two years of life (hazard ratio 1.99, 95 % CI 1.06, 3.72). Comprehensive care including highly active antiretroviral therapy to eligible HIV-infected women during pregnancy could reduce the burden of anaemia in children. Programmes for the prevention of mother-to-child transmission of HIV and antimalarial treatment to children could improve child survival in settings with high HIV prevalence

Six years survival on imatinib with no disease progression after diagnosis of metastatic duodenal gastrointestinal stromal tumour: a case report

Introduction: A duodenal Gastrointestinal Stromal Tumour (GIST) is a rare finding and until recently advanced disease had a poor prognosis. A PubMed search revealed no reports of more than five years survival of inoperable GIST on chemotherapy with WHO performance status zero. Case Presentation: A 68 year old female was diagnosed with unresectable GIST in the duodenum with metastasis to liver, pancreas and omentum in November 2001. She was commenced on imatinib mesylate (Glivec) chemotherapy. This case report was prepared from the medical records and radiology reports. She had good tolerance with stable disease. After six years her CT scan showed no disease progression and her WHO performance status was zero. Conclusion: This report supports the view that imatinib is a safe and effective drug in controlling disease progression in advanced metastatic GIST and plays an important role in improving the patient's quality of life

Carbon dynamics in a Boreal land-stream-lake continuum during the spring freshet of two hydrologically contrasting years

We studied in 2013 and 2014 the spring carbon dynamics in a Boreal landscape consisting of a lake and 15 inflowing streams and an outlet. The first year had weather and a hydrological regime typical of past years with a distinct spring freshet connected with the thaw of the average snowpack. The latter year had higher air temperatures which did not permit snow accumulation, despite similar winter precipitation. As such, there was hardly any spring freshet in 2014, and stream discharge peaked in January, i.e., the conditions resembled those predicted in the future climate. Despite the hydrological differences between the years, there were only small interannual differences in the stream CO2 and DOC concentrations. The relationship between the concentrations and discharge was stronger in the typical year. CO2 concentrations in medium-sized streams correlated negatively with the discharge, indicating dilution effect of melting snowpacks, while in large-sized streams the correlation was positive, suggesting stronger groundwater influence. The DOC pathway to these streams was through the subsurface soil layers, not the groundwater. The total amount of carbon transported into the lake was ca. 1.5-fold higher in the typical year than in the year with warm winter. In 2013, most of the lateral inputs took place during spring freshet. In 2014, the majority of inputs occurred earlier, during the winter months. The lateral CO2 signal was visible in the lake at 1.5 m depth. DOC dominated the carbon transport, and in both years, 12% of the input C was in inorganic form.Peer reviewe