Edge-Orders

Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs in linear time, respectively. While the former can be seen as the edge-variants of st-numberings, the latter are the edge-variants of Mondshein sequences and non-separating ear decompositions. The methods that we use for obtaining such edge-orders differ considerably in almost all details from the ones used for their vertex-counterparts, as different graph-theoretic constructions are used in the inductive proof and standard reductions from edge- to vertex-connectivity are bound to fail. As a first application, we consider the famous Edge-Independent Spanning Tree Conjecture, which asserts that every k-edge-connected graph contains k rooted spanning trees that are pairwise edge-independent. We illustrate the impact of the above edge-orders by deducing algorithms that construct 2- and 3-edge independent spanning trees of 2- and 3-edge-connected graphs, the latter of which improves the best known running time from O(n^2) to linear time

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals--increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [L. M. Lopatina and J. V. Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.Comment: 7 pages, including 2 postscript figures, uses REVTeX 4.

Hartree-Fock symmetry breaking around conical intersections

We study the behavior of Hartree-Fock (HF) solutions in the vicinity of conical intersections. These are here understood as regions of a molecular potential energy surface characterized by degenerate or nearly-degenerate eigenfunctions with identical quantum numbers (point group, spin, and electron number). Accidental degeneracies between states with different quantum numbers are known to induce symmetry breaking in HF. The most common closed-shell restricted HF instability is related to singlet-triplet spin degeneracies that lead to collinear unrestricted HF (UHF) solutions. Adding geometric frustration to the mix usually results in noncollinear generalized HF (GHF) solutions, identified by orbitals that are linear combinations of up and down spins. Near conical intersections, we observe the appearance of coplanar GHF solutions that break all symmetries, including complex conjugation and time-reversal, which do not carry good quantum numbers. We discuss several prototypical examples taken from the conical intersection literature. Additionally, we utilize a recently introduced a magnetization diagnostic to characterize these solutions, as well as a solution of a Jahn-Teller active geometry of H$_8^{+2}$.Comment: accepted to JCP December 2017, published online January 201

Health-Related Quality of Life and Needs of Care and Support of Adult Tanzanians with Cancer: A Mixed-Methods Study.

Cancer is among the three leading causes of death in low income countries and the highest increase with regard to incidence figures for cancer diseases are found in these countries. This is the first report of the health-related quality of life (HRQOL) and needs of care and support of adult Tanzanians with cancer. A mixed-methods design was used. The study was conducted at Ocean Road Cancer Institute (ORCI) in Dar es Salaam, Tanzania. One hundred and one patients with a variety of cancer diagnoses treated and cared for at ORCI answered the Kiswahili version of the EORTC QLQ-C30 investigating HRQOL. Thirty-two of the patients participated in focus group interviews discussing needs of care and support. Data from focus group interviews were analyzed with content analysis. The findings show that the patients, both women and men, report a low quality of life, especially with regard to physical, role, and social function and a high level of symptoms and problems especially with financial difficulties and pain. Financial difficulties are reported to a remarkably high extent by both women and men. The patients, both women and men report least problems with emotional function. A content analysis of the interview data revealed needs of food and water, hygienic needs, emotional needs, spiritual needs, financial needs, and needs of closeness to cancer care and treatment services. The high score for pain points out that ORCI is facing severe challenges regarding care and treatment. However, when considering this finding it should be noted that the pain subscale of the Kiswahili version of the EORTC QLQ-C30 did not reach acceptable internal consistency and showed less than satisfactory convergent validity. This also applies to the subscales cognitive function and global health/quality of life. Attention should be drawn to meet the identified needs of Tanzanian cancer patients while hospitalized but also when at home. Increased accessibility of mosquito nets, pads, and pain-killers would help to fulfil some needs

Characterisation of a candidate dual AGN

We present Chandra and optical observations of a candidate dual AGN discovered serendipitously while searching for recoiling black holes via a cross-correlation between the serendipitous XMM source catalog (2XMMi) and SDSS-DR7 galaxies with a separation no larger than ten times the sum of their Petrosian radii. The system has a stellar mass ratio M$_{1}$/M$_{2}\approx 0.7$. One of the galaxies (Source 1) shows clear evidence for AGN activity in the form of hard X-ray emission and optical emission-line diagnostics typical of AGN ionisation. The nucleus of the other galaxy (Source 2) has a soft X-ray spectrum, bluer colours, and optical emission line ratios dominated by stellar photoionisation with a "composite" signature, which might indicate the presence of a weak AGN. When plotted on a diagram with X-ray luminosity vs [OIII] luminosity both nuclei fall within the locus defined by local Seyfert galaxies. From the optical spectrum we estimate the electron densities finding n$_{1} < 27$ e$^{-}$ cm$^{-3}$ and n$_{2} \approx 200$ e$^{-}$ cm$^{-3}$. From a 2D decomposition of the surface brightness distribution we infer that both galaxies host rotationally supported bulges (Sersic index $< 1$). While the active nature of Source 1 can be established with confidence, whether the nucleus of Source 2 is active remains a matter of debate. Evidence that a faint AGN might reside in its nucleus is, however, tantalising.Comment: 16 pages, 9 figures. Accepted for publication on MNRAS. Comments welcom

Studies on Venous Function after Deep Venous Thrombosis

Background The incidence of deep venous thrombosis (DVT) is estimated to be about 1-2/1000 per year of which approximately 4 % are located in the arm veins. Some of the most important late effects of a DVT are chronic venous dysfunction and the development of post-thrombotic syndrome (PTS). Objective diagnosis with detailed information on disease extent and location and global venous function is often important for clinical management of the patient. Color duplex ultrasonography (CDU) and computerized strain-gauge plethysmography (CSGP) are currently available non-invasive methods to study venous function after earlier DVT. Aims The aim of this thesis was to study venous function after earlier deep venous thrombosis assessed by CDU and CSGP; to study how findings with those methods are related to long-term sequelae, and development of postthrombotic diseases after different types of DVT. Study I and II These studies were performed to assess the efficiency of CSGP for evaluation of venous outflow capacity of the upper extremities, to receive reference values and to describe venous function using CSGP and CDU in patients with earlier primary upper extremity deep venous thrombosis (UEDVT). Thirty-four healthy controls and 32 patients with earlier UEDVT were included. The results showed that CSGP is easy to handle and can be used in a reproducible way to study venous function in the upper extremities. CSGP reference values were established for upper extremities. Patients with earlier UEDVT had reduced venous outflow, residual thrombus was a common finding, and one third had a moderate grade of PTS. CSGP and CDU are useful methods that can provide objective information regarding venous function after UEDVT. Study III This study was performed to determine whether asymptomatic deep venous thrombosis (ADVT) following minor surgery affects venous function and contributes to development of PTS. Eighty-three patients operated for Achilles tendon rupture were included; 38 patients with postoperative ADVT and 45 patients without (control group). The follow-up examinations five years after the operation consisted of CSGP, CDU and clinical scoring. More than 50 % of patients with ADVT developed post-thrombotic changes according to CDU, but these changes did not affect global venous function. Eight percent of ADVT patients and 4 % of control group patients developed PTS. Therefore, PTS is not a common sequel to ADVT after minor orthopaedic surgery. Study IV This follow-up study included 83 patients with postoperative DVT examined after a mean of 7 years. There was two series of patients, 45 with symptomatic deep venous thrombosis (SDVT) and 38 with ADVT. The objective was to describe long-term effect of SDVT and ADVT on venous function and subsequent incidence of PTS in patients operated for Achilles tendon rupture. Examinations comprised CSGP, CDU and clinical scoring. The results showed that post-operative DVT after minor surgery consists mainly of distal DVTs and is associated with a low risk for PTS, found in approximately 10 % of the patients. Deep venous reflux was more common in SDVT than in ADVT patients (84 % vs. 55 %). Abnormal plethysmographic results were seen in only a few patients without difference between the two groups. This indicates that DVT provoked by minor orthopaedic surgery represents a transient risk factor with minor long-term sequelae. In summary This thesis concerns studies of venous function and evaluation of clinical sequelae and frequency of PTS in patients with previous primary upper extremity DVT and in patients with postoperative DVT following minor orthopaedic surgery. In general, these studies show that the clinical signs as well as symptoms stated by the patients in these types of DVT are rather non-specific and often consist of pain, paresthesias, cramps, swelling and functional impairment. Therefore, in addition to the clinical examination, objective assessment of venous function and evaluation of the extent of disease are of value. Ultrasonograhy and plethysmograpy are non-invasive tests that can be used for this purpose