On a Tree and a Path with no Geometric Simultaneous Embedding

Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous embedding if there exists a set of points P and a bijection M: P -> V that induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it is known that two caterpillars always admit a geometric simultaneous embedding and that two trees not always admit one, the question about a tree and a path is still open and is often regarded as the most prominent open problem in this area. We answer this question in the negative by providing a counterexample. Additionally, since the counterexample uses disjoint edge sets for the two graphs, we also negatively answer another open question, that is, whether it is possible to simultaneously embed two edge-disjoint trees. As a final result, we study the same problem when some constraints on the tree are imposed. Namely, we show that a tree of depth 2 and a path always admit a geometric simultaneous embedding. In fact, such a strong constraint is not so far from closing the gap with the instances not admitting any solution, as the tree used in our counterexample has depth 4.Comment: 42 pages, 33 figure

Pattern densities in fluid dimer models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.Comment: 38 pages, 3 figure

Convexity in partial cubes: the hull number

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some earlier results in the literature. On the other hand we provide a polynomial-time algorithm to determine the hull number of planar partial cube quadrangulations. Instances of the hull number problem for partial cubes described include poset dimension and hitting sets for interiors of curves in the plane. To obtain the above results, we investigate convexity in partial cubes and characterize these graphs in terms of their lattice of convex subgraphs, improving a theorem of Handa. Furthermore we provide a topological representation theorem for planar partial cubes, generalizing a result of Fukuda and Handa about rank three oriented matroids.Comment: 19 pages, 4 figure

Electron Exchange Coupling for Single Donor Solid-State Qubits

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller.Comment: 10 Pages, 8 Figures. To appear in Physical Review

A radium assay technique using hydrous titanium oxide adsorbent for the Sudbury Neutrino Observatory

As photodisintegration of deuterons mimics the disintegration of deuterons by neutrinos, the accurate measurement of the radioactivity from thorium and uranium decay chains in the heavy water in the Sudbury Neutrino Observatory (SNO) is essential for the determination of the total solar neutrino flux. A radium assay technique of the required sensitivity is described that uses hydrous titanium oxide adsorbent on a filtration membrane together with a beta-alpha delayed coincidence counting system. For a 200 tonne assay the detection limit for 232Th is a concentration of 3 x 10^(-16) g Th/g water and for 238U of 3 x 10^(-16) g U/g water. Results of assays of both the heavy and light water carried out during the first two years of data collection of SNO are presented.Comment: 12 pages, 4 figure

Systemic perturbations of the kynurenine pathway precede progression to dementia independently of amyloid-β

Increasing evidence suggests that kynurenine pathway (KP) dyshomeostasis may promote disease progression in dementia. Studies in Alzheimer's disease (AD) patients confirm KP dyshomeostasis in plasma and cerebrospinal fluid (CSF) which correlates with amyloid-β and tau pathology. Herein, we performed the first comprehensive study assessing baseline levels of KP metabolites in participants enrolling in the Australian Imaging Biomarkers Flagship Study of Aging. Our purpose was to test the hypothesis that changes in KP metabolites may be biomarkers of dementia processes that are largely silent. We used a cross-sectional analytical approach to assess non-progressors (N = 73); cognitively normal (CN) or mild cognitive impairment (MCI) participants at baseline and throughout the study, and progressors (N = 166); CN or MCI at baseline but progressing to either MCI or AD during the study. Significant KP changes in progressors included increased 3-hydroxyanthranilic acid (3-HAA) and 3-hydroxyanthranilic acid/anthranilic acid (3-HAA/AA) ratio, the latter having the largest effect on the odds of an individual being a progressor (OR 35.3; 95% CI between 14 and 104). 3-HAA levels were hence surprisingly bi-phasic, high in progressors but low in non-progressors or participants who had already transitioned to MCI or dementia. This is a new, unexpected and interesting result, as most studies of the KP in neurodegenerative disease show reduced 3-HAA/AA ratio after diagnosis. The neuroprotective metabolite picolinic acid was also significantly decreased while the neurotoxic metabolite 3-hydroxykynurenine increased in progressors. These results were significant even after adjustment for confounders. Considering the magnitude of the OR to predict change in cognition, it is important that these findings are replicated in other populations. Independent validation of our findings may confirm the utility of 3-HAA/AA ratio to predict change in cognition leading to dementia in clinical settings

Alzheimer’s disease cerebrospinal fluid biomarkers are not influenced by gravity drip or aspiration extraction methodology

Introduction: Cerebrospinal fluid (CSF) biomarkers, although of established utility in the diagnostic evaluation of Alzheimer's disease (AD), are known to be sensitive to variation based on pre-analytical sample processing. We assessed whether gravity droplet collection versus syringe aspiration was another factor influencing CSF biomarker analyte concentrations and reproducibility. Methods: Standardized lumbar puncture using small calibre atraumatic spinal needles and CSF collection using gravity fed collection followed by syringe aspirated extraction was performed in a sample of elderly individuals participating in a large long-term observational research trial. Analyte assay concentrations were compared. Results: For the 44 total paired samples of gravity collection and aspiration, reproducibility was high for biomarker CSF analyte assay concentrations (concordance correlation [95%CI]: beta-amyloid1-42 (Aβ42) 0.83 [0.71 - 0.90]), t-tau 0.99 [0.98 - 0.99], and phosphorylated tau (p-tau) 0.82 [95 % CI 0.71 - 0.89]) and Bonferroni corrected paired sample t-tests showed no significant differences (group means (SD): Aβ42 366.5 (86.8) vs 354.3 (82.6), p = 0.10; t-tau 83.9 (46.6) vs 84.7 (47.4) p = 0.49; p-tau 43.5 (22.8) vs 40.0 (17.7), p = 0.05). The mean duration of collection was 10.9 minutes for gravity collection and <1 minute for aspiration. Conclusions: Our results demonstrate that aspiration of CSF is comparable to gravity droplet collection for AD biomarker analyses but could considerably accelerate throughput and improve the procedural tolerability for assessment of CSF biomarkers

Does It Really Work? Re-Assessing the Impact of Pre-Departure Cross-Cultural Training on Expatriate Adjustment

Cultural adjustment is considered to be a prerequisite for expatriate success abroad. One way to enhance adjustment is to provide employees with knowledge and awareness of appropriate norms and behaviors of the host country through cross-cultural training (CCT). This article analyzes the impact of pre-departure CCT on expatriate adjustment and focuses on variations in participation, length and the comprehensiveness of training. Unlike previous research, the study focuses on the effectiveness of pre-departure CCT for non-US employees expatriated to a broad range of host country settings. Employing data from 339 expatriates from 20 German Multinational Corporations (MNCs) the study finds CCT has little if any effect on general, interactional or work setting expatriate adjustment. However, a significant impact of foreign language competence was found for all three dimensions of expatriate adjustment. We used interviews with 20 expatriates to supplement our discussion and provide further implications for practice