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Let R be a simply connected closed region in the Euclidean plane E2 whose boundary is a simple closed curve C. A triangular map, or simply "map," is a representation of R as the union of a finite number of disjoint point sets called cells, where the cells are of three kinds, vertices, edges, and faces (said to be of dimension 0, 1, and 2, respectively), where each vertex is a single point, each edge is an open arc whose ends are distinct vertices, and each face is a simply connected open region whose boundary consists of the closure of the union of three edges. Two cells of different dimension are incident if one is contained in the boundary of the other.
For a formal definition of “map” the reader is referred to (7, §2). The maps in this paper are rooted by specifying an orientation for one of the edges. This also specifies a root vertex, the negative end of the root, and a root face, the face on the left of the root edge. Counting is, as usual, defined on isomorphism classes.
Regular maps of even valence have been enumerated in a recent paper by Tutte. In this paper we determine the average number of trees in such maps, and include similar results for regular tri valent maps, that is, maps with three edges incident on every vertex. In the development for the latter, a formula for the number of trivalent maps with 2t vertices is produced.
It is the purpose of this paper to show that many of the enumerative techniques available for counting rooted plane trees may be extended to tree-rooted maps, that is, rooted maps in which a spanning tree is distinguished as root tree. For example, tree-rooted maps are enumerated by partition, and the average number of trees in a rooted map with n edges is determined. An enumerative similarity between Hamiltonian rooted maps (that is, rooted maps with a distinguished Hamiltonian polygon) and tree-rooted maps is discussed. A 1-1 correspondence is established between treerooted maps with n edges and Hamiltonian rooted trivalent maps with 2n + 1 vertices in which the root vertex is exceptional, being divalent, both of which are in 1-1 correspondence with non-separable Hamiltonian-rooted triangularized digons with n internal vertices, where both the latter are as defined in (2).
To understand increasing rates of hepatitis C virus (HCV) infection in Tennessee, we conducted testing, risk factor analysis and a nested case–control study among persons who use drugs. During June–October 2016, HCV testing with risk factor assessment was conducted in sexually transmitted disease clinics, family planning clinics and an addiction treatment facility in eastern Tennessee; data were analysed by using multivariable logistic regression. A nested case–control study was conducted to assess drug-using risks and behaviours among persons who reported intranasal or injection drug use (IDU). Of 4753 persons tested, 397 (8.4%) were HCV-antibody positive. HCV infection was significantly associated with a history of both intranasal and IDU (adjusted odds ratio (aOR) 35.4, 95% confidence interval (CI) 24.1–51.9), IDU alone (aOR 52.7, CI 25.3–109.9), intranasal drug use alone (aOR 2.6, CI 1.8–3.9) and incarceration (aOR 2.7, CI 2.0–3.8). By 4 October 2016, 574 persons with a reported history of drug use; 63 (11%) were interviewed further. Of 31 persons who used both intranasal and injection drugs, 26 (84%) reported previous intranasal drug use, occurring 1–18 years (median 5.5 years) before their first IDU. Our findings provide evidence that reported IDU, intranasal drug use and incarceration are independent indicators of risk for past or present HCV infection in the study population.
Major depressive disorder (MDD) is a common and disabling condition with well-established heritability and environmental risk factors. Gene–environment interaction studies in MDD have typically investigated candidate genes, though the disorder is known to be highly polygenic. This study aims to test for interaction between polygenic risk and stressful life events (SLEs) or childhood trauma (CT) in the aetiology of MDD.
The RADIANT UK sample consists of 1605 MDD cases and 1064 controls with SLE data, and a subset of 240 cases and 272 controls with CT data. Polygenic risk scores (PRS) were constructed using results from a mega-analysis on MDD by the Psychiatric Genomics Consortium. PRS and environmental factors were tested for association with case/control status and for interaction between them.
PRS significantly predicted depression, explaining 1.1% of variance in phenotype (p = 1.9 × 10−6). SLEs and CT were also associated with MDD status (p = 2.19 × 10−4 and p = 5.12 × 10−20, respectively). No interactions were found between PRS and SLEs. Significant PRSxCT interactions were found (p = 0.002), but showed an inverse association with MDD status, as cases who experienced more severe CT tended to have a lower PRS than other cases or controls. This relationship between PRS and CT was not observed in independent replication samples.
CT is a strong risk factor for MDD but may have greater effect in individuals with lower genetic liability for the disorder. Including environmental risk along with genetics is important in studying the aetiology of MDD and PRS provide a useful approach to investigating gene–environment interactions in complex traits.
This work experimentally examines the detachment of liquid droplets from both oleophilic and oleophobic fibres, using an atomic force microscope. The droplet detachment force was found to increase with increasing fibre diameter and forces were higher for philic fibres than phobic fibres. We also considered the detachment of droplets situated on the intersection of two fibres and arrays of fibres (such as found in fibrous mats or filters) and found that the required detachment forces were higher than for similarly sized droplets on a single fibre, though not as high as expected based on theory. A model was developed to predict the detachment force, from single fibres, which agreed well with experimental results. It was found that the entire dataset (single and multiple fibres) could be best described by power law relationships.
Patients with major depressive disorder (MDD) present with highly heterogeneous symptom profiles. We aimed to examine whether individual differences in amygdala activity to emotionally salient stimuli were related to heterogeneity in lifetime levels of depressive and subthreshold manic symptoms among adults with MDD.
We compared age- and gender-matched adults with MDD (n = 26) with healthy controls (HC, n = 28). While undergoing functional magnetic resonance imaging, participants performed an implicit emotional faces task: they labeled a color flash superimposed upon initially neutral faces that dynamically morphed into one of four emotions (angry, fearful, sad, happy). Region of interest analyses examined group differences in amygdala activity. For conditions in which adults with MDD displayed abnormal amygdala activity versus HC, within-group analyses examined amygdala activity as a function of scores on a continuous measure of lifetime depression-related and mania-related pathology.
Adults with MDD showed significantly greater right-sided amygdala activity to angry and happy conditions than HC (p < 0.05, corrected). Multiple regression analyses revealed that greater right-amygdala activity to the happy condition in adults with MDD was associated with higher levels of subthreshold manic symptoms experienced across the lifespan (p = 0.002).
Among depressed adults with MDD, lifetime features of subthreshold mania were associated with abnormally elevated amygdala activity to emerging happy faces. These findings are a first step toward identifying biomarkers that reflect individual differences in neural mechanisms in MDD, and challenge conventional mood disorder diagnostic boundaries by suggesting that some adults with MDD are characterized by pathophysiological processes that overlap with bipolar disorder.
Depression in the context of bipolar disorder (BDd) is often misdiagnosed as unipolar disorder depression (UDd) leading to poor clinical outcomes for many bipolar sufferers. We examined neural circuitry supporting emotion regulation in females with either BDd or UDd as a first stage toward identifying biomarkers that may differentiate BDd from UDd.
Fifty-seven females aged 18–45 years participated in this study: 23 with UDd, 18 with bipolar disorder type I depression (BDId) and 16 healthy females. During 3-T functional magnetic resonance imaging (fMRI), the participants performed an emotional face n-back (EFNBACK) task, that is an n-back task with high (2-back) and low (0-back) memory load conditions flanked by two positive, negative or neutral face distracters. This paradigm examines executive control with emotional distracters–emotion regulation.
High memory load with neutral face distracters elicited greater bilateral and left dorsal anterior midcingulate cortex (dAMCC) activity in UDd than in healthy and BDId females respectively, and greater bilateral putamen activity in both depressed groups versus healthy females. High memory load with happy face distracters elicited greater left putamen activity in UDd than in healthy females. Psychotropic medication was associated with greater putamen activity to these contrasts in UDd females.
During high memory load with neutral face distracters, elevated dAMCC activity in UDd suggests abnormal recruitment of attentional control circuitry to maintain task performance, whereas elevated putamen activity unrelated to psychotropic medication in BDId females may suggest an attentional bias toward ambiguous neutral face distracters. Differential patterns of functional abnormalities in neural circuitry supporting attentional control during emotion regulation, especially in the dAMCC, is a promising neuroimaging measure to distinguish UDd from BDId in females.
We report on the morphology of heavily phosphorous doped silicon films grown by ultra high vacuum chemical vapor deposition at temperatures of ∼550° C. The effects of PH3 on epitaxial films have been examined for silicon deposited using SiH4 and Si2H6. It is found that films grown using silane experience an increase in surface roughness with increasing phosphine partial pressure. AFM and RHEED studies indicate 3-D growth. As epitaxy progresses, it is believed that phosphorus segregation on the growing film surface greatly diminishes the adsorption and surface mobility of the silicon bearing species. Initial Si deposition results in a pitted surface, but as growth advances and the phosphorus coverage increases, growth within the pits decreases the surface roughness. In contrast to SiH4, it is found that Si2H6 provides excellent quality, smooth films even at high PH3 partial pressures.
The effect of surface and grain-boundary diffusion on interconnect reliability is addressed by extending the theory of thermal grooving to arbitrary grain-boundary flux. For a periodic array of grain boundaries, three regimes are identified: (1) equilibrium, (2) global steady state, and (3) local steady state. These regimes govern the stability of polycrystalline materials subjected to large electric (electromigration) or mechanical (stress voiding) fields, especially in thin films where grain size approximates film thickness.
Increasing MOSFET performance requires scaling, the systematic reduction in device dimensions. Tunneling leakage, however, provides an absolute scaling limit for SiO2of about 1.5 nm. Power limitations and device reliability are likely to pose softer limits slightly above 2 nm. We have investigated the use of high permittivity materials such as TiO2, ZrO2, and their silicates as potential replacements for SiO2. We have synthesized titanium nitrate (Ti(NO3)4or TN), zirconium nitrate (Zr(NO3)4or ZrN), and hafnium nitrate (Hf(NO3)4or HfN) as hydrogen and carbon free deposition precursors. Several problems arise in the use of these films including the formation of an amorphous low permittivity interfacial layer. For TiO2this layer is formed by silicon up diffusion. Surface nitridation retards the formation of the interfacial layer. We discuss the effects of both thermal and remote plasma surface nitridation treatments on the properties of the film stack. ZrO2and HfO2appear to form a thermal layer of silicon oxide between the high permittivity film and the silicon and have excess oxygen in the bulk of the film.
A known liquid mixture of [(CH3CH2)2N]3 Ta=NCH2CH3 and [(CH3CH2)2N]3Ta[ð2-CH3CH2N=CH(CH3)] was studied to deposit Ta2O5 and TaN thin films by CVD. Films were deposited at temperatures below 400°C using oxygen for oxide and ammonia for nitride, respectively. XRD analysis revealed that as-deposited amorphous tantalum oxide films were converted to hexagonal Ta2O5 after annealing under oxygen, while tantalum nitride thin films contained cubic TaN as deposited. The low viscosity, thermal stability, and sufficient volatility of the precursor allows direct liquid injection to deliver the precursor, which results in high deposition rate and uniformity of the deposited films.
Sodium-covered silica films formed on silicon substrates have been examined by X-ray photoemission spectroscopy (XPS) and X-ray absorption spectroscopy (EXAFS) in ultra-high vacuumconditions at 300K. The results show that sodium diffuses into the silica layer on a reversible manner and that it modifies the silica network in order to create its own site. Sodium atoms are surrounded by oxygen atoms at an average distance of 2.3 Å and by a second shell which is assigned to silicon atoms located at 3.8 Å. At high Na concentrations, sodium atoms are also present in the close environment of one sodium atom.
Tetrakis(dimethylamino)titanium (TDMAT) is an important precursor for TiN, TiCN, and TiSiN thin films in chemical vapor deposition. In order to better understand how the gas phase chemistry influences the formation of these films, the decomposition of TDMAT has been studied in a high-temperature flow reactor (HTFR) by molecular beam mass spectrometry (MBMS). Two kinetic regimes have been observed as a function of temperature. Rate expressions and mechanistic implications will be presented. Further studies are in progress to identify the gas phase species relevant to the decomposition mechanism of TDMAT.
Hysteresis effect of barium strontium titanate (BST) thin films for gate dielectric application has been studied. It is found that the “counterclockwise” hysteresis has strong sweep voltage and operating temperature dependence. It can be reduced or eliminated by proper thermal annealing or by using a barrier layer. A charge trapping and detrapping mechanism has been proposed.
Continuous polycrystalline SiCN films with high nucleation density have been successfully deposited by using CH3NH2, as carbon source gas in an ECR-CVD reactor. Fom the kinetic point of view, using CH3NH2, as carbon source could provide more abundant active carbon species in the gas phase to enhance the carbon incorporation in the SiCN films. The compositions of the SiCN films analyzed from Rutherford Backscattering Spectroscopy showed that higher [CH3NH2,]/[SiH4] ratio led to higher carbon content in the films. Moreover, a lower carbon content was measured when the film was deposited at higher substrate temperature. The direct band gap of the aforementioned SiCN films determined using PzR is around 4.4 eV, indicating a wide band gap material for blue-UV optoelectronics.
Etch rates up to 1200 Åmin−1 for Ta2O5 were achieved in both SF6/Ar and Cl2/Ar discharges under Inductively Coupled Plasma conditions. The etch rates with N2/Ar or CH4/H2/Ar chemistries were an order of magnitude lower. There was no effect of post deposition annealing on the Ta2O5 etch rates, at least up to 800 °C. Selectivities to Si of ∼1 were achieved at low source powers, but at higher powers the Si typically etched 4-7 times faster than Ta 20 5. UV illumination during ICP etching in both SF6/Ar and Cl2/Ar produced significant enhancements (up to a factor of 2) in etch rates due to photo-assisted desorption of the TaFx products. The UV illumination is an alternative to employing elevated sample temperatures during etching to increase the volatility of the etch products and may find application where the thermal budget should be minimized during processing.
Reactive-magnetron-sputtered ZrO2 thin film has been deposited on Si directly for gate dielectric application. Both structural and electrical properties of the ZrO2 film have been investigated. An amorphous structure for 30Å ZrO2 and a semi-amorphous structure for 200Å ZrO2 have been revealed. The sputtered film shows a good stoichiometry and a good structural stability of ZrO2 based on the X-ray photoelectron spectroscopy and Rutherford backscattering spectroscopy data. Thin equivalent oxide thickness of about 11.5Å was obtained without the consideration of quantum mechanical effects. A low leakage of less than 10−2 A/cm2 at ±1V relative to the flat band voltage was obtained for this 11.5Å equivalent oxide thickness Pt/ZrO2/Si structure. High effective dielectric breakdown and superior reliability properties have been demonstrated for ZrO2 gate dielectric.