Complexity of links in 3-manifolds

We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a closed orientable 3-manifold and L is a link contained in M. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal number of tetrahedra in a triangulation of M containing L in its 1-skeleton. Slightly adapting Matveev's recent theory of roots for graphs, we carefully analyze the behaviour of c under connected sum away from and along the link. We show in particular that c is almost always additive, describing in detail the circumstances under which it is not. To do so we introduce a certain (0,2)-root for a pair X, we show that it is well-defined, and we prove that X has the same complexity as its (0,2)-root. We then consider, for links in the 3-sphere, the relations of c with the crossing number and with the hyperbolic volume of the exterior, establishing various upper and lower bounds. We also specialize our analysis to certain infinite families of links, providing rather accurate asymptotic estimates.Comment: 24 pages, 6 figure

Notes on the complexity of 3-valent graphs in 3-manifolds

A theory of complexity for pairs (M,G) with M an arbitrary closed 3-manifold and G a 3-valent graph in M was introduced by the first two named authors, extending the original notion due to Matveev. The complexity c is known to be always additive under connected sum away from the graphs, but not always under connected sum along (unknotted) arcs of the graphs. In this article we prove the slightly surprising fact that if in M there is a sphere intersecting G transversely at one point, and this point belongs to an edge e of G, then e can be canceled from G without affecting the complexity. Using this fact we completely characterize the circumstances under which complexity is additive under connected sum along graphs. For the set of pairs (M,K) with K a knot in M, we also prove that any function that is fully additive under connected sum along knots is actually a function of the ambient manifold only.Comment: 15 pages, 6 figure

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische Zeitschrif

Evaporating waterbody effects in a simplified urban neighbourhood: A RANS analysis

The incorporation of nature-based solutions comprising green and blue infrastructure is often touted as a way to cool cities and enhance pollutant removal. However, there is little agreement between different methodologies to measure the effect of any single intervention. Here, we present 3D steady RANS simulations to investigate the influence of waterbody on in-canyon flow structure, temperature (T*) and water vapour (!*) distribution in a simplified urban neighbourhood. A novel solver that captures evaporation effects is developed and validated against wind tunnel experiments. Simulations are performed under neutral atmospheric conditions for forced -and mixed-convection cases and different air-water temperature differences, indicative of either daytime or night-time conditions. Results under forced convection show minimal impact on the flow structure, whilst T* and !* effects are distributed primarily over and around the water surface. However, the mixed-convection case shows that a cooler waterbody weakens the principal vortex in the open square, whilst T* and !* effects reach further upwind and are more widely distributed in the spanwise direction. A warmer waterbody is shown to disrupt the skimming flow structure, indicating a possible heat and pollutant removal mechanism from around the waterbody and also downwind canyons

Sub-Nyquist Field Trial Using Time Frequency Packed DP-QPSK Super-Channel Within Fixed ITU-T Grid

Sub-Nyquist time frequency packing technique was demonstrated for the first time in a super channel field trial transmission over long-haul distances. The technique allows a limited spectral occupancy even with low order modulation formats. The transmission was successfully performed on a deployed Australian link between Sydney and Melbourne which included 995 km of uncompensated SMF with coexistent traffic. 40 and 100 Gb/s co-propagating channels were transmitted together with the super-channel in a 50 GHz ITU-T grid without additional penalty. The super-channel consisted of eight sub-channels with low-level modulation format, i.e. DP-QPSK, guaranteeing better OSNR robustness and reduced complexity with respect to higher order formats. At the receiver side, coherent detection was used together with iterative maximum-a-posteriori (MAP) detection and decoding. A 975 Gb/s DP-QPSK super-channel was successfully transmitted between Sydney and Melbourne within four 50GHz WSS channels (200 GHz). A maximum potential SE of 5.58 bit/s/Hz was achieved with an OSNR=15.8 dB, comparable to the OSNR of the installed 100 Gb/s channels. The system reliability was proven through long term measurements. In addition, by closing the link in a loop back configuration, a potential SE*d product of 9254 bit/s/Hz*km was achieved

From building regulations and local health rules to the new local building codes. A national survey in Italy on the prescriptive and performance requirements for a new performance approach

BACKGROUND: World Health Organization has highlighted the need to strengthen the relationship between health and built environment factors, such as inappropriate housing conditions. Building Regulations and Local Health Rules provide safety and building hygiene in construction practices. Currently the Italian Government is giving rise to a Building Regulation Type and the paper aims to verify the present contents of recent innovative Local Health Rules and Building Regulations of several Italian municipalities for supporting the performance approach of the future Building Regulations including hygienic issues. METHODS: The analysis examines both Building Regulations and Local Health Rules of a sample of about 550 cities, analysing some specific fields of interest: urban field, outdoor issues, housing features, housing restrictions, and qualitative aspects. RESULTS: The analysis focuses on some specific aspects defining the general data reported in Building Regulations and Local Health Rules, in particular around surfaces, heights, lighting and aeration ratio, basements and semi-basements, gas radon, building greenery, etc. CONCLUSION: The investigation permitted to have a wide vision on the present State of the Art in order to highlight some innovative aspects and design approaches of Building Regulations and Local Health Rules. New perspectives in the new regulations should have a performance approach, starting also from the recent SARS-CoV-2 pandemic

Multislice computed tomography SYNTAX score for coronary artery disease evaluation prior to transcatheter aortic valve implantation

Background: Coronary computed tomography angiography (CCTA) is a useful tool for the evaluation of coronary anatomy prior to both surgical and transcatheter aortic valve implantation (TAVI). Multislice Computed Tomography (MSCT) SYNTAX score (SXscore) strongly correlates with the traditional angiographic SXscore, and the latter has proven to predict cardiovascular events in patients with coronary artery disease (CAD) referred to TAVI. Purpose: The aim of the study is to evaluate the feasibility and accuracy of the calculation of MSCT SXscore in TAVI patients, compared to the gold standard angiographic SXscore. Materials and methods: We evaluated 65 patients eligible for TAVI who underwent both CCTA and invasive coronary angiography (ICA) prior to valve replacement. CCTA was compared to ICA in terms of sensitivity, specificity, and positive and negative predictive values. CCTA performance was evaluated at 3 levels: patient level, vessellevel and segmentlevel. MSCT SXscore was calculated, when possible (i.e. only in fullyevaluable scans), and compared to the angiographic SXscore. Results: Overall CCTA diagnostic performance was good, with high sensitivity and negative predictive values (97.2% and 96.0%, respectively) and good agreement with ICA (k=0.81). As expected, specificity and positive predictive values were lower (82.8% and 87.5%, respectively). At vessellevel, the circumflex artery (CA) was more often misdiagnosed than the other arteries. We were able to calculate MSCT SXscore in 50/65 scans (76.9%). The correlation between MSCT and angiographic SXscore was excellent (Pearson's R=0.965, P<0.001). Conclusions: MSCT SXscore emerges as an interesting tool with strong agreement with angiographic SXscore, providing a noninvasive ambulatory alternative to assess CAD severity in TAVI patients

Living together apart: Perceived concealment as signal of exclusion in marital relationships

This article examines how perceiving concealment in close relationships influences marital well-being. It suggests that the perception of concealment from a partner signals separateness from one's partner and contributes to feelings of perceived partner exclusion. These feelings of exclusion, in turn, should negatively affect relational quality. These predictions are tested in a prospective study among 199 newlywed couples. Results suggest that perceiving concealment reduced marital adjustment and trust and increased conflict over time. Importantly, change in perceived partner exclusion mediated these effects. This article demonstrates that the perception of concealment (a) has deleterious effects on relational well-being in the long run and (b) is harmful in part because it elicits feelings of exclusion. © 2009 by the Society for Personality and Social Psychology, Inc