Branched covers of the sphere and the prime-degree conjecture

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate surface cover" is an abstract branch datum, a priori not coming from a branched cover, but satisfying the Riemann-Hurwitz formula. The old Hurwitz problem asks which candidate surface covers are realizable by branched covers. It is now known that all candidate covers are realizable when the candidate covered surface has positive genus, but not all are when it is the 2-sphere. However a long-standing conjecture asserts that candidate covers with prime degree are realizable. To a candidate surface cover one can associate one Y -> X between 2-orbifolds, and in a previous paper we have completely analyzed the candidate surface covers such that either X is bad, spherical, or Euclidean, or both X and Y are rigid hyperbolic orbifolds, thus also providing strong supporting evidence for the prime-degree conjecture. In this paper, using a variety of different techniques, we continue this analysis, carrying it out completely for the case where X is hyperbolic and rigid and Y has a 2-dimensional Teichmueller space. We find many more realizable and non-realizable candidate covers, providing more support for the prime-degree conjecture

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

Pequeños vertebrados del relleno kárstico del Pleistoceno Superior de Avetrana (Apulia, Sur de Italia)

The fossiliferous deposit (karst cavity) in La Grave, a locality near the small town of Avetrana (Taranto, south­ern Italy), has yielded numerous fossils of vertebrates. The remains of large mammals have been the subject of several studies. This paper examines the remains of small vertebrates and identifies four taxa of amphibians (Bufo bufo, Bufotes gr. B. viridis, Hyla gr. H. Arborea and Rana (s.l.) sp.), four taxa of reptiles (Testudo hermanni, Podarcis sp., Zamenis gr. Z. longissimus, Natrix natrix), and nine taxa of small mammals (Erinaceus europaeus, Crocidura suaveolens, Arvicola italicus, Microtus (Terricola) savii, Microtus (Microtus) arvalis, Apodemus gr. A. sylvaticus - A. flavicollis, Hystrix (Acanthion) vinogradovi, Oryctolagus cuniculus and Lepus corsicanus). From a biochronological point of view, the data on small and large vertebrates indicate an age between the beginning of the Late Pleistocene (MIS 5e) and the central part of MIS 3. The most recent fossiliferous layer (bed 8) is likely to have been deposited during a cooler period when compared to the previous layers.The data from small fossil vertebrates combined with those emerging from the large mammals and birds evidence the presence, near the karstic cavity, of open spaces (prairies) with pools of water, bordered by wooded areas and, not far, the presence of a rocky coastline.El depósito (cavidad kárstica) de La Grave, localidad cercana a la pequeña ciudad de Avetrana (Tarento, Italia meridional), ha dado lugar a numerosos fósiles de vertebrados. Los restos de grandes mamíferos han sido objeto de varios estudios. En este trabajo se examinan los restos de pequeños vertebrados y se identifican cuatro taxones de anfibios (Bufo bufo, Bufotes gr. B. viridis, Hyla gr. H. Arborea and Rana (s.l.) sp.), cuatro de reptiles (Testudo hermanni, Podarcis sp., Zamenis gr. Z. longissimus, Natrix natrix), y nueve de pequeños mamíferos (Erinaceus europaeus, Crocidura suaveolens, Arvicola italicus, Microtus (Terricola) savii, Microtus (Microtus) arva­lis, Apodemus gr. A. sylvaticus - A. flavicollis, Hystrix (Acanthion) vinogradovi, Oryctolagus cuniculus and Lepus corsicanus). Desde un punto de vista biocronológico, los datos sobre los vertebrados pequeños y grandes indican una edad entre el comienzo del Pleistoceno tardío (MIS 5e) y la parte central del MIS 3. Es probable que el estrato fosilífero más reciente (nivel 8) se haya depositado durante un período más frío en comparación con las capas anteriores. Los datos de pequeños vertebrados fósiles combinados con los que proceden de los grandes mamífe­ros y aves evidencian la presencia, cerca de la cavidad kárstica, de espacios abiertos (praderas) con charcos de agua, bordeados por zonas boscosas y, no muy lejos, la presencia de una costa rocosa

Noncyclic covers of knot complements

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\Phi (c)$ sheets.Comment: 29 pages, 8 figures, from Ph.D. thesis at Columbia University; Acknowledgments added; Content correcte

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

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