On ideal triangulations of surfaces up to branched transit equivalences

We consider triangulations of closed surfaces S with a given set of vertices V; every triangulation can be branched that is enhanced to a Delta-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V point-wise fixed. We extend a well known connectivity result for `naked' triangulations; in particular in the generic case when S has negative Euler-Poincare' characteristic c(S), we show that branched triangulations are equivalent to each other if c(S) is even, while this holds also for odd c(S) possibly after the complete inversion of one of the two branchings. Moreover we show that under a mild assumption, two branchings on a same triangulation are connected via a sequence of inversions of ambiguous edges (and possibly the total inversion of one of them). A natural organization of the b-flips in subfamilies gives rise to restricted transit equivalences with non trivial (even infinite) quotient sets. We analyze them in terms of certain preserved structures of differential topological nature carried by any branched triangulations; in particular a pair of transverse foliations with determined singular sets contained in V, including as particular cases the configuration of the vertical and horizontal foliations of the square of an Abelian differential on a Riemann surface.Comment: 22 pages, 11 figure

Trends in High Nature Value farmland studies: A systematic review

Background. Since the High Nature Value (HNV) concept was defined in the early 1990s, several studies on HNV farmland has been increasing over the past 30 years in Europe, highlighting the interest by scientific community of HNV farming systems supporting biodiversity conservation. The aim of this study was to evaluate the trends and main gaps on HNV farmland peer-reviewed publications in order to contribute to the effectiveness of future research in this field. Methods. Searches were conducted using the databases Web of SciencesTM and Scopus in order to identify only peer-reviewed articles on HNV farmland, published prior to July 2017. The inclusion and exclusion criteria were developed a priori. Data as year, country, type of document, subject area, taxa studied and biodiversity metrics assessed were extracted and explored in order to analyse the spatial and temporal distribution of the concept, including the main topics addressed in HNV farmland literature. Results. After screening 308 original articles, 90 were selected for this review. HNV farmland studies involved several disciplines, mainly biodiversity and conservation and environmental sciences and ecology. Most peer-reviewed articles focused on HNV farming were conducted in Spain, Italy, Ireland and Portugal. The main studied taxa were plants and birds. Taxonomic diversity was the biodiversity metric more often used to assess the biodiversity status on HNV farmland areas. A positive correlation was found between HNV farmland area and HNV farmland studies conducted in respective countries. Discussion. The HNV farmland research subject is a relative novel approach, and this systematic review provides a comprehensive overview about the main topics in the HNV farmland peer-reviewed literature contributing to highlight the main gaps and provide some considerations in order to assist the performance of HNV farming systems and conservation policies, addressed to sustain high levels of biodiversity

Critical behavior in spherical and hyperbolic spaces

We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: $d$-dimensional spheres and hyperboloids. In the first part of the paper, by applying the Ginzburg criterion, we find that for large correlation length the Gaussian approximation is valid on the hyperboloid for any dimension $d\geq 2$, while it is not trustable on the sphere for any dimension. This is understood in terms of various notions of effective dimension, such as the spectral and Hausdorff dimension. In the second part of the paper, we apply functional renormalization group methods to develop a different perspective on such phenomena, and to deduce them from a renormalization group analysis. By making use of the local potential approximation, we discuss the consequences of having a fixed scale in the renormalization group equations. In particular, we show that in the case of spheres there is no true phase transition, as symmetry restoration always occurs at large scales. In the case of hyperboloids, the phase transition is still present, but as the only true fixed point is the Gaussian one, mean field exponents are valid also in dimensions lower than four.Comment: 24 pages, 5 figures; several improvements in the presentation and small corrections, 2 figures adde

Ideal triangulations of 3-manifolds up to decorated transit equivalences

We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to the b-transit equivalence generated by isotopy and ideal branched moves which keep V pointwise fixed. We extend a well known connectivity result for naked triangulations by showing that branched ideal triangulations of (M, V) are equivalent to each other. A pre-branching is a system of transverse orientations at the 2-facets of T verifying a certain global constraint; pre-branchings are considered up to a natural pb-transit equivalence. If M is oriented, every branching b induces a pre-branching w(b) and every b-transit induces a pb-transit. The quotient set of pre-branchings up to transit equivalence is far to be trivial; we get some information about it and we characterize the pre-branchings of type w(b). Pre-branched and branched moves are naturally organized in subfamilies which give rise to restricted transit equivalences. In the branching setting we revisit early results about the sliding transit equivalence and outline a conceptually different approach to the branched connectivity and eventually also to the naked one. The basic idea is to point out some structures of differential topological nature which are carried by every branched ideal triangulation, are preserved by the sliding transits and can be modified by the whole branched transits. The non ambiguous transit equivalence already widely studied on pre-branchings lifts to a specialization of the sliding equivalence on branchings; we point out a few specific insights, again in terms of carried structures preserved by the non ambiguous and which can be modified by the whole sliding transits.Comment: 29 pages, 22 figure

On the number of relevant operators in asymptotically safe gravity

The asymptotic safety scenario of gravity conjectures that (i) the quantum field theory of gravity exists thanks to the presence of a non-trivial ultraviolet fixed point of the renormalization group, and that (ii) the fixed point has only a finite number of relevant perturbations, i.e. a finite number of UV-stable directions (or in other words, a finite number of free parameters to be fixed experimentally). Within the f(R) approximation of the functional renormalization group equation of gravity, we show that assuming the first half of the conjecture to be true, the remaining half follows from general arguments, that is, we show that assuming the existence of a non-trivial fixed point, the fact that the number of relevant directions is finite is a general consequence of the structure of the equations.Comment: 5 pages; v3: one typo corrected (thanks to Juergen Dietz for pointing it out

The Investigation of the UNC-6/Netrin and UNC-40/DCC-mediated Synaptic Partner Recognition Pathway

Organisms receive, process, and respond to environmental cues via intricate neural circuits that form during development. Proper development of neuronal circuits is therefore critical to brain function. To form these circuits, a neuron must first extend its axons to the appropriate target. After reaching this target region, it must recognize its correct synaptic partners from multiple incorrect partners and form appropriate synapses. It is well understood how axons reach their target regions, but little is known about how neurons select the correct partners once there, a process called synaptic partner recognition (SPR). Our work aims to elucidate the genetic programs that specify correct SPR in sensory circuits in the nematode Caenorhabditis elegans. We used the fluorescent trans-synaptic marker, Neuroligin 1-mediated GFP Reconstitution Across Synaptic Partners (NLG-1 GRASP). Using this marker, we discovered a role for an UNC-6/Netrin and UNC-40/DCC-mediated axon guidance pathway gene that functions in SPR. Interestingly, synaptic component localization in mutants of this gene is normal, indicating that the reduced SPR is not the result of a secondary defect in cell polarity or protein trafficking. Finally, we found that this gene functions in the UNC-6/Netrin and UNC-40/DCC SPR pathway previously described by our laboratory. Most remarkably, we found that the function of this gene in the SPR pathway is molecularly distinct from its previously characterized signaling pathways. The characterization of the novel role of this gene may give insights into the mechanism of sensory circuit formation