Enumerating Cyclic Orientations of a Graph

Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic orientations has been addressed in the literature. In this paper, we pose the problem of efficiently enumerating all the \emph{cyclic} orientations of an undirected connected graph with $n$ vertices and $m$ edges, observing that it cannot be solved using algorithmic techniques previously employed for enumerating acyclic orientations.We show that the problem is of independent interest from both combinatorial and algorithmic points of view, and that each cyclic orientation can be listed with $\tilde{O}(m)$ delay time. Space usage is $O(m)$ with an additional setup cost of $O(n^2)$ time before the enumeration begins, or $O(mn)$ with a setup cost of $\tilde{O}(m)$ time

Quantum Algorithm for Triangle Finding in Sparse Graphs

This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the recent $\tilde O(n^{5/4})$-query algorithm given by Le Gall [FOCS 2014] for triangle finding over dense graphs (here $n$ denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with $O(n^{5/4-\epsilon})$ queries for some constant $\epsilon>0$ whenever the graph has at most $O(n^{2-c})$ edges for some constant $c>0$.Comment: 13 page

Diffusion Limited Aggregation on a Cylinder

We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes the cluster to reach the m-th layer of the cylinder is at most of order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily small density. In addition, we provide an upper bound on the rate at which the "arms" grow. This bound is valid for a large class of base graphs G, including discrete tori of dimension at least 3. It is also shown that for any base graph G, the density of the DLA process on a G-cylinder is related to the rate at which the arms of the cluster grow. This implies, that for any vertex transitive G, the density of DLA on a G-cylinder is bounded by 2/3.Comment: 1 figur

Absorption and optical selection rules of tunable excitons in biased bilayer graphene

Biased bilayer graphene, with its easily tunable band gap, presents itself as the ideal system to explore the excitonic effect in graphene-based systems. In this paper we study the excitonic optical response of such a system by combining a tight-binding model with the solution of the Bethe-Salpeter equation, the latter being solved in a semianalytical manner, requiring a single numerical quadrature, thus allowing for a transparent calculation. With our approach we start by analytically obtaining the optical selection rules, followed by the computation of the absorption spectrum for the case of a biased bilayer encapsulated in hexagonal boron nitride, a system which has been the subject of a recent experimental study. Excellent agreement is seen when we compare our theoretical prediction with the experimental data.N.M.R.P. acknowledges support from the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. J.C.G.H. acknowledges the Center of Physics for a grant funded by the UIDB/04650/2020 strategic project. N.M.R.P. also acknowledges support from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3), COMPETE 2020, PORTUGAL 2020, FEDER, and the FCT through projects POCI-01-0145-FEDER-028114, POCI-01-0145-FEDER-02888, and PTDC/NANOPT/29265/2017

A New Advanced Backcross Tomato Population Enables High Resolution Leaf QTL Mapping and Gene Identification.

Quantitative Trait Loci (QTL) mapping is a powerful technique for dissecting the genetic basis of traits and species differences. Established tomato mapping populations between domesticated tomato (Solanum lycopersicum) and its more distant interfertile relatives typically follow a near isogenic line (NIL) design, such as the S. pennellii Introgression Line (IL) population, with a single wild introgression per line in an otherwise domesticated genetic background. Here, we report on a new advanced backcross QTL mapping resource for tomato, derived from a cross between the M82 tomato cultivar and S. pennellii This so-called Backcrossed Inbred Line (BIL) population is comprised of a mix of BC2 and BC3 lines, with domesticated tomato as the recurrent parent. The BIL population is complementary to the existing S. pennellii IL population, with which it shares parents. Using the BILs, we mapped traits for leaf complexity, leaflet shape, and flowering time. We demonstrate the utility of the BILs for fine-mapping QTL, particularly QTL initially mapped in the ILs, by fine-mapping several QTL to single or few candidate genes. Moreover, we confirm the value of a backcrossed population with multiple introgressions per line, such as the BILs, for epistatic QTL mapping. Our work was further enabled by the development of our own statistical inference and visualization tools, namely a heterogeneous hidden Markov model for genotyping the lines, and by using state-of-the-art sparse regression techniques for QTL mapping

Understanding the electromagnetic response of Graphene/Metallic nanostructures hybrids of different dimensionality

Plasmonic excitations, such as surface-plasmonpolaritons (SPPs) and graphene-plasmons (GPs), carry large momenta and are thus able to confine electromagnetic fields to small dimensions. This property makes them ideal platforms for subwavelength optical control and manipulation at the nanoscale. The momenta of these plasmons are even further increased if a scheme of metal-insulator-metal and graphene-insulator-metal are used for SPPs and GPs, respectively. However, with such large momenta, their far-field excitation becomes challenging. In this work, we consider hybrids of graphene and metallic nanostructures and study the physical mechanisms behind the interaction of far-field light with the supported high momenta plasmon modes. While there are some similarities in the properties of GPs and SPPs, since both are of the plasmon-polariton type, their physical properties are also distinctly different. For GPs we find two different physical mechanism related to either GPs confined to isolated cavities or large area collective grating couplers. Strikingly, we find that, although the two systems are conceptually different, under specific conditions, they can behave similarly. By applying the same study to SPPs, we find a different physical behavior, which fundamentally stems from the different dispersion relations of SPPs as compared to GPs. Furthermore, these hybrids produce large field enhancements that can also be electrically tuned and modulated making them the ideal candidates for a variety of plasmonic devices.N.M.R. P. and F. H.L.K. acknowledge support from the European Commission through the Project "Graphene-Driven Revolutions in ICT and Beyond" (Ref. No. 881603, CORE 3). N. M.R. P. and T.G.R. acknowledge COMPETE 2020, PORTUGAL 2020, FEDER and the Portuguese Foundation for Science and Technology (FCT) through Project POCI-01-0145-FEDER-028114. F.H.L.K. acknowledges financial support from the Government of Catalonia through the SGR Grant, and from the Spanish Ministry of Economy and Competitiveness through the "Severo Ochoa" Programme for Centres of Excellence in RD (SEV-2015-0522); support by Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA Program, and the Mineco Grants Ramo ' n y Cajal (RYC-2012-12281, Plan Nacional (FIS2013-47161-P and FIS2014-59639-JIN) and the Agency for Management of University and Research Grants (AGAUR) 2017 SGR 1656. This work was supported by the ERC TOPONANOP under Grant Agreement No. 726001 and the MINECO Plan Nacional Grant 2D-NANOTOP under Reference No. FIS2016-81044-P

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure