TY - CONF AB - We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding ' : G ! M of a graph G into a 2manifold M maps the vertices in V (G) to distinct points and the edges in E(G) to interior-disjoint Jordan arcs between the corresponding vertices. In applications in clustering, cartography, and visualization, nearby vertices and edges are often bundled to a common node or arc, due to data compression or low resolution. This raises the computational problem of deciding whether a given map ' : G ! M comes from an embedding. A map ' : G ! M is a weak embedding if it can be perturbed into an embedding ψ: G ! M with k' "k < " for every " > 0. A polynomial-time algorithm for recognizing weak embeddings was recently found by Fulek and Kyncl [14], which reduces to solving a system of linear equations over Z2. It runs in O(n2!) O(n4:75) time, where 2:373 is the matrix multiplication exponent and n is the number of vertices and edges of G. We improve the running time to O(n log n). Our algorithm is also conceptually simpler than [14]: We perform a sequence of local operations that gradually "untangles" the image '(G) into an embedding (G), or reports that ' is not a weak embedding. It generalizes a recent technique developed for the case that G is a cycle and the embedding is a simple polygon [1], and combines local constraints on the orientation of subgraphs directly, thereby eliminating the need for solving large systems of linear equations. AU - Akitaya, Hugo AU - Fulek, Radoslav AU - Tóth, Csaba ID - 309 TI - Recognizing weak embeddings of graphs ER - TY - JOUR AB - We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, Gq. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. We exemplify our approach by considering a quantum rotor interacting with a bath of bosons, and demonstrate that extracting the value of q from closed-form solutions in the perturbative regime allows one to predict the behavior of the system for arbitrary values of the impurity-bath coupling strength, in good agreement with nonperturbative calculations. Furthermore, the value of the deformation parameter allows one to predict at which coupling strengths rotor-bath interactions result in a formation of a stable quasiparticle. The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, but also provides valuable insights into hidden symmetries of interacting many-particle systems. AU - Yakaboylu, Enderalp AU - Shkolnikov, Mikhail AU - Lemeshko, Mikhail ID - 5794 IS - 25 JF - Physical Review Letters SN - 00319007 TI - Quantum groups as hidden symmetries of quantum impurities VL - 121 ER - TY - JOUR AB - Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton ID - 87 IS - 5 JF - Annals of Applied Probability TI - Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics VL - 28 ER - TY - JOUR AB - The phytohormone auxin is the information carrier in a plethora of developmental and physiological processes in plants(1). It has been firmly established that canonical, nuclear auxin signalling acts through regulation of gene transcription(2). Here, we combined microfluidics, live imaging, genetic engineering and computational modelling to reanalyse the classical case of root growth inhibition(3) by auxin. We show that Arabidopsis roots react to addition and removal of auxin by extremely rapid adaptation of growth rate. This process requires intracellular auxin perception but not transcriptional reprogramming. The formation of the canonical TIR1/AFB-Aux/IAA co-receptor complex is required for the growth regulation, hinting to a novel, non-transcriptional branch of this signalling pathway. Our results challenge the current understanding of root growth regulation by auxin and suggest another, presumably non-transcriptional, signalling output of the canonical auxin pathway. AU - Fendrych, Matyas AU - Akhmanova, Maria AU - Merrin, Jack AU - Glanc, Matous AU - Hagihara, Shinya AU - Takahashi, Koji AU - Uchida, Naoyuki AU - Torii, Keiko U AU - Friml, Jirí ID - 192 IS - 7 JF - Nature Plants TI - Rapid and reversible root growth inhibition by TIR1 auxin signalling VL - 4 ER - TY - JOUR AB - The intercellular transport of auxin is driven by PIN-formed (PIN) auxin efflux carriers. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping auxin into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM. Which of these two mechanisms dominates is a matter of debate. Here, we addressed the issue with a mathematical modeling approach. We demonstrate that the efficiency of secretory transport depends on SV size, half-life of PINs on the PM, pH, exocytosis frequency and PIN density. 3D structured illumination microscopy (SIM) was used to determine PIN density on the PM. Combining this data with published values of the other parameters, we show that the transport activity of PINs in SVs would have to be at least 1000× greater than on the PM in order to produce a comparable macroscopic auxin transport. If both transport mechanisms operated simultaneously and PINs were equally active on SVs and PM, the contribution of secretion to the total auxin flux would be negligible. In conclusion, while secretory vesicle-mediated transport of auxin is an intriguing and theoretically possible model, it is unlikely to be a major mechanism of auxin transport inplanta. AU - Hille, Sander AU - Akhmanova, Maria AU - Glanc, Matous AU - Johnson, Alexander J AU - Friml, Jirí ID - 14 IS - 11 JF - International Journal of Molecular Sciences TI - Relative contribution of PIN-containing secretory vesicles and plasma membrane PINs to the directed auxin transport: Theoretical estimation VL - 19 ER - TY - JOUR AB - We study how a block of genome with a large number of weakly selected loci introgresses under directional selection into a genetically homogeneous population. We derive exact expressions for the expected rate of growth of any fragment of the introduced block during the initial phase of introgression, and show that the growth rate of a single-locus variant is largely insensitive to its own additive effect, but depends instead on the combined effect of all loci within a characteristic linkage scale. The expected growth rate of a fragment is highly correlated with its long-term introgression probability in populations of moderate size, and can hence identify variants that are likely to introgress across replicate populations. We clarify how the introgression probability of an individual variant is determined by the interplay between hitchhiking with relatively large fragments during the early phase of introgression and selection on fine-scale variation within these, which at longer times results in differential introgression probabilities for beneficial and deleterious loci within successful fragments. By simulating individuals, we also investigate how introgression probabilities at individual loci depend on the variance of fitness effects, the net fitness of the introduced block, and the size of the recipient population, and how this shapes the net advance under selection. Our work suggests that even highly replicable substitutions may be associated with a range of selective effects, which makes it challenging to fine map the causal loci that underlie polygenic adaptation. AU - Sachdeva, Himani AU - Barton, Nicholas H ID - 39 IS - 4 JF - Genetics SN - 00166731 TI - Replicability of introgression under linked, polygenic selection VL - 210 ER - TY - JOUR AB - We analyze the theoretical derivation of the beyond-mean-field equation of state for two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. We show that at zero temperature our theory — considering Gaussian fluctuations on top of the mean-field equation of state — is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex–antivortex pairs. By doing so, we determine the Berezinskii–Kosterlitz–Thouless (BKT) critical temperature — at which the renormalized superfluid density jumps to zero — as a function of the inter-atomic potential strength. We find that the Nelson–Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover. AU - Bighin, Giacomo AU - Salasnich, Luca ID - 420 IS - 17 JF - International Journal of Modern Physics B TI - Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover VL - 32 ER - TY - JOUR AB - Genomes of closely-related species or populations often display localized regions of enhanced relative sequence divergence, termed genomic islands. It has been proposed that these islands arise through selective sweeps and/or barriers to gene flow. Here, we genetically dissect a genomic island that controls flower color pattern differences between two subspecies of Antirrhinum majus, A.m.striatum and A.m.pseudomajus, and relate it to clinal variation across a natural hybrid zone. We show that selective sweeps likely raised relative divergence at two tightly-linked MYB-like transcription factors, leading to distinct flower patterns in the two subspecies. The two patterns provide alternate floral guides and create a strong barrier to gene flow where populations come into contact. This barrier affects the selected flower color genes and tightlylinked loci, but does not extend outside of this domain, allowing gene flow to lower relative divergence for the rest of the chromosome. Thus, both selective sweeps and barriers to gene flow play a role in shaping genomic islands: sweeps cause elevation in relative divergence, while heterogeneous gene flow flattens the surrounding "sea," making the island of divergence stand out. By showing how selective sweeps establish alternative adaptive phenotypes that lead to barriers to gene flow, our study sheds light on possible mechanisms leading to reproductive isolation and speciation. AU - Tavares, Hugo AU - Whitley, Annabel AU - Field, David AU - Bradley, Desmond AU - Couchman, Matthew AU - Copsey, Lucy AU - Elleouet, Joane AU - Burrus, Monique AU - Andalo, Christophe AU - Li, Miaomiao AU - Li, Qun AU - Xue, Yongbiao AU - Rebocho, Alexandra B AU - Barton, Nicholas H AU - Coen, Enrico ID - 38 IS - 43 JF - PNAS SN - 00278424 TI - Selection and gene flow shape genomic islands that control floral guides VL - 115 ER - TY - CONF AB - There is currently significant interest in operating devices in the quantum regime, where their behaviour cannot be explained through classical mechanics. Quantum states, including entangled states, are fragile and easily disturbed by excessive thermal noise. Here we address the question of whether it is possible to create non-reciprocal devices that encourage the flow of thermal noise towards or away from a particular quantum device in a network. Our work makes use of the cascaded systems formalism to answer this question in the affirmative, showing how a three-port device can be used as an effective thermal transistor, and illustrates how this formalism maps onto an experimentally-realisable optomechanical system. Our results pave the way to more resilient quantum devices and to the use of thermal noise as a resource. AU - Xuereb, André AU - Aquilina, Matteo AU - Barzanjeh, Shabir ED - Andrews, D L ED - Ostendorf, A ED - Bain, A J ED - Nunzi, J M ID - 155 TI - Routing thermal noise through quantum networks VL - 10672 ER - TY - JOUR AB - Cuprate superconductors have long been thought of as having strong electronic correlations but negligible spin-orbit coupling. Using spin- and angle-resolved photoemission spectroscopy, we discovered that one of the most studied cuprate superconductors, Bi2212, has a nontrivial spin texture with a spin-momentum locking that circles the Brillouin zone center and a spin-layer locking that allows states of opposite spin to be localized in different parts of the unit cell. Our findings pose challenges for the vast majority of models of cuprates, such as the Hubbard model and its variants, where spin-orbit interaction has been mostly neglected, and open the intriguing question of how the high-temperature superconducting state emerges in the presence of this nontrivial spin texture. AU - Gotlieb, Kenneth AU - Lin, Chiu-Yun AU - Serbyn, Maksym AU - Zhang, Wentao AU - Smallwood, Christopher L. AU - Jozwiak, Christopher AU - Eisaki, Hiroshi AU - Hussain, Zahid AU - Vishwanath, Ashvin AU - Lanzara, Alessandra ID - 5767 IS - 6420 JF - Science SN - 0036-8075 TI - Revealing hidden spin-momentum locking in a high-temperature cuprate superconductor VL - 362 ER -