Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Simulation of transition dynamics to high confinement in fusion plasmas

The transition dynamics from the low (L) to the high (H) confinement mode in magnetically confined plasmas is investigated using a first-principles four-field fluid model. Numerical results are in close agreement with measurements from the Experimental Advanced Superconducting Tokamak - EAST. Particularly, the slow transition with an intermediate dithering phase is well reproduced by the numerical solutions. Additionally, the model reproduces the experimentally determined L-H transition power threshold scaling that the ion power threshold increases with increasing particle density. The results hold promise for developing predictive models of the transition, essential for understanding and optimizing future fusion power reactors

Experiments on Column Base Stiffness of Long-Span Cold-Formed Steel Portal Frames Composed of Double Channels

Cold-formed steel haunched portal frames are popular structures in industrial and housing applications. They are mostly used as sheds, garages, and shelters, and are common in rural areas. Cold-formed steel portal frames with spans of up to 30m (100 ft) are now being constructed in Australia. As these large structures are fairly new to the market, there is limited data on their feasibility and design recommendations. An experimental program was carried out on a series of portal frame systems composed of back-to-back channels for the columns, rafters, and knee braces. The system consisted of three frames connected in parallel with purlins to simulate a free standing structure, with an approximate span of 14 m (46 ft), column height of 5.3 m (17 ft), and apex height of 7 m (23 ft). Several configurations were tested including variations in the knee connection, sleeve stiffeners in the columns and rafters, and loading of either vertical or combined horizontal and vertical loads. Deflections were recorded at various locations to measure global and local movements of the structural members, as well as column base reactions and base rotations. It was determined that the column bases are semi-rigid and further column base connection tests were completed to quantify column base connection stiffness for bending about the column major and minor axes, as well as twist. Results of the column base connection stiffness are presented as well as the implications for frame design

Structurally specific thermal fluctuations identify functional sites for DNA transcription

We report results showing that thermally-induced openings of double stranded DNA coincide with the location of functionally relevant sites for transcription. Investigating both viral and bacterial DNA gene promoter segments, we found that the most probable opening occurs at the transcription start site. Minor openings appear to be related to other regulatory sites. Our results suggest that coherent thermal fluctuations play an important role in the initiation of transcription. Essential elements of the dynamics, in addition to sequence specificity, are nonlinearity and entropy, provided by local base-pair constraints

Lengthscales and Cooperativity in DNA Bubble Formation

It appears that thermally activated DNA bubbles of different sizes play central roles in important genetic processes. Here we show that the probability for the formation of such bubbles is regulated by the number of soft AT pairs in specific regions with lengths which at physiological temperatures are of the order of (but not equal to) the size of the bubble. The analysis is based on the Peyrard- Bishop-Dauxois model, whose equilibrium statistical properties have been accurately calculated here with a transfer integral approach

Fast and flexible Bayesian species distribution modelling using Gaussian processes

1. Species distribution modelling (SDM) is widely used in ecology, and predictions of species distributions inform both policy and ecological debates. Therefore, methods with high predictive accuracy and those that enable biological interpretation are preferable. Gaussian processes (GPs) are a highly flexible approach to statistical modelling and have recently been proposed for SDM. GP models fit smooth, but potentially complex response functions that can account for high-dimensional interactions between predictors. We propose fitting GP SDMs using deterministic numerical approximations, rather than Markov chain Monte Carlo methods in order to make GPs more computationally efficient and easy to use. 2. We introduce GP models and their application to SDM, illustrate how ecological knowledge can be incorporated into GP SDMs via Bayesian priors and formulate a simple GP SDM that can be fitted efficiently. This model can be fitted either by learning the hyperparameters or by using a fixed approximation to them. Using a subset of the North American Breeding Bird Survey data set, we compare the out-of-sample predictive accuracy of these models with several commonly used SDM approaches for both presence/absence and presence-only data. 3. Predictive accuracy of GP SDMs fitted by Laplace approximation was greater than boosted regression trees, generalized additive models (GAMs) and logistic regression when trained on presence/absence data and greater than all of these models plus MaxEnt when trained on presence-only data. GP SDMs fitted using a fixed approximation to hyperparameters were no less accurate than those with MAP estimation and on average 70 times faster, equivalent in speed to GAMs. 4. As well as having strong predictive power for this data set, GP SDMs offer a convenient method for incorporating prior knowledge of the species' ecology. By fitting these methods using efficient numerical approximations, they may easily be applied to large data sets and automatically for many species. An r package, GRaF, is provided to enable SDM users to fit GP models

Superconductivity-enhanced bias spectroscopy in carbon nanotube quantum dots

We study low-temperature transport through carbon nanotube quantum dots in the Coulomb blockade regime coupled to niobium-based superconducting leads. We observe pronounced conductance peaks at finite source-drain bias, which we ascribe to elastic and inelastic cotunneling processes enhanced by the coherence peaks in the density of states of the superconducting leads. The inelastic cotunneling lines display a marked dependence on the applied gate voltage which we relate to different tunneling-renormalizations of the two subbands in the nanotube. Finally, we discuss the origin of an especially pronounced sub-gap structure observed in every fourth Coulomb diamond

W-Extended Fusion Algebra of Critical Percolation

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.Comment: 30 page

SLE local martingales in logarithmic representations

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of representations where L_0 is not diagonalizable - a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation with the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE(kappa=6) describing the exploration path in critical percolation, and its relation with the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of kappa, thus at all central charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result