Higher harmonics and ac transport from time dependent density functional theory

We report on dynamical quantum transport simulations for realistic molecular devices based on an approximate formulation of time-dependent Density Functional Theory with open boundary conditions. The method allows for the computation of various properties of junctions that are driven by alternating bias voltages. Besides the ac conductance for hexene connected to gold leads via thiol anchoring groups, we also investigate higher harmonics in the current for a benzenedithiol device. Comparison to a classical quasi-static model reveals that quantum effects may become important already for small ac bias and that the full dynamical simulations exhibit a much lower number of higher harmonics. Current rectification is also briefly discussed.Comment: submitted to J. Comp. Elec. (special issue

Nested Sequential Monte Carlo Methods

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.Comment: Extended version of paper published in Proceedings of the 32nd International Conference on Machine Learning (ICML), Lille, France, 201

Sequential Monte Carlo for Graphical Models

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs

Capacity estimation of two-dimensional channels using Sequential Monte Carlo

We derive a new Sequential-Monte-Carlo-based algorithm to estimate the capacity of two-dimensional channel models. The focus is on computing the noiseless capacity of the 2-D one-infinity run-length limited constrained channel, but the underlying idea is generally applicable. The proposed algorithm is profiled against a state-of-the-art method, yielding more than an order of magnitude improvement in estimation accuracy for a given computation time

Locating-dominating sets in twin-free graphs

A locating-dominating set of a graph $G$ is a dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \ne N(v) \cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-domination number of $G$, denoted $\gamma_L(G)$, is the minimum cardinality of a locating-dominating set in $G$. It is conjectured [D. Garijo, A. Gonz\'alez and A. M\'arquez. The difference between the metric dimension and the determining number of a graph. Applied Mathematics and Computation 249 (2014), 487--501] that if $G$ is a twin-free graph of order $n$ without isolated vertices, then $\gamma_L(G)\le \frac{n}{2}$. We prove the general bound $\gamma_L(G)\le \frac{2n}{3}$, slightly improving over the $\lfloor\frac{2n}{3}\rfloor+1$ bound of Garijo et al. We then provide constructions of graphs reaching the $\frac{n}{2}$ bound, showing that if the conjecture is true, the family of extremal graphs is a very rich one. Moreover, we characterize the trees $G$ that are extremal for this bound. We finally prove the conjecture for split graphs and co-bipartite graphs.Comment: 11 pages; 4 figure

Estimation of Pulmonary Arterial Volume Changes in the Normal and Hypertensive Fawn-Hooded Rat from 3D Micro-CT data

In the study of pulmonary vascular remodeling, much can be learned from observing the morphological changes undergone in the pulmonary arteries of the rat lung when exposed to chronic hypoxia or other challenges which elicit a remodeling response. Remodeling effects include thickening of vessel walls, and loss of wall compliance. Morphometric data can be used to localize the hemodynamic and functional consequences. We developed a CT imaging method for measuring the pulmonary arterial tree over a range of pressures in rat lungs. X-ray micro-focal isotropic volumetric imaging of the arterial tree in the intact rat lung provides detailed information on the size, shape and mechanical properties of the arterial network. In this study, we investigate the changes in arterial volume with step changes in pressure for both normoxic and hypoxic Fawn-Hooded (FH) rats. We show that FH rats exposed to hypoxia tend to have reduced arterial volume changes for the same preload when compared to FH controls. A secondary objective of this work is to quantify various phenotypes to better understand the genetic contribution of vascular remodeling in the lungs. This volume estimation method shows promise in high throughput phenotyping, distinguishing differences in the pulmonary hypertensive rat model