The hidden burden of adult allergic rhinitis : UK healthcare resource utilisation survey

Funding Funding for this survey was provided by Meda Pharma.Peer reviewedPublisher PD

Three osculating walkers

We consider three directed walkers on the square lattice, which move simultaneously at each tick of a clock and never cross. Their trajectories form a non-crossing configuration of walks. This configuration is said to be osculating if the walkers never share an edge, and vicious (or: non-intersecting) if they never meet. We give a closed form expression for the generating function of osculating configurations starting from prescribed points. This generating function turns out to be algebraic. We also relate the enumeration of osculating configurations with prescribed starting and ending points to the (better understood) enumeration of non-intersecting configurations. Our method is based on a step by step decomposition of osculating configurations, and on the solution of the functional equation provided by this decomposition

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour.Comment: 10 pages, 3 figure

A Cost-based Optimizer for Gradient Descent Optimization

As the use of machine learning (ML) permeates into diverse application domains, there is an urgent need to support a declarative framework for ML. Ideally, a user will specify an ML task in a high-level and easy-to-use language and the framework will invoke the appropriate algorithms and system configurations to execute it. An important observation towards designing such a framework is that many ML tasks can be expressed as mathematical optimization problems, which take a specific form. Furthermore, these optimization problems can be efficiently solved using variations of the gradient descent (GD) algorithm. Thus, to decouple a user specification of an ML task from its execution, a key component is a GD optimizer. We propose a cost-based GD optimizer that selects the best GD plan for a given ML task. To build our optimizer, we introduce a set of abstract operators for expressing GD algorithms and propose a novel approach to estimate the number of iterations a GD algorithm requires to converge. Extensive experiments on real and synthetic datasets show that our optimizer not only chooses the best GD plan but also allows for optimizations that achieve orders of magnitude performance speed-up.Comment: Accepted at SIGMOD 201

Non collinear magnetism and single ion anisotropy in multiferroic perovskites

The link between the crystal distortions of the perovskite structure and the magnetic exchange interaction, the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya (DM) interaction are investigated by means of density-functional calculations. Using BiFeO$_3$ and LaFeO$_3$ as model systems, we quantify the relationship between the oxygen octahedra rotations, the ferroelectricity and the weak ferromagnetism (wFM). We recover the fact that the wFM is due to the DM interaction induced by the oxygen octahedra rotations. We find a simple relationship between the wFM, the oxygen rotation amplitude and the ratio between the DM vector and the exchange parameter such as the wFM increases with the oxygen octahedra rotation when the SIA does not compete with the DM forces induced on the spins. Unexpectedly, we also find that, in spite of the $d^5$ electronic configuration of Fe$^{3+}$, the SIA is very large in some structures and is surprisingly strongly sensitive to the chemistry of the $A$-site cation of the $A$BO$_3$ perovskite. In the ground $R3c$ state phase we show that the SIA shape induced by the ferroelectricity and the oxygen octahedra rotations are in competition such as it is possible to tune the wFM "on" and "off" through the relative size of the two types of distortion

The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table

First-principles calculations in crystalline structures are often performed with a planewave basis set. To make the number of basis functions tractable two approximations are usually introduced: core electrons are frozen and the diverging Coulomb potential near the nucleus is replaced by a smoother expression. The norm-conserving pseudopotential was the first successful method to apply these approximations in a fully ab initio way. Later on, more efficient and more exact approaches were developed based on the ultrasoft and the projector augmented wave formalisms. These formalisms are however more complex and developing new features in these frameworks is usually more difficult than in the norm-conserving framework. Most of the existing tables of norm- conserving pseudopotentials, generated long ago, do not include the latest developments, are not systematically tested or are not designed primarily for high accuracy. In this paper, we present our PseudoDojo framework for developing and testing full tables of pseudopotentials, and demonstrate it with a new table generated with the ONCVPSP approach. The PseudoDojo is an open source project, building on the AbiPy package, for developing and systematically testing pseudopotentials. At present it contains 7 different batteries of tests executed with ABINIT, which are performed as a function of the energy cutoff. The results of these tests are then used to provide hints for the energy cutoff for actual production calculations. Our final set contains 141 pseudopotentials split into a standard and a stringent accuracy table. In total around 70.000 calculations were performed to test the pseudopotentials. The process of developing the final table led to new insights into the effects of both the core-valence partitioning and the non-linear core corrections on the stability, convergence, and transferability of norm-conserving pseudopotentials. ...Comment: abstract truncated, 17 pages, 25 figures, 8 table

Renewed methane increase for five years (2007–2011) observed by solar FTIR spectrometry

Trends of column-averaged methane for the time period (1996, Sep 2011) are derived from the mid-infrared (mid-IR) solar FTIR time series at the Zugspitze (47.42° N, 10.98° E, 2964 m a.s.l.) and Garmisch (47.48° N, 11.06° E, 743 m a.s.l.). Trend analysis comprises a fit to the de-seasonalized time series along with bootstrap resampling for quantifying trend uncertainties. We find a positive trend during [1996, 1998] of 9.0 [3.2, 14.7] ppb yr&lt;sup&gt;−1&lt;/sup&gt; for Zugspitze (95% confidence interval), an insignificant growth during [1999, mid 2006] of 0.8 [−0.1, 1.7] ppb yr&lt;sup&gt;−1&lt;/sup&gt; (Zugspitze), and a significant renewed increase during [mid 2006, Sep 2011] of 5.1 [4.2, 6.0] ppb yr&lt;sup&gt;−1&lt;/sup&gt; for Garmisch, which is in agreement with 4.8 [3.8, 5.9] ppb yr&lt;sup&gt;−1&lt;/sup&gt; for Zugspitze. &lt;br&gt;&lt;/br&gt; The agreement of methane trends at the two closely neighboring FTIR sites Zugspitze and Garmisch within the uncertainties indicates a good station-to-station consistency as a basis for future trend analyses by the ground-based mid-IR FTIR network on the global scale. Furthermore, the Zugspitze FTIR trend for the time interval [Jul 2006, Jun 2009] is found to agree with the trend derived from SCIAMACHY (WFM-DOAS v2.0.2) data within the 95% confidence intervals. In case a 1000-km pixel selection radius around the Zugspitze is used, the confidence interval is narrower for the FTIR trend (6.9 [4.2, 9.5] ppb yr&lt;sup&gt;−1&lt;/sup&gt;) compared to SCIAMACHY (7.1 [5.1, 8.6] ppb yr&lt;sup&gt;−1&lt;/sup&gt;). If, however, a loosened pixel selection is used (&amp;approx;1000-km half-width latitudinal band), the SCIAMACHY trend significance interval is narrower (6.8 [5.1, 8.6] ppb yr&lt;sup&gt;−1&lt;/sup&gt;) compared to Zugspitze FTIR (5.7 [3.0, 8.3] ppb yr&lt;sup&gt;−1&lt;/sup&gt;). &lt;br&gt;&lt;/br&gt; While earlier studies using surface network data revealed changes of 8.0 ± 0.6 ppb in 2007, 6.4 ± 0.6 ppb in 2008, and 4.7 ± 0.6 ppb in 2009 (Dlugokencky et al., 2011), our updated result proves that the renewed methane increase meanwhile has been persisting for &gt;5 years [mid 2006, Sep 2011]. This is either the longest and largest positive trend anomaly since the beginning of systematic observations more than 25 years ago or the onset of a new period of strongly increasing CH&lt;sub&gt;4&lt;/sub&gt; levels in the atmosphere. Several scenarios have been developed to explain the persistent increase observed, mainly invoking an increase in emissions from natural wetlands, an increase in fossil fuel-related emissions or a decrease in OH concentrations. However, more work is needed to fully attribute this increase to a particular source or sink