A Linear Iterative Unfolding Method

A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of removing this smearing effect from the measured distribution is called unfolding, and is a delicate problem in signal processing, due to the well-known numerical ill behavior of this task. Various methods were invented which, given some assumptions on the initial probability distribution, try to regularize the unfolding problem. Most of these methods definitely introduce bias into the estimate of the initial probability distribution. We propose a linear iterative method, which has the advantage that no assumptions on the initial probability distribution is needed, and the only regularization parameter is the stopping order of the iteration, which can be used to choose the best compromise between the introduced bias and the propagated statistical and systematic errors. The method is consistent: "binwise" convergence to the initial probability distribution is proved in absence of measurement errors under a quite general condition on the response function. This condition holds for practical applications such as convolutions, calorimeter response functions, momentum reconstruction response functions based on tracking in magnetic field etc. In presence of measurement errors, explicit formulae for the propagation of the three important error terms is provided: bias error, statistical error, and systematic error. A trade-off between these three error terms can be used to define an optimal iteration stopping criterion, and the errors can be estimated there. We provide a numerical C library for the implementation of the method, which incorporates automatic statistical error propagation as well.Comment: Proceedings of ACAT-2011 conference (Uxbridge, United Kingdom), 9 pages, 5 figures, changes of corrigendum include

A strongly polynomial algorithm for generalized flow maximization

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of steps, an arc can be identified that must be tight in every dual optimal solution, and thus can be contracted. As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.Comment: minor correction

Ab initio study of mixed clusters of water and N,N′-dimethylethyleneurea

Intermolecular interactions between a single water and two N,N′-dimethylethyleneurea (DMEU) molecules have been investigated using local and density-fitting approximations of the standard Moller-Plesset perturbation theory (DF-LMP2) with the aug-ccpVTZ basis set. Six stable configurations have been found. In the first three, the water molecule intercalates between two DMEU molecules. In the next three configurations, the water molecule is attached to a stacked DMEU dimer, and these structures are more stable than the first three. These results support the view that DMEU molecules can form contact pairs in dilute aqueous solutions. © 2011

Approximating Minimum Cost Connectivity Orientation and Augmentation

We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation covering a nonnegative crossing $G$-supermodular demand function, as defined by Frank. An important example is $(k,\ell)$-edge-connectivity, a common generalization of global and rooted edge-connectivity. Our algorithm is based on a non-standard application of the iterative rounding method. We observe that the standard linear program with cut constraints is not amenable and use an alternative linear program with partition and co-partition constraints instead. The proof requires a new type of uncrossing technique on partitions and co-partitions. We also consider the problem setting when the cost of an edge can be different for the two possible orientations. The problem becomes substantially more difficult already for the simpler requirement of $k$-edge-connectivity. Khanna, Naor, and Shepherd showed that the integrality gap of the natural linear program is at most $4$ when $k=1$ and conjectured that it is constant for all fixed $k$. We disprove this conjecture by showing an $\Omega(|V|)$ integrality gap even when $k=2$

Effect of positional inaccuracies on multielectrode results

This paper investigates the effect of electrode positioning errors on the inverted pseudosection. Instead of random spacing errors (as usually assumed in geoelectrics) we exactly measured this effect among field conditions. In the field, in spite of the greatest possible care, the electrode positions contain some inaccuracy: either in case of dense undergrowth, or varied topography, or very rocky field. In all these cases, it is not possible to put the electrodes in their theoretical position. As a consequence, the position data will contain some error. The inaccuracies were exactly determined by using a laser distance meter. The geometrical data from real field conditions and by using Wenner-α, Wenner-β, pole-dipole and pole-pole arrays were then considered over homogeneous half space. As we have found, the positioning errors can be regarded as insignificant, even in case of relatively uncomfortable field conditions. However, in case of very rocky surface the distortions are more significant, but it is still possible to make some corrections: either by neglecting a few electrode positions with the greatest positioning error, or to minimize the inline errors, even on the price that offline deviations are high

Evolutionary trees: an integer multicommodity max-flow-min-cut theorem

In biomathematics, the extensions of a leaf-colouration of a binary tree to the whole vertex set with minimum number of colour-changing edges are extensively studied. Our paper generalizes the problem for trees; algorithms and a Menger-type theorem are presented. The LP dual of the problem is a multicommodity flow problem, for which a max-flow-min-cut theorem holds. The problem that we solve is an instance of the NP-hard multiway cut problem

Theoretical study of the role of the tip in enhancing the sensitivity of differential conductance tunneling spectroscopy on magnetic surfaces

Based on a simple model for spin-polarized scanning tunneling spectroscopy (SP-STS) we study how tip magnetization and electronic structure affects the differential conductance (dI/dV) tunneling spectrum of an Fe(001) surface. We take into account energy dependence of the vacuum decay of electron states, and tip electronic structure either using an ideal model or based on ab initio electronic structure calculation. In the STS approach, topographic and magnetic contributions to dI/dV can clearly be distinguished and analyzed separately. Our results suggest that the sensitivity of STS on a magnetic sample can be tuned and even enhanced by choosing the appropriate magnetic tip and bias setpoint, and the effect is governed by the effective spin-polarization.Comment: 22 pages manuscript, 4 figures; http://link.aps.org/doi/10.1103/PhysRevB.83.21441