Fine-grained dichotomies for the Tutte plane and Boolean #CSP

Jaeger, Vertigan, and Welsh [15] proved a dichotomy for the complexity of evaluating the Tutte polynomial at fixed points: The evaluation is #P-hard almost everywhere, and the remaining points admit polynomial-time algorithms. Dell, Husfeldt, and Wahl\'en [9] and Husfeldt and Taslaman [12], in combination with Curticapean [7], extended the #P-hardness results to tight lower bounds under the counting exponential time hypothesis #ETH, with the exception of the line $y=1$, which was left open. We complete the dichotomy theorem for the Tutte polynomial under #ETH by proving that the number of all acyclic subgraphs of a given $n$-vertex graph cannot be determined in time $exp(o(n))$ unless #ETH fails. Another dichotomy theorem we strengthen is the one of Creignou and Hermann [6] for counting the number of satisfying assignments to a constraint satisfaction problem instance over the Boolean domain. We prove that all #P-hard cases are also hard under #ETH. The main ingredient is to prove that the number of independent sets in bipartite graphs with $n$ vertices cannot be computed in time $exp(o(n))$ unless #ETH fails. In order to prove our results, we use the block interpolation idea by Curticapean [7] and transfer it to systems of linear equations that might not directly correspond to interpolation.Comment: 16 pages, 1 figur

Single crystal growth and electron spectroscopy of d1-systems

One of the most intriguing aspects of transition metal oxides is the wide variety and richness of their physical properties. Microscopic understanding of the unconventional behavior of this class of materials is at the heart of modern solid state physics research. The many body nature of the problem forms a true intellectual challenge requiring modern experimental and theoretical methods. There is a need for well-defined materials which can serve as model systems. The class of the RETiO3 (RE = rare earth) materials forms in this context a very interesting 'playground' for the quantitative study of the properties and excitation spectra of correlated oxides. It has the relatively simple perovskite crystal structure, and the Ti ions have (formally) only one electron in their 3d shell so that complications related to atomic multiplet effects can be avoided. Yet, the orbital degeneracy together with the presence of a small band gap lead to a number of interesting physics which are then subject of a flurry of detailed experimental and theoretical studies. Efforts are being made for a quantitative analysis as to test the accuracy of various theoretical approaches. Here we report on a detailed experimental study of the electronic structure of the RETiO3 system. The study aims to address one of the long standing topics in theoretical solid state physics, namely the single-particle spectral weight distribution in Mott-Hubbard systems in the vicinity of the metal-insulator transition. In view of the existing discussions in the literature, it turned out to be crucial to use well defined samples: we have to grow titanate single crystals with well defined stoichiometry and doping. This activity in fact forms the basis of this thesis work and much effort is also put into the characterization of the crystals using various methods including x-ray and neutron diffraction, as well as magnetic, transport and thermodynamic measurements. We have used photoelectron spectroscopy to investigate the electronic structure of the RETiO3 system. Although many photoemission studies have been reported in the literature, it is also realized more and more that those published results may not be representative for the material due to the extreme surface sensitivity of the particular photoemission technique used in those studies. This is important since the electronic structure of the surface is very different from the bulk, especially for strongly correlated systems. Essential aspect of the work is therefore to carefully optimize the conditions for this type of experiments as to make sure that the spectra obtained are truely representative for the bulk material. Only in this manner we can do a critical and quantitative evaluation of the various advanced many-body models currently available trying to describe the excitation spectra of strongly correlated systems. The main result of our spectroscopic study is as follows: we have utilized bulk-sensitive x-ray photoelectron spectroscopy to study the valence band spectral weight distribution of d1 Mott insulators LaTiO3 and YTiO3. We observed appreciable differences in the spectra, reflecting the difference in the one-electron band width W. We also found that the Ti 3d spectra of both materials are much broader than the occupied 3d bands calculated by band theories. The mean-field inclusion of the Hubbard U explains the band gap but produces even narrower bands, indicating the complete breakdown of standard mean-field theories in describing excitation spectra. We associate the observed spectra with the propagation of a hole in a system with surprisingly well suppressed charge fluctuations thereby showing characteristics of a t-J model. Upon doping we observe the creation of the new state at the Fermi level which is accompanied by a rapid decrease of the spectral intensity at about 1 eV binding energy. This rapid transfer of spectral weight characterizes the correlated nature of this material, and distinguishes this material clearly from ordinary band semiconductors. Surprisingly, we find also a large difference in the speed of transfer of spectral weight when comparing doping using excess oxygen or using Sr substitution. LDA+DMFT calculations suggest that this could be related to the fact that the Sr material has a smaller crystal field splitting in the t2g levels than the oxygen excess sample, yielding an effectively larger degeneracy and thus a smaller effective U versus W ratio

Local search for stable marriage problems with ties and incomplete lists

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun eds., Springer LNA

Deep convolutional networks for automated detection of posterior-element fractures on spine CT

Injuries of the spine, and its posterior elements in particular, are a common occurrence in trauma patients, with potentially devastating consequences. Computer-aided detection (CADe) could assist in the detection and classification of spine fractures. Furthermore, CAD could help assess the stability and chronicity of fractures, as well as facilitate research into optimization of treatment paradigms. In this work, we apply deep convolutional networks (ConvNets) for the automated detection of posterior element fractures of the spine. First, the vertebra bodies of the spine with its posterior elements are segmented in spine CT using multi-atlas label fusion. Then, edge maps of the posterior elements are computed. These edge maps serve as candidate regions for predicting a set of probabilities for fractures along the image edges using ConvNets in a 2.5D fashion (three orthogonal patches in axial, coronal and sagittal planes). We explore three different methods for training the ConvNet using 2.5D patches along the edge maps of 'positive', i.e. fractured posterior-elements and 'negative', i.e. non-fractured elements. An experienced radiologist retrospectively marked the location of 55 displaced posterior-element fractures in 18 trauma patients. We randomly split the data into training and testing cases. In testing, we achieve an area-under-the-curve of 0.857. This corresponds to 71% or 81% sensitivities at 5 or 10 false-positives per patient, respectively. Analysis of our set of trauma patients demonstrates the feasibility of detecting posterior-element fractures in spine CT images using computer vision techniques such as deep convolutional networks.Comment: To be presented at SPIE Medical Imaging, 2016, San Dieg

Computer-assisted polyp matching between optical colonoscopy and CT colonography: a phantom study

Potentially precancerous polyps detected with CT colonography (CTC) need to be removed subsequently, using an optical colonoscope (OC). Due to large colonic deformations induced by the colonoscope, even very experienced colonoscopists find it difficult to pinpoint the exact location of the colonoscope tip in relation to polyps reported on CTC. This can cause unduly prolonged OC examinations that are stressful for the patient, colonoscopist and supporting staff. We developed a method, based on monocular 3D reconstruction from OC images, that automatically matches polyps observed in OC with polyps reported on prior CTC. A matching cost is computed, using rigid point-based registration between surface point clouds extracted from both modalities. A 3D printed and painted phantom of a 25 cm long transverse colon segment was used to validate the method on two medium sized polyps. Results indicate that the matching cost is smaller at the correct corresponding polyp between OC and CTC: the value is 3.9 times higher at the incorrect polyp, comparing the correct match between polyps to the incorrect match. Furthermore, we evaluate the matching of the reconstructed polyp from OC with other colonic endoluminal surface structures such as haustral folds and show that there is a minimum at the correct polyp from CTC. Automated matching between polyps observed at OC and prior CTC would facilitate the biopsy or removal of true-positive pathology or exclusion of false-positive CTC findings, and would reduce colonoscopy false-negative (missed) polyps. Ultimately, such a method might reduce healthcare costs, patient inconvenience and discomfort.Comment: This paper was presented at the SPIE Medical Imaging 2014 conferenc