Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

A Logarithmic Image Prior for Blind Deconvolution

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the L0 “norm” is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primal-dual approach and one via majorization-minimization.

Hierarchical clustering of flow cytometry data for the study of conventional central chondrosarcoma

We have investigated the use of hierarchical clustering of flow cytometry data to classify samples of conventional central chondrosarcoma, a malignant cartilage forming tumor of uncertain cellular origin, according to similarities with surface marker profiles of several known cell types. Human primary chondrosarcoma cells, articular chondrocytes, mesenchymal stem cells, fibroblasts, and a panel of tumor cell lines from chondrocytic or epithelial origin were clustered based on the expression profile of eleven surface markers. For clustering, eight hierarchical clustering algorithms, three distance metrics, as well as several approaches for data preprocessing, including multivariate outlier detection, logarithmic transformation, and z-score normalization, were systematically evaluated. By selecting clustering approaches shown to give reproducible results for cluster recovery of known cell types, primary conventional central chondrosacoma cells could be grouped in two main clusters with distinctive marker expression signatures: one group clustering together with mesenchymal stem cells (CD49b-high/CD10-low/CD221-high) and a second group clustering close to fibroblasts (CD49b-low/CD10-high/CD221-low). Hierarchical clustering also revealed substantial differences between primary conventional central chondrosarcoma cells and established chondrosarcoma cell lines, with the latter not only segregating apart from primary tumor cells and normal tissue cells, but clustering together with cell lines from epithelial lineage. Our study provides a foundation for the use of hierarchical clustering applied to flow cytometry data as a powerful tool to classify samples according to marker expression patterns, which could lead to uncover new cancer subtypes.

Differences in Median Ultraviolet Light Transmissions of Serial Homeopathic Dilutions of Copper Sulfate, Hypericum perforatum, and Sulfur

Homeopathic remedies are produced by potentising, that is, the serial logarithmic dilution and succussion of a mother tincture. Techniques like ultraviolet spectroscopy, nuclear magnetic resonance, calorimetry, or thermoluminescence have been used to investigate their physical properties. In this study, homeopathic centesimal (c) potencies (6c to 30c) of copper sulfate, Hypericum perforatum, and sulfur as well as succussed water controls were prepared. Samples of these preparations were exposed to external physical factors like heat, pressure, ultraviolet radiation, or electromagnetic fields to mimic possible everyday storage conditions. The median transmissions from 190nm to 340nm and 220nm to 340nm were determined by ultraviolet light spectroscopy on five measurement days distributed over several months. Transmissions of controls and potencies of sulfur differed significantly on two of five measurement days and after exposure to physical factors. Transmissions of potencies exposed to ultraviolet light and unexposed potencies of copper sulfate and Hypericum perforatum differed significantly. Potency levels 6c to 30c were also compared, and wavelike patterns of higher and lower transmissions were found. The Kruskal-Wallis test yielded significant differences for the potency levels of all three substances. Aiming at understanding the physical properties of homeopathic preparations, this study confirmed and expanded the findings of previous studies.

Sampling-Design Effects on Properties of Species-Area Relationships - A Case Study from Estonian Dry Grassland Communities

Despite widespread use of species-area relationships (SARs), dispute remains over the most representative SAR model. Using data of small-scale SARs of Estonian dry grassland communities, we address three questions: (1) Which model describes these SARs best when known artifacts are excluded? (2) How do deviating sampling procedures (marginal instead of central position of the smaller plots in relation to the largest plot; single values instead of average values; randomly located subplots instead of nested subplots) influence the properties of the SARs? (3) Are those effects likely to bias the selection of the best model? Our general dataset consisted of 16 series of nested-plots (1 cm(2)-100 m(2), any-part system), each of which comprised five series of subplots located in the four corners and the centre of the 100-m(2) plot. Data for the three pairs of compared sampling designs were generated from this dataset by subsampling. Five function types (power, quadratic power, logarithmic, Michaelis-Menten, Lomolino) were fitted with non-linear regression. In some of the communities, we found extremely high species densities (including bryophytes and lichens), namely up to eight species in 1 cm(2) and up to 140 species in 100 m(2), which appear to be the highest documented values on these scales. For SARs constructed from nested-plot average-value data, the regular power function generally was the best model, closely followed by the quadratic power function, while the logarithmic and Michaelis-Menten functions performed poorly throughout. However, the relative fit of the latter two models increased significantly relative to the respective best model when the single-value or random-sampling method was applied, however, the power function normally remained far superior. These results confirm the hypothesis that both single-value and random-sampling approaches cause artifacts by increasing stochasticity in the data, which can lead to the selection of inappropriate models.

Diffusion-weighted imaging of the parotid gland: Influence of the choice of b-values on the apparent diffusion coefficient value

PURPOSE: To determine how the ADC value of parotid glands is influenced by the choice of b-values. MATERIALS AND METHODS: In eight healthy volunteers, diffusion-weighted echo-planar imaging (DW-EPI) was performed on a 1.5 T system, with b-values (in seconds/mm2) of 0, 50, 100, 150, 200, 250, 300, 500, 750, and 1000. ADC values were calculated by two alternative methods (exponential vs. logarithmic fit) from five different sets of b-values: (A) all b-values; (B) b=0, 50, and 100; (C) b=0 and 750; (D) b=0, 500, and 1000; and (E) b=500, 750, and 1000. RESULTS: The mean ADC values for the different settings were (in 10(-3) mm2/second, exponential fit): (A) 0.732+/-0.019, (B) 2.074+/-0.084, (C) 0.947+/-0.020, (D) 0.890+/-0.023, and (E) 0.581+/-0.021. ADC values were significantly (P <0.001) different for all pairwise comparisons of settings (A-E) of b-values, except for A vs. D (P=0.172) and C vs. D (P=0.380). The ADC(B) was significantly higher than ADC(C) or ADC(D), which was significantly higher than ADC(E). ADC values from exponential vs. logarithmic fit (P=0.542), as well as left vs. right parotid gland (P=0.962), were indistinguishable. CONCLUSION: The ADC values calculated from low b-value settings were significantly higher than those calculated from high b-value settings. These results suggest that not only true diffusion but also perfusion and saliva flow may contribute to the ADC.

Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto

We have recently derived a factorization formula for the Higgs-boson production cross section in the presence of a jet veto, which allows for a systematic resummation of large Sudakov logarithms of the form αn s lnm(pveto T /mH), along with the large virtual corrections known to affect also the total cross section. Here we determine the ingredients entering this formula at two-loop accuracy. Specifically, we compute the dependence on the jet-radius parameter R, which is encoded in the two-loop coefficient of the collinear anomaly, by means of a direct, fully analytic calculation in the framework of soft-collinear effective theory. We confirm the result obtained by Banfi et al. from a related calculation in QCD, and demonstrate that factorization-breaking, soft-collinear mixing effects do not arise at leading power in pveto T /mH, even for R = O(1). In addition, we extract the two-loop collinear beam functions numerically. We present detailed numerical predictions for the jet-veto cross section with partial next-to-next-to-next-to-leading logarithmic accuracy, matched to the next-to-next-to-leading order cross section in fixed-order perturbation theory. The only missing ingredients at this level of accuracy are the three-loop anomaly coefficient and the four-loop cusp anomalous dimension, whose numerical effects we estimate to be small.

Transverse-momentum spectra of electroweak bosons near threshold at NNLO

We obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.

Calculating track thrust with track functions

In e+e− event shapes studies at LEP, two different measurements were sometimes performed: a “calorimetric” measurement using both charged and neutral particles and a “track-based” measurement using just charged particles. Whereas calorimetric measurements are infrared and collinear safe, and therefore calculable in perturbative QCD, track-based measurements necessarily depend on nonperturbative hadronization effects. On the other hand, track-based measurements typically have smaller experimental uncertainties. In this paper, we present the first calculation of the event shape “track thrust” and compare to measurements performed at ALEPH and DELPHI. This calculation is made possible through the recently developed formalism of track functions, which are nonperturbative objects describing how energetic partons fragment into charged hadrons. By incorporating track functions into soft-collinear effective theory, we calculate the distribution for track thrust with next-to-leading logarithmic resummation. Due to a partial cancellation between nonperturbative parameters, the distributions for calorimeter thrust and track thrust are remarkably similar, a feature also seen in LEP data.

Determination of α_{s} from the QCD static energy

We compare lattice data for the short-distance part of the static energy in 21 flavor quantum chromodynamics (QCD) with perturbative calculations, up to next-to-next-to-next-to leading-logarithmic accuracy. We show that perturbation theory describes very well the lattice data at short distances, and exploit this fact to obtain a determination of the product of the lattice scale r0 with the QCD scale ΛMS. With the input of the value of r0, this provides a determination of the strong coupling αs at the typical distance scale of the lattice data. We obtain αs1.5  GeV0.3260.019, which provides a novel determination of αs with three-loop accuracy (including resummation of the leading ultrasoft logarithms), and constitutes one of the few low-energy determinations of αs available. When this value is evolved to the Z-mass scale MZ, it corresponds to αsMZ0.11560.00220.0021.

Using state variables to model the response of tumour cells to radiation and heat: a novel multi-hit-repair approach

In order to overcome the limitations of the linear-quadratic model and include synergistic effects of heat and radiation, a novel radiobiological model is proposed. The model is based on a chain of cell populations which are characterized by the number of radiation induced damages (hits). Cells can shift downward along the chain by collecting hits and upward by a repair process. The repair process is governed by a repair probability which depends upon state variables used for a simplistic description of the impact of heat and radiation upon repair proteins. Based on the parameters used, populations up to 4-5 hits are relevant for the calculation of the survival. The model describes intuitively the mathematical behaviour of apoptotic and nonapoptotic cell death. Linear-quadratic-linear behaviour of the logarithmic cell survival, fractionation, and (with one exception) the dose rate dependencies are described correctly. The model covers the time gap dependence of the synergistic cell killing due to combined application of heat and radiation, but further validation of the proposed approach based on experimental data is needed. However, the model offers a work bench for testing different biological concepts of damage induction, repair, and statistical approaches for calculating the variables of state.