Error analysis for filtered back projection reconstructions in Besov spaces

Filtered back projection (FBP) methods are the most widely used reconstruction algorithms in computerized tomography (CT). The ill-posedness of this inverse problem allows only an approximate reconstruction for given noisy data. Studying the resulting reconstruction error has been a most active field of research in the 1990s and has recently been revived in terms of optimal filter design and estimating the FBP approximation errors in general Sobolev spaces. However, the choice of Sobolev spaces is suboptimal for characterizing typical CT reconstructions. A widely used model are sums of characteristic functions, which are better modelled in terms of Besov spaces $\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$. In particular $\mathrm{B}^{\alpha,1}_1(\mathbb{R}^2)$ with $\alpha \approx 1$ is a preferred model in image analysis for describing natural images. In case of noisy Radon data the total FBP reconstruction error $$\|f-f_L^\delta\| \le \|f-f_L\|+ \|f_L - f_L^\delta\|$$ splits into an approximation error and a data error, where $L$ serves as regularization parameter. In this paper, we study the approximation error of FBP reconstructions for target functions $f \in \mathrm{L}^1(\mathbb{R}^2) \cap \mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)$ with positive $\alpha \not\in \mathbb{N}$ and $1 \leq p,q \leq \infty$. We prove that the $\mathrm{L}^p$-norm of the inherent FBP approximation error $f-f_L$ can be bounded above by \begin{equation*} \|f - f_L\|_{\mathrm{L}^p(\mathbb{R}^2)} \leq c_{\alpha,q,W} \, L^{-\alpha} \, |f|_{\mathrm{B}^{\alpha,p}_q(\mathbb{R}^2)} \end{equation*} under suitable assumptions on the utilized low-pass filter's window function $W$. This then extends by classical methods to estimates for the total reconstruction error.Comment: 32 pages, 8 figure

Managing the intake of new patients into a physician panel over time

This article focuses on balancing supply and demand for physicians and panel patients on a tactical level to ensure a manageable workload for the physician and access to care for patients. Patients are part of the physician’s panel if they visit the physician somewhat regularly. For the first time, we propose deterministic integer linear programs that decide on the intake of new patients into panels over time, taking into account the future panel development. The main objective is to minimize the deviation between the expected panel workload and the physician’s capacity over time. We classify panel patients with respect to age and the number of visits in a period and assume a transition probability from one visit category to another from one period to the next. We can include stationary patient attributes and consider several physicians together. The programs work with aggregation levels for the new patients’ demand concerning the patient attributes. We conduct experiments with parameters based on real-world data. We consider the transition between visit categories and the new patients’ demand to be stochastic in a discrete-event simulation. We define upper bounds on the number of patients in a patient class to be accepted in a period through solving the programs several times with different demand inputs. Even in this uncertain environment, we can significantly reduce the expected differences between workload and capacity over time, taking into account several future periods instead of one. Using a detailed classification of new patients decreases the expected differences further

Bullying girls - Changes after brief strategic family therapy: A randomized, prospective, controlled trial with one-year follow-up

Background: Many girls bully others. They are conspicuous because of their risk-taking behavior, increased anger, problematic interpersonal relationships and poor quality of life. Our aim was to determine the efficacy of brief strategic family therapy (BSFT) for bullying-related behavior, anger reduction, improvement of interpersonal relationships, and improvement of health-related quality of life in girls who bully, and to find out whether their expressive aggression correlates with their distinctive psychological features. Methods: 40 bullying girls were recruited from the general population: 20 were randomly selected for 3 months of BSFT. Follow-up took place 12 months after the therapy had ended. The results of treatment were examined using the Adolescents' Risk-taking Behavior Scale (ARBS), the State-Trait Anger Expression Inventory (STAXI), the Inventory of Interpersonal Problems (IIP-D), and the SF-36 Health Survey (SF-36). Results: In comparison with the control group (CG) (according to the intent-to-treat principle), bullying behavior in the BSFT group was reduced (BSFT-G from n = 20 to n = 6; CG from n = 20 to n = 18, p = 0.05) and statistically significant changes in all risk-taking behaviors (ARBS), on most STAXI, IIP-D, and SF-36 scales were observed after BSFT. The reduction in expressive aggression (Anger-Out scale of the STAXI) correlated with the reduction on several scales of the ARBS, IIP-D, and SF-36. Follow-up a year later showed relatively stable events. Conclusions: Our findings suggest that bullying girls suffer from psychological and social problems which may be reduced by the use of BSFT. Expressive aggression in girls appears to correlate with several types of risk-taking behavior and interpersonal problems, as well as with health-related quality of life. Copyright (c) 2006 S. Karger AG, Basel

Phosphonated Agents and Their Antiangiogenic and Antitumorigenic Use

Phosphonic acid agents are synthesized and characterized which are potent inhibitors of angiogenesis, tumorigenesis and metalloproteinase activity. Their method of use for the inhibition of angiogenesis and metalloproteinase and the treatment of tumors is also shown

Phosphonated Agents and Their Antiangiogenic and Antitumorigenic Use

Phosphonic acid agents are synthesized and characterized which are potent inhibitors of angiogenesis, tumorigenesis and metalloproteinase activity. Their method of use for the inhibition of angiogenesis and metalloproteinase and the treatment of tumors is also shown

Precision tools and models to narrow in on the 750 GeV diphoton resonance

The hints for a new resonance at 750 GeV from ATLAS and CMS have triggered a significant amount of attention. Since the simplest extensions of the standard model cannot accommodate the observation, many alternatives have been considered to explain the excess. Here we focus on several proposed renormalisable weakly-coupled models and revisit results given in the literature. We point out that physically important subtleties are often missed or neglected. To facilitate the study of the excess we have created a collection of 40 model files, selected from recent literature, for the Mathematica package SARAH. With SARAH one can generate files to perform numerical studies using the tailor-made spectrum generators FlexibleSUSY and SPheno. These have been extended to automatically include crucial higher order corrections to the diphoton and digluon decay rates for both CP-even and CP-odd scalars. Additionally, we have extended the UFO and CalcHep interfaces of SARAH, to pass the precise information about the effective vertices from the spectrum generator to a Monte-Carlo tool. Finally, as an example to demonstrate the power of the entire setup, we present a new supersymmetric model that accommodates the diphoton excess, explicitly demonstrating how a large width can be obtained. We explicitly show several steps in detail to elucidate the use of these public tools in the precision study of this model.Comment: 184 pages, 24 figures; model files available at http://sarah.hepforge.org/Diphoton_Models.tar.gz; v2: added a few clarifications and reference

Possible Digenic Disease in a Caucasian Family with COL4A3 and COL4A5 Mutations

Microscopic hematuria is a common feature of patients with Alport syndrome, a familial nephropathy due to mutations in COL4A3, COL4A4 or COL4A5. These genes encode for α3, α4, and α5 type IV collagen polypeptide chains (collagen IV α345), crucial for the structural component of the glomerular basement membrane. Even patients with mild phenotype, namely isolated microhematuria (X-linked females with thin basement membrane on electron microscopy or heterozygous carriers of COL4A3 or COL4A4 mutations), can potentially progress to proteinuria and to end-stage renal disease. Recent pedigree analyses provided evidence for digenic inheritance of Alport syndrome by concomitant mutations in COL4A3/COL4A4 or COL4A4/COL4A5. We describe a Caucasian family with concomitant COL4A3 and COL4A5 mutations, consisting of a novel c.4484A>G COL4A3 (p.Gln1495Arg) mutation and a previously reported c.1871G>A COL4A5 (p.Gly624Asp) mutation. Our segregation analysis raises the possibility that Alport syndrome resembles also digenic inheritance by COL4A3/COL4A5

Invertible residual networks in the context of regularization theory for linear inverse problems

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings