Local Infiltrations in Patients with Radiculopathy or Chronic Low Back Pain Due to Segment Degeneration—Only A Diagnostic Value?

The purpose of this study was to investigate the differences in the therapeutic effectiveness of CT-assisted infiltration of a local anesthetic + corticosteroid between nerve root and facet joint capsule in patients with chronic complaints. In this prospective trial with a 12-month follow-up, a total of 250 patients with chronic low back pain and radiculopathy were assigned to two groups. In the first group, patients with specific lumbar pain due to spondyloarthritis received periarticular facet joint capsule infiltration (FJI). In the second group, patients with monoradicular pain received periradicular infiltration (PRI) via an extraforaminal selective nerve block. Clinical improvement after FJI and PRI regarding pain (NRS), function (ODI), satisfaction (McNab), and health related quality of life (SF-36) were compared. Minimally clinically important difference (MCID) served as the threshold for therapeutic effectiveness evaluation. A total of 196 patients were available for final analysis. With respect to the pain reduction and functional improvement (ODI, NRSoverall, and NRSback), the PRI group performed significantly better (ptreatment < 0.001) and longer over time (ptreatment × time 0.001) than the FJI group. Regarding pain and function, only PRI demonstrated a durable improvement larger than MCID. A significant and durable therapeutic value was found only after receiving PRI but not after FJI in patients with chronic pain

Computable classifications of continuous, transducer, and regular functions

We develop a systematic algorithmic framework that unites global and local classification problems for functional separable spaces and apply it to attack classification problems concerning the Banach space C[0,1] of real-valued continuous functions on the unit interval. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear, pointwise linear-time Lipshitz functions is $\Sigma^0_2$-complete. We show that a function $f\colon [0,1] \rightarrow \mathbb{R}$ is (binary) transducer if and only if it is continuous regular; interestingly, this peculiar and nontrivial fact was overlooked by experts in automata theory. As one of many consequences, our $\Sigma^0_2$-completeness result covers the class of transducer functions as well. Finally, we show that the Banach space $C[0,1]$ of real-valued continuous functions admits an arithmetical classification among separable Banach spaces. Our proofs combine methods of abstract computability theory, automata theory, and functional analysis.Comment: Revised argument in Section 5; results unchange

A Formal Proof of PAC Learnability for Decision Stumps

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoretic subtleties arise when carrying it out fully formally. Our proof is structured so as to separate reasoning about deterministic properties of a learning function from proofs of measurability and analysis of probabilities.Comment: 13 pages, appeared in Certified Programs and Proofs (CPP) 202

Essays on persistence in growth rates and the success of the British Premium Bond

This dissertation contributes new evidence to two areas of research. The first two essays aim at analyzing persistence in growth rates of operating performance as an important factor for firm valuations. In this context, in-depth analyses on both the predictive power as well as the predictability of persistence in growth rates are performed. The two central research questions are: Do investors overestimate the predictive power of a high persistence in sales growth rates? Is it possible to predict a high future persistence in growth rates based on a set of firm-specific financial indicators? In the third essay, a very successful British lottery bond is in the focus of interest, the Premium Bond. Although monthly return is solely based on a lottery and therefore uncertain, this financial product is very popular. The study aims to explain what makes the Premium Bond and generally lottery-linked deposit accounts successful. The individual risk tolerance of an investor, the skewness of the prize distribution, and explanations based on the cumulative prospect theory are analyzed in detail

Predicting above-median and below-median growth rates

Multiannual periods of consecutive above-median or below-median growth rates in operating performance, called runs, have a substantial influence on firm valuations. For estimating the probability of an above-median or below-median run and utilizing information efficiently, we employ a stepwise regression to automatically identify the parsimonious indicator-specific set of economically and empirically meaningful variables. Our novel approach uses logit models to distinguish firms that will persistently grow above or below the median over a period of up to 6 years. The predictive power for sales growth rates is highest to discriminate between above-median and below-median growth rates, while the future behaviour of operating income and net income growth rates can partially be explained for below-median growth rates

Enhancing UML State Machines with Aspects

Separation of Concerns (SoC) is an important issue to reduce the complexity of software. Recent advances in programming language research show that Aspect-Oriented Programming (AOP) may be helpful for enhancing the SoC in software systems: AOP provides a means for describing concerns which are normally spread throughout the whole program at one location. The arguments for introducing aspects into programming languages also hold for modeling languages. In particular, modeling state-crosscutting behavior is insufficiently supported by UML state machines. This often leads to model elements addressing the same concern scattered all over the state machine. We present an approach to aspect-oriented state machines, which show considerably better modularity in modeling state-crosscutting behavior than standard UML state machines