Mutual Dimension

We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We show that these quantities satisfy the main desiderata for a satisfactory measure of mutual algorithmic information. Our main theorem, the data processing inequality for mutual dimension, says that, if $f:\mathbb{R}^m \rightarrow \mathbb{R}^n$ is computable and Lipschitz, then the inequalities $mdim(f(x):y) \leq mdim(x:y)$ and $Mdim(f(x):y) \leq Mdim(x:y)$ hold for all $x \in \mathbb{R}^m$ and $y \in \mathbb{R}^t$. We use this inequality and related inequalities that we prove in like fashion to establish conditions under which various classes of computable functions on Euclidean space preserve or otherwise transform mutual dimensions between points.Comment: This article is 29 pages and has been submitted to ACM Transactions on Computation Theory. A preliminary version of part of this material was reported at the 2013 Symposium on Theoretical Aspects of Computer Science in Kiel, German

Investigating the impact of carbohydrate and peptide attachment to multivalent scaffolds on influenza inhibition

Hämagglutinin (HA) des Influenzavirus ist eine mögliche Zielstruktur für antivirale Therapeutika. Aus der Menge experimenteller HA-Inhibitoren stechen die kürzlich beschriebenen Q-beta-Sialoside aufgrund ihrer hohen Affinität und akkuraten, multivalenten Abbildung der Rezeptorbindungsstellengeometrie hervor. Anknüpfend an diese Eigenschaften beschreibt die vorliegende Arbeit die Erweiterung der Q-beta-Sialosidplattform durch neuartige Varianten und Anwendungsgebiete. Verschiedene Strategien für die Entfernung von Lipopolysacchariden aus Kapsidproben wurden untersucht, wobei sich das Verfahren der Cloud Point als am besten geeignet herausstellte. Das gereinigte Material war geeignet für in vivo Versuche. Teilsialylierte Kaspidvarianten wurden auf ihre inhibitorische Aktivität untersucht und im Vergleich der Ergebnisse mit statistischen Berechnungen Hinweise auf einen vorherrschend trivalenten Bindungsmodus zwischen Q-beta-Sialosiden und HA gefunden. Die Arbeit beinhaltet die ersten Beispiele heterobifunktionaler Q-beta-Sialoside, die verschiedene Sialinsäureliganden oder Kombinationen aus Zuckern und Fluoreszenzfarbstoffen aufweisen. Die fluoreszenzmarkierten Kapside wurden in Mukus-Mobilitätsstudien angewendet und ihre Undurchgängigkeit der äußeren Mukusbarriere visualisiert. Mehrere Sialinsäureester wurden als potenzielle ladungsmaskierte Liganden für erhöhte Mukusgängigkeit untersucht. Ein zweiter Schwerpunkt der Arbeit war die Entwicklung eines peptidbasierten HA-Inhibitors. Eine Gruppe von aus HA-bindenden Antikörpern und Lactoferrin abgeleiteten Peptiden wurde mit Hilfe der mikroskaligen Thermophorese auf ihre Affinität zu HA oder Influenza A/X31 (H3N2) getestet. Die vorläufigen Resultate weisen auf eine gute Bindung mehrerer Kandidaten hin. Multivalente Peptid-Polymer-Konjugate wurden auf Basis von linearem Polygylcerol niedrigen Molekulargewichts synthetisiert, jedoch zeigte keines eine Inhibierung der getesteten Influenzastämme.The influenza virus hemagglutinin (HA) attracts much attention as a target widely unexploited by licensed therapeutics. From the numerous experimental HA inhibitors, the recently reported Q-beta sialosides stand out through their affinity and accurate, multivalent reflection of the receptor binding site geometry. Building upon these characteristics, this work expands the variety of the Q-beta sialoside platform with novel variants and explores new areas of application. Several strategies were compared to remove lipopolysaccharides from capsid preparations, determining cloud point extraction as the most suitable. The purified material shown to be suitable for in vivo experiments. The inhibitory activities of partially sialylated capsids were compared to statistical models to obtain evidence for the prevalence of trivalent interactions between Q-beta sialosides and HA. Moreover, this work contains the first examples of heterobifunctional Q sialosides, bearing multiple sialic acid (SA) ligands or combinations of sugars and fluorescent dyes. Fluorescently labeled Q-beta sialosides were applied in mucus mobility studies to visualize their entrapment in the outer mucus layer. Several SA esters were examined as potential masked-charge ligands to increase mucus permeation. A second focal point of the thesis was the design of a novel, peptide-based HA inhibitor. A library of peptides derived from HA-binding antibodies and lactoferrin was investigated using microscale thermophoresis for binding to recombinant HA or influenza A/X31 (H3N2) concentrate. Preliminary results indicated good affinity for some candidates. Multivalent polymer-peptide conjugates of several peptides were synthesized by immobilization on low molecular weight linear polyglycerol. However, none of the conjugates was able to inhibit influenza strains A/X31 (H3N2) or A/PR8 (H1N1) in a hemagglutination inhibition test

A Mode-Based Averaged Power Converter Model for Large Transients

Power converters employ high-frequency switching between multiple switch states, each of which causes the system to exhibit a different dynamic behavior. Averaged models are a common simplification used for describing the behavior in one or two specific cycles of switch states, also called operating modes. In this context, we propose extending the method of Sun et al. (2001), which allows averaging in two operating modes, to a converter model with four operating modes. We show in simulations that our model results in a reasonable approximation of the true moving average of the original switching converter model during large transients that pass through multiple operating modes

esys-escript 5.6

Escript is a programming tool for implementing mathematical models in python using the finite element method (FEM). As users do not access the data structures it is very easy to use and scripts can run on desktop computers as well as highly parallel supercomputer without changes. Application areas for escript include earth mantle convection, geophysical inversion, earthquakes, porous media flow, reactive transport, plate subduction, erosion, and tsunamis

esys-escript 5.5

Escript is a programming tool for implementing mathematical models in python using the finite element method (FEM). As users do not access the data structures it is very easy to use and scripts can run on desktop computers as well as highly parallel supercomputer without changes. Application areas for escript include earth mantle convection, geophysical inversion, earthquakes, porous media flow, reactive transport, plate subduction, erosion, and tsunamis

Electromyographic Activity of Hamstrings and Quadriceps Muscle during Jumping and Landing: Pilot Study

Background and Purpose. The purpose of this pilot study was to see if there was a difference in amount of electromyographic (EMG) activity in the quadriceps (vastus medialis and vastus lateralis) compared to amount of EMG activity in the hamstrings (biceps femoris and semitendinosus) in active male and female subjects during vertical jumping and landing. In addition, we looked at the amount of knee flexion that occurred in the male and female subjects shortly after landing from a vertical jump. Methods EMG activity was recorded using a Noraxon TeleMyo DTS telemetry unit with a sampling rate of 1 kHz. EMG data was recorded during vertical jumping and landing. EMG activity in two quadriceps muscles (vastus medialis and vastus lateralis) and two hamstring muscles (biceps femoris and semitendinosus) were monitored during the experiment. The subject was also captured on video using the NiNox 125/250 FPS camera system. Subjects consisted of two male and two female athletes in good physical condition with no previous knee pathologies. Results Differences were found in the quadriceps to hamstring ratio when comparing female to male participants in both single jump (Female 4.42:1, Male 2.38:1) and triple jump landing (Female 5.46:1, Male 1.90:1). Females generally showed higher percent of maximal voluntary contraction in the quadriceps than the males when compared for both jumps. Remarkable differences in knee flexion upon landing were not found between genders in either test. Conclusion The results of this study showed quadriceps dominance in females as compared to males when landing from a jump. Previous studies have theorized that this level of dominance creates tensile force on the ACL, leading to increased incidence of ACL tears. Strength training focused on hamstring activation with a proper quadriceps to hamstring muscles ratio should be implemented when preventing ACL injuries especially in the female population. Further research is needed to confirm these conclusions and demonstrate clinical relevance

The Effect of Patient Financial Liability on Physical Therapy Utilization and Patient Reported Outcomes for Patients With Low Back Pain: An Instrumental Variable Analysis

Low back pain (LBP) is the most common orthopedic complaint managed by physical therapists in the United States. Insurance plans that require greater patient financial liability per physical therapy visit are thought to disincentivize participation in recommended physical therapy plans of care. The primary purpose of this investigation was to use instrumental variable regression to investigate the effect of insurancemediated patient financial liability per visit on physical therapy visit count and functional patient reported outcomes. The secondary purpose of the study was to examine the generalizability of results to the broader excluded patient population—and beyond to patients that seek physical therapy for LBP. Insurance-mediated patient financial liability per visit was a poor instrument with an inconsistent effect that trended against the hypothesized direction. The instrument had no statistically or clinically important effect on visit count, and no subsequent clinically important change in patient reported outcome. A comparison of baseline patient information and “index” values for predicted visit count and change in patient reported outcome identified few potential clinically important differences, yielding the conclusion that results of the primary investigation are likely generalizable to a broader patient population with LBP. These results suggest patient financial liability per visit is a poor instrument with currently available data; however, any results from large observational analyses would likely generalize to a larger patient population with LBP