A sheaf theoretic approach to measure theory

The topos $extrm{Sh}(mathcal{F})$ of sheaves on a $sigma$-algebra $mathcal{F}$ is a natural home for measure theory. The collection of measures is a sheaf, the collection of measurable real valued functionsis a sheaf, the operation of integrationis a natural transformation, and the concept of almost-everywhere equivalence is a Lawvere-Tierney topology. The sheaf of measurable real valued functions is the Dedekind real numbers object in $extrm{Sh}(mathcal{F})$ and the topology of ``almost everywhere equivalence`` is the closed topologyinduced by the sieve of negligible sets The other elements of measure theory have not previously been described using the internallanguage of $extrm{Sh}(mathcal{F})$. The sheaf of measures, and the natural transformation of integration, are here described using the internal languages of $extrm{Sh}(mathcal{F})$ and $widehat{mathcal{F}}$, the topos of presheaves on $mathcal{F}$.These internal constructions describe corresponding components in any topos $mmathscr{E}$ with a designatedtopology $j$. In the case where $mmathscr{E}=widehat{mathcal{L}}$ is the topos of presheaves on a locale, and$j$ is the canonical topology, then the presheaf of measures is a sheaf on $mathcal{L}$. A definition of the measure theory on $mathcal{L}$ is given, and it is shown that when$extrm{Sh}(mathcal{F})simeqextrm{Sh}(mathcal{L})$, or equivalently, when $mathcal{L}$ is the locale of closed sieves in $mathcal{F}$this measure theory coincides with the traditional measure theory of a $sigma$-algebra $mathcal{F}$.In doing this, the interpretation of the topology of ``almost everywhere' equivalence is modified so as to better reflect non-Boolean settings.Given a measure $mu$ on $mathcal{F}$, the Lawvere-Tierney topology that expressesthe notion of ``$mu$-almost everywhere equivalence' induces a subtopos $extrm{Sh}_{mu}(mathcal{L})$. If this subtopos is Boolean, and if $mu$ is locally finite, then the Radon-Nikodym theorem holds, so that for any locally finite $ullmu$, the Radon-Nikodym derivative $frac{du}{dmu}$ exists

Time for a plant structural economics spectrum

We argue that tree and crown structural diversity can and should be integrated in the whole-plant economics spectrum. Ecologists have found that certain functional trait combinations have been more viable than others during evolution, generating a trait trade-off continuum which can be summarized along a few axes of variation, such as the "worldwide leaf economics spectrum" and the "wood economics spectrum." However, for woody plants the crown structural diversity should be included as well in the recently introduced "global spectrum of plant form and function," which now merely focusses on plant height as structural factor. The recent revolution in terrestrial laser scanning (TLS) unlocks the possibility to describe the three dimensional structure of trees quantitatively with unprecedented detail. We demonstrate that based on TLS data, a multidimensional structural trait space can be constructed, which can be decomposed into a few descriptive axes or spectra. We conclude that the time has come to develop a "structural economics spectrum" for woody plants based on structural trait data across the globe. We make suggestions as to what structural features might lie on this spectrum and how these might help improve our understanding of tree form-function relationships

Öko-Lebensmittel - das komplexe Zusammenspiel von Einflussfaktoren und Auswirkungen

Vorteile des Konsums ökologisch erzeugter Lebensmittel werden oft auf gesundheitliche Effekte reduziert. Ziel der Arbeit ist es, das komplexe Zusammenspiel der zahlreichen Einflussfaktoren und Auswirkungen des Konsums ökologischer Lebensmittel a ufzuzeigen. Basierend auf aktueller Literatur wurden entsprechend dem Ansatz der Ernährungsökologie mit der Modellierungstechnik NutriMod Faktoren aus den Dimensionen Gesundheit, Umwelt, Wirtschaft und Gesellschaft erfasst und in ihrer Vernetztheit dargestellt. Im resultierenden Modell können zahlreiche direkte und indirekte Zusammenhänge aufgezeigt, sowie Wirkketten und Rückkopplungen identifiziert werden, innerhalb der Dimensionen und dimensionenübergreifend. Durch die Abbildung von Mehrdimensionalität und Vernetztheit von Einflussfaktoren und Auswirkungen liefert das Modell für das kontrovers diskutierte Thema Öko-Landbau Grundlagen für weitere Forschung und für politische Entscheidungen im Sinne einer nachhaltigen Entwicklung

Abstract and proportional myoelectric control for multi-fingered hand prostheses

Powered hand prostheses with many degrees of freedom are moving from research into the market for prosthetics. In order to make use of the prostheses’ full functionality, it is essential to study efficient ways of high dimensional myoelectric control. Human subjects can rapidly learn to employ electromyographic (EMG) activity of several hand and arm muscles to control the position of a cursor on a computer screen, even if the muscle-cursor map contradicts directions in which the muscles would act naturally. But can a similar control scheme be translated into real-time operation of a dexterous robotic hand? We found that despite different degrees of freedom in the effector output, the learning process for controlling a robotic hand was surprisingly similar to that for a virtual two-dimensional cursor. Control signals were derived from the EMG in two different ways, with a linear and a Bayesian filter, to test how stable user intentions could be conveyed through them. Our analysis indicates that without visual feedback, control accuracy benefits from filters that reject high EMG amplitudes. In summary, we conclude that findings on myoelectric control principles, studied in abstract, virtual tasks can be transferred to real-life prosthetic applications. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s10439-013-0876-5) contains supplementary material, which is available to authorized users

Artificial proprioceptive feedback for myoelectric control

The typical control of myoelectric interfaces, whether in laboratory settings or real-life prosthetic applications, largely relies on visual feedback because proprioceptive signals from the controlling muscles are either not available or very noisy. We conducted a set of experiments to test whether artificial proprioceptive feedback, delivered non-invasively to another limb, can improve control of a two-dimensional myoelectrically-controlled computer interface. In these experiments, participants’ were required to reach a target with a visual cursor that was controlled by electromyogram signals recorded from muscles of the left hand, while they were provided with an additional proprioceptive feedback on their right arm by moving it with a robotic manipulandum. Provision of additional artificial proprioceptive feedback improved the angular accuracy of their movements when compared to using visual feedback alone but did not increase the overall accuracy quantified with the average distance between the cursor and the target. The advantages conferred by proprioception were present only when the proprioceptive feedback had similar orientation to the visual feedback in the task space and not when it was mirrored, demonstrating the importance of congruency in feedback modalities for multi-sensory integration. Our results reveal the ability of the human motor system to learn new inter-limb sensory-motor associations; the motor system can utilize task-related sensory feedback, even when it is available on a limb distinct from the one being actuated. In addition, the proposed task structure provides a flexible test paradigm by which the effectiveness of various sensory feedback and multi-sensory integration for myoelectric prosthesis control can be evaluated

Machine learning from wristband sensor data for wearable, noninvasive seizure forecasting

Objective: Seizure forecasting may provide patients with timely warnings to adapt their daily activities and help clinicians deliver more objective, personalized treatments. Although recent work has convincingly demonstrated that seizure risk assessment is in principle possible, these early approaches relied largely on complex, often invasive setups including intracranial electrocorticography, implanted devices, and multichannel electroencephalography, and required patient-specific adaptation or learning to perform optimally, all of which limit translation to broad clinical application. To facilitate broader adaptation of seizure forecasting in clinical practice, noninvasive, easily applicable techniques that reliably assess seizure risk without much prior tuning are crucial. Wristbands that continuously record physiological parameters, including electrodermal activity, body temperature, blood volume pulse, and actigraphy, may afford monitoring of autonomous nervous system function and movement relevant for such a task, hence minimizing potential complications associated with invasive monitoring and avoiding stigma associated with bulky external monitoring devices on the head. Methods: Here, we applied deep learning on multimodal wristband sensor data from 69 patients with epilepsy (total duration > 2311 hours, 452 seizures) to assess its capability to forecast seizures in a statistically significant way. Results: Using a leave-one-subject-out cross-validation approach, we identified better-than-chance predictability in 43% of the patients. Time-matched seizure surrogate data analyses indicated forecasting not to be driven simply by time of day or vigilance state. Prediction performance peaked when all sensor modalities were used, and did not differ between generalized and focal seizure types, but generally increased with the size of the training dataset, indicating potential further improvement with larger datasets in the future. Significance: Collectively, these results show that statistically significant seizure risk assessments are feasible from easy-to-use, noninvasive wearable devices without the need of patient-specific training or parameter optimization

Global loss of imprinting leads to widespread tumorigenesis in adult mice

SummaryLoss of imprinting (LOI), commonly observed in human tumors, refers to loss of monoallelic gene regulation normally conferred by parent-of-origin-specific DNA methylation. To test the function of LOI in tumorigenesis, we developed a model by using transient demethylation to generate imprint-free mouse embryonic stem cells (IF-ES cells). Embryonic fibroblasts derived from IF-ES cells (IF-MEFs) display TGFβ resistance and reduced p19 and p53 expression and form tumors in SCID mice. IF-MEFs exhibit spontaneous immortalization and cooperate with H-Ras in cellular transformation. Chimeric animals derived from IF-ES cells develop multiple tumors arising from the injected IF-ES cells within 12 months. These data demonstrate that LOI alone can predispose cells to tumorigenesis and identify a pathway through which immortality conferred by LOI lowers the threshold for transformation

The cost-effectiveness of oral contraceptives compared to ‘no hormonal treatment’ for endometriosis-related pain: An economic evaluation

<div><p>Objective</p><p>To develop a preliminary cost-effectiveness model that compares oral contraceptives and ‘no hormonal treatment’ for the treatment of endometriosis-related pain.</p><p>Methods</p><p>A <i>de novo</i> preliminary state transition (Markov) model was developed. The model was informed by systematic literature review and expert opinion. The uncertainty around the results was assessed both by deterministic and probabilistic sensitivity analyses. The economic evaluation was conducted from National Health Service (NHS) England perspective. The main outcome measure was incremental cost per quality-adjusted life year (QALY), with cost-effectiveness plane and cost-effectiveness acceptability curves presented for alternative willingness-to-pay thresholds.</p><p>Results</p><p>Oral contraceptives dominated ‘no hormonal treatment’ and provided more QALYs at a lower cost than ‘no hormonal treatment’, with a cost-effectiveness probability of 98%. A one-way sensitivity analysis excluding general practitioner consultations showed that oral contraceptives were still cost-effective.</p><p>Conclusions</p><p>The analyses showed that oral contraceptives could be an effective option for the treatment of endometriosis, as this treatment was shown to provide a higher level of QALYs at a lower cost, compared to ‘no hormonal treatment’. The results are subject to considerable parameter uncertainty as a range of assumptions were required as part of the modelling process.</p></div

Effects of bearing clearance on the chatter stability of milling process

In the present study, the influences of the bearing clearance, which is a common fault for machines, to the chatter stability of milling process are examined by using numerical simulation method. The results reveal that the presence of bearing clearance could make the milling process easier to enter the status of chatter instability and can shift the chatter frequency. In addition, the spectra analysis to vibration signals obtained under the instable milling processes show that the presence of bearing clearance could introduce more frequency components to the vibration responses but, however, under both the stable and instable milling processes, the generated frequency components will not violate the ideal spectra structures of the vibration responses of the milling process, which are usually characterized by the tooth passing frequency and its associated higher harmonics for the stable milling process and by the complex coupling of the tooth passing frequency and the chatter frequency for the instable milling process. This implies that, even under the case with bearing clearance fault, the stability of the milling process can still be determined by viewing the frequency spectra of the vibration responses. Moreover, the phenomena of the chatter frequency shift and the generation of more components provide potential ways to detect the bearing clearance in machines. (C) 2010 Elsevier Ltd. All rights reserved