Variational principles for fluid dynamics on rough paths

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Solution properties of the incompressible Euler system with rough path advection

The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport velocity possesses an additional rough-in-time, divergence-free vector field. In recent work, we have demonstrated that this system can be derived from Clebsch and Hamilton-Pontryagin variational principles that possess a perturbative geometric rough path Lie-advection constraint. In this paper, we prove the local well-posedness of the system in -Sobolev spaces with integer regularity and establish a Beale-Kato-Majda (BKM) blow-up criterion in terms of the -norm of the vorticity. In dimension two, we show that the -norms of the vorticity are conserved, which yields global well-posedness and a Wong-Zakai approximation theorem for the stochastic version of the equation.publishedVersionPaid open acces

Interpreting Neural Networks through the Polytope Lens

Mechanistic interpretability aims to explain what a neural network has learned at a nuts-and-bolts level. What are the fundamental primitives of neural network representations? Previous mechanistic descriptions have used individual neurons or their linear combinations to understand the representations a network has learned. But there are clues that neurons and their linear combinations are not the correct fundamental units of description: directions cannot describe how neural networks use nonlinearities to structure their representations. Moreover, many instances of individual neurons and their combinations are polysemantic (i.e. they have multiple unrelated meanings). Polysemanticity makes interpreting the network in terms of neurons or directions challenging since we can no longer assign a specific feature to a neural unit. In order to find a basic unit of description that does not suffer from these problems, we zoom in beyond just directions to study the way that piecewise linear activation functions (such as ReLU) partition the activation space into numerous discrete polytopes. We call this perspective the polytope lens. The polytope lens makes concrete predictions about the behavior of neural networks, which we evaluate through experiments on both convolutional image classifiers and language models. Specifically, we show that polytopes can be used to identify monosemantic regions of activation space (while directions are not in general monosemantic) and that the density of polytope boundaries reflect semantic boundaries. We also outline a vision for what mechanistic interpretability might look like through the polytope lens.Comment: 22/11/22 initial uploa

Access to Artemisinin-Based Anti-Malarial Treatment and its Related Factors in Rural Tanzania.

Artemisinin-based combination treatment (ACT) has been widely adopted as one of the main malaria control strategies. However, its promise to save thousands of lives in sub-Saharan Africa depends on how effective the use of ACT is within the routine health system. The INESS platform evaluated effective coverage of ACT in several African countries. Timely access within 24 hours to an authorized ACT outlet is one of the determinants of effective coverage and was assessed for artemether-lumefantrine (Alu), in two district health systems in rural Tanzania. From October 2009 to June 2011we conducted continuous rolling household surveys in the Kilombero-Ulanga and the Rufiji Health and Demographic Surveillance Sites (HDSS). Surveys were linked to the routine HDSS update rounds. Members of randomly pre-selected households that had experienced a fever episode in the previous two weeks were eligible for a structured interview. Data on individual treatment seeking, access to treatment, timing, source of treatment and household costs per episode were collected. Data are presented on timely access from a total of 2,112 interviews in relation to demographics, seasonality, and socio economic status. In Kilombero-Ulanga, 41.8% (CI: 36.6-45.1) and in Rufiji 36.8% (33.7-40.1) of fever cases had access to an authorized ACT provider within 24 hours of fever onset. In neither of the HDSS site was age, sex, socio-economic status or seasonality of malaria found to be significantly correlated with timely access. Timely access to authorized ACT providers is below 50% despite interventions intended to improve access such as social marketing and accreditation of private dispensing outlets. To improve prompt diagnosis and treatment, access remains a major bottle neck and new more innovative interventions are needed to raise effective coverage of malaria treatment in Tanzania

Naturopathic Care for Anxiety: A Randomized Controlled Trial ISRCTN78958974

BACKGROUND: Anxiety is a serious personal health condition and represents a substantial burden to overall quality of life. Additionally anxiety disorders represent a significant cost to the health care system as well as employers through benefits coverage and days missed due to incapacity. This study sought to explore the effectiveness of naturopathic care on anxiety symptoms using a randomized trial. METHODS: Employees with moderate to severe anxiety of longer than 6 weeks duration were randomized based on age and gender to receive naturopathic care (NC) (n = 41) or standardized psychotherapy intervention (PT) (n = 40) over a period of 12 weeks. Blinding of investigators and participants during randomization and allocation was maintained. Participants in the NC group received dietary counseling, deep breathing relaxation techniques, a standard multi-vitamin, and the herbal medicine, ashwagandha (Withania somnifera) (300 mg b.i.d. standardized to 1.5% with anolides, prepared from root). The PT intervention received psychotherapy, and matched deep breathing relaxation techniques, and placebo. The primary outcome measure was the Beck Anxiety Inventory (BAI) and secondary outcome measures included the Short Form 36 (SF-36), Fatigue Symptom Inventory (FSI), and Measure Yourself Medical Outcomes Profile (MY-MOP) to measure anxiety, mental health, and quality of life respectively. Participants were blinded to the placebo-controlled intervention. RESULTS: Seventy-five participants (93%) were followed for 8 or more weeks on the trial. Final BAI scores decreased by 56.5% (p<0.0001) in the NC group and 30.5% (p<0.0001) in the PT group. BAI group scores were significantly decreased in the NC group compared to PT group (p = 0.003). Significant differences between groups were also observed in mental health, concentration, fatigue, social functioning, vitality, and overall quality of life with the NC group exhibiting greater clinical benefit. No serious adverse reactions were observed in either group. RELEVANCE: Many patients seek alternatives and/or complementary care to conventional anxiety treatments. To date, no study has evaluated the potential of a naturopathic treatment protocol to effectively treat anxiety. Knowledge of the efficacy, safety or risk of natural health products, and naturopathic treatments is important for physicians and the public in order to make informed decisions. INTERPRETATION: Both NC and PT led to significant improvements in patients' anxiety. Group comparison demonstrated a significant decrease in anxiety levels in the NC group over the PT group. Significant improvements in secondary quality of life measures were also observed in the NC group as compared to PT. The whole system of naturopathic care for anxiety needs to be investigated further including a closer examination of the individual components within the context of their additive effect. TRIAL REGISTRATION: Controlled-Trials.com ISRCTN78958974

Clinical and laboratory phenotypes in juvenile-onset Systemic Lupus Erythematosus across ethnicities in the UK.

Funder: LUPUS UKSystemic lupus erythematosus (SLE) is a systemic autoimmune/inflammatory disease. Patients diagnosed with juvenile-onset SLE (jSLE), when compared to individuals with adult-onset SLE, develop more severe organ involvement, increased disease activity and greater tissue and organ damage. In adult-onset SLE, clinical characteristics, pathomechanisms, disease progression and outcomes do not only vary between individuals and age groups, but also ethnicities. However, in children and young people, the influence of ethnicity on disease onset, phenotype and outcome has not been investigated in detail. In this study, we investigated clinical and laboratory characteristics in pediatric SLE patients from different ethnic backgrounds (White Caucasian, Asian, Black African/Caribbean) accessing data from a national cohort of jSLE patients (the UK JSLE Cohort Study). Among jSLE patients in the UK, ethnicity affects both the disease's clinical course and outcomes. At diagnosis, Black African/Caribbean jSLE patients show more "classical" laboratory and clinical features when compared to White Caucasian or Asian patients. Black African/Caribbean jSLE patients exhibit more renal involvement and more frequently receive cyclophosphamide and rituximab. Studies targeting ethnicity-specific contributors to disease expression and phenotypes are necessary to improve our pathophysiological understanding, diagnosis and treatment of jSLE

Clinical and laboratory phenotypes in juvenile-onset Systemic Lupus Erythematosus across ethnicities in the UK.

Funder: LUPUS UKSystemic lupus erythematosus (SLE) is a systemic autoimmune/inflammatory disease. Patients diagnosed with juvenile-onset SLE (jSLE), when compared to individuals with adult-onset SLE, develop more severe organ involvement, increased disease activity and greater tissue and organ damage. In adult-onset SLE, clinical characteristics, pathomechanisms, disease progression and outcomes do not only vary between individuals and age groups, but also ethnicities. However, in children and young people, the influence of ethnicity on disease onset, phenotype and outcome has not been investigated in detail. In this study, we investigated clinical and laboratory characteristics in pediatric SLE patients from different ethnic backgrounds (White Caucasian, Asian, Black African/Caribbean) accessing data from a national cohort of jSLE patients (the UK JSLE Cohort Study). Among jSLE patients in the UK, ethnicity affects both the disease's clinical course and outcomes. At diagnosis, Black African/Caribbean jSLE patients show more "classical" laboratory and clinical features when compared to White Caucasian or Asian patients. Black African/Caribbean jSLE patients exhibit more renal involvement and more frequently receive cyclophosphamide and rituximab. Studies targeting ethnicity-specific contributors to disease expression and phenotypes are necessary to improve our pathophysiological understanding, diagnosis and treatment of jSLE

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong