A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields

In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of complex numbers [11, page 30]. In this article, we derive from Ax's theorem transcendency results in the context of differential valued exponential fields. In particular, we obtain results for exponential Hardy fields, Logarithmic-Exponential power series fields and Exponential-Logarithmic power series fields.Comment: 6 pages, to appear in Archiv der Mathemati

Turbulence closure with small, local neural networks: Forced two-dimensional and β\beta-plane flows

We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced two-dimensional turbulence on the $\beta$-plane at high Reynolds numbers (Re$\sim$25000) using simple 2-layer Convolutional Neural Networks (CNN) having only O(1000)parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8-10 layers; we obtain stable, accurate, and long-term online or a posteriori solutions at 16X downscaling factors. Our methodology significantly improves training efficiency and speed of online Large Eddy Simulations (LES) runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor. We minimize a loss between the SGS vorticity flux divergence (computed from the high-resolution solver) and that obtained from the CNN-modeled deviatoric stress tensor, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non-local dependence on coarse fields; it also aligns with our physical conception that small-scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2-layer CNN-parameterizations are more likely to be interpretable and generalizable because of their intrinsic low dimensionality.Comment: 27 pages, 13 figure

Incidence and risk factors of exercise-related knee disorders in young adult men

Background: Musculoskeletal disorders and injuries are common causes of morbidity and loss of active, physically demanding training days in military populations. We evaluated the incidence, diagnosis, and risk factors of knee disorders and injuries in male Finnish military conscripts. Methods: The study population comprised 5 cohorts of 1000 men performing their military service, classified according to birth year (1969, 1974, 1979, 1984, and 1989). Follow-up time for each conscript was the individual conscript's full, completed military service period. Data for each man were collected from a standard pre-information questionnaire used by defense force healthcare officials and from all original medical reports of the garrison healthcare centers. Background variables for risk factor analysis included the conscripts' service data, i.e., service class (A, B), length of military service, age, height, weight, body mass index (BMI), underweight, overweight, obesity, smoking habit, education, diseases, injuries, and subjective symptoms. Results: Of the 4029 conscripts, 853 visited healthcare professionals for knee symptoms during their military service, and 103 of these had suffered a knee injury. Independent risk factors for the incidence of knee symptoms were: older age; service class A; overweight (BMI 25.0-29.9 kg/m(2)); smoking habit; comprehensive school education only; and self-reported previous symptoms of the musculoskeletal, respiratory, and gastrointestinal system. The majority of visits to garrison healthcare services due to knee symptoms occurred during the first few months of military service. Knee symptoms were negatively correlated with self-reported mental and behavioral disorders. Conclusions: The present study highlights the frequency of knee disorders and injuries in young men during physically demanding military training. One-fifth of the male conscripts visited defense force healthcare professionals due to knee symptoms during their service period. Independent risk factors for the incidence of knee symptoms during military service were age at military service; military service class A; overweight; smoking habit; comprehensive school education only; and self-reported previous symptoms of the musculoskeletal system, respiratory system, or gastrointestinal system. These risk factors should be considered when planning and implementing procedures to reduce knee disorders and injuries during compulsory military service.Peer reviewe

Practical assessment of neural network applications

This paper reports the initial results of a joint research project carried out by Aston University and Lloyd's Register to develop a practical method of assessing neural network applications. A set of assessment guidelines for neural network applications were developed and tested on two applications. These case studies showed that it is practical to assess neural networks in a statistical pattern recognition framework. However there is need for more standardisation in neural network technology and a wider takeup of good development practice amongst the neural network community

Effect of the ionic liquid [bmim]Cl and high pressure on the activity of cellulase

The effect of the ionic liquid 1-butyl-3-methylimidazolium chloride ([bmim]Cl) and of high pressure on the activity of cellulase from Aspergillus niger were studied separately and in combination. The enzyme activity decreased with increasing concentrations of [bmim]Cl, reaching 50% the value in aqueous buffer with 20% [bmim]Cl. However, when the enzyme is held in 10% [bmim]Cl and is then assayed in 1% [bmim]Cl, it showed only 8% reduction of activity. These results can be explained by the fact that the activity of the enzyme in [bmim]Cl is linearly correlated with the decrease of the thermodynamic water activity (aw). Under pressure the enzyme activity varied from less 60% (at 200MPa) to equal (at 400 MPa), compared to atmospheric pressure. In 10% [bmim]Cl under pressure, cellulase activity is improved compared to atmospheric pressure, varying from equal (at 600 MPa) to 1.7-fold higher (at 100 MPa). This opens the possibility to improve cellulase activity in ionic liquids, and possibly of other enzymes, by carrying out the reaction under pressure

Development of standardized method for the determination of the degradation of nitric oxide (NO) in the air by photocatalytic materials: Inter-laboratory validation tests

International audienceThe need of a uniform experimental procedure for assessing the performance of photocatalytic inorganic materials contained in building materials led the European Committee for Standardization (CEN/TC386/WG2) to elaborate a Technical Specification (TS).Taking into consideration the importance of the effects which will be of possible variations in the implementation of the reference method, parallel photocatalytic tests according to the TS were performed in the current study. 6 European labs were participated in an inter-laboratory exercise where the experiments had to be done in a special design CEN reactor using LED system. The experimental procedure and conditions were taken from the draft TS and were referred to the average irradiance, inlet NO & NO 2 concentration, T o C and RH inside the reactor, flow and reactor net volume. Identical photocatalytic samples were provided to all participants. The results obtained from the 6 labs showed a variation between 18% and 31% on the photocatalytic NO conversion while the mean value was 26%. The corresponding photocatalytic rate was ranged between 2600 μg/m 2 h and 4100 μg/m 2 h presenting a mean value of 3400 μg/m 2 h. The homogeneity of the lamp and the homogeneity of the deposition of TiO 2 are the main factors impacting the results