On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Relative validity of a semiquantitative food frequency questionnaire designed for schoolchildren in western Greece

<p>Abstract</p> <p>Background</p> <p>The use of food frequency questionnaires (FFQs) has become increasingly important in epidemiologic studies. During the past few decades, a wide variety of nutritional studies have used the semiquantitative FFQ as a tool for assessing and evaluating dietary intake. One of the main concerns in a dietary analysis is the validity of the collected dietary data.</p> <p>Methods</p> <p>This paper discusses several methodological and statistical issues related to the validation of a semiquantitative FFQ. This questionnaire was used to assess the nutritional habits of schoolchildren in western Greece. For validation purposes, we selected 200 schoolchildren and contacted their respective parents. We evaluated the relative validity of 400 FFQs (200 children's FFQs and 200 parents' FFQs).</p> <p>Results</p> <p>The correlations between the children's and the parents' questionnaire responses showed that the questionnaire we designed was appropriate for fulfilling the purposes of our study and in ranking subjects according to food group intake.</p> <p>Conclusion</p> <p>Our study shows that the semiquantitative FFQ provides a reasonably reliable measure of dietary intake and corroborates the relative validity of our questionnaire.</p

Development of a food frequency questionnaire to estimate habitual dietary intake in Japanese children

<p>Abstract</p> <p>Background</p> <p>Food frequency questionnaires (FFQ) are used for epidemiological studies. Because of the wide variations in dietary habits within different populations, a FFQ must be developed to suit the specific group. To date, no FFQ has been developed for Japanese children. In this study, we developed a FFQ to assess the regular dietary intake of Japanese children. The FFQ included questions regarding both individual food items and mixed dishes.</p> <p>Methods</p> <p>Children (3-11 years of age, n = 621) were recruited as subjects. Their parents or guardians completed a weighed dietary record (WDR) for each subject in one day. We defined FOOD to be not only as a single food item but also as a mixed dish. The dieticians conceptually grouped similar FOODs as FOOD types. We used a contribution analysis and a multiple regression analysis to select FOOD types.</p> <p>Results</p> <p>We obtained a total of 586 children's dietary data (297 boys and 289 girls). In addition, we obtained 1,043 FOODs. Dieticians grouped into similar FOODs, yielding 275 FOOD types. A total of 115 FOOD types were chosen using a contribution analysis and a multiple regression analysis, then we excluded overlapping items. FOOD types that were eaten by fewer than 15 subjects were excluded; 74 FOOD types remained. We also added liver-based dishes that provided a high amount of retinol. A total of 75 FOOD types were finally determined for the FFQ. The frequency response formats were classified into four type categories: seven, eight, nine and eleven, according to the general intake frequency of each FOOD type. Information on portion size was obtained from the photographs of each listed FOOD type in real scale size, which was the average amount of the children's portion sizes.</p> <p>Conclusions</p> <p>Using both a contribution analysis and a multiple regression analysis, we developed a 75-food item questionnaire from the study involving 586 children. The next step will involve the verification of FFQ reproducibility and validity.</p

Longitudinal machine learning modeling of MS patient trajectories improves predictions of disability progression

Background and Objectives: Research in Multiple Sclerosis (MS) has recently focused on extracting knowledge from real-world clinical data sources. This type of data is more abundant than data produced during clinical trials and potentially more informative about real-world clinical practice. However, this comes at the cost of less curated and controlled data sets. In this work we aim to predict disability progression by optimally extracting information from longitudinal patient data in the real-world setting, with a special focus on the sporadic sampling problem. Methods: We use machine learning methods suited for patient trajectories modeling, such as recurrent neural networks and tensor factorization. A subset of 6682 patients from the MSBase registry is used. Results: We can predict disability progression of patients in a two-year horizon with an ROC-AUC of 0.85, which represents a 32% decrease in the ranking pair error (1-AUC) compared to reference methods using static clinical features. Conclusions: Compared to the models available in the literature, this work uses the most complete patient history for MS disease progression prediction and represents a step forward towards AI-assisted precision medicine in MS

Identification of IKr Kinetics and Drug Binding in Native Myocytes

Determining the effect of a compound on IKr is a standard screen for drug safety. Often the effect is described using a single IC50 value, which is unable to capture complex effects of a drug. Using verapamil as an example, we present a method for using recordings from native myocytes at several drug doses along with qualitative features of IKr from published studies of HERG current to estimate parameters in a mathematical model of the drug effect on IKr. IKr was recorded from canine left ventricular myocytes using ruptured patch techniques. A voltage command protocol was used to record tail currents at voltages from −70 to −20 mV, following activating pulses over a wide range of voltages and pulse durations. Model equations were taken from a published IKr Markov model and the drug was modeled as binding to the open state. Parameters were estimated using a combined global and local optimization algorithm based on collected data with two additional constraints on IKrI–V relation and IKr inactivation. The method produced models that quantitatively reproduce both the control IKr kinetics and dose dependent changes in the current. In addition, the model exhibited use and rate dependence. The results suggest that: (1) the technique proposed here has the practical potential to develop data-driven models that quantitatively reproduce channel behavior in native myocytes; (2) the method can capture important drug effects that cannot be reproduced by the IC50 method. Although the method was developed for IKr, the same strategy can be applied to other ion channels, once appropriate channel-specific voltage protocols and qualitative features are identified