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

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

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster

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

An embedding of ℂ in ℂ 2 with hyperbolic complement

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46249/1/208_2005_Article_BF01445264.pd

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

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

The individual-cell-based cryo-chip for the cryopreservation, manipulation and observation of spatially identifiable cells. I: Methodology

<p>Abstract</p> <p>Background</p> <p>Cryopreservation is the only widely applicable method of storing vital cells for nearly unlimited periods of time. Successful cryopreservation is essential for reproductive medicine, stem cell research, cord blood storage and related biomedical areas. The methods currently used to retrieve a specific cell or a group of individual cells with specific biological properties after cryopreservation are quite complicated and inefficient.</p> <p>Results</p> <p>The present study suggests a new approach in cryopreservation, utilizing the Individual Cell-based Cryo-Chip (i3C). The i3C is made of materials having appropriate durability for cryopreservation conditions. The core of this approach is an array of picowells, each picowell designed to maintain an individual cell during the severe conditions of the freezing - thawing cycle and accompanying treatments. More than 97% of cells were found to retain their position in the picowells throughout the entire freezing - thawing cycle and medium exchange. Thus the comparison between pre-freezing and post-thawing data can be achieved at an individual cell resolution. The intactness of cells undergoing slow freezing and thawing, while residing in the i3C, was found to be similar to that obtained with micro-vials. However, in a fast freezing protocol, the i3C was found to be far superior.</p> <p>Conclusions</p> <p>The results of the present study offer new opportunities for cryopreservation. Using the present methodology, the cryopreservation of individual identifiable cells, and their observation and retrieval, at an individual cell resolution become possible for the first time. This approach facilitates the correlation between cell characteristics before and after the freezing - thawing cycle. Thus, it is expected to significantly enhance current cryopreservation procedures for successful regenerative and reproductive medicine.</p