Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

RyR1-targeted drug discovery pipeline integrating FRET-based high-throughput screening and human myofiber dynamic Ca2+ assays.

Elevated cytoplasmic [Ca2+] is characteristic in severe skeletal and cardiac myopathies, diabetes, and neurodegeneration, and partly results from increased Ca2+ leak from sarcoplasmic reticulum stores via dysregulated ryanodine receptor (RyR) channels. Consequently, RyR is recognized as a high-value target for drug discovery to treat such pathologies. Using a FRET-based high-throughput screening assay that we previously reported, we identified small-molecule compounds that modulate the skeletal muscle channel isoform (RyR1) interaction with calmodulin and FK506 binding protein 12.6. Two such compounds, chloroxine and myricetin, increase FRET and inhibit [3H]ryanodine binding to RyR1 at nanomolar Ca2+. Both compounds also decrease RyR1 Ca2+ leak in human skinned skeletal muscle fibers. Furthermore, we identified compound concentrations that reduced leak by > 50% but only slightly affected Ca2+ release in excitation-contraction coupling, which is essential for normal muscle contraction. This report demonstrates a pipeline that effectively filters small-molecule RyR1 modulators towards clinical relevance

On the Universality of Linear Recurrences Followed by Nonlinear Projections

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.Comment: Accepted at HLD 2023: 1st Workshop on High-dimensional Learning Dynamic

Unmodifiable variables related to thyroid cancer incidence

The incidence of thyroid cancer is significantly different between male and female patients. Thyroid cancer is also the only form of cancer where age can be considered a staging variable. Identifying biological prognostic factors such as age or sex is important as it helps select an optimal personalized therapy. The present analysis is an observational, prospective study that enrolled all patients with thyroid disease who were operated upon at a single center. The study aimed to determine the most frequent age at presentation, the predominance of one sex over the other, the incidence of malignant thyroid disease, and the relative risk for each sex to develop thyroid carcinoma. The incidence of thyroid carcinoma was higher for women than for men, with a higher relative risk in the female subgroup. Incidence was also highest in the 50-60-year-old group. Given that studies show better survival for women and for younger patients, even when presenting with advanced disease, compared with older, male patients, such prognostic indicators should be a factor in the treatment decision

Does sex of the patient play a role in survival for MSI colorectal cancer?

Microsatellite instability (MSI) is a feature of colorectal tumors that develops as a result of inactivation of the DNA mismatch repair system. It is found in about 15% of all colorectal cancers and is an important prognostic molecular marker when assessing patients with colorectal cancer. It can influence prognosis and treatment decisions in both the advanced and early stages. Although in early stages this marker suggests a favorable prognosis and presents an important argument against adjuvant treatment in stage II disease, in metastatic stages it no longer associated with such an optimistic outcome. The present trial is a prospective, single-center study which included 122 colorectal cancer patients who were tested for MSI using immunohistochemistry. The trial included patients with stage II to IV colorectal cancer, treated in the Prof. Dr. Agrippa Ionescu Emergency Hospital, Bucharest, Romania. Follow-up data were collected during a 24-month period. The study attempted to determine whether differences exist in overall survival for MSI (microsatellite instability) vs. MSS (microsatellite stable) colorectal cancer and to ascertain whether sex of the patient influences prognosis in MSI patients, irrespective of stage or treatment. Results demonstrated no significant differences in survival for MSI vs MSS colorectal patients, and patients’ gender proved not to influence the outcome in MSI patients

Disease Knowledge Transfer across Neurodegenerative Diseases

We introduce Disease Knowledge Transfer (DKT), a novel technique for transferring biomarker information between related neurodegenerative diseases. DKT infers robust multimodal biomarker trajectories in rare neurodegenerative diseases even when only limited, unimodal data is available, by transferring information from larger multimodal datasets from common neurodegenerative diseases. DKT is a joint-disease generative model of biomarker progressions, which exploits biomarker relationships that are shared across diseases. Our proposed method allows, for the first time, the estimation of plausible, multimodal biomarker trajectories in Posterior Cortical Atrophy (PCA), a rare neurodegenerative disease where only unimodal MRI data is available. For this we train DKT on a combined dataset containing subjects with two distinct diseases and sizes of data available: 1) a larger, multimodal typical AD (tAD) dataset from the TADPOLE Challenge, and 2) a smaller unimodal Posterior Cortical Atrophy (PCA) dataset from the Dementia Research Centre (DRC), for which only a limited number of Magnetic Resonance Imaging (MRI) scans are available. Although validation is challenging due to lack of data in PCA, we validate DKT on synthetic data and two patient datasets (TADPOLE and PCA cohorts), showing it can estimate the ground truth parameters in the simulation and predict unseen biomarkers on the two patient datasets. While we demonstrated DKT on Alzheimer's variants, we note DKT is generalisable to other forms of related neurodegenerative diseases. Source code for DKT is available online: https://github.com/mrazvan22/dkt.Comment: accepted at MICCAI 2019, 13 pages, 5 figures, 2 table

Carbon Speciation and Solubility in Silicate Melts

To improve our understanding of the Earth's global carbon cycle, it is critical to characterize the distribution and storage mechanisms of carbon in silicate melts. Presently, the carbon budget of the deep Earth is not well constrained and is highly model-dependent. In silicate melts of the uppermost mantle, carbon exists predominantly as molecular carbon dioxide and carbonate, whereas at greater depths, carbon forms complex polymerized species. The concentration and speciation of carbon in silicate melts is intimately linked to the melt's composition and affects its physical and dynamic properties. Here we review the results of experiments and calculations on the solubility and speciation of carbon in silicate melts as a function of pressure, temperature, composition, polymerization, water concentration, and oxygen fugacity

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure