Convergence, Finiteness and Periodicity of Several New Algorithms of p-adic Continued Fractions

$p$-adic continued fractions, as an extension of the classical concept of classical continued fractions to the realm of $p$-adic numbers, offering a novel perspective on number representation and approximation. While numerous $p$-adic continued fraction expansion algorithms have been proposed by the researchers, the establishment of several excellent properties, such as the Lagrange Theorem for classic continued fractions, which indicates that every quadratic irrationals can be expanded periodically, remains elusive. In this paper, we present several new algorithms that can be viewed as refinements of the existing $p$-adic continued fraction algorithms. We give an upper bound of the length of partial quotients when expanding rational numbers, and prove that for small primes $p$, our algorithm can generate periodic continued fraction expansions for all quadratic irrationals. As confirmed through experimentation, one of our algorithms can be viewed as the best $p$-adic algorithm available to date. Furthermore, we provide an approach to establish a $p$-adic continued fraction expansion algorithm that could generate periodic expansions for all quadratic irrationals in $\mathbb{Q}_p$ for a given prime $p$

Graph Transformer Network for Flood Forecasting with Heterogeneous Covariates

Floods can be very destructive causing heavy damage to life, property, and livelihoods. Global climate change and the consequent sea-level rise have increased the occurrence of extreme weather events, resulting in elevated and frequent flood risk. Therefore, accurate and timely flood forecasting in coastal river systems is critical to facilitate good flood management. However, the computational tools currently used are either slow or inaccurate. In this paper, we propose a Flood prediction tool using Graph Transformer Network (FloodGTN) for river systems. More specifically, FloodGTN learns the spatio-temporal dependencies of water levels at different monitoring stations using Graph Neural Networks (GNNs) and an LSTM. It is currently implemented to consider external covariates such as rainfall, tide, and the settings of hydraulic structures (e.g., outflows of dams, gates, pumps, etc.) along the river. We use a Transformer to learn the attention given to external covariates in computing water levels. We apply the FloodGTN tool to data from the South Florida Water Management District, which manages a coastal area that is prone to frequent storms and hurricanes. Experimental results show that FloodGTN outperforms the physics-based model (HEC-RAS) by achieving higher accuracy with 50% improvement while speeding up run times by at least 500x

Hybrid high-order methods for elliptic PDEs on curved and complicated domains

International audienceWe introduce a variant of the hybrid high-order method (HHO) employing Nitsche’s boundary penalty techniques for the Poisson problem on the curved and complicated Lipschitz domain. The proposed method has two advantages: Firstly, there are no face unknowns introduced on the boundary of the domain, which avoids the computation of the parameterized mapping for the face unknowns on the curved domain boundary. Secondly, using Nitsche’s boundary penalty techniques for weakly imposing Dirichlet boundary conditions one can obtain the stability and optimal error estimate independent of the number and measure of faces on the domain boundary. Finally, a numerical experiment is presented in this chapter to confirm the theoretical results

Ataxia-telangiectasia in China: a case report of a novel ATM variant and literature review

BackgroundAtaxia-telangiectasia (A-T) is a multisystem genetic disorder involving ataxia, oculocutaneous telangiectasia, and immunodeficiency caused by biallelic pathogenic variants in the ATM gene. To date, most ATM variants have been reported in the Caucasian population, and few studies have focused on the genotype–phenotype correlation of A-T in the Chinese population. We herein present a Chinese patient with A-T who carries compound heterozygous variants in the ATM gene and conducted a literature review for A-T in China.Case presentationA 7-year-old Chinese girl presented with growth retardation, ataxia, medium ocular telangiectasia, cerebellar atrophy, and elevated serum alpha-fetoprotein (AFP) level, which supported the suspicion of A-T. Notably, the serum levels of immunoglobulins were all normal, ruling out immunodeficiency. Exome sequencing and Sanger sequencing revealed two likely pathogenic ATM variants, namely NM_000051.4: c.4195dup (p.Thr1399Asnfs*15) and c.6006 + 1G>T (p.?), which were inherited from her father and mother, respectively. From the Chinese literature review, we found that there was a marked delay in the diagnosis of A-T, and 38.9% (7/18) of A-T patients did not suffer from immunodeficiency in China. No genotype–phenotype correlation was observed in this group of A-T patients.ConclusionThese results extend the genotype spectrum of A-T in the Chinese population and imply that the diagnosis of A-T in China should be improved

MemDA: Forecasting Urban Time Series with Memory-based Drift Adaptation

Urban time series data forecasting featuring significant contributions to sustainable development is widely studied as an essential task of the smart city. However, with the dramatic and rapid changes in the world environment, the assumption that data obey Independent Identically Distribution is undermined by the subsequent changes in data distribution, known as concept drift, leading to weak replicability and transferability of the model over unseen data. To address the issue, previous approaches typically retrain the model, forcing it to fit the most recent observed data. However, retraining is problematic in that it leads to model lag, consumption of resources, and model re-invalidation, causing the drift problem to be not well solved in realistic scenarios. In this study, we propose a new urban time series prediction model for the concept drift problem, which encodes the drift by considering the periodicity in the data and makes on-the-fly adjustments to the model based on the drift using a meta-dynamic network. Experiments on real-world datasets show that our design significantly outperforms state-of-the-art methods and can be well generalized to existing prediction backbones by reducing their sensitivity to distribution changes.Comment: Accepted by CIKM 202

Public-key Cryptosystems and Signature Schemes from p-adic Lattices

In 2018, the longest vector problem and closest vector problem in local fields were introduced, as the p-adic analogues of the shortest vector problem and closest vector problem in lattices of Euclidean spaces. They are considered to be hard and useful in constructing cryptographic primitives, but no applications in cryptography were given. In this paper, we construct the first signature scheme and public-key encryption cryptosystem based on p-adic lattice by proposing a trapdoor function with the orthogonal basis of p-adic lattice. These cryptographic schemes have reasonable key size and efficiency, which shows that p-adic lattice can be a new alternative to construct cryptographic primitives and well worth studying

MegaCRN: Meta-Graph Convolutional Recurrent Network for Spatio-Temporal Modeling

Spatio-temporal modeling as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the underlying heterogeneity and non-stationarity implied in the graph streams, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (METR-LA and PEMS-BAY) and a large-scale spatio-temporal dataset that contains a variaty of non-stationary phenomena. Our model outperformed the state-of-the-arts to a large degree on all three datasets (over 27% MAE and 34% RMSE). Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle locations and time slots with different patterns and be robustly adaptive to different anomalous situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.Comment: Preprint submitted to Artificial Intelligence. arXiv admin note: substantial text overlap with arXiv:2211.1470

Advanced manufacturing process design for Mesenchymal Stromal Cell therapies

For decades, the potential immunomodulatory effects of Mesenchymal Stromal Cells (MSCs) have prompted numerous cell-therapy clinical investigations targeting various diseases such as graft-versus-host disease and autoimmune diseases. Despite their ubiquitous usage in clinical trials, significant challenges related to their manufacturing and biological variabilities have led to poorly reproducible outcomes of therapeutic efficacy. Therefore, identification of validated critical quality attributes (CQAs) correlative to therapeutic function is of great interest to the MSC community. Such CQAs would also permit identification of critical process parameters (CPPs) to achieve and maintain MSC quality while producing a high yield. In this study, we designed and tested a “smart” feedback-controlled hollow fiber-based bioreactor for maintaining nutrient and waste levels for human umbilical cord tissue-derived MSC expansions. The bioreactor platform is a semi-autonomous system complete with in-line sensors, modeling, data-driven controllers, and an automated sampling platform. The small-scale system reduced costs, labor, time, and perturbations and improved yields of MSC products using a hollow fiber cartridge that closely models the basic design of the large-scale Quantum Cell Expansion System. Our feedback-controlled bioreactor responded to in-line glucose and lactate levels while recorded pH and dissolved oxygen measurements. This information was fed into a controller, which auto-calculates cell growth rates based on our developed mathematical model, and subsequently regulated media feed rates to support cell growth and nutrient requirements. Compared to the manual expansion process, the automated expansion processes showed higher yields and comparative therapeutic potency of MSCs, indicated by indolamine 2,3-dioxygenase assay and T cell proliferation assay. Future directions of our study propose to correlate metabolites and secreted proteins in culture media as putative CQAs that can be used as in-line predictors of MSC yield and therapeutic potency. Moreover, we aim to maintain a metabolic and secretory profile throughout MSC expansions enabled by real-time modulation of CPPs and scale up of the “smart” bioreactor. The proposed bioprocess for MSC products can be adapted and applied to industrial cell therapy manufacturing and can enable high-yield and high-quality products while minimizing variabilities. Please click Additional Files below to see the full abstract