On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

HierarchyNet : learning to summarize source code with heterogeneous representations

Code representation is important to machine learning models in the code-related applications. Existing code summarization approaches primarily leverage Abstract Syntax Trees (ASTs) and sequential information from source code to generate code summaries while often overlooking the critical consideration of the interplay of dependencies among code elements and code hierarchy. However, effective summarization necessitates a holistic analysis of code snippets from three distinct aspects: lexical, syntactic, and semantic information. In this paper, we propose a novel code summarization approach utilizing Heterogeneous Code Representations (HCRs) and our specially designed HierarchyNet. HCRs adeptly capture essential code features at lexical, syntactic, and semantic levels within a hierarchical structure. HierarchyNet processes each layer of the HCR separately, employing a Heterogeneous Graph Transformer, a Tree-based CNN, and a Transformer Encoder. In addition, HierarchyNet demonstrates superior performance compared to fine-tuned pre-trained models, including CodeT5, and CodeBERT, as well as large language models that employ zero/few-shot settings, such as CodeLlama, StarCoder, and CodeGen. Implementation details can be found at https://github.com/FSoft-AI4Code/HierarchyNet

Adding marrow adiposity and cortical porosity to femoral neck areal bone mineral density improves the discrimination of women with nonvertebral fractures from controls

Advancing age is accompanied by a reduction in bone formation and remodeling imbalance, which produces microstructural deterioration. This may be partly caused by a diversion of mesenchymal cells towards adipocytes rather than osteoblast lineage cells. We hypothesized that microstructural deterioration would be associated with an increased marrow adiposity, and each of these traits would be independently associated with nonvertebral fractures and improve discrimination of women with fractures from controls over that achieved by femoral neck (FN) areal bone mineral density (aBMD) alone. The marrow adiposity and bone microstructure were quantified from HR‐pQCT images of the distal tibia and distal radius in 77 women aged 40 to 70 years with a recent nonvertebral fracture and 226 controls in Melbourne, Australia. Marrow fat measurement from HR‐pQCT images was validated using direct histologic measurement as the gold standard, at the distal radius of 15 sheep, with an agreement (R2 = 0.86, p < 0.0001). Each SD higher distal tibia marrow adiposity was associated with 0.33 SD higher cortical porosity, and 0.60 SD fewer, 0.24 SD thinner, and 0.72 SD more‐separated trabeculae (all p < 0.05). Adjusted for age and FN aBMD, odds ratios (ORs) (95% CI) for fracture per SD higher marrow adiposity and cortical porosity were OR, 3.39 (95% CI, 2.14 to 5.38) and OR, 1.79 (95% CI, 1.14 to 2.80), respectively. Discrimination of women with fracture from controls improved when cortical porosity was added to FN aBMD and age (area under the receiver‐operating characteristic curve [AUC] 0.778 versus 0.751, p = 0.006) or marrow adiposity was added to FN aBMD and age (AUC 0.825 versus 0.751, p = 0.002). The model including FN aBMD, age, cortical porosity, trabecular thickness, and marrow adiposity had an AUC = 0.888. Results were similar for the distal radius. Whether marrow adiposity and cortical porosity indices improve the identification of women at risk for fractures requires validation in prospective studies. © 2019 American Society for Bone and Mineral Research

The Spectrum of Neurological and White Matter Changes and Premutation Status Categories of Older Male Carriers of the FMR1 Alleles Are Linked to Genetic (CGG and FMR1 mRNA) and Cellular Stress (AMPK) Markers

The fragile X premutation (PM) allele contains a CGG expansion of 55–200 repeats in the FMR1 gene’s promoter. Male PM carriers have an elevated risk of developing neurological and psychiatric changes, including an approximately 50% risk of the fragile X-associated tremor/ataxia syndrome (FXTAS). The aim of this study was to assess the relationships of regional white matter hyperintensities (wmhs) semi-quantitative scores, clinical status, motor (UPDRS, ICARS, Tremor) scales, and cognitive impairments, with FMR1-specific genetic changes, in a sample of 32 unselected male PM carriers aged 39–81 years. Half of these individuals were affected with FXTAS, while the non-FXTAS group comprised subcategories of non-affected individuals and individuals affected with non-syndromic changes. The dynamics of pathological processes at the cellular level relevant to the clinical status of PM carriers was investigated using the enzyme AMP-activated protein kinase (AMPK), which is a highly sensitive cellular stress-sensing alarm protein. This enzyme, as well as genetic markers – CGG repeat number and the levels of the FMR1 mRNA – were assessed in blood lymphoblasts. The results showed that the repeat distribution for FXTAS individuals peaked at 85–90 CGGs; non-FXTAS carriers were distributed within the lowest end of the PM repeat range, and non-syndromic carriers assumed an intermediate position. The size of the CGG expansion was significantly correlated, across all three categories, with infratentorial and total wmhs and with all motor scores, and the FMR1 mRNA levels with all the wmh scores, whilst AMPK activity showed considerable elevation in the non-FXTAS combined group, decreasing in the FXTAS group, proportionally to increasing severity of the wmhs and tremor/ataxia. We conclude that the size of the CGG expansion relates to the risk for FXTAS, to severity of infratentorial wmhs lesions, and to all three motor scale scores. FMR1 mRNA shows a strong association with the extent of wmhs, which is the most sensitive marker of the pathological process. However, the AMPK activity findings – suggestive of a role of this enzyme in the risk of FXTAS – need to be verified and expanded in future studies using larger samples and longitudinal assessment

Software development offshoring competitiveness: A case study of ASEAN countries

With the success of offshoring within the American software industry, corporate executives are moving their software developments overseas. The member countries of the Association of Southeast Asian Nations (ASEAN) have become a preferred destination. However, there is a lack of published studies on the region's software competitiveness in comparison to other offshoring countries. This research uses five country factors identified by subject-matter experts to compare the ASEAN's software offshoring competitiveness against 25 selected countries in the world. It analyzes the region's competitiveness from various perspectives such as Government vision and policy, Information and Communication Technology (ICT) Industry's global maturity, Information and Communication Technology framework, Wages, and Human Capital development. The findings are relevant for Western countries looking to partner with ASEAN countries for software offshoring purpose

Learning to Represent Programs with Code Hierarchies

When used to process source code, graph neural networks have been shown to produce impressive results for a wide range of software engineering tasks. Existing techniques, however, still have two issues: (1) long-term dependency and (2) different code components are treated as equals when they should not be. To address these issues, we propose a method for representing code as a hierarchy (Code Hierarchy), in which different code components are represented separately at various levels of granularity. Then, to process each level of representation, we design a novel network architecture, HIRGAST, which combines the strengths of Heterogeneous Graph Transformer Networks and Tree-based Convolutional Neural Networks to learn Abstract Syntax Trees enriched with code dependency information. We also propose a novel pretraining objective called Missing Subtree Prediction to complement our Code Hierarchy. The evaluation results show that our method significantly outperforms other baselines in three downstream tasks: any-code completion, code classification, and code clone detection