Continuous Extension Research Articles

On a continuation of quaternionic and octonionic logarithm along curves and the winding number

This paper deals with the problem of finding a continuous extension of the hypercomplex (quaternionic or octonionic) logarithm along (quaternionic or octonionic) paths which avoid the origin. The main difficulty depends upon this fact: while a branch of the complex logarithm can be defined in a small open neighbourhood of a strictly negative real point, no continuous branch of the hypercomplex logarithm can be defined in any open set which contains a strictly negative real point. To overcome this difficulty, we use the logarithmic manifold introduced in [4]: in general, the existence of a lift of a path to this manifold is not guaranteed and, indeed, the problem of lifting a path to the logarithmic manifold is completely equivalent to the problem of finding a continuation of the hypercomplex logarithm along this path.The second part of the paper scrutinizes the existence of a notion of winding number (with respect to the origin) for hypercomplex loops that avoid the origin, even though it is known that the definition of winding number for such loops is not natural in Rn when n is greater than 2. The surprise is that, in the hypercomplex setting, the new definition of winding number introduced in this paper can be given and has full meaning for a large class of hypercomplex loops (untwisted loops with companion that avoid the origin).Finally an original but rather natural notion of homotopy for these hypercomplex loops (the c-homotopy) is presented and it is proved to be suitable to comply with the intrinsic geometrical meaning of the winding number for this class of loops, namely, two such hypercomplex loops are c-homotopic if, and only if, they have the same winding number.

A Continuous Extension of Gene Set Enrichment Analysis Using the Likelihood Ratio Test Statistics Identifies Vascular Endothelial Growth Factor as a Candidate Pathway for Alzheimer's Disease via ITGA5.

Alzheimer's disease (AD) involves brain neuropathologies such as amyloid plaque and hyperphosphorylated tau tangles and is accompanied by cognitive decline. Identifying the biological mechanisms underlying disease onset and progression based on quantifiable phenotypes will help understand disease etiology and devise therapies. Our objective was to identify molecular pathways associated with hallmark AD biomarkers and cognitive status, accounting for variables such as age, sex, education, and APOE genotype. We introduce a pathway-based statistical approach, extending the gene set likelihood ratio test to continuous phenotypes. We first analyzed independently each of the three phenotypes (amyloid-β, tau, cognition) using continuous gene set likelihood ratio tests to account for covariates, including age, sex, education, and APOE genotype. The analysis involved 634 subjects with data available for all three phenotypes, allowing for the identification of common pathways. We identified 14 pathways significantly associated with amyloid-β; 5 associated with tau; and 174 associated with cognition, which showed a larger number of pathways compared to biomarkers. A single pathway, vascular endothelial growth factor receptor binding (VEGF-RB), exhibited associations with all three phenotypes. Mediation analysis showed that among the VEGF-RB family genes, ITGA5 mediates the relationship between cognitive scores and pathological biomarkers. We presented a new statistical approach linking continuous phenotypes, gene expression across pathways, and covariates like sex, age, and education. Our results reinforced VEGF RB2's role in AD cognition and demonstrated ITGA5's significant role in mediating the AD pathology-cognition connection.

Numerical simulation of airflow temperature field and cooling in high temperature coal seam working face

With the continuous extension of coal mining depth, the risk of heat exhaustion from high temperatures gets worse. In this paper, we first identified the main heat sources of the high-temperature coal seam working face. The effects of air supply volume on the temperature evolution of working face were then investigated by numerical simulation. The air supply volume to effectively cool the working face was calculated using a new method, sigma heat difference. A mechanical cooling method, an air cooler in the intake airway, was proposed, and the accuracy of the sigma heat difference method was confirmed through numerical simulation and field measurements. The results show that: (1) The aggregate thermal energy emitted by the heat sources located in the mining working face is 688.2177 kW, with mechanical equipment heat dissipation accounting for the main part; (2) The numerical simulation shows that the temperature of the airflow of the roadway steadily drops as the airflow velocity from the inlet airway increases. Yet extremely high inlet airflow velocities lead to narrower change ranges of the air temperature of the working face; (3) The air supply volume required to effectively cool the working face is determined by the sigma heat difference method to be 1972.2 m3/min, which provides a basis for numerical simulation of inlet air velocity for cooling; (4) The Field measurement and numerical modelling demonstrate that the sigma heat difference method is reasonable. The research conclusions provide theoretical guidance for dealing with heat hazards in coal mining faces.

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

Existence of a Hölder Continuous Extension on Embedded Balls of the 3-Torus for the Periodic Navier Stokes Equations

Uniformly continuous extension in L-uniform convergence tower spaces

Using an extension theorem for continuous mappings between quantale-valued convergence tower spaces that we obtained in a previous paper, we prove an extension theorem for uniformly continuous mappings between quantale-valued uniform convergence spaces. To this end, we define and study suitable uniform diagonal axioms and uniform regularity for quantale-valued uniform convergence tower spaces.

Covering properties of $ C_{p}\left(Y|X\right) $

<abstract><p>Let $ X $ be an infinite Tychonoff space, and $ Y $ be a topological subspace of $ X $. In this paper, we study some covering properties of the subspace $ C_{p}\left(Y|X\right) $ of $ C_{p}\left(Y\right) $ consisting of those functions $ f\in C\left(Y\right) $ which admit a continuous extension to $ X $ equipped with the relative topology of $ C_{p}\left(Y\right) $. Among other results, we show that $ \left(i\right) $ $ C_{p}(Y|X) $ has a fundamental bounded resolution if and only if $ Y $ is countable; when $ X $ is realcompact and $ Y $ is closed in $ X $, we have $ \left(ii\right) $ if $ C_{p}(Y|X) $ admits a resolution of convex compact sets that swallows the local null sequences in $ C_{p}(Y|X) $, then $ Y $ is countable and discrete; $ \left(iii\right) $ if $ C_{p}(Y|X) $ admits a compact resolution that swallows the compact sets, then $ Y $ is also countable and discrete, and, as a corollary, we deduce that $ C_{p}(Y|X) $ admits a compact resolution that swallows the compact sets if and only if $ C_{p}(Y|X) $ is a Polish space. We also prove that $ \left(iv\right) $ for a metrizable space $ X $, $ C_{p}\left(X\right) $ is a quasi-$ \left(LB\right) $-space if and only if $ X $ is $ \sigma $-compact, and hence for a subspace $ Y $ of $ X $, the space $ C_{p}\left(Y|X\right) $ is a quasi-$ \left(LB\right) $-space. We include some examples and observations that answer natural questions raised in this paper.</p></abstract>

Successful Aging: Theoretical Concepts, Determinants, and Interventions

Over the past few decades, the concept of successful aging has become an increasingly relevant topic in various scientific disciplines, including medicine, biology, psychology, sociology, gerontology, and andragogy. On of the main reasons for this is the continuous extension of the average lifespan, resulting in a higher proportion of older individuals in the general population. Consequently, there is a growing need for understand the challenges faced by this age group and to identify factors contributing to successful aging and the preservation of quality of life in old age. While there is still no unanimously adopted definition of successful aging, what is certain is that successful aging is much more than the absence if disease. It represents a holistic concept encopmpassing the physical, mental, emotional, and social well-being of older individuals, resulting from the complex interplay of personal and environmental factors. Therefore, the study of successful aging requires a multdisciplinary approach to gain a deeper understanding of the complexity of this phenomenon, and to develop strategies that support older individuals in living fulfilling and healthy lives. The aim of this paper is to provide theoretically grounded and empirically supported information about successful aging, its determinants, and interventions aimed at improving the quality of life in old age. Furthermore, this work aims to raise awareness of the importance of this topic and stimulate further interest in it, both among proffesionals and the general public.

Time-frequency analysis on flat tori and Gabor frames in finite dimensions

We provide the foundations of a Hilbert space theory for the short-time Fourier transform (STFT) where the flat tori TN2=R2/(Z×NZ)=[0,1]×[0,N] act as phase spaces. We work on an N-dimensional subspace SN of distributions periodic in time and frequency in the dual S0′(R) of the Feichtinger algebra S0(R) and equip it with an inner product. To construct the Hilbert space SN we apply a suitable double periodization operator to S0(R). On SN, the STFT is applied as the usual STFT defined on S0′(R). This STFT is a continuous extension of the finite discrete Gabor transform from the lattice onto the entire flat torus. As such, sampling theorems on flat tori lead to Gabor frames in finite dimensions. For Gaussian windows, one is lead to spaces of analytic functions and the construction allows to prove a necessary and sufficient Nyquist rate type result, which is the analogue, for Gabor frames in finite dimensions, of a well known result of Lyubarskii and Seip-Wallstén for Gabor frames with Gaussian windows and which, for N odd, produces an explicit full spark Gabor frame. The compactness of the phase space, the finite dimension of the signal spaces and our sampling theorem offer practical advantages in some applications. We illustrate this by discussing a problem of current research interest: recovering signals from the zeros of their noisy spectrograms.

A monotone finite volume element scheme for diffusion equations on arbitrary polygonal grids

We develop a monotone finite volume element scheme for the diffusion problem on arbitrary polygonal grids inspired by the scheme in the literature ([35]). The main contributions of this paper include three aspects. Firstly, some auxiliary lines or points are introduced for any polygonal element so that it can be partitioned into two or more triangles, and one novel type of its control volume is concomitantly designed. In this paper, we mainly discuss quadrilateral grids. Secondly, some piecewise linear finite element spaces are imported for the trial spaces. Fictitious elements, continuous extensions and the nonlinear two-point flux idea can all be inherited from the triangular case. Therefore, the monotonicity of the scheme is easily proved only by the assembling of some triangles' element stiff matrices. Thirdly, the agreeable adaptability for distorted grids is completely borned. The strict convexity restriction on the grids can also be removed, the concave or severely distorted polygonal (such as quadrilateral) grids are transformed as the convex and general regular triangles. Finally, numerical results confirm its monotonicity, accuracy and stability.

Toward Morphologic Atlasing of the Human Whole Brain at the Nanoscale

Although no dataset at the nanoscale for the entire human brain has yet been acquired and neither a nanoscale human whole brain atlas has been constructed, tremendous progress in neuroimaging and high-performance computing makes them feasible in the non-distant future. To construct the human whole brain nanoscale atlas, there are several challenges, and here, we address two, i.e., the morphology modeling of the brain at the nanoscale and designing of a nanoscale brain atlas. A new nanoscale neuronal format is introduced to describe data necessary and sufficient to model the entire human brain at the nanoscale, enabling calculations of the synaptome and connectome. The design of the nanoscale brain atlas covers design principles, content, architecture, navigation, functionality, and user interface. Three novel design principles are introduced supporting navigation, exploration, and calculations, namely, a gross neuroanatomy-guided navigation of micro/nanoscale neuroanatomy; a movable and zoomable sampling volume of interest for navigation and exploration; and a nanoscale data processing in a parallel-pipeline mode exploiting parallelism resulting from the decomposition of gross neuroanatomy parcellated into structures and regions as well as nano neuroanatomy decomposed into neurons and synapses, enabling the distributed construction and continual enhancement of the nanoscale atlas. Numerous applications of this atlas can be contemplated ranging from proofreading and continual multi-site extension to exploration, morphometric and network-related analyses, and knowledge discovery. To my best knowledge, this is the first proposed neuronal morphology nanoscale model and the first attempt to design a human whole brain atlas at the nanoscale.

A Summary of Fatal Injury Surveillance Methods in Australian Agriculture and Their Impact on Safety Policies and Practices

ABSTRACT Agriculture is one of the most important and also hazardous industries in Australia. Having a sound knowledge and understanding of the circumstance of injury events is critical to developing evidence-based intervention programs. This paper aims to provide a brief historical snapshot of the development of data systems underpinning the assessment of fatal farm injury in Australia and how it has impacted on safety policy and practice. The first Australian studies used coronial information to explore agricultural fatalities, these studies reviewed paper-based records (in-situ) and collected the information for analysis and reporting. This task was laborious and costly. When the National Coronial Information System (NCIS) was established in 2000, this allowed access to coronial records online. Information provided about the deceased includes demographics, contextual details on the nature of the fatality and autopsy, toxicology, and police reports, as-well-as the coroner’s finding. Information from the NCIS, along with media reports, have been used to develop the farm fatality database. This information has been used to inform the safety goals and targets for farm commodity groups, identify key risks, provide long-term benchmark indicators and underpin the development of prevention materials and training resources. Without accurate, timely, concise and relevant data about injury occurring on farms, there is no evidence to drive policy and practice or to evaluate programs of work. As such, the continued utilization and extension of the NCIS data will prove crucial to further reducing the burden of preventable fatal injuries on Australian farms.

Research on prediction of coal-gas compound dynamic disaster based on ICSA-CNN

With the continuous extension of coal mining into deeper layers, the physical properties and structural characteristics of coal seams and surrounding rocks undergo changes, leading to alterations in corresponding indicator thresholds. This increases the potential risk of coal-gas compound dynamic disasters. In this study, based on data from a specific mine, the iForest and MICE methods were applied for data cleaning. Then, the GRA was used to select influential indicators, and an indicator system for the prediction of coal-gas compound dynamic disasters was established based on iForest-MICE-GRA. Subsequently, A coal-gas compound dynamic disaster prediction model based on ICSA-CNN is constructed by employing CNN from deep learning to establish the model framework and optimizing model hyperparameters through the ICSA. Other models were established for comparative validation, and the ICSA-CNN prediction model developed in this study exhibited the highest accuracy, demonstrating excellent robustness and generalization capabilities. By using the method of ICSA-CNN, this research provides a more reliable decision reference for the prediction and prevention of coal-gas compound dynamic disasters.

CLARA-A3: The third edition of the AVHRR-based CM SAF climate data record on clouds, radiation and surface albedo covering the period 1979 to 2023

Abstract. This paper presents the third edition of The Satellite Application Facility on Climate Monitoring's (CM SAF) cloud, albedo, and surface radiation dataset from advanced very-high-resolution radiometer (AVHRR) data, CLARA-A3. The content of earlier CLARA editions, namely cloud, surface albedo, and surface radiation products, has been extended with two additional surface albedo products (blue- and white-sky albedo), three additional surface radiation products (net shortwave and longwave radiation, and surface radiation budget), and two top of atmosphere radiation budget products (reflected solar flux and outgoing longwave radiation). The record length is extended to 42 years (1979–2020) by also incorporating results from the first version of the advanced very high resolution radiometer imager (AVHRR/1). A continuous extension of the climate data record (CDR) has also been implemented by processing an interim climate data record (ICDR) based on the same set of algorithms but with slightly changed ancillary input data. All products are briefly described together with validation results and intercomparisons with currently existing similar CDRs. The extension of the product portfolio and the temporal coverage of the data record, together with product improvements, is expected to enlarge the potential of using CLARA-A3 for climate change studies and, in particular, studies of potential feedback effects between clouds, surface albedo, and radiation. The CLARA-A3 data record is hosted by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) CM SAF and is freely available at https://doi.org/10.5676/EUM_SAF_CM/CLARA_AVHRR/V003 (Karlsson et al., 2023b).

Research on the application of transformer in computer vision

The Transformer is a deep neural network model that utilizes attention mechanisms to improve model performance. Initially, the Transformer gained significant attention in the field of natural language processing. In recent years, due to continuous improvements and extensions to the Transformer model structure, it has also achieved many important breakthroughs in computer vision(CV) tasks, attracting the interest of many researchers. However, there is a lack of comprehensive review articles on the application and development of the Transformer in computer vision. A summary of the Transformer’s applications and advancements in computer vision is given in this paper. It discusses the Transformer model’s fundamental ideas and organizational framework, and primarily introduces its applications in various fields such as image classification, object detection, and image generation, as well as the superiority of the Transformer+ convolutional neural network(CNN) fusion model. The paper provides a detailed analysis of classic models such as Vision Transformer(ViT), Detection Transformer(DETR) and discusses their strengths, weaknesses, and improvement methods. Finally, the paper summarizes and looks forward to the Transformer’s evolution in computer vision.

On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended (potentially into another phase of the universe) is generally unknown. Both questions have important physical implications. In this paper, we take a closer look at the geometrical structure of inflationary spacetimes and investigate these very questions. We first classify which past inflationary histories have a scalar curvature singularity and which might be extendible and/or non-singular in homogeneous and isotropic cosmology with flat spatial sections. Then, we derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Finally, we show that beyond homogeneity and isotropy, special continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in situations with very special initial conditions.

A linear exponential comonad in s-finite transition kernels and probabilistic coherent spaces

This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonad arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions.A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.

Collaborative evaluation study on 18 candidate diseases for newborn screening in 1.77 million samples.

Analytical and therapeutic innovations led to a continuous but variable extension of newborn screening (NBS) programmes worldwide. Every extension requires a careful evaluation of feasibility, diagnostic (process) quality and possible health benefits to balance benefits and limitations. The aim of this study was to evaluate the suitability of 18 candidate diseases for inclusion in NBS programmes. Utilising tandem mass spectrometry as well as establishing specific diagnostic pathways with second-tier analyses, three German NBS centres designed and conducted an evaluation study for 18 candidate diseases, all of them inherited metabolic diseases. In total, 1 777 264 NBS samples were analysed. Overall, 441 positive NBS results were reported resulting in 68 confirmed diagnoses, 373 false-positive cases and an estimated cumulative prevalence of approximately 1 in 26 000 newborns. The positive predictive value ranged from 0.07 (carnitine transporter defect) to 0.67 (HMG-CoA lyase deficiency). Three individuals were missed and 14 individuals (21%) developed symptoms before the positive NBS results were reported. The majority of tested candidate diseases were found to be suitable for inclusion in NBS programmes, while multiple acyl-CoA dehydrogenase deficiency, isolated methylmalonic acidurias, propionic acidemia and malonyl-CoA decarboxylase deficiency showed some and carnitine transporter defect significant limitations. Evaluation studies are an important tool to assess the potential benefits and limitations of expanding NBS programmes to new diseases.

Experimental study on time-dependent rheological properties and mechanical performance of cemented fine tailings backfill mixed with polypropylene fiber.

By preparing fine tailings slurry with different mass concentration and fiber content, the rheological parameters of slurry with different fiber content and curing time were tested. In addition, the influence law of fiber content and curing time on compressive strength was analyzed through the prepared fine tailings backfill samples, and the microstructure characteristics of fine tailings backfill were further studied. The results show that when the fiber content is 0.2 ~ 1.2%, the yield stress and plastic viscosity of the slurry increase with the increase of fiber content, and the thixotropy of the slurry also shows the same change characteristics. The bridge effect of fiber makes it easier for forming network structure, which increase the slurry rheology. When the curing time ranges from 0h to 2.5h, the increasing of curing time leads to the increasing trend of rheological parameters, and also increases the thixotropy of slurry. However, the increase of rheological parameters will continuously decrease when the curing time exceeds 1h, indicating that the influence of curing time on yield stress and thixotropy will gradually weaken with the continuous extension of curing time. When the curing age increases from 3 to 56days, the compressive strength of the fine tailings backfill increases with the curing age, but the increasing range of compressive strength decreases gradually. When the fiber content ranges from 0.2 to 1.2%, the compressive strength of backfill increases first and then decreases with the increase of fiber content, and reaches the maximum value when the fiber content is 0.6%. The extension of curing time reduces the generation of large-scale pore structure, which promotes the formation of more compact microstructure of backfill.

Measures for waste and by-product recycling and circular economy of whole industry chain of traditional Chinese medicine resources facing carbon peak and carbon neutrality (dual carbon) goals

It has become a common consensus that resource conservation and intensive recycling for improving resource utilization efficiency is an important way to achieve carbon peak and carbon neutrality(dual carbon). Traditonal Chinese medicine(TCM)resources as national strategic resources are the material basis and fundamental guarantee for the development of TCM industry and health services. However, the rapid growth of China's TCM industry and the continuous expansion and extension of the industrial chain have exposed the low efficiency of TCM resources. Resource waste and environmental pollution caused by the treatment and discharge of TCM waste have emerged as major problems faced by the development of the industry, which has aroused wide concern. Considering the dual carbon goals, this paper expounds the role and potential of TCM resource recycling and circular economy industry development. Taking the typical model of TCM resource recycling as the case of circular economy industry in reducing carbon source and increasing carbon sink, this paper puts forward the suggestions for the TCM circular economy industry serving the double carbon goals. The suggestions mainly include strengthening the policy and strategic leading role of the double carbon goals, building an objective evaluation system of low-carbon emission reduction in the whole industrial chain of TCM resources, building an industrial demonstration park for the recycling of TCM resources, and promoting the establishment of a circular economy system of the whole industrial chain of TCM resources. These measures are expected to guide the green transformation of TCM resource industry from linear economic model to circular economy model, provide support for improving the utilization efficiency and sustainable development of TCM resources, and facilitate the low-carbon and efficient development of TCM resource industry and the achievement of the double carbon goals.

Thermo‐Kinematic Constraints on Restoration of the Eastern Sichuan Fold‐And‐Thrust Belt, South China

AbstractKinematic restoration of the eastern Sichuan fold‐and‐thrust belt (ESFTB) in South China is calibrated with a new thermo‐kinematic model combining analog models, discrete element method, and thermochronology data. Thermo‐kinematic analysis provides constraints on the onset, rate, and lateral variation of deformation and exhumation. Results show that the ESFTB experienced a northwestward thrusting and periodic exhumation. Its evolution was characterized by five major stages based on the deformation characteristics; (a) Shortening above a basal decollement and formation of large imbricates separated by narrow synclines during 170–130 Ma; (b) Transition stage during 130–100 Ma; (c) Stepping up of deformation to shallow decollement levels and shaping of the thick‐skinned domain during 100–70 Ma; (d) Shaping of the thin‐skinned domain during 70–20 Ma; and (e) Continuous exhumation and structural modification from 20 Ma to present. The changes in the exhumation rate have been tectonic responses to the subduction retreat of the Paleo‐Pacific Plate and the eastward growth of the Tibetan Plateau. The westward subduction of the Paleo‐Pacific Plate resulted in northwestward shortening across South China, progressive deformation of the ESFTB, and rapid exhumation from the Late Jurassic to the Late Cretaceous. The crustal extension associated with the rollback of the Paleo‐Pacific slab accounted for the Mesozoic exhumation rate decrease until the Miocene. The accelerated cooling of the thin‐skinned domain of the ESFTB since the Miocene was a response to the eastward growth of the Tibetan Plateau, while the continuous slow exhumation in the thick‐skinned domain was related to the continuous crustal extension in South China.