Limit Point Research Articles

Limit points of (signless) Laplacian spectral radii of linear trees

We study limit points of the spectral radii of Laplacian matrices of graphs. We adapted the method used by J. B. Shearer in 1989, devised to prove the density of adjacency limit points of caterpillars, to Laplacian limit points. We show that this fails, in the sense that there is an interval for which the method produces no limit points. Then we generalize the method to Laplacian limit points of linear trees and prove that it generates a larger set of limit points. The results of this manuscript may provide important tools for proving the density of Laplacian limit points in [4.38+,∞).

Journey over Destination: Dynamic Sensor Placement Enhances Generalization

Abstract Reconstructing complex, high-dimensional global fields from limited data points is a challenge across various scientific and industrial domains. This is particularly important for recovering spatio-temporal fields using sensor data from, for example, laboratory-based scientific experiments, weather forecasting, or drone surveys. Given the prohibitive costs of specialized sensors and the inaccessibility of
certain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of machine learning algorithms trained to reconstruct fields given a limited dataset is of critical importance. In this study, we introduce a general
approach that employs moving sensors to enhance data exploitation during the training of an attention based neural network, thereby improving field reconstruction. The training of sensor locations is accomplished using an end-to-end workflow, ensuring
differentiability in the interpolation of field values associated to the sensors, and is simple to implement using differentiable programming. Additionally, we have incorporated a correction mechanism to prevent sensors from entering invalid regions within the domain. We evaluated our method using two distinct datasets; the results show that our approach enhances learning, as evidenced by improved test scores.

P38 Experimental evidence of ecto-5′-nucleotidase (CD73) modulation in psoriasis-like inflammation

Abstract Introduction and aims Adenosine is an endogenous purine nucleoside that, by binding to adenosine receptors, modulates inflammation and immune responses. Psoriasis is a chronic immune-mediated inflammatory skin disease characterized by keratinocyte hyperproliferation and abnormal differentiation. A2A and A2B adenosine receptors modulate keratinocyte proliferation and their expression was found to be altered in psoriatic epidermis. Ecto-5′-nucleotidase (CD73) is an enzyme that hydrolyses extracellular adenosine monophosphate and represents a key control point for extracellular adenosine accumulation. CD73 is involved in the regulation of local immune response and tissue barrier function. As changes in CD73 expression and activity have been associated with other autoimmune diseases, the aim of this study was to investigate CD73 involvement in skin inflammation using in vitro and in vivo approaches. Methods In vitro experiments were performed on human keratinocyte (HaCaT) cell lines stimulated with tumour necrosis factor-α, interleukin (IL)-17A, IL-6 and IL-1α (10 ng mL−1 each), and in vivo, on the mouse model of imiquimod-induced psoriasis-like inflammation on the right ear, which was also performed on CD73−/− mice and their wildtype counterpart. CD73 expression in cell lysates and ear homogenates were evaluated using Western blot analysis. Results We found that CD73 expression was significantly increased (N = 3 wells, P < 0.05) in cytokine-treated HaCaTs compared with unstimulated cells. In vivo experiments showed increased CD73 expression on psoriatic lesions (P < 0.001, N = 3). In CD73−/− mice, imiquimod-induced lesions were exacerbated compared with the development of lesions in wildtype mice as shown by ear thickness (0.190 ± 0.02 mm, knockout mice vs. 0.138 ± 0.02 mm, wildtype mice; P < 0.05, N = 5), erythema and scaling. Conclusions Our preliminary Results show involvement of CD73 in the development of psoriasis-like inflammation, suggesting that CD73 may represent a new therapeutic target in the treatment of skin diseases. Further investigations are needed to provide an in-depth study of CD73 localization in inflamed skin.

Periodic Behaviour of General Systems

A continuous function on the product of compact metric spaces to itself and back to the same space is known as a genera system. Where each element's orbit is an infinite sequence and where the first two elements are the same as given and next to it depends on the two elements prior to it form stronger conditions for the orbit. We could define an m-step dynamical system by extending the definition of a compact metric space to its m-times product. Because the system's current state frequently depends directly on the conditions of previous terms, this system appears more realistic. The basic theorems regarding periodic points and their related points, such as fixed point, limit points, recurrent points, will be proved in this paper. We also define the topological transitivity and its properties. In the end we find periodic points with periods one and two for affine maps and periodicity of tent map in dynamical system and generalised dynamical system.

Convergence of the numerical approximations and well-posedness: Nonlocal conservation laws with rough flux

We study a class of nonlinear nonlocal conservation laws with discontinuous flux, modeling crowd dynamics and traffic flow. The discontinuous coefficient of the flux function is assumed to be of bounded variation (BV) and bounded away from zero, and hence the spatial discontinuities of the flux function can be infinitely many with possible accumulation points. Strong compactness of the Godunov and Lax-Friedrichs type approximations is proved, providing the existence of entropy solutions. A proof of the uniqueness of the adapted entropy solutions is provided, establishing the convergence of the entire sequence of finite volume approximations to the adapted entropy solution. As per the current literature, this is the first well-posedness result for the aforesaid class and connects the theory of nonlocal conservation laws (with discontinuous flux), with its local counterpart in a generic setup. Some numerical examples are presented to display the performance of the schemes and explore the limiting behavior of these nonlocal conservation laws to their local counterparts.

Markoff–Lagrange spectrum of one‐sided shifts

AbstractFor the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed point of a substitution for the alternating lexicographic order. For orders defined by cylinders, we show that the solutions are ‐adic sequences, where is a certain infinite set of substitutions that contains Sturmian morphisms. We also consider a similar problem for symmetric ternary shifts, which is applicable to the multiplicative version of the Markoff–Lagrange spectrum.

Initial load factor adjustment through genetic algorithm for the generalized displacement control method: Implementation on non-rigid origami analysis

The nonlinear analysis of structural systems relies on effective nonlinear solution schemes, known as nonlinear solvers or path-following methods. This paper explores the challenge of determining the initial load factor in such analyses, with a particular focus on complex origami structures. This study presents a novel approach that leverages genetic algorithms (GA) to efficiently determine the initial load factor for the generalized displacement method. Building upon the concept of stiffness parameters, our method offers a systematic solution. In this work, GA serves as a tool to discover the appropriate initial load factor based on changes in the stiffness parameter, providing a more rational and user-friendly approach. To demonstrate the practical applicability of our approach, we apply it to a range of complex origami problems, including the folding of Miura-ori, folding of an egg-box origami, bending of an egg-box origami, and folding of an arc Miura-ori. These examples, along with a truss example, encompass highly nonlinear behaviors, including limit points, extreme stiffness fluctuations, snap-through, and snap-back. Our results showcase the effectiveness of our method in accurately tuning the initial load factor to capture and track intricate nonlinear behaviors. Furthermore, it offers the flexibility to fine-tune the distribution of points along the path and manage the resolution of the depicted equilibrium path. This versatility underscores its potential applications in fields such as deployable structures and complex large deformation structural analysis.

CSRNet: Focusing on critical points for depth completion

Depth completion is an effective method for generating dense depth maps from sparse ones. In recent studies, the majority of points, which we call standard points, often exhibit sub-optimal performance. This issue arises from the need to fit only very few points, termed as challenging points, which consist of noises and regions with discontinuous depth in the ground-truth. On the other hand, traditional evaluations can not recognize this situation, and are dominated by these limited challenging points, whose performance improvements may not significantly benefit related tasks. In contrast, standard points, which are critical for these tasks, are not effectively measured. This discrepancy highlights the need for a more targeted approach and evaluation method for depth completion. In order to solve the above problems, we propose a standard-point-enhancing learning paradigm. This paradigm aims to improve the performance on standard points, which consists of a Cascaded Segmentation-to-Regression Networks (CSRNet) and a Mining L1 loss. CSRNet includes two branches: DSNet and DRNet. DSNet uses segmentation to generate a coarse depth map, providing challenging-point-insensitive information. DRNet adopts a coarse-to-fine approach to learn the residual depth map between the coarse depth map and the ground-truth depth map. In addition, our Mining L1 loss leverages the segmentation results to filter out potential challenging points. This approach allows the network to concentrate more effectively on standard points. Lastly, we introduce the Minimum Error (ME) Curves as a new way to measure the performance of predicted depth maps in a flexible and comprehensive manner, irrespective of whether the points are standard or challenging. Experimental results on the KITTI and NYUDv2 datasets show that our approach significantly improves accuracy on the majority of points.

Barriers to Enrollment of National Health Insurance Scheme in Uttargaya Rural Municipality, Rasuwa

The Social Health Security Program (SHSP) is a social protection program of the Government of Nepal that aims to enable all citizens to access quality and effective healthcare services without any financial burden. A cross-sectional household-based and quantitative in-nature study was conducted in Rasuwa district. This study's population was residents of Uttargaya rural municipality wards no 4 and 5. How different factors are related to SHI enrolment. Ethnicity (p=<0.001), religion (p=<0.001), IWI grade (p=0.010), know about health insurance (p=<0.001), the behavior of service providers (p=<0.001), neighbors enrollment (p=<0.001), discussed SHI with neighbors (p=0.001), and family members agreed to enroll (p=0.002) were significantly associated with enrollment in SHI whereas others factors did not show any significant association with enrollment in social health insurance. This study found that enrollment was significantly associated with different independent variables. Poor knowledge of SHI, unfriendly behaviors of service providers, lack of trust, and unaffordability of premium costs were identified as barriers. Furthermore, Inappropriate timing of premium collection, limited services point, feeling that enrollment was not necessary, long queue, inadequate number of enrollment assistant and mandatory refer card were also reasons for not enrolling in SHI.

The dimensions of deep-layer soil desiccation and its impact on xylem hydraulic conductivity in dryland tree plantations

Abstract. In water-limited areas, planted trees can extract substantial amounts of soil water from deep layers (> 200 cm) to meet their high water demand, resulting in deep soil desiccation, which influences not only regional water cycling but also the sustainability of trees per se in drylands. However, the specific dimensions of deep soil desiccation in relation to both the soil moisture limitation and the maximum root water uptake (RWU) depth are still not well determined. Whether the dimensions depend on tree species and how they will affect trees' xylem hydraulic conductivity are also unclear, restricting our ability to predict the fate of dryland tree plantations. Therefore, we studied the spatiotemporal distribution of deep soil moisture deficit (DSMD) for two typical planted trees, apple (Malus pumila Mill.) and black locust (Robinia pseudoacacia L.), based on published data and multiple field samplings on China's Loess Plateau. The results indicated that the lowest deep soil moisture (DSM; units of gravimetric percent, i.e., grav-%) occurred under the planted trees aged 24–28 years at all sites. The lowest DSMD varied around −0.6, which was close to the DSMD at the permanent wilting point (PWP, grav-%), regardless of tree species and site, although shallow (< 200 cm) soil moisture was not reduced to the point of limitation. This suggests that PWP is a reliable indicator of the moisture limitation of deep-layer soil desiccation for the tree species examined. The corresponding depth of soil moisture use reached 18.0–22.0 m for these old planted trees at different sites, while it was more than 25 m for R. pseudoacacia in the drier site of Mizhi. Furthermore, the mean values of native percentage loss of hydraulic conductivity of planted trees' branches xylem reached 74.9 %–96.5 % in the plantations sampled in this study, indicating that tree mortality may occur. The findings help predict the sustainability of planted trees in semi-arid regions with a thick vadose zone.

Determination of the Fixed Point of Lotka-Volterra Function

The paper focuses on the Lotka-Volterra function in its discrete form. The purpose of the study was to determine the fixed points of the function. The study employs the Banach Fixed Point Theorem and Contraction Mapping in Metric Space on the function to demonstrate the uniqueness of the fixed points and its continuous stability after several iterations, using the fixed points as the initial conditions. The study has shown that $(0,0),\left(0,\frac{\alpha-1}{\beta}\right),\left(\frac{1+\gamma}{\delta},0\right)$ and $\left(\frac{1+\gamma}{\delta},\frac{\alpha-1}{\beta}\right) $are the fixed points of the function, with the initial pair serving as a trivial one and the other three solely depending on the parameter values for the behavior of the function. The outcome of the limit points of the function as the fixed points after several iterations forms a fixed orbit structure of the function, irrespective of the value of the parameter. The study also showed the uniqueness of the fixed points, demonstrating the stability and continuity of the function in its steady state.

Simultaneous prediction of petrophysical properties and formation layered thickness from acoustic logging data using a modular cascading residual neural network (MCARNN) with physical constraints

Predicting petrophysical properties from logging data using deep neural networks (DNNs) improves the efficiency of subsurface exploration. Traditional methods, however, heavily rely on data pre-processing. Therefore, a novel Modular Cascading Residual Neural Network (MCARNN) is proposed to simultaneously retrieve layered thickness and petrophysical properties of porous media directly from raw acoustic logging data without pre-processing. The MCARNN mainly comprises two cascading modules: the first is tasked with retrieving layered thickness, while the second one further reconstructs petrophysical properties based on the thickness information. To more accurately simulate the uncertainties of the real world, we incorporate some known geophysical knowledge, including the distribution range of actual petrophysical parameters, physical constraints among porous medium parameters, configurations of logging instruments, and stratified geological models. During this process, all Biot's porous parameters are independently randomized to cover a wide range of geological rock types. Furthermore, to enhance MCARNN's generalization ability under different random noise distributions, we independently generate the training and testing datasets using distinct numerical algorithms, thus preventing the “inverse crime” phenomenon. Additionally, varying levels of Gaussian white noises are added to the training dataset, and the transmitter-receiver configuration of the logging instrument is varied to enhance the training dataset. Two numerical experiments are implemented to validate the reliability and superiority of the MCARNN. It is shown that the proposed MCARNN can not only accurately predict porous petrophysical parameters when the background layer configurations are known but also be able to simultaneously reconstruct layered thickness and petrophysical parameters with low model misfit. Notably, MCARNN successfully predicts the porous velocity dispersion curves within a broad frequency band based on limited frequency points—a task typically requiring auxiliary equations in traditional inversion methods, demonstrating the advanced predictive capability of the proposed MCARNN. Through this research, we not only address the deficiencies in existing real-world logging datasets in terms of sample volume and label reliability but also effectively integrate rock physics models with data-driven neural networks, providing a novel and effective pathway for reservoir parameter prediction in the field of geophysical logging.

Irradiation-Hardening Model of TiZrHfNbMo0.1 Refractory High-Entropy Alloys.

In order to find more excellent structural materials resistant to radiation damage, high-entropy alloys (HEAs) have been developed due to their characteristics of limited point defect diffusion such as lattice distortion and slow diffusion. Specially, refractory high-entropy alloys (RHEAs) that can adapt to a high-temperature environment are badly needed. In this study, TiZrHfNbMo0.1 RHEAs are selected for irradiation and nanoindentation experiments. We combined the mechanistic model for the depth-dependent hardness of ion-irradiated metals and the introduction of the scale factor f to modify the irradiation-hardening model in order to better describe the nanoindentation indentation process in the irradiated layer. Finally, it can be found that, with the increase in irradiation dose, a more serious lattice distortion caused by a higher defect density limits the expansion of the plastic zone.

Schur multipliers of C⁎-algebras, group-invariant compactification and applications to amenability and percolation

Let Γ be a countable discrete group. Given any sequence (fn)n≥1 of ℓp-normalized functions (p∈[1,2)), consider the associated positive definite matrix coefficients 〈fn,ρ(⋅)fn〉 of the right regular representation ρ. We construct an orthogonal decomposition of the corresponding Schur multipliers on the reduced group C⁎-algebra or the uniform Roe algebra of Γ. We identify this decomposition explicitly via the limit points of the orbits (f˜n)n≥1 in the group-invariant compactification of the quotient space constructed by Varadhan and the first author in [14]. We apply this result and use positive-definiteness to provide two (quite different) characterizations of amenability of Γ – one via a variational approach and the other using group-invariant percolation on Cayley graphs constructed by Benjamini, Lyons, Peres and Schramm [1]. These results underline, from a new point of view to the best of our knowledge, the manner in which Schur multipliers capture geometric properties of the underlying group Γ.

Full-Section Deformation Monitoring of High-Altitude Fault Tunnels Based on Three-Dimensional Laser Scanning Technology.

In traditional tunnel monitoring, the characteristic points of an object within a tunnel are measured to obtain information about the object. Considering the limitations of the traditional method in measuring the complex surface structure of tunnels, such as limited monitoring points, a long measurement period, and low precision, this study introduces an approach that uses three-dimensional (3D) laser scanning for monitoring tunnel cross-section deformation. Using this approach, the soft surrounding rock of a high-altitude ultralong tunnel was taken as the monitoring object. The test tunnel was first scanned using a 3D laser scanner, and the collected data were processed. The internal structural data of the tunnel were subsequently compared with its actual contour lines and the data of its primary branch and secondary lining on different dates. The results indicate that the arch roof of the tunnel tended to be stable within a certain time range when the positions of the primary branch and secondary lining were at different measuring points with different pile numbers. The deformation of the pile number on the left and right sides did not generally exceed 0.02 m, except at a few measuring points. A comparison between the actual cross section of the initial branch and that of the designed section showed that the actual elevation of the arch of the initial branch of the tunnel was greater than its designed elevation by no more than 0.3 m. Hence, through this study, a convenient and practical method is presented for monitoring deformation in complex curved tunnel structures.

CdIn2Se4@chitosan heterojunction nanocomposite with ultrahigh photocatalytic activity under sunlight driven photodegradation of organic pollutants

This research focused on synthesizing a CdIn2Se4@Ch nanocomposite by doping CdIn2Se4 into chitosan using a photolysis assisted ultrasonic process. The aim was to enhance the photodegradation efficiency of ofloxacin and 2,4-dichlorophenoxyacetic acid under sunlight. The synthesized CdIn2Se4@Ch nanocomposite was investigated via different techniques, including XRD, XPS, FTIR, TEM, DSC, TGA, UV–Vis and PL. The study also investigated the influence of various reaction parameters, including the effects of inorganic and organic ions. The synthesized nanocomposite demonstrated exceptional efficiency, achieving 86 % and 95 % removal rates, with corresponding rate constants of 0.025 and 0.047 min-1. This performance surpasses that of CdIn2Se4 by approximately 1.35 and 2.25 times, respectively. The values of COD were decreased to 78 and 86 % for ofloxacin and 2,4-dichlorophenoxyacetic, while the TOC values decreased to 71 and 84 %, respectively, from their premier values. The improvement in performance is associated with the introduction of CdIn2Se4 into chitosan, resulting in the self-integration of Cd into the catalyst. This creates a localized accumulation point for electrons, enhancing the efficiency of charge separation and further reducing the surface charge of chitosan. Experimental evidence suggests that superoxide and hydroxyl radicals play a significant role in the photodegradation of pollutants. Additionally, the nanocomposite exhibits excellent stability and can be reused up to five times, indicating remarkable stability and reusability of the developed photocatalyst.

Cellular and Molecular Mechanisms of Heterotopic Ossification in Fibrodysplasia Ossificans Progressiva.

Fibrodysplasia ossificans progressiva (FOP) is a debilitating genetic disorder characterized by recurrent episodes of heterotopic ossification (HO) formation in muscles, tendons, and ligaments. FOP is caused by a missense mutation in the ACVR1 gene (activin A receptor type I), an important signaling receptor involved in endochondral ossification. The ACVR1R206H mutation induces increased downstream canonical SMAD-signaling and drives tissue-resident progenitor cells with osteogenic potential to participate in endochondral HO formation. In this article, we review aberrant ACVR1R206H signaling and the cells that give rise to HO in FOP. FOP mouse models and lineage tracing analyses have been used to provide strong evidence for tissue-resident mesenchymal cells as cellular contributors to HO. We assess how the underlying mutation in FOP disrupts muscle-specific dynamics during homeostasis and repair, with a focus on muscle-resident mesenchymal cells known as fibro-adipogenic progenitors (FAPs). Accumulating research points to FAPs as a prominent HO progenitor population, with ACVR1R206H FAPs not only aberrantly differentiating into chondro-osteogenic lineages but creating a permissive environment for bone formation at the expense of muscle regeneration. We will further discuss the emerging role of ACVR1R206H FAPs in muscle regeneration and therapeutic targeting of these cells to reduce HO formation in FOP.

One-dimensional Schrödinger operator with decaying white noise potential

In this paper, we consider a random one-dimensional Schrödinger operator Hω on the half line which has, as its potential term, Gaussian white noise multiplied by a decaying factor. Although the potential term is not an ordinary function, but a distribution, it is possible to realize Hω as a symmetric operator in L2([0, ∞); dt) as was pointed out by the present author [Minami, Lect. Notes Math. 1299, 298 (1986)], and it will be shown that Hω is actually self-adjoint with probability one. When the white noise in Hω is replaced by random functions of a specific type, [Kotani and Ushiroya, Commun. Math. Phys. 115, 247 (1988)] made a precise analysis of the positive part of the spectrum. According to them, if the decaying factor is not square integrable, the positive part of the spectrum typically consists of singular continuous and dense pure-point parts, which are separated by a threshold number. On the other hand, the positive part of the spectrum is purely absolutely continuous when the decaying factor is square integrable. In this work, we shall focus on the case of square integrable decaying factor, and prove the absolute continuity of the positive part of the spectrum of Hω. We shall further prove that the negative part of the spectrum of Hω is discrete, with no accumulation points other than 0.

Improving spatial transferability of deep learning models for small-field crop yield prediction

Predicting crop yield using deep learning (DL) and remote sensing is a promising technique in agriculture. In smallholder agriculture (<2 ha), where 84% of the farms operate globally, it is crucial to build a model that can be useful across several fields (high spatial transferability). However, enhancing spatial model transferability in a small-scale setting faces significant challenges, including spatial autocorrelation, heterogeneity and scale dependence of spatial dynamics, as well as the need to address limited data points. This study aimed to test the hypothesis that spatial cross validation (SCV) is a more suitable model validation practice than random cross validation (RCV) to enhance model transferability for spatial prediction in a small-scale farming setting. We compared the performances of DL models that predict crop yield for several settings including three crop types and two DL architectures based on RCV with and without overlapping samples and SCV. Notably, we conducted model performance tests on external, equally sized fields instead of the field used for training. We used high resolution RGB imagery taken with a drone as input. Our results show that the models using SCV outperformed those using RCV when the models were tested on external fields (on average r = 0.37 for SCV, r = 0.18 for RCV with overlap and r = 0.07 without), even though the models using SCV showed a substantially lower performance for cross validation (CV) than those using RCV (r with SCV and RCV w/o overlap = 0.73 and 0.98/0.73, respectively). The results suggest that RCV leads to over-optimism by overfitting the spatial structure and remembering image-specific information (so called memorization). Our study offers the first empirical evidence in agriculture that SCV is preferable to RCV in small field settings for making DL models more transferable.

Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle

For the Riesz and logarithmic potentials, we consider greedy energy sequences (an)n=0∞ on the unit circle S1, constructed in such a way that for every n≥1, the discrete potential generated by the first n points a0,…,an−1 of the sequence attains its minimum value (say Un) at an. We obtain asymptotic formulae that describe the behavior of Un as n→∞, in terms of certain bounded arithmetic functions with a doubling periodicity property. As previously shown in [8], after properly translating and scaling Un, one obtains a new sequence (Fn) that is bounded and divergent. We find the exact value of liminfFn (the value of limsupFn was already given in [8]), and show that the interval [liminfFn,limsupFn] comprises all the limit points of the sequence (Fn).