Functional Limit Research Articles

Security Risks in the Encryption of Database Connection Strings

ABSTRACTBackgroundThere exists an important and open problem with the encrypting of database connection strings in that related connection strings start with well known identical initial sub‐strings. When these initial sub‐strings are longer than the encrypting algorithm's block size, the resulting encrypted text for related database connection strings will have identical initial sub‐strings which could increase the chance of breaking the encryption key used to encrypt the connection strings.AimsThe objective of our work was to find a simple, easy to implement, well known algorithm that would eliminate the identical initial sub‐strings in the encrypted text of related database connection strings.MethodsOur methodology was to apply an obfuscation function to the database connection strings before encrypting them with the 3DES and AES encryption algorithms. The obfuscation functions we chose for our tests were the Roman Keyword cipher or the Greek Scytale cipher.DiscussionThe results of applying the two obfuscation functions to the related database connection strings before encrypting them with the symmetric encryption algorithms. This process effectively eliminated the commonality in the encrypted text of the database connection strings.ConclusionWhile both the Keyword and Scytale obfuscation functions were able to eliminate the commonality in the encrypted text. We found that the Scytale function was superior to the Keyword function due to some minor limitations of the Keyword functions and the fact that the Scytale function geometrically increased the number of possible known strings within the plain text connection string before encryption.

Magnetic and electrical stimulation in complex rehabilitation for myelodysplasia in children: a clinical randomized study

Introduction. Myelodysplasia (MD) in children is accompanied by disorders of the musculoskeletal system and pelvic functions, causing a decrease in activity and restriction of participation in society, leading to disability and contributing to social isolation. The rehabilitation potential, determined by the International Classification of Functioning, Disability and Health (ICF), is realized when the child is active and participates in the processes of life. The improvement of methods and technologies for the rehabilitation of children with MD remains relevant. Aim. To study the effect of medical rehabilitation in children with MD on the development of motor skills in all children and self-care in children over the age of 1 year. Materials and methods. The study included 117 children diagnosed with male and female MD between the ages of 6 months and 13 years, 11 months and 30 days (average age 6 years and 9 ± 6 months). The diagnosis of the functioning of the body was performed in the categorical profile of the ICF using a ranking system for the degree of disorders / limitations of functioning. The subjects are divided into three groups. Patients of group I received physical rehabilitation, ergotherapy, magnetic stimulation of the spinal cord (MS) and electromyostimulation (EMS); group II — physical rehabilitation, ergotherapy and MS; group III — standard physical therapy techniques, massage, ergotherapy, therapy with sinusoidal modulated currents (SMT-therapy) on the muscles of the lower extremities. Results and discussion. The effectiveness of consistent use of MS, EMS during physical exercises for the development of motor skills, classes with an occupational therapist on self-service skills has been demonstrated in children with MD, which is confirmed by positive dynamics in mobility and self-service skills assessed using functional scales and questionnaires. Medical rehabilitation increases muscle strength in children with MMD, and the combined use of MS with EMS during targeted exercises contributes to the effective development of motor functions. The development of motor skills and classes with an occupational therapist increase the level of independence in children with MD. Conclusion. Medical rehabilitation with the inclusion of MS and EMS during the performance of targeted exercises contributes to the better development of motor skills and improves self-care in children with MD.

Modified quantum regression theorem and consistency with Kubo-Martin-Schwinger condition

Abstract We show that the long-time limit of the two-point correlation function obtained via the standard quantum regression theorem, a standard tool to compute correlation functions in open quantum systems, does not respect the Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the system-bath coupling. We then follow the recently developed Heisenberg operator method for open quantum systems and by applying a ``{\it weak}" Markov approximation, derive a new modified version of the quantum regression theorem that not only respects the KMS condition but further predicts exact answers for certain paradigmatic models in specific limits. We also show that in cases where the modified quantum regression theorem does not match with exact answers, it always performs better than the standard quantum regression theorem.

De Sitter S matrix for the masses

We define an S matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch coordinates relevant for early Universe cosmology. It enjoys many of the same properties as its Minkowski counterpart, for instance: it is insensitive to total derivatives and field redefinitions in the action; it can be extracted as a particular “on shell” limit of time-ordered correlation functions; and for low-point scattering, kinematics strongly constrains its possible structures. We present explicit formulas relating inflationary observables—namely in-in equal-time correlators and wavefunction coefficients at the conformal boundary—to these S matrix elements. This new formalism will allow modern amplitude methods to be applied directly in cosmology and hence provide a wider range of more accurate theoretical predictions for upcoming sky surveys. Published by the American Physical Society 2024

Gaussian fluctuations of spatial averages of a system of stochastic heat equations

. We consider a system of d non-linear stochastic heat equations driven by an m-dimensional space-time white noise on R + × R . In this article, we study the asymptotic behavior of spatial averages over large intervals [ − R , R ] . We establish a rate of convergence to a multivariate normal distribution in the Wasserstein distance and a functional central limit theorem.

Physics-aware cross-domain fusion aids learning-driven computer-generated holography

The rapid advancement of computer-generated holography has bridged deep learning with traditional optical principles in recent years. However, a critical challenge in this evolution is the efficient and accurate conversion from the amplitude to phase domain for high-quality phase-only hologram (POH) generation. Existing computational models often struggle to address the inherent complexities of optical phenomena, compromising the conversion process. In this study, we present the cross-domain fusion network (CDFN), an architecture designed to tackle the complexities involved in POH generation. The CDFN employs a multi-stage (MS) mechanism to progressively learn the translation from amplitude to phase domain, complemented by the deep supervision (DS) strategy of middle features to enhance task-relevant feature learning from the initial stages. Additionally, we propose an infinite phase mapper (IPM), a phase-mapping function that circumvents the limitations of conventional activation functions and encapsulates the physical essence of holography. Through simulations, our proposed method successfully reconstructs high-quality 2K color images from the DIV2K dataset, achieving an average PSNR of 31.68 dB and SSIM of 0.944. Furthermore, we realize high-quality color image reconstruction in optical experiments. The experimental results highlight the computational intelligence and optical fidelity achieved by our proposed physics-aware cross-domain fusion.

Partial Meanings that a Teacher Mobilizes for Learning Limits at the School Level

Objective: The objective of this study is to analyze the partial meanings of the function limit object in a variable that a teacher mobilizes when teaching the Calculus unit at the school level. Theoretical Framework: For the analysis of the partial meanings of the mathematical object, the epistemic configurations proposed by the OntoSemiotic Approach to Mathematical Cognition and Instruction (OSA) were used. Method: The study is qualitative in nature and its methodological design is an instrumental-descriptive case study.. To carry out the analysis of the meanings mobilized by the teacher, a semi-structured interview, teaching material, field notes from class observation and the notes of two students of the course were used. Results and Discussion: The results obtained revealed that the teacher preferentially mobilizes the last two epistemic configurations of the mathematical object and to a limited extent some primary objects of other configurations. Research Implications: The research provides a reflection for the pedagogical practices of teachers regarding the epistemic richness of the mathematical object, mainly to Chilean teachers, who must teach said object promoting all its partial meanings according to the requirements of the Chilean school curriculum. Originality/Value: The research lies in the importance of the pedagogical practices that teachers should consider when teaching said object, in particular, the mathematical richness of the partial meanings of the object.

Maintaining Cyber Resilience in the Reconfigurable Networks with Immunization and Improved Network Game Methods.

The paper proposes a technique for protecting reconfigurable networks that implements topology rebuilding, which combines immunization and network gaming methods, as a solution for maintaining cyber resilience. Immunization presumes an adaptive set of protective reconfigurations destined to ensure the functioning of a network. It is a protective reconfiguration aimed to preserve/increase the functional quality of the system. Network nodes and edges are adaptively reorganized to counteract an invasion. This is a functional component of cyber resilience. It can be implemented as a global strategy, using knowledge of the whole network structure, or a local strategy that only works with a certain part of a network. A formal description of global and local immune strategies based on hierarchical and peer-to-peer network topologies is presented. A network game is a kind of the well-defined game model in which each situation generates a specific network, and the payoff function is calculated based on the constructed networks. A network game is proposed for analyzing a network topology. This model allows quickly identifying nodes that require disconnection or replacement when a cyber attack occurs, and understanding which network sectors might be affected by an attack. The gaming method keeps the network topology resistant to unnecessary connections. This is a structural component of cyber resilience. The basic network game method has been improved by using the criterion of maximum possible path length to reduce the number of reconfigurations. Network optimization works together with immunization to preserve the structural integrity of the network. In an experimental study, the proposed method demonstrated its effectiveness in maintaining system quality within given functional limits and reducing the cost of system protective restructuring.

Remote sensing image segmentation of gully erosion in a typical black soil area in Northeast China based on improved DeepLabV3+ model

Gully erosion, a cause of soil degradation and reduced crop yields is widespread in the diffuse river and hillock regions of Northeast China. The surface conditions in gully erosion areas are complex, and manual extraction methods are inefficient, hindering gully erosion monitoring progress. Accurate extraction of gullies is essential for effective environmental monitoring and management. In this study, we propose an improved deep learning network, named DD-DA (the DeepLabV3+ deep network with dual attention mechanism), for automatic and precise gully erosion extraction from 2 m resolution Gaofen-6 remote sensing images from the Heshan Farm area. The DD-DA model builds upon the DeepLabV3+ network architecture with targeted optimizations. Firstly, ResNet50 replaces the original backbone network of DeepLabV3+, enhancing feature extraction capabilities. Second, the Convolutional Block Attention Module (CBAM) integrates spatial and channel attention, improving the model's capacity to capture the shape and texture features of gully erosion. Finally, the Dice loss function is adopted to address the limitations of the traditional cross-entropy loss function, particularly in handling unbalanced datasets. To promote deep learning applications in gully erosion monitoring in Northeast China, a gully erosion dataset was constructed. Experiments on gully erosion datasets show that DD-DA can achieve high Mean Intersection over Union (MIoU) (79.21 %), Pixel Accuracy (96.17 %), Recall (87.66 %), F1-Score (86.48 %), and Precision (86.08 %) simultaneously, which significantly outperform traditional image processing methods and recently deep learning networks. Overall, DD-DA efficiently and accurately segment gully erosion in agricultural fields, significantly improving the extraction of gully erosion features from high-resolution remote sensing images, particularly in the black soil regions of northeastern China. Meanwhile, this study offers a solution for the rapid monitoring of gully erosion and provides substantial technical support for extracting other land degradation features, such as soil salinization and desertification.

Tame topology in Hensel minimal structures

We are concerned with topology of Hensel minimal structures on non-trivially valued fields K, whose axiomatic theory was introduced in a recent paper by Cluckers–Halupczok–Rideau. We additionally require that every definable subset in the imaginary sort RV, binding together the residue field Kv and value group vK, be already definable in the plain valued field language. This condition is satisfied by several classical tame structures on Henselian fields, including Henselian fields with analytic structure, V-minimal fields, polynomially bounded o-minimal structures with a convex subring, and almost real closed fields with real analytic structure. In this article, we establish many results concerning definable functions and sets. These are, among others, existence of the limit for definable functions of one variable, a closedness theorem, several non-Archimedean versions of the Łojasiewicz inequalities, an embedding theorem for regular definable spaces, and the definable ultranormality and ultraparacompactness of definable Hausdorff LC-spaces.

Change in mental health service utilization from pre- to post-COVID-19 period in the United States

ObjectivesThis study aimed to explore the change in mental health service utilization before and after the COVID-19 pandemic as well as determine the association of various sociodemographic characteristics and comorbidities on the utilization pattern. MethodsData from the National Health Interview Survey (NHIS) 2019 and 2022 were explored in this study. Along with the univariate analysis, bivariate analysis was conducted using the Chi-square and Cochran-Armitage trend tests. Stepwise binary logistic regression was implemented to find the best-fitted model and examine the effects of different factors on mental healthcare utilization. We also conducted a subgroup analysis for the variables that showed heterogeneous changes in utilization from 2019 to 2022. ResultsAnalysis of a total of 53,856 complete cases showed that the percentage of mental healthcare utilization changed from 20% in 2019 to 23.31% in 2022. Logistic regression results showed that the odds of mental health service utilization in the post-COVID period is 1.41 times of the pre-COVID [95% CI odds ratio (OR) = (1.26, 1.58)]. Sex, age, race, education, income group, insurance coverage, birth country, marital status, limitations of social functioning, having a place for healthcare, symptoms and history of depression/anxiety, diabetes, and hypertension had significant effects on the odds of receiving mental healthcare. Subgroup analysis revealed that the utilization changed significantly from 2019 to 2022 for age group “18–34” [OR = 1.41, 95% CI = (1.26, 1.58)], “35–49” [OR = 1.35, 95% CI = (1.21, 1.50)], and “50–64” [OR = 1.12, 95% CI = (1.01, 1.24)], while for the age group “above 64” was not significant. ConclusionPre- and post-COVID periods were found to be significantly different in terms of the utilization of mental healthcare utilization. Changes in the utilization was also found to differ in terms of different age groups.

수학 학습 촉진을 위한 애니메이션 자료 제작 연구: 파이썬 라이브러리 Manim을 기반으로

Objectives The purpose of this study is to propose guidelines for producing animation materials as a way to help students understand the characteristics of mathematics and mathematical concepts and principles, and to in-troduce Manim, an effective mathematics animation material production tool. Methods We investigated animation production principles that can be helpful in the math animation production process, and applied them to already produced math animation materials to find out their suitability as math ani-mation production principles. In addition, the scope of GeoGebra's animation implementation functions, which are used in the production of mathematical materials, was confirmed, and the possibilities of supplementing the limi-tations of various functions revealed here were explored through Manim. and we looked at the process of produc-ing animation materials using Manim and the results. Results As a result of analyzing whether the animation production principles adopted and applied are valid for the production of mathematics animation materials, we found some requirements that should be modified and sup-plemented from the perspective of mathematics education, and derived improved guidelines for the production of mathematics animation materials. GeoGebra, one of the production tools, has an animation composition func-tion, but there were limitations in its implementation functions, such as setting text condition input and repeating the target hiding operation. In comparison, although Manim requires an understanding of basic Python grammar, it was found to have great advantages in producing mathematical animation materials, such as intuitive com-mands, convenient property change function, free expression ordering, and various animation effects. Conclusions Previous animation production research has not sufficiently considered the abstract nature of math concepts. accordingly, the need for improved guidelines that cover the expression of mathematical concepts, and the use of formulas as the main object of animation has emerged. GeoGebra has limitations in its animation com-position function, so the need for it is increasing along with the expansion of new mathematical animation material creation tools that go beyond that function. accordingly, it was confirmed that Manim, which uses simple com-mands as an alternative production tool, is a very specialized tool for creating mathematical animations.

Hindlimb kinematics, kinetics, and muscle dynamics during sit-to-stand and sit-to-walk transitions in emus (Dromaius novaehollandiae).

Terrestrial animals not only need to walk and run but also lie prone to rest and then stand up. Sit-to-stand (STS) and sit-to-walk (STW) transitions are vital behaviours little studied in species other than humans so far, but likely impose biomechanical constraints on limb design because they involve near-maximal excursions of limb joints that should require large length changes and force production from muscles. By integrating data from experiments into musculoskeletal simulations, we analysed joint motions, ground reaction forces, and muscle dynamics during STS and STW in a large terrestrial, bipedal, and cursorial bird: the emu (Dromaius novaehollandiae, ∼30 kg). Simulation results suggest that in both STS and STW, emus operate near the functional limits (∼50 % of shortening/lengthening) of some of their hindlimb muscles, particularly in distal muscles with limited capacity for length change and leverage. Both movements involved high muscle activations (> 50 %) and force generation of the major joint extensor muscles early in the transition. STW required larger net joint moments and non-sagittal motions than STS, entailing greater demands for muscle capacity. Whilst our study involves multiple assumptions, our findings lay the groundwork for future studies to understand, for example, how tendon contributions may reduce excessive muscle demands, especially in the distal hindlimb. As the first investigation into how an avian species stands up, this study provides a foundational framework for future comparative studies investigating organismal morphofunctional specialisations and evolution, offering potential robotics and animal welfare applications.

CONCEPT IMAGE AND CONCEPT DEFINITION SCHEMES AS TOOLS FOR ANALYZING STUDENTS’ COMPREHENSION OF LIMIT OF A FUNCTION

This paper aims to analyze one’s understanding of limit of a function based on Concept Image and Concept Definition schemes, which can be used as powerful tools in research that have mathematical comprehension as part of their object of study. For that, we developed and applied a set of tasks involving limits of functions to students who had already been in a Calculus course. Vinner’s study about concept image and concept definition was the theoretical framework of this paper. The results obtained let us observe the plurality of interpretations about limits and other adjacent concepts, which allowed us to trace, in this paper, a reflection upon the cognitive conflicts concerning the (lack of) understanding of these concepts.

Low energy limit from high energy expansion in mass gapped theory

We present a method to extract the low energy behavior of physical observables from their high energy expansions, systematically calculable via the operator product expansion (OPE), in asymptotically free and mass-gapped theories. By applying the inverse Laplace transform to correlation functions, their analytic structure is modified such that low-energy information connects with high energy expansions. Furthermore, this transformation alleviates the renormalon problem, enabling a more straightforward application of the OPE compared to the OPE before the transformation. We demonstrate that the low energy limit of correlation functions can be accurately extracted using the OPE in the two dimensional O(N) nonlinear σ model, serving as a first testing ground.

Development of an improved mass transfer model for condensation with dynamic feedback regulation

In the field of condensation research, accurate and efficient numerical simulation models are highly desired. One of the widely used phase change mass transfer models is known as the Lee model. However, this model has limitations due to uncertainties in the mass transfer intensity factor, which can lead to simulation failures and impede large-scale engineering applications. This study presents an improved mass transfer model which employs a tuning function to dynamically and accurately modify the mass transfer intensity factor in each two-phase cell via feedback adjustment. This approach enables immediate and customized adjustment of the factor for each grid within the limit of the tuning function, significantly reducing the errors caused by repeated artificial adjustments and related uncertainties. The adjustment capabilities of the hyperbolic tangent and softsign functions are evaluated. The softsign function is superior in both regulation efficiency and accuracy. The model's accuracy is verified by comparing with previous experiments and simulations, as well as by the one-dimensional Stefan problem. The proposed model achieves high prediction accuracy, reduces the risk of simulation dispersion, and significantly enhances computational efficiency with the iteration number reduced by nearly half under certain conditions compared to the Lee model. Furthermore, the new model shows robustness as the prediction accuracy is insensitive to variations in critical parameters. The improved model is expected to provide valuable assistance for future research and applications in flow condensation with outstanding computational accuracy, efficiency, and stability.

Exponential stability and non-weighted L 2-gain analysis for switched neutral systems with unstable subsystems

Exponential stability and non-weighted L 2 -gain are studied for switched neutral systems with unstable subsystems. Initially, a time scheduling strategy is introduced to formulate switching-signal-based multiple discontinuous Lyapunov functions. Multiple discontinuous Lyapunov functions can be applied to each subsystem, thereby relaxing the limitations of traditional Lyapunov functions. Meanwhile, mode-dependent average dwell times are utilised to design fast and slow switching signals, ensuring stability in switched neutral systems where the switching between unstable and stable subsystems is arbitrary. Moreover, in the presence of external disturbances, the non-weighted L 2 -gain performance is discussed. Sufficient conditions are proposed to achieve the stability of switched neutral systems and non-weighted L 2 -gain performance using the linear matrix inequality method. The validity of this study is ultimately demonstrated through simulation examples.

GaN System-on-Chip: Pushing the Limits of Integration and Functionality

GaN System-on-Chip: Pushing the Limits of Integration and Functionality

Measure-Theoretic Analysis of Stochastic Competence Sets and Dynamic Shapley Values in Banach Spaces

We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path continuity and moment estimates. The dynamic Shapley value is rigorously defined as a càdlàg stochastic process with an axiomatic characterization. We derive a martingale representation for this process and establish its asymptotic properties, including a strong law of large numbers and a functional central limit theorem under α-mixing conditions. This framework provides a rigorous basis for analyzing dynamic value attribution in abstract spaces, with potential applications to economic and game-theoretic models.

Absolute quantitation of human serum cystatin C: candidate reference method by 15N-labeled recombinant protein isotope dilution UPLC-MS/MS.

Serum cystatin C (CysC) is a reliable and ideal endogenous marker for accurately assessing early changes in glomerular filtration rate (GFR), surpassing the limitations of creatinine-based estimated GFR. To improve the precision of GFR calculation, the development of strategies for accurately measuring serum CysC is crucial. In this study, the full-length CysC pure product and fully recombinant 15N-labeled CysC internal standard were subjected to protein cleavage. Subsequently, an LC-MS/MS method was developed for the absolute quantification ofserum CysC. The traceability of the method was assigned calibrator using the amino acid reference measurement procedure (RMP). It involved calibrating the instrument using an amino acid reference material with known amino acid concentrations for calibration and comparison purposes. The total imprecision of the method was determined to be≤8.2 %, and a lower functional limit of quantification (LLoQ) was achieved. The recoveries ranged from 97.36 to 103.26 %. The relative bias between this candidate RMP for measurement of ERM-DA471-IFCC and the target value was 1.74 %. The linearity response was observed within the concentration range of 0.21-10.13 mg/L, with a high R2 value of 0.999. The results obtained using our method was consistent with those obtained using other certified RMPs. With the establishment of this highly selective and accurate serum CysC measurement method, it is now possible to assess the correlation between immunoassay results of serum CysC and the intended target when discrepancies are suspected in the clinical setting.