As Convergence Research Articles

ON I-DEFERRED STATISTICAL CONVERGENCE OF ORDER Α FOR COMPLEX UNCERTAIN SEQUENCES

In this paper, we introduce the concepts of I-deferred statistical convergence almost surely of order α, I-deferred statistical convergence in measure of order α, I-deferred statistical convergence in mean of order α, I-deferred statistical convergence in distribution of order α, I-deferred statistical convergence in uniformly almost surely of order α and some relationships among them are discussed.

Quantitative convergence of the nonlocal Allen–Cahn equation to volume-preserving mean curvature flow

AbstractWe prove a quantitative convergence result of the nonlocal Allen–Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative entropy method, which has been used in the recent literature to prove weak–strong uniqueness results for mean curvature flow and convergence of the Allen–Cahn equation. A crucial difference in this work is a new notion of gradient flow calibrations. We add a tangential component to the velocity field in order to prove the Gronwall estimate for the relative energy. This allows us to derive the optimal convergence rate without having to show the closeness of the Lagrange-multipliers.

An augmented complex-valued gradient-descent total least-squares algorithm for noncircular signals

In this paper, we propose a novel augmented complex-valued gradient-descent total least-squares (ACGDTLS) adaptive filter for processing noisy input and output noncircular complex-valued signals. First, a Rayleigh quotient cost function is formulated by incorporating augmented complex-valued statistics and the output-to-input-noise-ratio within the widely linear error-in-variable model, whereby the ACGDTLS is developed using the gradient-descent approach. Next, rigorous analysis is conducted to establish a conservative step-size bound guaranteeing mean convergence, a closed-form expression for the steady-state mean-squared deviation, and the algorithm’s computational complexity. Finally, through simulations conducted in system identification, wind/speech prediction, and stereophonic acoustic echo cancellation, the analytical findings are validated, and the proposed ACGDTLS filter demonstrates superior estimation accuracy compared to the augmented complex-valued least-mean-square algorithm and two state-of-the-art bias-compensated methods. Remarkably, this performance advantage persists across a wide range of step-sizes, input noise variances, and output noise variances.

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Statement of Retraction: Convergence in quadratic mean of averaged stochastic gradient algorithms without strong convexity nor bounded gradient

Analytical model of an active noise control system for performance analysis of adaptive algorithms in HVAC system

In real-world acoustic scenarios related to the problem with the low-frequency noise such as HVAC systems, the signal is a stochastic, non-stationary and time-varying process where the performance of the active noise control technique mainly depends on the characteristics of the adaptive filtering techniques. In this paper, a method for analytical modeling of active noise control of signals in MATLAB/Simulink is presented, in which the acquisition of audio signals is provided by using a National Instruments control and acquisition module. For the realization of the active noise control, an adaptive filtering system model for signal analysis has been developed, using three adaptive algorithms (LMS,RLS and NLMS). The analysis of the characteristics of each of the three investigated adaptive algorithms is performed according to four parameters: Mean Square Error (MSE), convergence speed, stability and robustness. The conclusions are presented through a comparative analysis of the results obtained from the implemented methodology. The individual characteristics and parameters that are observed for correct adaptation and optimal results of each of the adaptive filters are explained in detail.

Pointwise Convergence of Noncommutative Fourier Series

This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods and mean convergence of the associated noncommutative Fourier series. Based on this framework, this paper studies the refined counterpart of pointwise convergence of these Fourier series. As a key ingredient, we develop a noncommutative bootstrap method and establish a general criterion of maximal inequalities for approximate identities of noncommutative Fourier multipliers. Based on this criterion, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to 1 1 pointwise, so that the associated Fourier multipliers on noncommutative L p L_p -spaces satisfy the pointwise convergence for all p > 1 p>1 . In a similar fashion, we also obtain results for a large subclass of groups (as well as quantum groups) with the Haagerup property and the weak amenability. We also consider the analogues of Fejér and Bochner-Riesz means in the noncommutative setting. Our approach heavily relies on the noncommutative ergodic theory in conjunction with abstract constructions of Markov semigroups, inspired by quantum probability and geometric group theory. Finally, we also obtain as a byproduct the dimension free bounds of the noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies.

Secure distributed estimation via an average diffusion LMS and average likelihood ratio test

Secure distributed estimation algorithms are designed to protect against a spectrum of attacks by exploring different attack models and implementing strategies to enhance the resilience of the algorithm. These models encompass diverse scenarios such as measurement sensor attacks and communication link attacks, which have been extensively investigated in existing literature. This paper, however, focuses on a specific type of attack: the multiplicative sensor attack model. To counter this, the paper introduces the Average diffusion least mean square (ADLMS) algorithm as a viable solution. Furthermore, the paper introduces the Average Likelihood Ratio Test (ALRT) detector, which provides a straightforward detection criterion. In the presence of communication link attacks, the paper considers the manipulation attack model and presents an ALRT adversary detector. The analysis extends to these ALRT detectors, encompassing the calculation of adversary detection probability and false alarm probability, both achieved in closed form. The paper also provides the mean convergence analysis of the proposed ADLMS algorithm. Simulation results reveal that the proposed algorithms exhibit enhanced performance compared to the DLMS algorithm, while the incremental complexity remains only marginally higher than that of the DLMS algorithm.

Is military spending converging across middle eastern countries and Turkiye? A comprehensive unit root test analysis

AbstractThe Middle East is a region of chronic insecurity due to internal and external tensions. These tensions and insecurity have made the Middle East one of the world's leading regions in military armaments. This study investigates the stochastic convergence of military burden in 10 selected Middle Eastern countries using comprehensive unit root analysis. Stochastic convergence for each country from 1977 to 2020 is examined using conventional, structural break, nonlinear, and Fourier‐based unit root tests. Empirical results provide strong evidence of convergence with regional averages in Bahrain, Saudi Arabia, and Oman. There is also some evidence of convergence in the case of Israel, Egypt, Kuwait, Lebanon, and Turkiye. However, evidence for the existence of convergence in Iran and Jordan is weak.

Multi-state Markovian-random walk adaptive filter for time-varying block sparse system identification

This paper presents a higher order multi-state Markov model for block sparsity model of a system impulse response. To capture the time-varying behavior of the system, a random walk model for temporal evolution is incorporated; resulting in a two-dimensional multi-state Markov-Random walk model across spatial and temporal domains. Additionally, a block batch data structure is utilized for the adaptive filter design. The proposed adaptive filter is aimed to find the Maximum A Posteriori (MAP) estimator of the batch time-varying impulse response. The associated optimization problem is demonstrated to be convex and efficiently solvable through the Steepest-Descent (SD) approach. Furthermore, the final recursion of the proposed adaptive filter is derived and a mean convergence analysis of the algorithm is provided. Simulation results show the effectiveness of the proposed algorithm under severe time-varying conditions of the system impulse response, where alternative algorithms may exhibit divergence or poor convergence. Synthetic experiments and real-world experiments using acoustic channel estimation further validate the superiority of the proposed algorithm.

Near‐Surface Wind Convergence Along the Sea Ice Edge in the Greenland Sea: Its Mean State and Shaping Process

AbstractAt mid‐latitudes, a narrow band of near‐surface wind convergence (NSWC) overlies the western boundary currents in long‐term climatology as a response to steep sea surface temperature gradients. The underlying dynamics shaping mean convergence in the mid‐latitude region have been investigated in detail. In polar regions, surface temperature gradients are intense along the sea ice edges. However, literature concerning NSWC near sea ice edges is limited. This study investigates time‐mean NSWC along sea ice edges and its shaping processes, focusing on the Greenland Sea, based on atmospheric reanalysis. In cold‐season climatology, positive NSWC overlies the sea ice edge, resulting in a localized upward motion reaching the free atmosphere. The mean NSWC was insensitive to sea ice thickness and surface roughness in the regional model. This study suggests that, in addition to local atmospheric boundary processes, extreme NSWC events play a vital role in shaping the mean distribution. Although these features are similar to those along the Gulf Stream, atmospheric fronts appear to play a relatively minor role in the Greenland Sea. Instead, the frequent cyclone generation near the sea ice edge and the anticyclonic circulation over Greenland in conjunction with the transient synoptic circulation seem essential. In the warm season, positive NSWC was virtually missing in the Greenland Sea, unlike in the Gulf Stream region, reflecting the shallow virtual temperature response to the surface thermal forcing. This study contributes to understanding the mechanisms by which sea ice variability affects large‐scale atmospheric circulation in remote regions.

Auxiliary model‐based recursive least squares and stochastic gradient algorithms and convergence analysis for feedback nonlinear output‐error systems

SummaryThis paper deals with the problem of the parameter estimation for feedback nonlinear output‐error systems. The auxiliary model‐based recursive least squares algorithm and the auxiliary model‐based stochastic gradient algorithm are derived for parameter estimation. Based on the stochastic process theory, the convergence of the proposed algorithms are proved. The simulation results indicate that the proposed algorithms can estimate the parameters of feedback nonlinear output‐error systems effectively.

Change readiness in organizations: an affective cognitive process for convergent sensemaking

PurposeThis conceptual paper aims to present a new, integrated model for change readiness that focuses on affective sensemaking among intra-organizational members. Change processes are often hindered by lack of preparedness, which can be justified by organizational members' emotional resistance to change and divergent understandings of its meaning. Our paper proposes a normative model depicting the interactive process between middle-managers and employees until convergence of meaning is achieved and the organization is ready to change.Design/methodology/approachThe authors offer a conceptual process model that describes how employees prepare for organizational change. The model illustrates how emotionally laden narratives enable employees to make sense of organizational change communicated by middle managers.FindingsThe sensemaking process is initiated by the negative emotions employees often experience when organizational change is first presented. Then middle managers must transform the negative felt emotions into positive valence via the strategic use of narratives that contain an affective component. This is done to increase the likelihood that convergent sensemaking takes place. Until this stage, intra-organizational members holding different perspectives about the need to change, engage in discussions in which the conflicting views are supported by the instrumental and systematic use of emotional tools with different valence.Research limitations/implicationsFirst, we contribute to the change readiness literature by offering a detailed process for managers to influence individual readiness for change in their organizations. Our paper proposes a normative model depicting the interactive process between middle-managers and employees until convergence of meaning is achieved and the organization is ready to change. Future work needs to empirically test our model.Practical implicationsWe contribute to the sensemaking literature by integrating positive and negative valence into the process for understanding organizational change. Finally, we contribute to our practical understanding of convergent sensemaking processes through the strategic use of narratives in organizations.Social implicationsOur paper proposes a normative model depicting the interactive process between middle-managers and employees until convergence of meaning is achieved and the organization is ready to organizational and social change.Originality/valueOur main contributions are three-fold. First, we contribute to the change readiness literature by offering a detailed process for managers to influence individual readiness for change in their organizations. Secondly, we contribute to the sensemaking literature by integrating positive and negative valence into the process for understanding organizational change. Finally, we contribute to our understanding of convergent sensemaking processes through the strategic use of narratives.

Study on stochastic convergence of China’s carbon emission efficiency

ABSTRACT Carbon emission efficiency (CEE) and its stochastic convergence are important indicators for achieving the strategic goal of carbon peaking and carbon neutrality. Thus, this paper firstly estimates the CEE of 30 provinces in China from 1995 to 2019 with the super efficiency of the SBM model. Then the panel unit root test method is adopted to test its stochastic convergence. The results show that the overall CEE has not reached the effective level, and the CEE level varies greatly among regions. There is a stochastic divergence of CEE in most regions from 1995 to 2001. While the CEE of most regions changes to convergence after 2002. From 1995 to 2019, the CEE of the western, northeast, and southwest regions diverge. While the CEE of the national level, the eastern, central regions, and the other six regions in the eight major economic zones converged stochastically. Among the divergent areas, the CEE of Heilongjiang, Guangxi, and Sichuan provinces are the main contributors to the CEE divergence. Therefore, it is the key to narrowing the differences in regional low-carbon development in China by significantly improving the CEE of each province.

A note about almost uniform convergence on D-poset of intuitionistic fuzzy sets

The aim of this contribution is studying the almost uniform convergence on D-poset of intuitionistic fuzzy sets. We prove the connection between almost everywhere convergence of random variables in Kolmogorov probability space and almost uniform convergence of observables in the mentioned D-poset. We define a product operation on D-poset of intuitionistic fuzzy sets and prove the existence of a joint observable, too.

Transiting toward sustainable development: stochastic convergence of energy diversification using a newly constructed index.

An optimal energy mix is a sine qua non for sustainable development. However, the global energy mix is sub-optimally dominated by fossils which endangers energy security and threatens the attainment of sustainable development. Understanding the convergence of energy series can assist the transition path to optimal energy mix and sustainable development. Thus, research on the convergence of several energy series has gained prominence in recent years. This study extends this important niche in the literature on the convergence of natural resources and environmental series by examining the convergence in energy diversification along several dimensions for a panel of 79 lower-middle, higher-middle, and high-income countries. As a departure from the existing studies, the study employs a novel methodology that allows abrupt or smooth changes through the Fourier approximation of smooth breaks, while including factor structures to test for the presence of unit roots in the relative energy diversification series. The results provide evidence of convergence of the energy diversification series in the majority of the considered countries, with 90% of the sample demonstrating convergence. A disaggregated country analysis was conducted and the findings show that 93% of the lower-middle-income countries are converging, while 95% of the upper-middle-income countries and 87% of the high-income countries are converging. Policy implications of the findings are also discussed.

“The Gates of Eternal Life”: Metamorphosis and Performativity in Middle to Late Byzantine Sculpted Church Doors (with a Case Study of a Wallachian Wooden Door)

In recent years, there has been a growing interest in analyzing the manufacturing techniques of Byzantine church doors in laboratory settings. However, the connection between the iconography and significance of the décor of church doors and their liturgical performativity, as well as their parallels with iconostases in Byzantium, remained a relatively underexplored area of study. This article seeks to delve deeper into these intersections. By focusing on the relationship between the iconography of church doors in Middle to Late Byzantium and their connection to the sacred space and liturgical practices, I aim to shed light on how these artworks played a crucial role in the sacred experience of the Byzantines. This exploration will not highlight only the aesthetic evolution of church door artwork but also emphasize the communal and embodied nature of the religious experience during the Byzantine era. Their intricate designs were not merely decorative elements but served as portals to the divine, enriching the salvation journey of worshippers as they crossed the threshold into the liturgical spaces. By conducting an examination of the development of door iconography and their symbolism throughout the empire’s history, the transformation of narrative depictions from the Middle Byzantine era to the Palaiologan period, culminating in a convergence of symbolic meanings within the sacred space of the church, is delineated. This transformation is further exemplified by a sculpted church door from the Principality of Wallachia. By bridging the gap between art history and religious studies, this article aims to rekindle interest in the profound symbolism and significance of Byzantine church doors and their relation to sacred liturgical space, offering a broader perspective on an important aspect of Byzantine heritage.

Climate Change Is Leading to a Convergence of Global Climate Distribution

AbstractThe impact of changes in global temperatures and precipitation on climate distribution remains unclear. Taking the annual global average temperatures and precipitation as the origin, this study determined the climate distribution with the distances of temperature and precipitation from their global averages as the X and Y axes. The results showed that during 1980–2019, the global temperature distribution converged toward the mean (convergence), while the precipitation distribution moved away from the mean (divergence). The combined effects of both led to a convergence in the global climate distribution. During 2025–2100, significant climate convergence is observed under two emission scenarios (SSP245 and SSP585). However, the climate convergence and the area of change in climate type remains insignificant only under SSP126, suggesting that the diversity of the global climate pattern can be maintained under a sustainable emission pathway (SSP126), whereas high emission pathways will lead to greater uniformity in global climate.

Limit Law for Zagreb and Wiener Indices of Random Exponential Recursive Trees

The Wiener index is the sum of distances of all pairs of nodes in a graph; and the Zagreb index is defined as the sum of squares of the degrees of nodes in a rooted tree. In this note, we calculate the first two moments of the Wiener and Zagreb indices of random exponential recursive trees (random ERTs) from two systems of recurrence relations. Then, by an application of the contraction method, we characterize the limit law for a scaled Zagreb index of ERTs. Via the martingale convergence theorem, we also show the almost sure convergence and quadratic mean convergence of an appropriately scaled Wiener index that is indicative of the distance of two randomly chosen nodes.

Convergence of aquatic products consumption: A disaggregated analysis in European countries

Several benefits of consuming fishery and aquaculture products have been documented by the extant literature. However, the literature has been largely silent on few dimensions of aquaculture products, including the convergence of aquatic products consumption. An importance of investigating the convergence of aquatic products is that it provides hindsight on which countries should be the focus of exporters of the products. Convergence analysis of aquatic products consumption provides information that is relevant to the need to boost local production of aquatic products, and to conserve foreign exchange earnings. The aim of this study is to investigate the convergence of total aquatic products consumption per capita in 27 European Union countries plus United Kingdom, during 1993–2019. We have further considered the convergence of the components of total aquatic products consumption, which include aquatic animals, cephalopods, crustaceans, demersal fish, freshwater fish, marine fish, molluscs, and pelagic fish. Additionally, we have examined conditional convergence by evaluating the determinants of convergence of total aquatic products consumption. Using recently introduced unit root tests that provide for both smooth and sharp breaks, the results provide support for stochastic convergence of total aquatic products consumption per capita. Using a new conditional convergence approach, the analysis demonstrates that population growth rate, real gross domestic product, and prices of aquatic products are factors that enable the convergence of total aquatic products. The results are not materially different across the components of total aquatic products consumption. The implications of the results are discussed in the paper.

Transcultural Adaptation of the Collaborative Model for Promoting Competence and Success for Students with Autism Spectrum Disorder (COMPASS)

ABSTRACT This study describes the transcultural adaptation of the Collaborative Model for Promoting Competence and Success for Students with Autism Spectrum Disorder (COMPASS) to Brazilian Portuguese (BP). A blind translation of the original version in English (OV) to the version in BP, blind back-translation of the BP version into English (BT), comparison of BT with OV to statistically verify the convergence (CO), minimum divergence (MD) and divergence of meaning (DM) between BT and OV, review of the BP version by a committee of experts, maintaining conceptual, idiomatic, semantic and cultural equivalence, and sending of the files to the author of the model, was carried out. 1372 items were translated from English to BP. After comparing BT/OV, 0.6% DM (9 items), 47.9% MD (657 items), and 51.5% CO (706 items) were found. 97 equivalences were made, 43 semantic and 54 conceptual. The author of the model received all files from steps 1 to 4. Having carried out this process, it is possible to state that COMPASS was transcultural adapted to BP. With the future availability of COMPASS in Brazil, we hope that it can contribute to the development of the quality of education for students with Autism Spectrum Disorder in the country.