Eventual Convergence Research Articles

Examining career trajectories of Norwegian PhD recipients: slower progression for women academics but not a leaky pipeline

ABSTRACT We use longitudinal data for the entire population of Norwegian PhD recipients over five decades to examine why only one-third of full professors in Norway are women, despite gender balance among current PhDs. We find that 90% of the lower female representation is due to lower female proportions in earlier PhD cohorts, increasing sizes of cohorts, and decreasing overall rates of promotion, which together we call ‘compositional/historical factors’. We find that the remaining imbalance is not caused by women dropping out, but rather by 14–18% slower average promotion rates calculated using hazard analysis. However, on average, women eventually catch up with men after about 20 years, although this differs by field. A similar hazard analysis for the US shows that women doctorates are less likely than men to enter tenure-track academia although more likely to enter non-tenure-track academia. This leads to larger US gender differences in advancement to full professorships and no eventual convergence. We suggest possible reasons for the differences between Norway and the US.

Diminishing legacy effects from forest fertilization on stand structure, vegetation community, and soil function

While there is consensus that fertilization with nitrogen (N) is a cost-effective way of increasing both forest biomass yield and timber harvest profitability, the strength and longevity of legacy effects are debated. To quantify legacy effects of past fertilization, we analysed 21 mixed Pinus sylvesteris and Picea abies stands. The stands, on average 23 years old at the time of this study, were either unfertilized (n=7), fertilized with 150 kg N ha−1 once 36 years ago (n=7), or twice, 45 and 36 years ago, respectively (n=7), during the previous stand rotation. We performed measurements on soil N mineralisation and N availability, forest growth, ground vegetation community composition, soil and vegetation C/N ratios and soil C and N stocks, many of which responded to legacy N fertilization earlier in stand development. Our results show that the legacy effects of fertilization during the previous stand rotation have diminished through time, indicating an eventual convergence of stand properties. Specifically, all significant effects present in the previous measurement period (over a decade ago), were weaker or completely absent in the current study (i.e. 36 years after fertilization and 23 years after initiation of the new stands). None-the-less, this indicates a longer legacy effect of N fertilization than what is normally considered and suggests that care should be taken to mitigate unwanted, long-term effects when utilizing N addition to promote tree growth in boreal forests.

Protection path of personal data and privacy in China: Moving from monism to dualism in civil law and then in criminal law

The relationship between privacy protection and personal data protection is legally and academically challenging. The PRC's civil law has evolved from the traditional monism of privacy right provision (protecting personal information) to the dualism of separating privacy protection and personal information protection. But when the private information within the privacy sphere involves personal information, the dualism protection is not absolute, but more delicate than it has been suggested.More importantly, there is little in the existing literature analysing the noteworthy divergence of the protection path of privacy and personal information in civil law and criminal law – or considering the reasonable convergence of the protection path under the civil and criminal law. China's Criminal Law has sought to protect privacy with personal information provision for more than a decade. But it is presently difficult to convert privacy content into private information for personal information protection purposes. Given the multifaceted forms of contemporary privacy invasion and comparative law trends and thoughts, we seek to build a protection framework for privacy in the information age under the criminal law – and continually updating it – so as to make use of the expression function of coherence law theory to nurture a culture of respecting individual privacy and trusting legal protection in the information technology environment. The eventual convergence of dualism protection of personal data and privacy in both civil law and criminal law corresponds to the doctrinal coherence in the information age and to policy considerations in the digital economy and society. Privacy is by default an inalienable right to protect dignity and liberty – while personal information can be a comprehensive interest, which values and balances security and purpose, in accordance with law, in a specific jurisdiction such as contemporary China. The dualism exemplifies criminal law's coordination with civil law in protection.

Monitoring of barricade pressure during the entire backfilling process for a high iron mine stope

The stability of the backfill barricade is an important foundation for safe mining production. The backfill material is transported to the underground mined-out area. During the backfilling process, it is difficult to directly monitor the curing process of backfill body and its lateral load on barricades. This severely affects the accurate formulation of the mining and backfilling strategy as well as effective control of associated costs. In order to investigate the change law of pressure on barricade, a continuous monitoring experiment was conducted by installing pressure sensors inside the barricade. The results indicated that the pressure on barricade showed an initial increase followed by a subsequent decrease and eventual convergence towards zero with the increase in backfill height and curing time. A barricade pressure prediction model was established for discontinuous backfilling conditions using a fitting method that characterizes the relationship between backfill height and barricade pressure through a Gaussian function. Finally, from both on-site monitoring and theoretical analysis, it was jointly demonstrated that the continuous filling of Luohe iron ore mine quarry has safety and feasibility.

Thermal-hydraulic-dynamic investigation of an inverted self-fluttering vortex generator

Static vortex generators initiate vortical structures; an active generator intensifies the vortices through local agitations. Flow-induced vibrations present a hybrid approach to enhance thermal mixing: the role of vortical redistribution. To further our series of study regarding the self-fluttering vortex generator, machine learning was utilized in this work to analyze a large set of experimental data which includes a broader range of design parameters in order to find a general rule of the onset of the large flapping motion and its effect on the overall thermal transport and frictional pressure loss characteristics. In addition, this paper presented the differences in thermal hydraulic efficiencies of a flapping vortex generator to an aggregation of traditional ones of the same configuration. Through machine-learning-aided analysis, we captured a striking behavior of the generator: the power-law regime spanning across different designs, bridging a shorter flow speed range each time. Such findings highlight the localization and specialization of such setups to certain flow conditions. We observe a saturation effect of the vortical redistribution process and the eventual convergence between pumping power and thermal performance. Among all interactions, we see a propensity toward lower-speed flows: higher efficiencies and better thermal transport– stands out as the characteristic of this flapping vortex generator.

Joint Power and Data Allocation in Multi-Carrier Full-Duplex Relaying Networks Operating With Finite Blocklength Codes

In this paper, we study a full-duplex (FD) relaying network operating with finite blocklength (FBL) codes. Based on Polyanskiy’s FBL model, we characterize the FBL reliability of the relaying network under both decode-and-forward (DF) and amplify-and-forward (AF) relaying schemes. Based on the characterisation, we provide reliability-optimal designs via optimal power allocation for both schemes in a single-carrier scenario. In particular, we prove that under the FD DF relaying scheme the (tightly approximated) overall error probability is convex in the transmit power at the relay. In addition, we show that minimizing the overall error probability of the FD AF relaying is equivalent to maximizing the overall signal to interference plus noise ratio (SINR), which is further proved to be pseudo-concave. Then, the designs for a single-carrier scenario are further extended to a multi-carrier scenario with a joint power and data allocation among carriers. In particular, for either the FD DF or FD AF relaying scheme, a joint optimization problem is reformulated to a single problem maximizing the reliability via finding and achieving the optimal SINRs, while auxiliary variables are introduced in FD AF relaying to facilitate the reformulation. Based on mathematical analysis, we respectively construct convex approximations and subsequently propose iterative algorithms, with which the error probability is reduced iteratively until an eventual convergence to an efficient suboptimal value. Hence, a corresponding suboptimal data and power allocation solution can be constructed for the multi-carrier scenario. Via numerical analysis, we validate our analytical model and the proposed allocation algorithms. The FD DF and FD AF relaying schemes are compared with direct transmission in both single-carrier and multi-carrier scenarios, and the benefits of applying FD relaying schemes and joint optimization among multiple carriers are observed.

Generalization error of GAN from the discriminator’s perspective

The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the memorization phenomenon, the eventual convergence to the empirical distribution. We consider a simplified GAN model with the generator replaced by a density and analyze how the discriminator contributes to generalization. We show that with early stopping, the generalization error measured by Wasserstein metric escapes from the curse of dimensionality, despite that in the long term, memorization is inevitable. In addition, we present a hardness of learning result for WGAN.

AdaptivePIDcontrol of robotic manipulators without equality/inequality constraints on control gains

AbstractThis article proposes two novel adaptive PID controllers for the trajectory tracking of robotic manipulators with known or unknown upper bound of the uncertainties, respectively. The designed controllers are shown to be not only robust with respect to the uncertainties but also adaptive with reference to the unknown manipulator and load parameters. Lyapunov stability analysis is included to prove eventual local asymptotic tracking. The salient features of the two proposed adaptive PID controllers are as follows: (1) they guarantee the eventual asymptotic convergence of the manipulator joint position and velocity tracking errors to zero with no need of any equality/inequality constraints on the controller gains when compared with the classical PID controller and the existing adaptive PID controllers; and (2) they offer better robustness against uncertainties than the existing classical PID controller, the adaptive PD controller, the linear active disturbance rejection controller, and the nonlinear disturbance observer based adaptive PID controller. Simulation studies and comprehensive comparisons demonstrate the superiorities of the two proposed adaptive PID controllers.

Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks.

Uncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof. Therefore the question remains, whether under stable conditions, in realistic situations found in IoT networks, this algorithm indeed converges. This paper demonstrates proof of the eventual convergence of the EWMA algorithm. The proof consists of two steps: it models the sensor network as the UOG (Uniform Opinion Graph) that enables the analytical approach to the problem, and then offers the mathematical proof of eventual convergence, using formalizations identified in the previous step. The paper demonstrates that the EWMA algorithm converges under all realistic conditions.

Opinion dynamics on tie-decay networks

In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.

Comparing immigrant commute travel adaptation across and within racial/ethnic groups

This research investigates differences in the adaptation process of immigrant commute distance and commute mode across and within three racial/ethnic groups—white, Hispanic, and Asian—in the United States to explore policies that facilitate immigrant travel in an efficient and sustainable way. A two-step analysis is conducted: the first step uses all US-born as the reference group, and the second step uses US-born of the same race/ethnicity as the reference. The second step overcomes a potential problem in existing research on immigrant travel adaptation: When all US-born are used as the reference group, the statistics mainly reflect the travel behavior of US-born white people, masking intrinsic travel differences among US-born racial/ethnic groups. Based on multi-level regression analysis of the 2017 National Household Travel Survey (NHTS) data, our results support existing findings of initial difference but eventual convergence of immigrant commute behavior with US-born, while highlighting white immigrants' persistence and Hispanic immigrants' low propensity in using non-automobile modes. Comparison results based on the two reference groups suggest that segmented assimilation due to racial/ethnic group membership is limited. Still, nuanced findings denote distinctive spatial mechanisms that affect immigrant and US-born Asians and highlight the short time window after immigrants' arrival in the U.S. during which policies might contribute to a continuation of their sustainable travel patterns.

The role of policy and legislation in mental health care

The interface of policy and legislation is crucial in making quality mental health care accessible in an effective manner. Shortage of psychiatrists and other mental health personnel in India poses a huge challenge in delivering mental health care. The social context is instrumental in subjecting the mentally ill to human rights violations and discriminations with low awareness, illiteracy, superstitions, denial, and the prevailing social perception of mental illness in India. The enormity of problem requires a multipronged approach supported by a robust policy with specific achievable goals. Mental health policy relies on the legal framework to achieve its goals, and ameliorate the lives of persons with mental disorders. Policy and legislation are two complementary approaches for improving mental health care and services. International developments in mental health care have brought a paradigm shift from “charity-” to “rights-” based approach which is very much reflected in India's first-ever Mental Health Policy, 2014, and the newly enacted Mental Healthcare Act, 2017. This shift entails a “participatory” approach for developing community-based facilities, services, and rehabilitation provisions. An analytical approach has been adopted to gauge the likely outcome of the combined role of this ambitious policy and law in light of existing mental health-care infrastructure and “social context.” An attempt has been made to highlight the main concerns and challenges in effective implementation of new law while putting forth feasible solutions to attain the policy goals. The paper concludes on a note that legal and health measures should work in tandem and eventual convergence be directed toward the best interest of mentally ill persons.

Self-focusing hybrid skyrmions in spatially varying canted ferromagnetic systems

Magnetic skyrmions are quasiparticle configurations in a magnetic film that can act as information carrying bits for ultrasmall, all-electronic nonvolatile memory. The skyrmions can be nucleated and driven by spin-orbit torque from a current driven in a heavy metal underlayer. Along its gyrotropic path, a Magnus force can cause a skyrmion to be annihilated at the boundaries. By combining interfacial and bulk Dzyaloshinskii-Moriya interactions (DMIs), for instance by using a B20 material on top of a heavy metal layer with high spin-orbit coupling, it is possible to engineer a hybrid skyrmion that will travel parallel to the racetrack with zero Magnus force. We show that by using a spatially varying interfacial DMI, a hybrid skyrmion will automatically self-focus onto such a track as its domain angle evolves along the path. Furthermore, using a gate driven voltage controlled magnetic anisotropy, we can control the trajectory of the hybrid skyrmion and its eventual convergence path and lane selection in a racetrack geometry.

Three‐dimensional anisotropic plasticity model for sand subjected to principal stress value change and axes rotation

AbstractA three‐dimensional (3D) anisotropic plasticity model for sand is formulated in this study to provide a constitutive description for both radial and principal stress axes rotation (PSAR) loading‐induced behavior under various conditions with a single set of model parameters. The model has zero elastic range, with plastic loading and flow direction dependent on both current stress and stress rate direction. Fabric tensor is introduced along with its evolution to achieve anisotropic plastic modulus, dilatancy, and flow rule formulations. Increase in plastic modulus under continuous PSAR achieves eventual convergence of strain accumulation. A unique decomposition of dilatancy controls the overall contraction and periodic dilatancy oscillation under PSAR. The performance of the model is first thoroughly evaluated based on drained/undrained, monotonic shear/PSAR tests on Toyoura sand, showing its effectiveness in reproducing the behavior of real sand. Discrete element method numerical test results are then adopted for comprehensive calibration of the model parameters, and then for validation of the model under 3D PSAR in any arbitrary direction. These comparisons highlight the model's capability in simulating the behavior of granular soil under 3D stress paths.

Prandtl number dependence of stratified turbulence

Abstract

Robustness of the Adaptive Bellman –Ford Algorithm: Global Stability and Ultimate Bounds

Self-stabilizing distance estimation algorithms are an important building block of many distributed systems, such as seen in the emerging field of aggregate computing. Their safe use in feedback systems or under persistent perturbations has not previously been formally analyzed. Self-stabilization only involves eventual convergence, and is not endowed with robustness properties associated with global uniform asymptotic stability and thus does not guarantee stability under perturbations or feedback. We formulate a Lyapunov function to analyze the Adaptive Bellman–Ford distance estimation algorithm and use it to prove global uniform asymptotic stability, a property which the classical Bellman–Ford algorithm lacks. Global uniform asymptotic stability assures a measure of robustness to structural perturbations, empirically observed by us in a previous work. We also show that the algorithm is ultimately bounded under bounded measurement error and device mobility and provide a tight bound on the ultimate bound and the time to attain it.

Finding Order in Chaos: Grappling with the Policy and Politics of Sustainable Energy Transition

Finding Order in Chaos: Grappling with the Policy and Politics of Sustainable Energy Transition

Efficiency of Best Response Dynamics with High Playing Rates in Potential Games

In this paper we design and analyze distributed best response dynamics to compute Nash equilibria in potential games. This algorithm uses local Poisson clocks for each player and does not rely on the usual but unrealistic assumption that players take no time to compute their best response. If this time (denotedδ) is taken into account, distributed best response dynamics (BRD) may suffer from overlaps: one player starts to play while another player has not changed its strategy yet. An overlap may lead to a decrease of the potential but we can show that they do not jeopardize eventual convergence to a Nash equilibrium. Our main result is to use a Markovian approach to show that the average execution time of the algorithm E[TBRD] can be bounded: 2δn log n/ log log n + O(n) ≤E[TBRD] ≤ 4e δn log n/ log log n+O(n), where ' is the Euler constant, n is the number of players and δ is the time taken by one player to compute its best response. These bounds are obtained by using an asymptotically optimal playing rate λ. Our analytic bound shows that 2δλ = log log n - log C, where C is a constant. This induces a large probability of overlap (p = 1 - C/ log1/2 n). In practice, numerical simulations also show that using high playing rates is efficient, with an optimal probability of overlap popt ≈ 0.78, for n up to 250. This shows that best response dynamics are unexpectedly efficient to compute Nash equilibria, even in a distributed setting.

Distributed best response dynamics with high playing rates in potential games

In this paper we design and analyze distributed best response dynamics to compute Nash equilibria in potential games. This algorithm uses local Poisson clocks for each player, and does not rely on the usual but unrealistic assumption that players take no time to compute their best response. If this time (denoted δ) is taken into account, distributed best response dynamics may suffer from overlaps: one player starts to play while another player has not changed its strategy yet. Overlaps may lead to drops of the potential but we can show that they do not jeopardize eventual convergence to a Nash equilibrium. Our main result is to use a Markovian approach to show that the average execution time of the algorithm can be bounded from above by eγδnlognloglogn(1+o(1)) and from below by δnlognloglogn(1+o(1)), where γ is the Euler constant, n is the number of players and δ is the time taken by one player to compute its best response. These bounds are obtained by using an asymptotically optimal playing rate λ. Our analytic bounds show that this λ is high: λˆ=loglogn−logloglognδ. This induces a large probability of overlap (pˆ=1−loglogn∕logn). In practice, numerical simulations also show that using high playing rates is efficient, with an optimal probability of overlap popt≈0.78 up to n=250. This implies that best response dynamics are unexpectedly efficient to compute Nash equilibria, even in a distributed setting.

Convergence rate analysis for the higher order power method in best rank one approximations of tensors

A popular and classical method for finding the best rank one approximation of a real tensor is the higher order power method (HOPM). It is known in the literature that the iterative sequence generated by HOPM converges globally, while the convergence rate can be superlinear, linear or sublinear. In this paper, we examine the convergence rate of HOPM in solving the best rank one approximation problem of real tensors. We first show that the iterative sequence of HOPM always converges globally and provide an explicit eventual sublinear convergence rate. The sublinear convergence rate estimate is in terms of the dimension and the order of the underlying tensor space. Then, we examine the concept of nondegenerate singular vector tuples and show that, if the sequence of HOPM converges to a nondegenerate singular vector tuple, then the global convergence rate is R-linear. We show that, for almost all tensors (in the sense of Lebesgue measure), all the singular vector tuples are nondegenerate, and so, the HOPM “typically” exhibits global R-linear convergence rate. Moreover, without any regularity assumption, we establish that the sequence generated by HOPM always converges globally and R-linearly for orthogonally decomposable tensors with order at least 3. We achieved this by showing that each nonzero singular vector tuple of an orthogonally decomposable tensor with order at least 3 is nondegenerate.