Exponential Growth Research Articles

Gradient flows of generalized relative entropy and functional inequalities on graphs

We derive the discrete forms of the porous medium equation and fast diffusion equation with drift terms on a finite graph as gradient flows of the m-relative entropy, with the global existence of solutions. We show the Łojasiewicz inequality to prove the convergence of solutions and some important functional inequalities. More specifically, the Łojasiewicz inequality holds near the stationary solution with exponent 12, which leads to the exactly exponential convergence rate with a finite trajectory length. It can also be applied to show the Talagrand-type inequality and the log-Sobolev-type inequality directly.

Exact convergence rate of the central limit theorem and polynomial convergence rate for branching processes in a random environment

Let (Zn) be a supercritical branching process in an independent and identically distributed (i.i.d.) random environment. The paper studies the properties of the estimator Mn=n−1∑k=0n−1(Zk+1/Zk) introduced by Dion and Esty in 1979. We introduce a related martingale and discuss its convergence and exponential convergence rate. On this basis the exact convergence rate of the central limit theorem for normalized Mn is given.

Study on Thermal Oxygen Aging Characteristics and Degradation Kinetics of PMR350 Resin.

The thermal stability and aging kinetics of polyimides have garnered significant research attention. As a newly developed class of high thermal stability polyimide, the thermal aging characteristics and degradation kinetics of phenylene-capped polyimide prepolymer (PMR350) have not yet been reported. In this article, the thermo-oxidative stability of PMR350 was investigated systematically. The thermal degradation kinetics of PMR350 resin under different atmospheres were also analyzed using the Flynn-Wall-Ozawa method, the Kissinger-Akahira-Sunose method, and the Friedman method. Thermogravimetric analysis (TGA) results revealed that the 5% thermal decomposition temperature (Td5%) of PMR350 in a nitrogen atmosphere was 29 °C higher than that in air, and the maximum thermal degradation rate was 0.0025%/°C, which is only one-seventh of that observed in air. Isothermal oxidative aging results indicated that the weight loss rate of PMR350 and the time-dependence relationship follow a first-order exponential growth function. PMR350 resin thermal decomposition reaction under air atmosphere includes one stage, with a degradation activation energy of approximately 57 kJ/mol. The reaction model g(α) fits the F2 model, and the integral form is given by g(α) = 1/(1 - α). In contrast, the thermal decomposition reaction under a nitrogen atmosphere consists of two stages, with degradation activation energies of 240 kJ/mol and 200 kJ/mol, respectively. The reaction models g(α) correspond to the A2 and D3 models, with the integral forms represented as g(α) = [-ln(1 - α)]2 and g(α) = [1 - (1 - α)1/3]2 due to the oxygen accelerating thermal degradation from multiple perspectives. Moreover, PMR350 resin maintained high hardness and modulus even after thermal aging at 350 °C for 300 h. The results indicate that the resin exhibits excellent resistance to thermal and oxygen aging. This study represents the first systematic analysis of the thermal stability characteristics of PMR350 resin, offering essential theoretical insights and data support for understanding the mechanisms of thermal stability modification in PMR350 and its engineering applications.

Predicting the Representative Elementary Volume by determining the evolution law of the convergence cone

In order to characterise a rock formation prior to subsurface operations, it is required to find a microscale rock volume for which the homogenised property does not fluctuate when the size of the sample is increased; the Representative Elementary Volume (REV). Its determination usually comes at the cost of a large number of simulations, making it overall a computationally expensive process. Therefore, many scientific studies have been dedicated to optimising the process of finding REV. Using statistical numerical methods, it is shown that the fluctuation of the effective property corresponds overall to a cone-like shape convergence. We suggest determining the generic evolution law of the cone of convergence, which can be used to predict the size of the REV and the effective physical property. This study is based on simulations of Stokes flow through idealised microstructures from which the permeability is upscaled. By tracing and plotting the convergence of permeability for multiple samples, the full cone of convergence appears. The cone shows exponential growth and decay, converging towards the effective permeability of the microstructure. By fitting a log-normal distribution on the collected data points, we show that the generic evolution law of the cone of convergence can always be described with two parameters, independently of the porosity. We show that the determined law of the cone also applies to real microstructures, despite the presence of natural heterogeneities. The new method allows us to reduce the computational costs of finding all characteristics related to REV by simulating several subsamples rather than the full-sized sample, unlocking thereby high-resolution samples which are often too computationally expensive. The use of a statistical model provides quantification of the precision level we can obtain on the REV determination.

Developing a process for assessing the safety of a digital mental health intervention and gaining regulatory approval: a case study and academic’s guide

BackgroundThe field of digital mental health has followed an exponential growth trajectory in recent years. While the evidence base has increased significantly, its adoption within health and care services has been slowed by several challenges, including a lack of knowledge from researchers regarding how to navigate the pathway for mandatory regulatory approval. This paper details the steps that a team must take to achieve the required approvals to carry out a research study using a novel digital mental health intervention. We used a randomised controlled trial of a digital mental health intervention called STOP (Successful Treatment of Paranoia) as a worked example.MethodsThe methods section explains the two main objectives that are required to achieve regulatory approval (MHRA Notification of No Objection) and the detailed steps involved within each, as carried out for the STOP trial. First, the existing safety of digital mental health interventions must be demonstrated. This can refer to literature reviews, any feasibility/pilot safety data, and requires a risk management plan. Second, a detailed plan to further evaluate the safety of the digital mental health intervention is needed. As part of this we describe the STOP study’s development of a framework for categorising adverse events and based on this framework, a tool to collect adverse event data.ResultsWe present literature review results, safety-related feasibility study findings and the full risk management plan for STOP, which addressed 26 possible hazards, and included the 6-point scales developed to quantify the probability and severity of typical risks involved when a psychiatric population receives a digital intervention without the direct support of a therapist. We also present an Adverse Event Category Framework for Digital Therapeutic Devices and the Adverse Events Checklist—which assesses 15 different categories of adverse events—that was constructed from this and used in the STOP trial.ConclusionsThe example shared in this paper serves as a guide for academics and professionals working in the field of digital mental health. It provides insights into the safety assessment requirements of regulatory bodies when a clinical investigation of a digital mental health intervention is proposed. Methods, scales and tools that could easily be adapted for use in other similar research are presented, with the expectation that these will assist other researchers in the field seeking regulatory approval for digital mental health products.

Avoid the “Pitfalls”: Specific Features of Organizational Change Governance

The exponential growth of technology contrasts with the slower linear relationships of organizational growth. In the face of constant changes in the world, it is important to understand whether an organization is ready to implement innovative ideas, since otherwise this will not increase its creativity and competitiveness. However, many organizations today are exactly the same as they were in the previous days. This situation mainly concerns the practice of interaction and change management. This means that the organization must be able to realize its potential at the same speed as new opportunities appear in the world. This empirical study is aimed at managing change in an organization, as well as addressing the question of how to act so that the implemented changes are comfortable, appropriate, useful and take root; how to ensure that a smart idea is executed well and ultimately delivers value. The real situation is researched from an observational point of view. An empirical model for managing organizational change in conditions of intense changes in the eco-environment and human nature itself is presented.

Ramping cells in the rodent medial prefrontal cortex encode time to past and future events via real Laplace transform

In interval reproduction tasks, animals must remember the event starting the interval and anticipate the time of the planned response to terminate the interval. The interval reproduction task thus allows for studying both memory for the past and anticipation of the future. We analyzed previously published recordings from the rodent medial prefrontal cortex [J. Henke et al., eLife10, e71612 (2021)] during an interval reproduction task and identified two cell groups by modeling their temporal receptive fields using hierarchical Bayesian models. The firing in the "past cells" group peaked at the start of the interval and relaxed exponentially back to baseline. The firing in the "future cells" group increased exponentially and peaked right before the planned action at the end of the interval. Contrary to the previous assumption that timing information in the brain has one or two time scales for a given interval, we found strong evidence for a continuous distribution of the exponential rate constants for both past and future cell populations. The real Laplace transformation of time predicts exponential firing with a continuous distribution of rate constants across the population. Therefore, the firing pattern of the past cells can be identified with the Laplace transform of time since the past event while the firing pattern of the future cells can be identified with the Laplace transform of time until the planned future event.

Adiabatic gauge potential and integrability breaking with free fermions

We revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos. We also study the so-called weak integrability breaking, which occurs if the dynamical effects of the perturbation do not appear at leading order in the perturbing parameter. A recent statement in the literature claimed that integrability breaking should generally lead to an exponential growth of the AGP norm with respect to the volume. However, afterwards it was found that weak integrability breaking is a counter-example, leading to a cross-over between polynomial and exponential growth. Here we show that in free fermionic systems the AGP norm always grows polynomially, if the perturbation is local with respect to the fermions, even if the perturbation strongly breaks integrability. As a by-product of our computations we also find, that in free fermionic spin chains there are operators which weakly break integrability, but which are not associated with known long range deformations.

Gravitational index of the heterotic string

The fundamental heterotic string has a tower of BPS states whose supersymmetric index has an exponential growth in the charges. We construct the saddle-point of the gravitational path integral corresponding to this index. The saddle-point configuration is a supersymmetric rotating non-extremal Euclidean black hole. This configuration is singular in the two-derivative theory. We show that the addition of higher-derivative terms in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supergravity resolves the singularity. In doing so, we extend the recently-developed “new attractor mechanism” to include the effect of higher-derivative terms. Remarkably, the one-loop, four-derivative F-term contribution to the prepotential leads to a precise match of the gravitational and microscopic index. We also comment, using the effective theory near the horizon, on the possibility of a string-size near-extremal black hole. Our results clarify the meaning of different descriptions of this system in the literature. The thermal state transitions to a winding condensate and a gas of strings without ever reaching a small black hole, while the index is captured by the rotating Euclidean black hole solution and is constant and thus smoothly connected to the microscopic ensemble.

Generative AI: hopes, controversies and the future of faculty roles in education

Purpose Generative artificial intelligence (GAI) has seen exponential growth in recent years due to its capability to generate original content through natural language processing and comprehensive language models. This paper aims to investigate the transformative impact of GAI on higher education, focusing on the evolving roles of faculty in the classroom. Design/methodology/approach Using a phenomenological perspective and a process approach, the study involved 25 semi-structured interviews with academicians in higher education. Findings The findings reveal that GAI currently creates biased and commercially driven learning environments, challenging traditional pedagogical models. Despite its potential for enhancing education, the autonomous nature of GAI often prioritizes commercial interests over pedagogical goals. Research limitations/implications The study is limited to faculty perspectives, suggesting future research should include student viewpoints and diverse educational contexts. Practical implications The study highlights the need for higher education institutions to develop comprehensive policies, provide training for faculty and students and design new courses that leverage GAI for personalized learning experiences and enhanced faculty research. Originality/value This paper contributes to the emerging literature on GAI’s impact on education, highlighting its dual nature as both a transformative tool and a potential threat to traditional educational roles and outcomes.

Modeling long-term, stage-structured dynamics of Tribolium castaneum (Coleoptera: Tenebrionidae) at food facilities with and without two types of long-lasting insecticide-incorporated netting.

The red flour beetle, Tribolium castaneum (Herbst) (Coleoptera: Tenebrionidae), is a cosmopolitan and destructive external-infesting pest at many food facilities. The use of deltamethrin- and α-cypermethrin-incorporated long-lasting insecticide-incorporated netting (LLIN) has shown incredible promise for the management of stored product insects. However, it is unknown how LLIN deployed within food facilities may affect the long-term population dynamics of T. castaneum compared to populations where no LLIN is present. Exposure to LLIN has been shown to affect mortality in the current generation and decrease progeny production in the subsequent generation. Thus, we modeled the long-term population dynamics of T. castaneum at food facilities over 15 generations by incorporating realistic estimates for mortality and progeny reduction after contact with LLIN compared to baseline growth by the species. We parameterized the model with estimates from the literature and used a four-stage structured population (eggs, larvae, pupae, and adults). The model was implemented using the package popbio in R. Our models suggest that deploying LLIN led to significant population reductions based on the estimates of mortality and progeny reduction from prior work, whereas the baseline model exhibited exponential population growth. In addition, there were differences in the frequencies of each life stage under each scenario modeled. As a result, it appears deploying LLIN may contribute to the local extirpation of T. castaneum within as few as 15 generations. Our work contributes to a growing literature about the effectiveness of incorporating LLIN into existing pest management programs for managing stored product insects in food facilities.

Exploring Chinese Tourists’ Well-Being Through a Confucian Lens: A Multi-Focal Model

ABSTRACT Despite exponential growth in research interest in the psychological benefits derived from travel experiences, existing conceptualizations of well-being in tourism predominantly adopt Western perspectives. This conceptual paper proposes a multifocal model for understanding tourist well-being through a Confucian lens. By comparing the five cardinal Confucian virtues with Aristotelian well-being perspectives, this multidimensional framework integrates traditional and modern well-being insights, depicting eleven dimensions of Chinese tourists’ psychological well-being. This manuscript contributes a multi-focal model of Chinese tourist well-being, which extends the traditional one-dimensional Confucian perspectives on well-being toward a two-dimensional framework which includes eudaimonic and hedonic aspects. Future studies should conduct empirical work designed to clarify conceptual and terminological ambiguity and advance discourse on the integration of Eastern perspectives into the study of tourist well-being.

Efficiency Boosts in Human Mobility Data Privacy Risk Assessment: Advancements within the PRUDEnce Framework

With the exponential growth of mobility data generated by IoT, social networks, and mobile devices, there is a pressing need to address privacy concerns. Our work proposes methods to reduce the computation of privacy risk evaluation on mobility datasets, focusing on reducing background knowledge configurations and matching functions, and enhancing code performance. Leveraging the unique characteristics of trajectory data, we aim to minimize the size of combination sets and directly evaluate risk for trajectories with distinct values. Additionally, we optimize efficiency by storing essential information in memory to eliminate unnecessary computations. These approaches offer a more efficient and effective means of identifying and addressing privacy risks associated with diverse mobility datasets.

Diversity in Action: Unveiling Flipkart’s Path to Inclusion and Excellence

This comprehensive case study explores the journey of Flipkart India Pvt. Ltd., tracing its trajectory from its inception to its current position as a pioneering force in the Indian e-commerce landscape. The study aims to outline the company’s exponential growth and potential by highlighting its pivotal milestones, strategic shifts, acquisitions, and the adaptive measures that have been instrumental in its evolutionary course. With a particular focus on the transformative influence of diversity, equity, and inclusion (DE&I) initiatives within Flipkart’s organizational framework, the study emphasizes the changing needs of the workforce and their need for inclusion in the workplace. By analyzing how DE&I efforts intersect with diverse operational domains, the study underscores their pivotal role in empowering a dynamic workforce and propelling societal progress. Flipkart’s journey as a pioneer of DE&I in the e-commerce industry has set a benchmark for enhancing workforce potential and demonstrating its direct impact on the business altogether. The authors of the study have drawn insights from a range of secondary and publicly available sources that offer a comprehensive view of the symbiotic relationship between corporate growth and DE&I initiatives, an imperative for businesses aspiring to expand, distinguish their brand, and foster innovation.

Social Networks as a Tool for Evidence-Based Health Education: Umbrella Review.

The number of people who access social networking sites continues to increase at an exponential rate. The use of technology is an essential skill for nursing professionals and its development represents a challenge in improving health education, promotion and care. The objective of this systematic review is to analyse the use of social networking sites by healthcare professionals as an intervention tool for evidence-based public health education. The protocol of this umbrella review was registered in the International Prospective Register of Systematic Reviews (CRD42023407249). Searches were carried out in MEDLINE (PubMed), Web of Science, CINAHL, PsycINFO (EBSCOhost), and Cochrane Library of Systematic Reviews, in February 2023. A narrative synthesis of the results was conducted. 1896 articles were found, of which 15 reviews fulfilled the inclusion criteria. Social networks broadened the profession; they were YouTube, X (formerly Twitter), Facebook, and Instagram. The target population was mainly young professionals, and they came across different topic areas that addressed health education. It is important to have information backed by scientific evidence to make health decisions. Health professionals active on social networking sites have a unique opportunity to educate the public about health by sharing scientific evidence in an accessible and clear way, which helps to combat misinformation.

Interaction of defects, martensitic transformation and slip in metastable body centred cubic crystals of Ti-10V-2Fe-3Al: A study via crystal plasticity finite element methods (CPFEM)

Metastable β titanium alloys are widely applied in many industries. These alloys can have plastic deformation via dislocation slip, twinning, stress-induced martensite (SIM), or a combination of these. These alloys fail in a ductile manner via a process of void nucleation, growth, and coalescence. Inherent defects, such as voids, are commonly attributed to poor mechanical properties. In this study, aspects of plastic anisotropy in damage accumulation are investigated for metastable crystals that deform by combined slip and SIM. The focus of this study is to understand the evolution of damage due to inherent voids in metastable Ti-10V-2Fe-3Al single crystals. This investigation is conducted using crystal plasticity-based 3D finite element (FE) calculations. A unit-cell FE model involving a spherical void is deformed under constant stress triaxiality and lode parameter. We investigated four triaxiality values at differing lode parameters in three crystal orientations. The void growth was found to be heavily dependent on crystal orientation at low triaxialities. At higher triaxialities, SIM is found to inhibit the void growth via accommodation of the required deformation in the surrounding material. Orientations aligned favourable with SIM undergo significantly less void growth. The accommodation of deformation in the surrounding matrix was found to help preserve the integrity of the void, preventing the localisation of deformation around the void. At lower lode parameter and at higher stress triaxiality this impedes the exponential growth of the void. While, at higher lode parameter with low triaxiality SIM was found to delay the collapse of the void into a crack like morphology. This study not only deepens our understanding of the mechanical behaviour of metastable β titanium alloys, but also unveils the complex interplay between inherent defects, stress-induced martensite, and slip-based plasticity within their crystalline structure, offering fresh perspectives on enhancing material performance.

Stress-Induced Production of Bioactive Oxylipins in Marine Microalgae.

Microalgae, stemming from a complex evolutionary lineage, possess a metabolic composition influenced by their evolutionary journey. They have the capacity to generate diverse polyunsaturated fatty acids (PUFAs), akin to those found in terrestrial plants and oily fish. Also, because of their numerous double bonds, these metabolic compounds are prone to oxidation processes, leading to the creation of valuable bioactive molecules called oxylipins. Moreover, owing to their adaptability across various environments, microalgae offer an intriguing avenue for biosynthesizing these compounds. Thus, modifying the culture conditions could potentially impact the profiles of oxylipins. Indeed, the accumulation of oxylipins in microalgae is subject to the influence of growth conditions, nutrient availability, and stressors, and adjusting these factors can enhance their production in microalgae culture. Consequently, the present study scrutinized the LC-MS/MS profiles of oxylipins from three marine microalgae species (two Haptagophytes and one Chlorophyte) cultivated in 1 L of photobioreactors under varying stress-inducing conditions, such as the introduction of H2O2, EtOAc, and NaCl, during their exponential growth phase. Approximately 50 oxylipins were identified, exhibiting different concentrations depending on the species and growth circumstances. This research suggests that microalgae metabolisms can be steered toward the production of bioactive oxylipins through modifications in the culture conditions. In this instance, the application of a low dose of hydrogen peroxide to Mi 124 appears to stimulate the production of nonenzymatic oxylipins. For Mi136, it is the application of salt stress that seems to increase the overall production of oxylipins. In the case of Mi 168, either a low concentration of H2O2 or a high concentration of AcOEt appears to have this effect.

Compact modeling of highly excited linear aggregates using generalized quantum particles

Calculation of nonlinear spectra of chromophore aggregates using response function theory when the number of contributing chromophores is large, and the level of excitation is high is extremely complicated. The main limitation is due to the exponential growth of computational time due to the aggregate size and number of excitations when considering an arbitrary excitation intensity. Non-perturbative calculation of spectra in this case becomes advantageous. We revisit our proposed model with exciton - exciton annihilation terms and apply it to large aggregates. We generalize the equations for both paulions and bosons with a parameter that allows smooth transition from one description to another. Intermediate statistics may also be valuable as molecular electronic excitations do not strictly obey either boson or paulion statistics. Specific approximations allow efficient calculation of pump-probe spectra for a large J aggregate.

The economophysical model of the propagation of innovation: the Ising model

The process of technical and economic justification of investment, analysis and evaluation of the effectiveness of innovation requires a tool for describing and modeling the process of distribution of technology in the industry. The work presents a model of propagation of innovation involving physical approaches, describing the market saturation point, i.e. the point at which the exponential growth of the innovation propagation speed is replaced by the logarithmic growth. The object of the study is the propagation of innovation, and the subject is the development of the market saturation point functional. The authors justified the implementation and described the approach to modeling of the process of saturation of the market with innovation by the physical Ising model. The value of the Ising model’s toolkit is presented by the Curie point in ferromagnets which characterizes the second order phase transition. The article presents the mathematical model of the compliance of physical parameters with economic ones: the amount of inter-company influence, barriers to implementation and breakthrough of innovation. The authors adduce the discussion of the limitations and applicability of this model as well as further potential directions of study of economophysical models. The tools developed by the authors can be used in all sectors of economics to improve their innovation activity level.

The 6 Whats Coaching Model: A Practical Guide to Structuring Professional Coaching Conversations

Coaching practice, which occurs largely in organizational contexts, has traditionally been seen as forward-looking dialogue that moves clients from intentions to goal attainment. Extensive research can be found attesting to the value of coaching experiences for personal and professional development. Yet, with exponential growth in this field, what is represented as coaching may take a wide variety of forms,  thereby obscuring and problematizing what the nature of professional coaching is, especially as articulated by professional coaching organizations. As well, with such diversity in coaching approaches, how can organizations fully appreciate what they are inviting into their environment when they choose to employ coaching as an HRD strategy? The 6 whats model aims to recenter awareness on the essential elements of a coaching conversation in order that the coherence of coaching practice is more consistent and that practice boundaries for this relatively new profession can be reaffirmed. It builds upon historical traditions within the coaching field and articulates the core elements of coaching conversations that are required so that coaching relationships remain within their legitimate domain of professional endeavor.