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Within Lorenz models, the three major kinds of butterfly effects (BEs) are the sensitive dependence on initial conditions (SDIC), the ability of a tiny perturbation to create an organized circulation at large distances, and the hypothetical role of small-scale processes in contributing to finite predictability, referred to as the first, second, and third kinds of butterfly effects (BE1, BE2, and BE3), respectively. A well-accepted definition of the butterfly effect is the BE1 with SDIC, which was rediscovered by Lorenz in 1963. In fact, the use of the term “butterfly” appeared in a conference presentation by Lorenz in 1972, when Lorenz introduced the BE2 as the metaphorical butterfly effect. In 2014, the so-called “real butterfly effect”, which is based on the features of Lorenz’s study in 1969, was introduced as the BE3.

We investigate error growth from small‐amplitude initial condition perturbations, simulated with a recent artificial intelligence‐based weather prediction model. From past simulations with standard physically‐based numerical models as well as from theoretical considerations it is expected that such small‐amplitude initial condition perturbations would grow very fast initially. This fast growth then sets a fixed and fundamental limit to the predictability of weather, a phenomenon known as the butterfly effect. We find however, that the AI‐based model completely fails to reproduce the rapid initial growth rates and hence would incorrectly suggest an unlimited predictability of the atmosphere. In contrast, if the initial perturbations are large and comparable to current uncertainties in the estimation of the initial state, the AI‐based model basically agrees with physically‐based simulations, although some deficits are still present. Plain Language Summary Even if perfect observations and models were available, the time interval for which weather forecasts can be accurate is limited. This limit is related to fundamental physical characteristics of the earth's atmosphere, which make small errors grow very fast and spread out, a feature known as the butterfly effect. In this article, we test if an artificial intelligence‐based weather prediction model is able to reproduce this butterfly effect. Therefore, we computed several weather forecasts that differed only very slightly in their starting conditions. We find, that in contrast to standard weather forecasting models, the initial difference grow only slowly in the AI‐based model and there is no indication of a butterfly effect at all. This provides an example of how machine learning models can fail to reproduce a fundamental physical principle, even though they can accurately mimic many observed behaviors. Key Points Current artificial‐intelligence‐based models cannot simulate the butterfly effect and incorrectly suggest unlimited atmospheric predictability Their error growth rate and structure remain similar to synoptic‐scale error growth regardless of the amplitude of the initial perturbation Synoptic‐scale error growth from current levels of initial condition uncertainty appears mostly realistic, except for a short initial decay

Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

Neurodegenerative diseases (NDDs) like Alzheimer’s disease (AD), Parkinson’s disease (PD), and amyotrophic lateral sclerosis (ALS) are defined by a myriad of complex aetiologies. Understanding the common biochemical molecular pathologies among NDDs gives an opportunity to decipher the overlapping and numerous cross-talk mechanisms of neurodegeneration. Numerous interrelated pathways lead to the progression of neurodegeneration. We present evidence from the past pieces of literature for the most usual global convergent hallmarks like ageing, oxidative stress, excitotoxicity-induced calcium butterfly effect, defective proteostasis including chaperones, autophagy, mitophagy, and proteosome networks, and neuroinflammation. Herein, we applied a holistic approach to identify and represent the shared mechanism across NDDs. Further, we believe that this approach could be helpful in identifying key modulators across NDDs, with a particular focus on AD, PD, and ALS. Moreover, these concepts could be applied to the development and diagnosis of novel strategies for diverse NDDs.

Ribavirin, 1-(β-D-Ribofuranosyl)-1H-1,2,4-triazole-3-carboxamide, which is included in the list of drugs recommended in the guidelines for the diagnosis and treatment of SARS-CoV-2 infection, has been the subject of experimental and theoretical investigation. The most thermodynamically stable polymorphic form was studied using 1H-14N NQR cross-relaxation, periodic DFT/QTAIM/RDS/3D Hirshfeld surfaces, and molecular docking. For the first time, a 1H-14N cross-relaxation spectrum of ribavirin was recorded and interpreted. Twelve resonance frequencies were assigned to four inequivalent nitrogen positions in the molecule using combined experimental techniques and solid-state quantum chemical calculations. The influence of the structural alteration on the NQR parameters was modeled using GGA/RPBE. The differences in the binding pattern of ribavirin, acadesine, inosine, guanosine, and favipiravir-ribofuranosyl in the solid state and the protein-ligand complex were assessed to elucidate the differences in the binding mechanism at the molecular level due to aglycone modification. The replacement of the carbon adjacent to the ribose with nitrogen, in conjunction with the absence of oxygen at the 2-position of the ring, resulted in an increased flexibility of the RBV structure in comparison to the favipiravir-ribofuranosyl structure. The present study identified the intramolecular hydrogen bond NH···N in RBV as playing a crucial role in the formation of a quasi-five-membered ring. However, this bond was proven to be too weak to force positioning of the amide group in the ring plane. The ribofuranosyl in RBV inhibits tautomerism and freezes the conformation of the amide group. The results of the molecular dynamics simulations demonstrated that RBV and favipiravir-ribofuranosyl incorporated into the RNA primer exhibited comparable stability within the protein binding region. The titular anti-butterfly (inverted butterfly) effect is associated with the consequences of both the changes in aglycone moiety and the neighborhood alteration. Seven structure-binding strength indices and six novel quadrupolar indices defined in this study have been proven to facilitate the evaluation of the similarity of binding motifs in the solid state and protein-ligand complex.

As pointed out by many researchers, replication plays a key role in the credibility of applied sciences and the confidence in all research findings. With regard, in particular, to energy finance and economics, replication papers are rare, probably because they are hampered by inaccessible data, but their aim is crucial. We consider two ways to avoid misleading results on the ostensible chaoticity of price series. The first one is represented by the proper mathematical definition of chaos and the related theoretical background, while the latter is represented by the hybrid approach that we propose here—i.e., consisting of considering the dynamical system underlying the price time series as a deterministic system with noise. We find that both chaotic and stochastic features coexist in the energy commodity markets, although the misuse of some tests in the established practice in the literature may say otherwise.

The purpose of this study was to achieve a specific unlocking of the butterfly effect: nanointerface-based electrochemical biosensing of adenosine triphosphate (ATP) and alkaline phosphatase (ALP). Based on the Faraday-cage concept reported first by our group, we built a new outer Helmholtz plane (OHP)-based electrochemical biosensor by using an unique nanocomposite involving three-dimensional graphene-Au nanoparticles (3D-GO-AuNPs), tetrahedral DNA nanostructures (TDNs), and separated ATP aptamers, in which methylene blue (MB) was employed as the electrochemical signal output. In this process, the prepared nanocomposites were attached favorably onto the TDN substrate electrode surface due to the interaction of ATP and its aptamer, creating a better OHP of the electrode owing to its large enough specific surface area; then a detection limit of 0.25 pM was calculated by 3 δ /slope. Whereas, the hydrolysis for ATP of ALP can hinder this binding process, therefore, the biosensor could be indirectly applied for ALP analysis with a detection limit of 0.21 mU/L (3 δ /slope). Since some small changes of the two targets will set off a whole series of changes in system, the OHP-extended biosensor provides a superior electrochemical platform for complex biological processes with causal relationships in clinical diagnosis and drug development, similar to the butterfly effect. Graphical abstract

The exploitation of the important features exhibited by the complex systems found in the surrounding natural and artificial space will improve computational model performance. Therefore, the purpose of the current paper is to use cellular automata as a tool simulating complexity, able to bring forth an interesting global behaviour based only on simple, local interactions. We show that, in the context of image segmentation, a butterfly effect arises when we perturb the neighbourhood system of a cellular automaton. Specifically, we enhance a classical GrowCut cellular automaton with chaotic features, which are also able to improve its performance (e.g., a Dice coefficient of 71% in case of 2D images). This enhanced GrowCut flavor (referred to as Band-Based GrowCut) uses an extended, stochastic neighbourhood, in which randomly-selected remote neighbours reinforce the standard local ones. We demonstrate the presence of the butterfly effect and an increase in segmentation performance by numerical experiments performed on synthetic and natural images. Thus, our results suggest that, by having small changes in the initial conditions of the performed task, we can induce major changes in the final outcome of the segmentation.

The 'butterfly effect' is an underlying principle of chaos theory- a branch of mathematics and physics developed by Edward Norton Lorenz in 1960s- resting on the notion that a small occurrence can influence a complex system. In the same vein, the butterfly effect as an interdisciplinary approach applied to sociohistorical studies describes how seemingly insignificant individual actions can initiate significant sociohistorical consequences within complex systems. Accordingly, the \"butterfly effect\" highlights the agency of individuals and the profound effects their choices can generate. Guided by this principle, the present study aims at exploring the alternate history presented in Kim Stanley Robinson's The Years of Rice and Salt (2002). The novel explores a pivotal point of divergence: what if the Black Death plague had annihilated 99% of Europe's population instead of a third. The Years of Rice and Salt also tries to speculate how the absence of European colonization and imperialism shapes the world, including the rise of new powers and the impact on cultural, political, and scientific advancements. Through the lens of the principle of the \"butterfly effect\", the study attempts to offer a comprehensive understanding of the intricate interplay between sociopolitical conflicts and individual agency within the novel's micro-macro structure and to explore diverse perspectives on how these forces interact, shaping the course of history in this alternate reality.

Introduction Adequate water intake is a low-cost and effectively non-invasive strategy for individual health outcomes. We aimed to demonstrate the efficacy of water intake intervention in intensive-labor and static-type workplaces. Method Smart drinking cups were provided to the participants, and a built-in application (App) associated with the cup was downloaded on their phones. The App collected and recorded the amount of drinking water consumed by the participants set reminders for drinking water and drinking water health education information. We assessed the data, including the amount of and time interval between water intake, sedentary time, the degree of physical and psychological importance of oneself, self-satisfaction, and physical fitness. Results After the intervention, water intake in the two companies significantly increased during the reminder period compared with the non-reminder period. A significant increase was noted in week 3 in the amount of water intake by the participants after using the App, and the total sedentary time considerably decreased. Furthermore, the interval between water consumption decreased compared with the preintervention interval. The systolic and diastolic blood pressure decreased in the participants working at the static-type and intensive-labor workplaces after the intervention, respectively. The participants ' lower limb muscle performance also improved significantly, and the emphasis on self-care was significantly improved. Conclusions The health-promoting effects of the water intake wellness intervention were akin to the butterfly effect. Besides significantly increasing water intake, the intervention improved other health behaviors, thereby benefiting physical and mental health. Hence, promoting water consumption in workplaces till it becomes a habit may benefit the employees.