Hierarchical Dynamical Systems Research Articles

Formalizing developmental phenomena as continuous-time systems: Relations between mathematics and language development.

We demonstrate how developmental theories may be instantiated as statistical models, using hierarchical continuous-time dynamic systems. This approach offers a flexible specification and an often more direct link between theory and model parameters than common modeling frameworks. We address developmental theories of the relation between the academic competencies of mathematics and language, using data from the online learning system Mindsteps. We use ability estimates from 160,164 observation occasions, across N = 4623 3rd to 9th grade students and five ability domains. Model development is step-by-step from simple to complex, with ramifications for theory and modeling discussed at each step.

Hierarchical dynamic regulation of Saccharomyces cerevisiaefor enhanced lutein biosynthesis.

Lutein, as a carotenoid with strong antioxidant capacity and an important component of macular pigment in the retina, has wide applications in pharmaceutical, food, feed, and cosmetics industries. Besides extraction from plant and algae, microbial fermentation using engineered cell factories to produce lutein has emerged as a promising route. However, intra-pathway competition between the lycopene cyclases and the conflict between cell growth and production are two major challenges. In our previous study, de novo synthesis of lutein had been achieved in Saccharomyces cerevisiae by dividing the pathway into two stages (δ-carotene formation and conversion) using temperature as the input signal to realize sequential cyclation of lycopene. However, lutein production was limited to microgram level, which is still too low to meet industrial demand. In this study, a dual-signal hierarchical dynamic regulation system was developed and applied to divide lutein biosynthesis into three stages in response to glucose concentration and culture temperature. By placing the genes involved in δ-carotene formation under the glucose-responsive ADH2 promoter and genes involved in the conversion of δ-carotene to lutein under temperature-responsive GAL promoters, the growth-production conflict and intra-pathway competition were simultaneously resolved. Meanwhile, the rate-limiting lycopene ε-cyclation and carotene hydroxylation reactions were improved by screening for lycopene ε-cyclase with higher activity and fine tuning of the P450 enzymes and their redox partners. Finally, a lutein titer of 19.92 mg/L (4.53 mg/g DCW) was obtained in shake-flask cultures using the engineered yeast strain YLutein-3S-6, which is the highest lutein titer ever reported in heterologous production systems.

A reconfigurable and magnetically responsive assembly for dynamic solar steam generation

Interfacial solar vapor generation is a promising technique to efficiently get fresh water from seawater or effluent. However, for the traditional static evaporation models, further performance improvement has encountered bottlenecks due to the lack of dynamic management and self-regulation on the evolving water movement and phase change in the evaporation process. Here, a reconfigurable and magnetically responsive evaporator with conic arrays is developed through the controllable and reversible assembly of graphene wrapped Fe3O4 nanoparticles. Different from the traditional structure-rigid evaporation architecture, the deformable and dynamic assemblies could reconfigure themselves both at macroscopic and microscopic scales in response to the variable magnetic field. Thus, the internal water transportation and external vapor diffusion are greatly promoted simultaneously, leading to a 23% higher evaporation rate than that of static counterparts. Further, well-designed hierarchical assembly and dynamic evaporation system can boost the evaporation rate to a record high level of 5.9 kg m−2 h−1. This proof-of-concept work demonstrates a new direction for development of high performance water evaporation system with the ability of dynamic reconfiguration and reassembly.

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations.

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Единство интеллекта и аффекта в множественной регуляции эмпатии

Background. The manuscript provides a synthetic review of the multiple understandings of the concept of empathy. Recent studies generally limit their focus to some aspects of empathy; alternatively, others adopt a top-down methodology for conceptualization of its dimensions rather than the analysis of the multiple regulation of processes that result in empathy. This review is timely and relevant not only because it compares various types of empathy but also because it provides an analysis of the involvement of various empathy processes in a wide plethora of relationships. Objective. The goa of the review was to establish the conceptual framework for the understanding of multiple types of empathy involvement in cognitive and affective/personality domains, as well as of theoretical discrepancies that can be overcome from the standpoint of unity of intellect and affect. Methods. This synthetic review elucidates fundamental dichotomies that are central to understanding of empathy (cognitive-affective; immediate-mediated; situational-dispositional etc) as well as the wide range of associations established between empathy, emotional intelligence, and unstable personality core traits such as the Dark Triad. Results. The results of the study are based on the systematic review of theories of empathy and suggest the need for differentiation between empathy as a product and empathy as a set of processes that might through different pathways achieve the same result and product — empathy. Thus, we argue that the seeming inconsistency between the multiple types of empathy can be resolved by postulating that it is subject to the principle of dynamic regulative systems (DRS) that allow for a rich combination of hierarchical structures of cognitive and emotional processes. This approach assumes that multiple processes underly regulation of empathy. This idea is rooted in Vygotsky’s idea of the unity of intellect and affect, pointing to the pivotal role of empathy as the binding and mediating trait between cognitive and personality/ affective domains. Conclusion. The review lays the foundation for the approach that omits the development of partial theories of empathy in favor of viewing it as a resulting product of multiple processes. Different types and forms of empathy that are frequently discussed in the literature reflect the development of hierarchical dynamic systems and processes.

ИНСТРУМЕНТЫ ОПТИМИЗАЦИИ МНОГОЧАСТИЧНОГО ФИЛЬТРА ДЛЯ ВЕРОЯТНОСТНЫХ МОДЕЛЕЙ ДИНАМИЧЕСКИХ СИСТЕМ

В работе предложены математические инструменты на основе достаточных статистик и декомпозиции выборок в сочетании с алгоритмами распределенных вычислений, позволяющие существенно повысить эффективность процедуры фильтрации. Filtering algorithms are used to assess the state of dynamic systems when solving various practical problems, such as voice synthesis and determining the geo-position and monitoring the movement of objects. In the case of complex hierarchical dynamic systems with a large number of time slices, the process of calculating probabilistic characteristics becomes very time-consuming due to the need to generate a large number of samples. The essence of optimization is to reduce the number of samples generated by the filter, increase their consistency and speed up computational operations. The paper offers mathematical tools based on sufficient statistics and sample decomposition in combination with distributed computing algorithms that can significantly improve the efficiency of the filtering procedure.

Technological process of rescue operations in conditions of mass destruction. System-integrative aspect and principles of organization

In the presented article, the author substantiates the feasibility of using the “process approach” in organizing emergency rescue operations in the conditions of destroyed buildings and structures. It is noted that the advantage of the process approach is that it can be used when considering various solutions to typical organizational and technological problems and predicting the processes of emergency rescue operations ERO. The author emphasizes that the process of conducting the ERO should be considered as a complex hierarchical multicomponent dynamic system, the levels of which are characterized by diverse coordinating relationships and a certain subordination. Taking into account this circumstance, new principles of organizing the production process of ERO in the conditions of mass destruction are justified. Of practical importance is the possibility of applying these principles in the development of methodological approaches to optimizing emergency rescue operations ERO processes, substantiating rational technologies for their implementation. In General, the article presents a new, original approach to the organization and conduct of rescue operations, based on the account of organizational and technological features of large-scale emergencies and the results of the study of the system-integrative aspect.

РОЗРОБКА МОДЕЛІ ЗНАНЬ ДЛЯ ІНФОРМАЦІЙНОЇ СИСТЕМИ ПІДТРИМКИ ПРИЙНЯТТЯ РІШЕНЬ АВІАЦІЙНИМ ОПЕРАТОРОМ ПРИ ВИНИКНЕННІ ОСОБЛИВИХ ВИПАДКІВ В ПОЛЬОТІ

Предметом вивчення в статті є методи, що дозволяють вирішити проблему невизначеності в процесі побудови систем підтримки прийняття рішень авіадиспетчера при виникненні особливих випадків в польоті. Метою є аналіз і обґрунтування вибору математичного апарату для побудови СППР авіадиспетчера. Завдання: аналіз ряду відомих методів інтелектуального аналізу даних, а саме: еволюційних алгоритмів, нейронних мереж, нечіткої логіки та байєсівських мереж з точки зору доцільності їх застосування при побудови систем підтримки прийняття рішень авіадиспетчера управління повітряним рухом при виникненні особливих випадків в польоті. Використовуваними методами є: методи аналізу і синтезу складних інформаційних систем, методи імітаційно-статистичного моделювання. Отримано такі результати. В результаті проведеного аналізу було встановлено, для побудови моделі СППР авіадиспетчера найбільш ефективним є використання апарату байєсівських мереж, який представляє собою перспективний ймовірнісний інструментарій, що дозволяє моделювати складні ієрархічні статичні та динамічні системи. Це обумовлено тим, що на відміну від популярних на даний час моделей "чорних скриньок" байєсівська мережа дозволяє отримати зрозуміле пояснення одержаних висновків, має їх логічну інтерпретацію, надає можливість врахування невизначеностей параметричного, статичного і структурного характеру і, що є особливо важливим, ґрунтується на фундаментальних положеннях теорії ймовірностей, яка розроблялась не одне сторіччя. Висновки. Напрямком подальших досліджень є побудова системи підтримки прийняття рішень авіадиспетчера з використанням байєсівських мереж і технології ймовірнісного програмування

Power law error growth in multi-hierarchical chaotic systems—a dynamical mechanism for finite prediction horizon

We propose a dynamical mechanism for a strictly finite prediction horizon, i.e. a scenatio of chaotic motion where asymptotically a more precise knowledge of the initial condition does note translate into a longer closeness of the forecast to the truth. For this, we propose a class of hierarchical dynamical systems which possess a scale dependent error growth rate in the form of a power law. Actually, this is motivated by and consistent with well known hierarchies of patterns in atmospheric dynamics. This scale dependent error growth rate in form of a power law translates in power law error growth over time instead of exponential error growth as in conventional chaotic systems. The consequence is a strictly finite prediction horizon, since in the limit of infinitesimal errors of initial conditions, the error growth rate diverges and hence additional accuracy is not translated into longer prediction times. By re-analyzing data of the National Center for Environmental Protect Global Forecast System, a weather prediction model, published by Harlim et al (2005 Phys. Rev. Lett. 94 228501) we show that such a power law error growth rate can indeed be found in numerical weather forecast models and estimate it average maximal prediction horizon to about 15 d.

Development of a hierarchical dynamic keyboard character recognition system using trajectory features and scale-invariant holistic modeling of characters

A robust, intuitive, effortless, and novel dynamic hand gesture based virtual keyboard system is developed in this study. Firstly, a new hierarchical approach is applied, which, based on self-coarticulation and position features, effectively sub-groups a large gesture vocabulary. Additionally, new trajectory features are proposed which shall extract the local structural statistics of the gestures. All state-of-art models are based on temporal trajectory features which are based on the frame-wise 2D sequential path it followed. Due to this, the trajectory features are path dependent and vulnerable to trajectory noises or any other variations in pattern, speed, or scale. In contrast to this, an image-based approach of gesture recognition has been proposed in this study, which is independent of the sequential gesturing path of the gesture. Since the image-models (a holistic view) are not obtained frame-wise, unlike existing image-models, they are pattern, speed, and scale invariant in nature and also immune to trajectory distortions. To this end, image-based features and significant trajectory features are fused to develop a hybrid hierarchical classification model which exhibits an exceptional increase in accuracy by 3.9% as compared to baseline non-hierarchical trajectory based model using an Artificial neural network (ANN). Classification models such as Voronoi diagram based classifier (VDBC) and neuro-fuzzy (NF) classifier have also been explored and displayed motivating performance. Reduction in misclassification has been observed for gestures such as ‘(and)’, ‘{and}’, ‘0 and O’, ‘Z and 2’. The present system can also identify any static/dynamic imposters present in the gesture environment.

Order reduction of hierarchical interconnected dynamical systems

Abstract. The simulation of large scale nonlinear dynamical interconnected systems, as they arise in all modern engineering disciplines, is a usual task. Due to the high complexity of the considered systems, the principle of thinking in hierarchical structures is essential and common among engineers. Therefore, this contribution proposes an approach for the numerical simulation of large systems, which keeps the hierarchical system structure alive during the entire simulation process while simultaneously exploiting it for order reduction purposes. This is accomplished by embedding the trajectory piecewise linear order reduction scheme in a modified variant of the component connection modeling for building interconnected system structures. The application of this concept is demonstrated by means of a widely used benchmark example and a modified variant of it.

Transitions between superstatistical regimes: Validity, breakdown and applications

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important rôle in analysis of hierarchical complex dynamical systems. Yet, its “canonical” formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.

Hierarchical linear dynamical systems for unsupervised musical note recognition

In this paper we develop a new framework for time series segmentation based on a Hierarchical Linear Dynamical System (HLDS), and test its performance on monophonic and polyphonic musical note recognition. The center piece of our approach is the inclusion of constraints in the filter topology, instead of on the cost function as normally done in machine learning. Just by slowing down the dynamics of the top layer of an augmented (multilayer) state model, which is still compatible with the recursive update equation proposed originally by Kalman, the system learns directly from data all the musical notes, without labels, effectively creating a time series clustering algorithm that does not require segmentation. We analyze the HLDS properties and show that it provides better classification accuracy compared to current state-of-the-art approaches.

Exponential consensus for hierarchical multi‐agent systems with switching topology and inter‐layer communication delay

This study studies the exponential state consensus problem for hierarchical multi-agent dynamical systems with switching topology and inter-layer communication delay. A Lyapunov function is introduced to quantify the total disagreement among the nodes of a hierarchical multi-agent system. By using the stability theory of switched system and graph theory of hierarchical network topology, delay dependent sufficient conditions are proposed to achieve the exponential hierarchical average consensus with the average dwell time of the switching law larger than a minimum bound. Illustrative examples are provided to verify the effectiveness of the proposed approach.

Flux Control at the Malonyl-CoA Node through Hierarchical Dynamic Pathway Regulation in Saccharomyces cerevisiae.

The establishment of a heterologous pathway in a microbial host for the production of industrially relevant chemicals at high titers and yields requires efficient adjustment of the central carbon metabolism to ensure that flux is directed toward the product of interest. This can be achieved through regulation at key branch points in the metabolic networks, and here we present a novel approach for dynamic modulation of pathway flux and enzyme expression levels. The approach is based on a hierarchical dynamic control system around the key pathway intermediate malonyl-CoA. The upper level of the control system ensures downregulation of endogenous use of malonyl-CoA for fatty acid biosynthesis, which results in accumulation of this pathway intermediate. The lower level of the control system is based on use of a novel biosensor for malonyl-CoA to activate expression of a heterologous pathway using this metabolite for production of 3-hydroxypropionic acid (3-HP). The malonyl-CoA sensor was developed based on the FapR transcription factor of Bacillus subtilis, and it demonstrates one of the first applications of a bacterial metabolite sensor in yeast. Introduction of the dual pathway control increased the production of 3-HP by 10-fold and can also be applied for production of other malonyl-CoA-derived products.

News from Rand Model Designer for Industry and Education

Rand Model Designer http://www.mvstudium.com) is a modern tool for modeling and simulation of hierarchical multicomponent event-driven dynamical systems. It was demonstrated in the series of MIM-conferences, including MIM-2013 (Senichenkov Yu. (2013)). It utilizes the UML-based object-oriented Model Vision Language for designing dynamical and hybrid systems, using modification of State Machines - large-scale multicomponent systems, such as: control systems with “inputs-outputs”, “physical” systems with “contacts-flows”, and novel variable structure component systems, particularly “agent” systems. The recently launched tool “Visual Debugger” includes new modifications of numerical solvers for sparse systems, for instance it is now possible to reorder each solved system to block-triangular form with the help of Tarjan’s algorithm in order to accelerate execution speed.

State consensus for hierarchical multi-agent dynamical systems with inter-layer communication time delay

This paper studies the consensus problem for hierarchical multi-agent dynamical systems with the inter-layer communication time-varying delay. This paper firstly finds a mathematical model for the hierarchical multi-agent dynamical systems with inter-layer communication time-varying delay, and then delay-dependent sufficient conditions are proposed for reaching a consensus based on Lyapunov function approach. A Lyapunov function is introduced to quantify the total disagreement among the nodes of a hierarchical network. All the results are in the form of linear matrix inequalities (LMIs). Simulation results are provided to verify the effectiveness of the proposed condition for agreement in networks with inter-layer communication time-delay.

Qualitative theory of p-adic dynamical systems

We consider a class of dynamical systems over the p-adic number field: hierarchical dynamical systems. We prove a strong variant of the Poincare theorem on the number of returns for such systems and show that hierarchical systems do not admit mixing. We describe hierarchical dynamical systems over the projective line and present an example of a nonhierarchical p-adic system that admits mixing: the p-adic baker’s transformation.

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

This paper proposes an eigenvector-based method for analysis and design of hierarchical networks for multi-agent systems. We first define the concept of eigen-connection by characterizing low rank information flow between layers based on the eigenvector of lower level interconnection structures. It is shown that the resulting intergroup interconnections affect only a few eigenvalues of interconnection structures in the lower layer, and we derive explicit expressions for shifted eigenvalues. Then a procedure for designing hierarchical networks that result in desirable eigenvalue distributions is proposed, where the eigen-connection is used for a key to move undesirable eigenvalues selectively. The effectiveness of the procedure is demonstrated by a numerical example.

The non-resonant, relativistic dynamics of circumbinary planets

We investigate the non-resonant, 3-D (spatial) model of the hierarchical system composed of point-mass stellar (or sub-stellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading relativistic corrections to the Newtonian gravity. The secular model of the system relies on the expansion of the perturbing Hamiltonian in terms of the ratio of semi-major axes $\alpha$, averaged over the mean anomalies. We found that the low-mass object in a distant orbit may excite large eccentricity of the inner binary when the mutual inclination of the orbits is larger than about of 60 deg. This is related to strong instability caused by a phenomenon which acts similarly to the Lidov-Kozai resonance (LKR). The secular system may be strongly chaotic and its dynamics unpredictable over the long-term time scale. Our study shows that in the Jupiter-- or brown dwarf-- mass regime of the low-massive companion, the restricted model does not properly describe the long-term dynamics in the vicinity of the LKR. The relativistic correction is significant for the parametric structure of a few families of stationary solutions in this problem, in particular, for the direct orbits configurations (with the mutual inclination less than 90 degrees). We found that the dynamics of hierarchical systems with small $\alpha \sim 0.01$ may be qualitatively different in the realm of the Newtonian (classic) and relativistic models. This holds true even for relatively large masses of the secondaries.