A.N. Gorban and O. Radulescu
Dynamical robustness of biological networks with hierarchical distribution of time scales
IET Syst. Biol., 2007, 1, (4), pp. 238–246

  Concepts of distributed robustness and r-robustness proposed by biologists to explain a variety of stability phenomena in molecular biology are analysed. Then, the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks is discussed. First, the following result for linear networks is obtained: for large multiscale systems with hierarchical distribution of time scales, the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. Similar phenomena are valid in the nonlinear case as well. As a numerical illustration, a model of signalling network is used for the important transcription factor NFkB.

A.N. Gorban and  A.Y. Zinovyev
The Mystery of Two Straight Lines in Bacterial Genome Statistics
Bulletin of Mathematical Biology (2007) DOI 10.1007/s11538-007-9229-6 (Online First)

  In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position-specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented.We demonstrate that the mean-field approximation, which is also known as context-free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature, respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.

Ovidiu Radulescu, Alexander N. Gorban, Sergei Vakulenko, Andrei Zinovyev
Hierarchies and modules in complex biological systems
In: Proceedings of European Conference on Complex Systems (paper ECCS06-114), Oxford, UK, September 2006. http://complexsystems.lri.fr/FinalReview/FILES/PDF/p114.pdf

  We review several mathematical methods allowing to identify modules and hierarchies with several levels of complexity in biological systems. These methods are based either on the properties of the input-output characteristic of the modules or on global properties of the dynamics such as the distribution of timescales or the stratification of attractors with variable dimension. We also discuss the consequences of the hierarchical structure on the robustness of biological processes. Stratified attractors lead to Waddington's type canalization effects. Successive application of the many to one mapping relating parameters of different levels in an hierarchy of models (analogue to the renormalization operation from statistical mechanics) leads to concentration and robustness of those properties that are common to many levels of complexity. Examples such as the response of the transcription factor NF·B to signalling, and the segmentation patterns in the development of Drosophila are used as illustrations of the theoretical ideas.

A.N. Gorban, T.G.Popova, A.Yu. Zinovyev
Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences
Physica A: Statistical and Theoretical Physics, 353C (2005), 365-387.
(Number 11 in TOP25 articles within the journal: Physica A: Statistical Mechanics and its Applications, APR - JUN 2005 Top25.pdf)

   Three results are presented. First, we prove the existence of a universal 7-cluster structure in all 143 completely sequenced bacterial genomes available in Genbank in August 2004, and explained its properties. The 7-cluster structure is responsible for the main part of sequence heterogeneity in bacterial genomes. In this sense, our 7 clusters is the basic model of bacterial genome sequence. We demonstrated that there are four basic ``pure" types of this model, observed in nature: ``parallel triangles", ``perpendicular triangles", degenerated case and the flower-like type.
  Second, we answered the question: how big are the position-specific information and the contribution connected with correlations between nucleotide. The accuracy of the mean-field (context-free) approximation is estimated for bacterial genomes.
  We show that codon usage of bacterial genomes is a multi-linear function of their genomic G+C-content with high accuracy (more precisely, by two similar functions, one for eubacterial genomes and the other one for archaea). Description of these two codon-usage trajectories is the third result.
All 143 cluster animated 3D-scatters are collected in a database and is made available on our web-site: http://www.ihes.fr/~zinovyev/7clusters.

A.N. Gorban, T.G.Popova, A.Yu. Zinovyev
Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences
In Silico Biology, 5 (2005), 0039.
Internet site CLUSTER STRUCTURE IN GENOME with analysis of all bacterial genomes.

  Coding information is the main source of heterogeneity (non-randomness) in the sequences of microbial genomes. The heterogeneity corresponds to a cluster structure in triplet distributions of relatively short genomic fragments (200-400bp). We found a universal 7-cluster structure in microbial genomic sequences and explained its properties. We show that codon usage of bacterial genomes is a multi-linear function of their genomic G+C-content with high accuracy. Based on the analysis of 143 completely sequenced bacterial genomes available in Genbank in August 2004, we show that there are four "pure" types of the 7-cluster structure observed. All 143 cluster animated 3D-scatters are collected in a database which is made available on our web-site (http://www.ihes.fr/~zinovyev/7clusters). The findings can be readily introduced into software for gene prediction, sequence alignment or microbial genomes classification.

A.N. Gorban, M. Kudryashev, T. Popova
On the Way to Protein Alphabet: Informational Classification of Amino Acids in Comparison to Other Classifications
E-print: http://arxiv.org/abs/q-bio.BM/0501019

  What proteins are made from, as the working parts of the living cells protein machines? To answer this question, we need a technology to disassemble proteins onto elementary functional details and to prepare lumped description of such details. This lumped description might have a multiple material realization (in amino acids). Our hypothesis is that informational approach to this problem is possible. We propose a way of hierarchical classification that makes the primary structure of protein maximally non-random and compare them with other classifications. The first step of the suggested research program is realized: the analysis of protein binary alphabet in comparison with other amino acid classifications.

A.N. Gorban, A. Yu. Zinovyev
PCA deciphers genome
E-print: http://arxiv.org/abs/q-bio.QM/0504013

  In this paper, we give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students learn how data visualization can help in genomic sequences analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they ``discover'' that the information in genome is encoded by non-overlapping triplets. Next, they learn to find gene positions. This exercise on principal component analysis and K-Means clustering gives a possibility for active study of the basic bioinformatics notions. In Appendix the program listings for MatLab are published.

A.N. Gorban, A.Yu. Zinovyev
The Mystery of Two Straight Lines in Bacterial Genome Statistics
E-print: http://arxiv.org/abs/q-bio.GN/0412015

  In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 175 known bacterial genomes (Genbank, March 2005) belong these lines with high accuracy, and these two lines are certainly different. The results of PCA analysis of codon usage and accuracy of mean--field (context--free) approximation are presented. The first two principal components correlate strongly with genomic G+C-content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. The eubacterial and archaeal genomes codon usage are clearly distributed along two third order curves with genomic G+C-content as a parameter.

A.N. Gorban, T.G. Popova, A.Yu. Zinovyev
Four basic symmetry types in the universal 7-cluster structure of 143 complete bacterial genomic sequences
E-print: http://arxiv.org/abs/q-bio/0410033

  The coding information is the main source of heterogeneity (non-randomness) in the sequences of bacterial genomes. This information can be naturally modeled by analysing cluster structures in the "in-phase" triplet distributions of relatively short genomic fragments (200-400bp). We found a universal 7-cluster structure in bacterial genomic sequences and explained its properties. We show that codon usage of bacterial genomes is a multi-linear function of their genomic G+C-content with high accuracy. Based on the analysis of 143 completely sequenced bacterial genomes available in Genbank in August 2004, we show that there are four "pure" types of the 7-cluster structure observed. All 143 cluster animated 3D-scatters are collected in a database and is made available on our web-site: http://www.ihes.fr/~zinovyev/7clusters. The finding can be readily introduced into any software for gene prediction, sequence alignment or bacterial genomes classification.

Gorban, A.N.
Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finite-dimensional asymptotics
E-print: http://arxiv.org/abs/cond-mat/0405451

  If we find a representation of an infinite-dimensional dynamical system as a nonlinear kinetic system with {\it conservation of supports} of distributions, then (after some additional technical steps) we can state that the asymptotics is finite-dimensional. This conservation of support has a {\it quasi-biological interpretation, inheritance} (if a gene was not presented initially in a isolated population without mutations, then it cannot appear at later time). These quasi-biological models can describe various physical, chemical, and, of course, biological systems. The finite-dimensional asymptotic demonstrates effects of {\it "natural" selection}. The estimations of asymptotic dimension are presented. The support of an individual limit distribution is almost always small. But the union of such supports can be the whole space even for one solution. Possible are such situations: a solution is a finite set of narrow peaks getting in time more and more narrow, moving slower and slower. It is possible that these peaks do not tend to fixed positions, rather they continue moving, and the path covered tends to infinity at $t \to \infty$. The {\it drift equations} for peaks motion are obtained. Various types of stability are studied. In example, models of cell division self-synchronization are studied. The appropriate construction of notion of typicalness in infinite-dimensional spaces is discussed, and the "completely thin" sets are introduced

A. Yu. Zinovyev, A. N. Gorban, T. G. Popova
Self-Organizing Approach for Automated Gene Identification
Open Sys. & Information Dyn., 10, 2003, 321-333

  Self-training technique for automated gene recognition both in entire genomes and in unassembled ones is proposed. It is based on a simple measure (namely, the vector of frequencies of non-overlapping triplets in sliding window), and needs neither predetermined information, nor preliminary learning. The sliding window length is the only one tuning parameter. It should be chosen close to the average exon length typical to the DNA text under investigation. An essential feature of the technique proposed is preliminary visualization of the set of vectors in the subspace of the first three principal components. It was shown, the distribution of DNA sites has the bullet-like structure with one central cluster (corresponding to non-coding sites) and three or six ank ones (corresponding to protein-coding sites). The bullet-like structure itself revealed in the distribution seems to be very interesting illustration of triplet usage in DNA sequence. The method was examined on several genomes (mitochondrion of P.wickerhamii, bacteria C.crescentus and primitive eukaryot S.cerevisiae). The percentage of truly predicted nucleotides exceeds 90%.
In October 2004 this paper was mentioned as one of the five most viewed paper published in the Journal since 1997 http://www.kluweronline.com/issn/1230-1612 .

A. N. Gorban, A. Yu. Zinovyev, T. G. Popova
Seven clusters in genomic triplet distributions
In Silico Biology, 3, 2003, 471-482 (0039), Online: http://arXiv.org/abs/cond-mat/0305681 29 May 2003

  Motivation: In several recent papers new algorithms were proposed for detecting coding regions without requiring learning dataset of already known genes. In this paper we studied cluster structure of several genomes in the space of codon usage. This allowed to interpret some of the results obtained in other studies and propose a simpler method, which is, nevertheless, fully functional. Results: Several complete genomic sequences were analyzed, using visualization of tables of triplet counts in a sliding window. The distribution of 64-dimensional vectors of triplet frequencies displays a well-detectable cluster structure. The structure was found to consist of seven clusters, corresponding to protein-coding information in three possible phases in one of the two complementary strands and in the non-coding regions. Awareness of the existence of this structure allows development of methods for the segmentation of sequences into regions with the same coding phase and non-coding regions. This method may be completely unsupervised or use some external information. Since the method does not need extraction of ORFs, it can be applied even for unassembled genomes. Accuracy calculated on the base-pair level (both sensitivity and specificity) exceeds 90%. This is not worse as compared to such methods as HMM, however, has the advantage to be much simpler and clear. Availability: The software and datasets are available at http://www.ihes.fr/~zinovyev/bullet

A. N. Gorban, A. Y. Zinovyev, D.C. Wunsch
Application of The Method of Elastic Maps In Analysis of Genetic Texts
Proceedings of IJCNN2003

  Method of elastic maps allows to construct efficiently 1D, 2D and 3D non-linear approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. We describe the idea of the method and demonstrate its applications in analysis of genetic sequences.

Alexander N. Gorban, Andrei Yu. Zinovyev, Tatyana G. Popova
Detecting simple cluster structure of triplet distributions in genetic texts
Bioinformatics, Submitted, 2003

 Motivation: In several recent papers new algorithms were proposed for detecting coding regions without requiring learning dataset of already known genes. In this paper we interpret some of these results and propose a simpler method.
 Results: Several complete genomic sequences were analyzed, using visualization of tables of triplet counts in a sliding window. The distribution of 64-dimensional vectors of triplet frequencies displays a well-detectable cluster structure. The structure was found to consist of seven clusters, corresponding to protein-coding information in three possible phases in one of the two complementary strands and in the non-coding regions. Awareness of the existence of this structure allows development of methods for the segmentation of sequences into regions with the same coding phase and non-coding regions. This method may be completely unsupervised or use some external information. Since the method does not need extraction of ORFs, it can be applied even for unassembled genomes. Accuracy calculated on the base-pair level (both sensitivity and specificity) exceeds 90%. This is not worse as compared to such methods as HMM, however, has the advantage to be much simpler.
 Availability: The software and datasets are available at http://www.ihes.fr/~zinovyev/bullet.

Горбань А.Н.,Попова Т.Г., Садовский М.Г.
Классификация нуклеотидных последовательностей по частотным словарям обнаруживает связь между их структурой и таксономическим положением организмов
Журнал общей биологии, 2003, том 64, № 1, с. 51–63

Цель работы - изучение связи между структурой нуклеотидной последователь-ности и таксономическим положением её носителя. Изучены классификации нуклео-тидных последовательностей бактериальных 16SРНК. Показано существование корре-ляции между таксономическим положением носителей и информационной структурой нуклеотидных последовательностей бактериальных 16SРНК. Две последовательности считались близкими по структуре, если близки их частотные словари в евклидовой метрике. Предложена процедура преобразования частотного словаря, которая выявляет особенности информационной структуры символьной последовательности. Проведено сравнительное исследование классификаций по реальным и преобразованным частот-ным словарям. Выделены информационно значимые сайты - главные факторы отли-чия - для полученных классов. Классификация реальных частотных словарей толщи-ны 3 наилучшим образом коррелирует с родом: род, как правило, целиком включён в один класс и исключения редки. В результате иерархической классификации по преоб-разованным частотным словарям на каждом этапе выделялись одна-две таксономиче-ские группы. Структурные различия полученных классов заключены в редком или, на-оборот, частом (по сравнению с ожидаемым) появлении некоторых слов, количество которых невелико.

Gorban A.N., Zinovyev A.Yu., Popova T.G.
Self-organizing approach for automated gene identification in whole genomes
Русское название: Метод автоматической идентификации белок кодирующих участков в геноме
Institut des Hautes Etudes Scientifiques Preprint. IHES. December 12, 2001
Online-version: arXiv:physics/0108016 v1 10 Aug 2001

 An approach based on using the idea of distinguished coding phase in explicit form for identication of protein-coding regions in whole genome has been proposed. For several genomes an optimal window length for averaging GC-content function and calculating codon frequencies has been found. Self-training procedure based on clustering in multidimensional space of triplet frequencies is proposed.

Gorban A.N., Zinovyev A.Yu., Popova T.G.
Statistical approaches to automated gene identification without teacher.
Русское название: Статистический подход к автоматической идентификации генов без учителя
Institut des Hautes Etudes Scientifiques Preprint. IHES M/01/34.
Online-version: http://www.ihes.fr/PREPRINTS/M01/Resu/resu-M01-34.html

 Overview of statistical methods of gene identification is made. Particular attention is given to the methods which need not a training set of already known genes. After analysis several statistical approaches are proposed for computational exon identification in whole genomes. For several genomes an optimal window length for averaging GC-content function and calculating codon frequencies has been found. Self-training procedure based on clustering in multidimensional codon frequencies space is proposed.

Gorban A.N., Popova T.G., Sadovsky M.G.
Classification Of Symbol Sequences Over Thier Frequency Dictionaries: Towards The Connection Between Structure And Natural Taxonomy
Русское название:Классификация последовательностей 16S-РНК по частотным словарям выявляет связь между структурой генов и таксономическим положением их носителей
Open Sys. & Information Dyn. 7: 1-17, 2000
Kluwer Academic Publishers

 The classifications of bacterial 16S RNA sequences developed over the real and transformed frequency dictionaries have been studied. Two sequences considered to be close each other, when their frequency dictionaries were close in Euclidean metrics. A procedure to transform a dictionary is proposed that makes clear some features of the information pattern of a symbol sequence. A comparative study of classifications developed over the real frequency dictionaries vs. the transformed ones has been carried out. A correlation between an information pattern of nucleotide sequences and taxonomy of the bearer of the sequence was found. The sites with high information value are found, that were the main factors of the difference between the classes in a classification. The classification of nucleotide sequences developed over the real frequency dictionaries of the thickness 3 reveals the best correlation to a gender of bacteria. A set of sequences of the same gender is included entirely into one class, as a rule, and the exclusions occur rarely. A hierarchical classification yields one or two taxonomy groups on each level of the classification. An unexpectedly often (in comparison to the expected), or unexpectedly rare occurrence of some sites within a sequence makes a basic difference between the structure patterns of the classes yielded; a number of those sites is not too great. Further investigations are necessary in order to compare the sites revealed with those determined due to other methodology.

Горбань А.Н., Хлебопрос Р.Г.
Демон Дарвина. Идея оптимальности и естественный отбор
М.: Наука. Гл. ред. физ. - мат. лит., 1988. - 208с. - (Пробл. науки и техн. прогресса).

 Популярная книга о принципе оптимальности в эволюции, о методологии математического моделирования, о Дарвине и естественном отборе.

 Аннотированное оглавление:
 ПРЕДИСЛОВИЕ: МИФ О МОДЕЛИРОВАНИИ
 ПЕРВЫЙ ШАГ Естественное и искусственное. Мир Эпиметея. У кого больше потомков - у мухи или у слона? Единая мера совершенства. Застывшая история. Царство матемазавров. Две ветви теории эволюции: возможен ли синтез? Проект читателя. Искусство сомневаться. Сомнения в принятом центральном тезисе. Вид с высоты, его достоинства и недостатки
 УГОЛ ЗРЕНИЯ Отделение смысла от бессмыслицы. Теория - модель - объект. Теория Дарвина и динамические модели Ньютона. Закон шага и закон цели. Эволюционные сценарии в физике и биологии. Достаточны ли первые принципы? Теория или метод? Вложение возможных миров. Логическое всеведение. Неосуществимые программы дают полезные результаты. Определение как автопортрет. Проблема синтеза.
 ИЗГОТОВЛЕНИЕ МОДЕЛЕЙ Восемь разновидностей моделей. Парадоксы и презумпция осмысленности. Незавершенные миры развивающейся физики. Рамка для неизвестных возможностей и в ней - Чебурашка. Простота без упрощений. Мысленный эксперимент - столкновение знаний. Имитационные модели. Две функции моделей: соответствие объектам и смыслообразование. Эффект зайца. Неужели физику легче, чем биологу? Проект двух следующих шагов.
 МОДЕЛЬ ДАРВИНА Дарвинизм - картина мира в биологии. Биосфера и ее генотень. Проблема организма. Триединая среда. Расстояние между генотипами. Иерархичность генотени. Радиус скрещивания и брачные предпочтения у дрозофилы. Динамическое объяснение иерархичности. Проблемы происхождения высших таксонов. Восстановление истории и вымирание динозавров. Сама модель. Что иерархично?
 ОТБОР ПО ПРИЗНАКУ Краб из Плимутской бухты. Цвет бабочки и промышленная революция. Запрограммированные случайности в фенотипе. Легенда о скромном хищнике. Парадокс выгоды. Решающий эксперимент по внедрению. Три типа устойчивости и оптимальности. Смысл "пользы". Альтруизм и динамика меток "свой - чужой". Проблема пола. Таинственные законы корреляции. Модели и реальность.
 ДЕМОН МЕНДЕЛЯ-ИОГАННСЕНА Открытие и переоткрытие. Развертывание простых моделей. Хромосома, локус, аллель и ген. Половое размножение и гены-грубияны. Размножение и отбор генов. Геноценоз как биоценоз и биоценоз как геноценоз. Благо рецессивности.
 НАСЛЕДОВАНИЕ Идея инварианта. Встречные пути. Четыре подразделения клеточной ДНК. Генетический ламаркизм. Единицы воспроизводства. Динамическая последовательность. Единицы функции. Способности и поведение. Плата за функцию. Обобщенный генотип. От наследуемых единиц к биосфере и обратно. Коэффициент размножения без предков и потомков. Сооптимальность и совершенство. Гены, полученные не от родителей. Где же организмы? Наследование без организмов - попытка определения.
 ИЗМЕНЧИВОСТЬ Изменение и разнообразие. Проблема нейтральных мутаций. Мозаичность условий и волны жизни. Релятивизация наследуемых единиц, шаг первый. Эволюция, безразличная к деталям изменчивости. Направленные и ненаправленные изменения. Релятивизация, шаг второй. Эволюция изменчивости.
 ГДЕ ЖЕ ГЛАВНАЯ МОДЕЛЬ?
 КОММЕНТАРИИ К СПИСКУ ЛИТЕРАТУРЫ
 СПИСОК ЛИТЕРАТУРЫ (129 наименований)

 ПОЖЕЛАНИЯ СТУДЕНТАМ
Книга может использоваться для составления рефератов по: теории эволюции и, в частности, теории отбора; принципам оптимальности в биологии и их происхождению; методологии математического моделирования в естественных науках.

Бугаенко Н.Н., Горбань А.Н., Садовский М.Г.
Определение информационной емкости нуклеотидных последовательностей
Электронный журнал "Наука Сибири"

 Рассматривается проблема определения информационной емкости нуклеотидных последовательностей. Получены выражения для восстановления частотных словарей высших порядков по низшим. Описаны особенности информационных характеристик реальных нуклеотидных последовательностей, достоверно отличающие их от случайных текстов.

Горбань А.Н., Смирнова Е.В., Чеусова Е.П.
Групповой стресс: динамика корреляций при адаптации и организация систем экологических факторов.
Препринт. ИВМ СО РАН, 1997. Рукопись депонирована в ВИНИТИ 17.07.97, № 2434В97. 54 с.

 В результате обработки многолетних наблюдений при сравнительном анализе популяций и групп, находящихся в различных экологических условиях (на Крайнем Севере и в средних широтах Сибири), получен вывод: наибольшую информацию о степени адаптированности популяции к экстремальным или просто изменившимся условиям несут корреляции между физиологическими параметрами.
 В типичной ситуации при увеличении адаптационной нагрузки уровень корреляций повышается, а в результате успешной адаптации - снижается. Показано, что этот эффект связан с организацией системы факторов, действующих на группу.
 Если система факторов организована в соответствии с принципом Либиха (монолимитирование) то с ростом адаптационного напряжения размерность облака точек, представляющего группу в пространстве физиологических параметров, снижается, растет сумма коэффициентов корреляции и, в то же время, растет разброс этого облака - возрастают дисперсии.
 Если происходит взаимное усиление давления различных факторов (синергичные системы), то, напротив, с ростом адаптационного напряжения размерность облака точек, представляющего группу в пространстве физиологических параметров, растет, падает сумма коэффициентов корреляции. Дисперсии в то же время возрастают - так же, как и в предыдущем случае.
 Рассматриваются два возможных способа повышения корреляций:

1. распределение (облако) точек, представляющих группу в пространстве параметров, более или менее равномерно вытягивается в небольшом числе направлений;
2. это облако точек распадается на несколько (как минимум, два) кластеров, которые расходятся в пространстве параметров на значительную величину; эти кластеры могут соответствовать различным типам реакции на адаптационную нагрузку.

 С помощью алгоритма автоматической классификации проведен анализ данных о состоянии липидного обмена плазмы крови при различных нагрузках. Показано, что в данном конкретном случае кластеризация отсутствует и имеет место первый способ увеличения корреляций.
 Полученный результат позволяет высказать гипотезу о том, что эффект повышения корреляций при увеличении адаптационного напряжения не связан с образованием изолированных подгрупп, соответствующих различным типам реакции на факторы среды. В соответствии с высказанной гипотезой, если исследуемая группа все же распадается на такие изолированные подгруппы, то увеличение корреляций при повышении адаптационного напряжения должно наблюдаться во всех этих подгруппах.
 Проведен анализ идей, лежащих в основе теории группового стресса.