Social network size and perceived network sufficiency as predictors of perceived health status

This study focused on the relationship between social network size (number of friends and relatives), perceived sufficiency of the network and self-rated health utilizing data from the National Survey of Personal Health Practices and Consequences, 1979. For men neither perceived sufficiency nor number of relatives were associated with self-rated health status. The number of friends was positively associated with health status. For women perceived network sufficiency was positively and significantly related to health status, independent of network size. The number of friends and relatives was not associated with self-rated health status. The sociodemographic variables accounted for most of the explained variance in health status for both males and females. Social networks may hold different meanings for women and men, and may require qualitative as well as quantitative analysis. There may have been insufficient variance in the major variables to produce meaningful results. ^

Mitochondrial Network Size Scaling in Budding Yeast

Mitochondria must grow with the growing cell to ensure proper cellular physiology and inheritance upon division. We measured the physical size of mitochondrial networks in budding yeast and found that mitochondrial network size increased with increasing cell size and that this scaling relation occurred primarily in the bud. The mitochondria-to-cell size ratio continually decreased in aging mothers over successive generations. However, regardless of the mother's age or mitochondrial content, all buds attained the same average ratio. Thus, yeast populations achieve a stable scaling relation between mitochondrial content and cell size despite asymmetry in inheritance.

From Personal Network to Institution Building: The Lifanyuan and the Formalization of Manchu-Mongol Relations

The Qing emperors, who ruled over China from 1644-1911, managed to bring large parts of Inner Asia under their control and extended the territory of China to an unprecedented degree. This paper maintains that the political technique of patronage with its formalized language, its emphasis on gift exchange and expressions of courtesy is a useful concept for explaining the integration of Inner Asian confederations into the empire. By re-interpreting the obligations of gift exchange, the Qing transformed the network of personal relationships, which had to be reinforced and consolidated permanently into a system with clearly defined rules. In this process of formalization, the Lifanyuan, the Court for the Administration of the Outer Regions, played a key role. While in the early years of the dynasty, it was responsible for collecting and disseminating information concerning the various patronage relationships with Inner Asian leaders, over the course of the 17th and 18th centuries its efforts were directed at standardizing and streamlining the contacts between ethnic minorities and the state. Through the Lifanyuan, the rules and principles of patronage were maintained in a modified form even in the later part of the dynasty, when the Qing exercised control in the outer regions more directly. The paper provides an explanation for the longevity and cohesiveness of the multi-ethnic Qing empire. Based on recently published Manchu and Mongolian language archival material and the Maussian concept of gift exchange the study sheds new light on the changing self-conception of the Qing emperors.

The game of contacts: Estimating the social visibility of groups

Estimating the sizes of hard-to-count populations is a challenging and important problem that occurs frequently in social science, public health, and public policy. This problem is particularly pressing in HIV/AIDS research because estimates of the sizes of the most at-risk populations-illicit drug users, men who have sex with men, and sex workers-are needed for designing, evaluating, and funding programs to curb the spread of the disease. A promising new approach in this area is the network scale-up method, which uses information about the personal networks of respondents to make population size estimates. However, if the target population has low social visibility, as is likely to be the case in HIV/AIDS research, scale-up estimates will be too low. In this paper we develop a game-like activity that we call the game of contacts in order to estimate the social visibility of groups, and report results from a study of heavy drug users in Curitiba, Brazil (n = 294). The game produced estimates of social visibility that were consistent with qualitative expectations but of surprising magnitude. Further, a number of checks suggest that the data are high-quality. While motivated by the specific problem of population size estimation, our method could be used by researchers more broadly and adds to long-standing efforts to combine the richness of social network analysis with the power and scale of sample surveys. (C) 2010 Elsevier B.V. All rights reserved.

Larger or broader : performance implications of size and diversity of the knowledge worker's egocentric network. [更多或更广：知识员工个人中心网络大小和 多样性对绩效的影响]

Management scholars and practitioners emphasize the importance of the size and diversity of a knowledge worker's social network. Constraints on knowledge workers’ time and energy suggest that more is not always better. Further, why and how larger networks contribute to valuable outcomes deserves further understanding. In this study, we offer hypotheses to shed insight on the question of the diminishing returns of large networks and the specific form of network diversity that may contribute to innovative performance among knowledge workers. We tested our hypotheses using data collected from 93 R&D engineers in a Sino-German automobile electronics company located in China. Study findings identified an inflection point, confirming our hypothesis that the size of the knowledge worker's egocentric network has an inverted U-shaped effect on job performance. We further demonstrate that network dispersion richness (the number of cohorts that the focal employee has connections to) rather than network dispersion evenness (equal distribution of ties across the cohorts) has more influence on the knowledge worker's job performance. Additionally, we found that the curvilinear effect of network size is fully mediated by network dispersion richness. Implications for future research on social networks in China and Western contexts are discussed.

Personal factors, communication and vision predict social participation in older adults

Social isolation is a predictor of morbidity and mortality in older people. Speech pathologists often consider that communication disabilities associated with normal ageing (sensory loss, language and discourse changes) contribute to social isolation. The aims of this study were to describe the functioning of older people using the International Classification of Functioning, Disability and Health (WHO, 2001) as a conceptual framework for language and sensory functioning, communicative activity, and social participation, and to explore the relationship between communication (both at an impairment level and an activity level), social participation and personal factors (demographics and emotional health). In a prospective study, 47 women and 28 men aged 62 to 98 years (mean=74 yrs) completed objective and subjective assessments of functioning and participation, and provided personal information. Assessments were individually conducted in a face- to-face interview situation with the primary researcher, who was a speech pathologist. Assessments revealed the sample had predominantly mild hearing and vision impairments, unimpaired naming ability, frequent involvement in a wide range of communication activities, and variable social network size and social activities participation. Social participation was shown to be associated with vision, communication activities, age, education and emotional health. Naming and hearing impairments were not reliable predictors of social participation. It was concluded that professionals interested in maintaining and improving social participation of older people could well consider these predictors in community-directed interventions. Speech pathologists should therefore promote older people's involvement in everyday communicative activities while also limiting the impact of communication-related impairments, so that social participation is maintained in our ageing population.

Predicting community responses to perturbations in the face of imperfect knowledge and network complexity

How best to predict the effects of perturbations to ecological communities has been a long-standing goal for both applied and basic ecology. This quest has recently been revived by new empirical data, new analysis methods, and increased computing speed, with the promise that ecologically important insights may be obtainable from a limited knowledge of community interactions. We use empirically based and simulated networks of varying size and connectance to assess two limitations to predicting perturbation responses in multispecies communities: (1) the inaccuracy by which species interaction strengths are empirically quantified and (2) the indeterminacy of species responses due to indirect effects associated with network size and structure. We find that even modest levels of species richness and connectance (similar to 25 pairwise interactions) impose high requirements for interaction strength estimates because system indeterminacy rapidly overwhelms predictive insights. Nevertheless, even poorly estimated interaction strengths provide greater average predictive certainty than an approach that uses only the sign of each interaction. Our simulations provide guidance in dealing with the trade-offs involved in maximizing the utility of network approaches for predicting dynamics in multispecies communities.

The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces self-sustained activity. Nonlocal connections, or shortcuts, are randomly introduced according to a specified connection probability. There is a range of connection probabilities for which neuron firing occurs, as well as a critical probability for which the firing ceases in the absence of time delay. The critical probability for nonlocal shortcuts depends on the network size according to a power-law. We also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes. (C) 2011 Elsevier B.V. All rights reserved.

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

Analysis and comparison of network performance with different network parameters

The purpose of this study was to analyze the network performance by observing the effect of varying network size and data link rate on one of the most commonly found network configurations. Computer networks have been growing explosively. Networking is used in every aspect of business, including advertising, production, shipping, planning, billing, and accounting. Communication takes place through networks that form the basis of transfer of information. The number and type of components may vary from network to network depending on several factors such as requirement and actual physical placement of the networks. There is no fixed size of the networks and they can be very small consisting of say five to six nodes or very large consisting of over two thousand nodes. The varying network sizes make it very important to study the network performance so as to be able to predict the functioning and the suitability of the network. The findings demonstrated that the network performance parameters such as global delay, load, router processor utilization, router processor delay, etc. are affected. The findings demonstrated that the network performance parameters such as global delay, load, router processor utilization, router processor delay, etc. are affected significantly due to the increase in the size of the network and that there exists a correlation between the various parameters and the size of the network. These variations are not only dependent on the magnitude of the change in the actual physical area of the network but also on the data link rate used to connect the various components of the network.

Redes Sociais Pessoais de Idosos Segundo o Sexo dos Filhos

Objetivos: O presente estudo tem como objetivo analisar as redes sociais pessoais de idosos portugueses com filhos segundo o sexo da descendência e o sexo do/a idoso/a, relativamente às características estruturais, funcionais e relacionais-contextuais. Metodologia: Para a avaliação das variáveis em estudo foram utilizados o Instrumento de Análise da Rede Social Pessoal, versão para idosos (IARSP – Idosos) (Guadalupe, 2010; Guadalupe & Vicente, 2012) para avaliar as dimensões da rede social pessoal e um inquérito por questionário para caracterização da amostra a nível sociodemográfico e sociofamiliar. Participantes: A amostra é constituída por 498 idosos com filhos, com uma média de idades de 75 anos (DP=7,487), entre os 65 anos e os 98 anos, maioritariamente do sexo feminino (60,8%), casados ou em união facto (58,4%) e com escolaridade (70,7%). A maioria dos idosos inquiridos reside em aglomerado populacional (90,8%) e não usufrui de apoio de respostas sociais (78,1%). Resultados: Na análise separámos 3 subamostras: idosos com filhos de ambos os sexos (n=218; 43,7%), idosos com filhos do sexo masculino (n=125; 25,2%) e idosos com filhos do sexo feminino (n=155; 31,2%). Os idosos com filhas apresentam valores mais elevados no apoio material e instrumental (p = 0,046), apoio informativo (p = 0,018), companhia social (p = 0,018) e reciprocidade de apoio (p < 0,001). O tamanho da rede é menor no caso dos idosos com filhas comparativamente aos que têm filhos de ambos os sexos (p = 0,012). Analisando separadamente as redes das idosas e dos idosos da amostra, assinalamos que nas redes de idosos do sexo masculino apenas houve diferença na reciprocidade (p = 0,016), sendo menos recíprocas as redes da subamostra com filhos apenas do sexo masculino; por sua vez, nas redes das idosas houve diferenças no tamanho da rede (p = 0,015) e na frequência de contactos (p = 0,019) sendo maior nas idosas com filhos de ambos sexos; na proporção de relações de vizinhança na rede (p = 0,005), sendo menor nas idosas que têm filhos de ambos os sexos; no apoio informativo (p = 0,022) e na reciprocidade (p = 0,005) sendo menores nas idosas com filhos do sexo masculino. Conclusões: O nosso estudo revela que o sexo dos filhos influencia as redes sociais pessoais dos pais e mães idosos/as a nível funcional, estrutural e relacional-contextual, sobretudo no caso das mulheres idosas, uma vez que as redes das idosas apresentam diferenças nas três dimensões, o que não se verifica nos pais idosos, verificando-se também que os idosos com filhas do sexo feminino têm redes mais centradas nas relações familiares. / Goals: This study aims to analyze the personal social networks structural, functional and relational-contextual characteristics of Portuguese seniors with offspring, according to their sex. Methodology: To the variables evaluation, we have used the Personal Social Network Analysis Instrument, Elderly Version (IARSP – Elderly) (Guadalupe, 2010; Guadalupe & Vicente, 2012) in order to evaluate the dimensions of the personal social network, and a questionnaire for demographic description. Participants: Our sample has 498 seniors with offspring, with an average of 75 years of age (DP = 7,487), between 65 and 98 years old, mostly females (60,8%), married (58,4%) with education (70,7%).The majority live on agglomeration (90,8%) and does not have the support of social services (78,1%). Results: In this analysis we've 3 groups: seniors with sons and daughters (n = 218; 43,7%), seniors with male offspring (n = 125; 25,2%) and seniors with female offspring ( n = 155; 31,2%). Seniors with daughters only shows higher values on material and instrumental support (p = 0,046), informative support (p = 0,018), social company (p = 0,018) and reciprocity support (p < 0,001). The network size is smaller on senior's with offspring, comparing the ones with sons and daughters (p = 0,012). On a separate analysis of the male and female seniors sample, it should be noticed that on the male seniors network there's been a difference on reciprocity only (p = 0,016) being less reciprocal the networks from the group exclusively with male sons; on the other end, on the female seniors network with sons and daughters there's been a difference on the network size (p = 0,015) and on the contact frequency (p = 0,019) being smaller on the seniors with offspring from both sex; on the proportion relation of network neighborhood (p = 0,005), smaller on the female seniors with sons and daughters; on informative support (p = 0,022) and on the reciprocity (p = 0,005), being smaller on the female seniors with male offspring. Conclusions: Our study reveals that the male and female offspring influences the personal social networks of senior mothers and fathers on a functional, structural and context-relational level, mostly on women, once that their network presents differences in the three dimension, something that does not happen with senior fathers, with the verification that the seniors with daughters do have social networks that are more centered in family relations.

Famílias Unipessoais Idosas: um estudo das redes sociais pessoais de idosos que vivem sós

Objetivos: O presente estudo tem como objetivo analisar as características estruturais, funcionais e relacionais-contextuais das redes sociais pessoais de famílias unipessoais idosas. Metodologia: Utilizámos para recolha de dados um questionário para caracterizar sociodemograficamente a amostra, o Instrumento de Análise da Rede Social Pessoal (versão para idosos) (IARSP-Idosos) (Guadalupe, 2010; Guadalupe e Vicente 2012) e a escala de solidão UCLA (Neto, 1989). Participantes: A amostra é constituída por 567 indivíduos com média de idades de 75,53 anos, maioritariamente do sexo feminino (63,0%; n = 357). Predominam os sujeitos casados (53,7%; n = 304), com filhos (87,8%; n = 498) e em situação de coabitação (n = 450; 79,4%). Contudo, 20,6% (n = 117) vivem sós, constituindo as famílias unipessoais. Resultados: As redes sociais dos idosos têm em média 7,99 elementos, predominantemente familiares (M = 76,89%). Os participantes percecionam um nível elevado de apoio por parte das suas redes. São redes coesas, pouco dispersas e os contactos entre os elementos são frequentes. As mulheres, os indivíduos solteiros, viúvos ou divorciados e os idosos sem filhos têm uma maior probabilidade de viverem sós (p < 0,05) e estes apresentam uma maior probabilidade de necessitar de apoio social formal (p < 0,05). As famílias unipessoais, quando comparadas com os que não vivem sós, apresentam um maior número de campos relacionais e maior proporção de relações de amizade e de vizinhança (p < 0,05). Têm menor perceção de apoio material e instrumental, informativo, companhia social, acesso a novos vínculos e reciprocidade de apoio (p < 0,05). Além disso, referem menor frequência de contactos e uma maior dispersão geográfica (p < 0,05). Nas famílias unipessoais, observou-se a existência de correlações negativas significativas (p < 0,05) entre a percepção de solidão e o tamanho da rede, a proporção das relações familiares na rede, o apoio emocional e informativo e a reciprocidade de apoio. CONCLUSÃO: Os idosos com famílias unipessoais percecionam menor apoio por parte das suas redes, tendo uma maior propensão à solidão. É fundamental, ao longo do ciclo vital, promover a quantidade e qualidade dos vínculos, no sentido de manter a efetividade do suporte das redes mesmo quando se vive só. / Objectives: The present study aims to analyze the structural, functional and relational-contextual characteristics of older single-person households. Methodology: We used as instruments a questionnaire to evaluate sociodemographic data, the Instrumento de Análise da Rede Social Pessoal (version for elderly people: IARSP-Idosos) (Guadalupe, 2010; Guadalupe e Vicente 2012) and the UCLA Loneliness Scale (Neto, 1989). Participants: The sample consists of 567 individuals with an average age of 75.53 years, mostly females (63.0%; n = 357). There is a predominance of married individuals (53.7%; n = 304) with children (87.8%; n = 498). Older people live mainly in cohabitation (n = 450; 79.4%), however 20.6% oh them live alone, constituting one-person households. Results: The elderly personal social networks have 8 elements, on average, with a predominance of family relationships (M = 76.89%). The participants perceived a high level of support from their networks. In general the networks are cohesive, with low dispersion and have frequent contacts. The women, single, widowed or divorced and childless elderly are more likely to live alone (p < 0.05) and to need social services support (p < 0.05). The single-person households, compared with those who do not live alone, have a greater number of relational fields and a higher proportion of friendships and neighborhood relations (p < 0.05). They have a lower perception of material and informative support, social company and acess to new ties and reciprocal support (p < 0.05). They also refer lowest frequency of contacts and a wider geographical dispersion (p < 0.05). In single-person households there was a negative significant correlation between the perception of loneliness and the social network size, the proportion of family relationships in the network, emotional and informational support and reciprocal support. Conclusions: The elderly single-person households perceived less support from their networks and a greater propensity to loneliness. It is critical to promot the quality of ties, rather then their quantity, throughout the life cycle, in order to maintain the network effectiveness even when the person lives alone.

Redes Sociais Pessoais de Idosos com e sem Filhos

Objetivos: O presente estudo tem como objectivo analisar as redes sociais e pessoais de idosos portugueses com filhos e sem filhos, relativamente às características estruturais, funcionais e relacionais-contextuais. Metodologia: Para a avaliação das variáveis em estudo foram utilizados: o Instrumento de Análise da Rede Social Pessoal, versão para idosos (IARSP – Idosos) (Guadalupe, 2010; Guadalupe & Vicente, 2012) para avaliar as dimensões da rede social pessoal; um inquérito por questionário para caracterização da amostra a nível sociodemográfico e sociofamiliar. Participantes: A amostra é constituída por 418 idosos, com uma média de idades de 76 anos (DP=7,62), entre os 65 anos e os 98 anos, maioritariamente do sexo feminino (63,9%), casados ou em união facto (51,0%) e com escolaridade (63,9,1%). A maioria dos idosos inquiridos vive com agregado familiar (80,4%) em zonas rurais (64,8) e não usufrui de qualquer tipo de apoio de resposta social (71,5%). Resultados: Os idosos com filhos são maioritários (n=364; 87,1%) e os sem filhos os minoritários (n=54; 12,9%) na nossa amostra. Dos que têm filhos, 29,9% (109) têm filhos únicos e 70,1% (255) têm mais do que um filho (67% com 1 ou 2 filhos), sendo os filhos maioritariamente de ambos os sexos (n=158; 43,4%). Os resultados sugerem que o facto de os idosos terem ou não terem filhos reflete-se sobretudo em diferenças nas características estruturais das redes. Os idosos com filhos apresentam uma média mais elevada no tamanho da rede, na proporção das relações de familiares, e satisfação da rede e reciprocidade de apoio (p ≤ 0,001), a nível das características funcionais. Já relativamente à proporção das relações de amizade, vizinhança na rede, são os idosos sem filhos que apresentam uma média substantivamente mais elevada (p ≤ 0,003) do que a outra subamostra, apresentando também uma maior durabilidade das relações interpessoais (p < 0,03). As correlações entre o número total de filhos/as com as características estruturais e funcionais da rede, indicam-nos que quanto maior é o número de filhos maior é o tamanho da rede, a proporção das relações familiares, o apoio emocional, a reciprocidade de apoio, a satisfação com a rede e com o suporte social. Conclusões: O nosso estudo revela que as redes sociais pessoais dos idosos diferenciam-se a nível estrutural segundo o facto de terem ou não filhos, mas também nalgumas variáveis funcionais. Os idosos com filhos apresentam redes mais alargadas e muito centradas nas relações familiares na rede (sensivelmente menos um terço) do que os idosos sem filhos. Os últimos apresentam redes menores (com cerca de 2 pessoas a menos) e mais investidas nas relações de amizade e de vizinhança (com proporções que representam mais do dobro destes vínculos). / Goals: The present study has the purpose to analyze the personal social networks of Portuguese elder with our without sons/daughters, in their structural, functional and contextual relations. Methodology: We used for the evaluation of the variables: The Personal Social Network Analysis Tool, regarding elderly people (IARSP – elderly people) (Guadalupe, 2010; Guadalupe & Vicente, 2012), to evaluate the personal social network dimensions; a survey through an inquiry to characterize the sample at sociodemographic and at sociofamily level. Participants: The sample includes 418 elderly with an average age of 76 years old (DP = 7,62) between 65 and 98 years old, mainly women (63,9%), married or living as a couple (51,0%) with education (63,9,1%). Most of the elderly people who answered the survey live in family household (80,4%) in rural areas (64,8) and do not benefit from any type of social services support (71,5%). Results: The majority is elderly people with sons/daughters (n=364, 87,1%) and the ones without are the minority (n= 54, 12,9%) in our sample. Within those who are parents, 29,9% (109) have only one child and 70,1% (255) have more than one child (67% with 1 or 2), and the children are mainly of both sexes (n= 158; 43,4%). The results suggest that the fact that the elderly have or not have children is reflected especially in differences in the structural characteristics of the networks. Elderly people with children have a higher average in the network size, in the proportion of family relationships, and satisfaction of the network and reciprocal support (p ≤ 0,001). Regarding the proportion of friendly relations, network neighborhood, are the elderly without children who have a substantially higher mean (p ≤ 0,003) than the other subsample, also featuring improved durability of interpersonal relationships (p < 0,003). The correlations between the total number of children/with the structural and functional characteristics of the network, indicate that the greater the number of children, the greater the size of the network, the proportion of family relationships, emotional, support, reciprocity support and satisfaction with social network. Conclusion: Our study reveals that the personal social networks of the elderly differ in the structural level, according to whether they have sons/daughters or not, but also in some functional variables. The elderly with children have networks much more broader and centered on family relationships (roughly one-third) than elderly without children. These elderly without children have smaller networks (about 2 fewer people) and more centered in relations of friendship and neighborhood (with proportions that are more than the double compared to the other subsample).

Stochastic ranking method for thermostatically controllable appliances to provide regulation services

Demand response can be used for providing regulation services in the electricity markets. The retailers can bid in a day-ahead market and respond to real-time regulation signal by load control. This paper proposes a new stochastic ranking method to provide regulation services via demand response. A pool of thermostatically controllable appliances (TCAs) such as air conditioners and water heaters are adjusted using direct load control method. The selection of appliances is based on a probabilistic ranking technique utilizing attributes such as temperature variation and statuses of TCAs. These attributes are stochastically forecasted for the next time step using day-ahead information. System performance is analyzed with a sample regulation signal. Network capability to provide regulation services under various seasons is analyzed. The effect of network size on the regulation services is also investigated.