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PubMed2006

Exploring photosynthesis evolution by comparative analysis of metabolic networks between chloroplasts and photosynthetic bacteria.

BACKGROUND: Chloroplasts descended from cyanobacteria and have a drastically reduced genome following an endosymbiotic event. Many genes of the ancestral cyanobacterial genome have been transferred to the plant nuclear genome by horizontal gene transfer. However, a selective set of metabolism pathways is maintained in chloroplasts using both chloroplast genome encoded and nuclear genome encoded enzymes. As an organelle specialized for carrying out photosynthesis, does the chloroplast metabolic network have properties adapted for higher efficiency of photosynthesis? We compared metabolic network properties of chloroplasts and prokaryotic photosynthetic organisms, mostly cyanobacteria, based on metabolic maps derived from genome data to identify features of chloroplast network properties that are different from cyanobacteria and to analyze possible functional significance of those features. RESULTS: The properties of the entire metabolic network and the sub-network that consists of reactions directly connected to the Calvin Cycle have been analyzed using hypergraph representation. Results showed that the whole metabolic networks in chloroplast and cyanobacteria both possess small-world network properties. Although the number of compounds and reactions in chloroplasts is less than that in cyanobacteria, the chloroplast's metabolic network has longer average path length, a larger diameter, and is Calvin Cycle -centered, indicating an overall less-dense network structure with specific and local high density areas in chloroplasts. Moreover, chloroplast metabolic network exhibits a better modular organization than cyanobacterial ones. Enzymes involved in the same metabolic processes tend to cluster into the same module in chloroplasts. CONCLUSION: In summary, the differences in metabolic network properties may reflect the evolutionary changes during endosymbiosis that led to the improvement of the photosynthesis efficiency in higher plants. Our findings are consistent with the notion that since the light energy absorption, transfer and conversion is highly efficient even in photosynthetic bacteria, the further improvements in photosynthetic efficiency in higher plants may rely on changes in metabolic network properties.

Arabidopsis↗
PubMed2006

Measuring specialization in species interaction networks.

BACKGROUND: Network analyses of plant-animal interactions hold valuable biological information. They are often used to quantify the degree of specialization between partners, but usually based on qualitative indices such as 'connectance' or number of links. These measures ignore interaction frequencies or sampling intensity, and strongly depend on network size. RESULTS: Here we introduce two quantitative indices using interaction frequencies to describe the degree of specialization, based on information theory. The first measure (d') describes the degree of interaction specialization at the species level, while the second measure (H2') characterizes the degree of specialization or partitioning among two parties in the entire network. Both indices are mathematically related and derived from Shannon entropy. The species-level index d' can be used to analyze variation within networks, while H2' as a network-level index is useful for comparisons across different interaction webs. Analyses of two published pollinator networks identified differences and features that have not been detected with previous approaches. For instance, plants and pollinators within a network differed in their average degree of specialization (weighted mean d'), and the correlation between specialization of pollinators and their relative abundance also differed between the webs. Rarefied sampling effort in both networks and null model simulations suggest that H2' is not affected by network size or sampling intensity. CONCLUSION: Quantitative analyses reflect properties of interaction networks more appropriately than previous qualitative attempts, and are robust against variation in sampling intensity, network size and symmetry. These measures will improve our understanding of patterns of specialization within and across networks from a broad spectrum of biological interactions.

Adaptation, Physiological↗
PubMed1995

Vimentin and CP49/filensin form distinct networks in the lens which are independently modulated during lens fibre cell differentiation.

The cells of the eye lens contain the type III intermediate filament protein vimentin, as well as two other intermediate filament proteins, CP49 and filensin. These two proteins appear to be unique to the differentiated lens fibre cell. Immunoblotting and confocal microscopy were used to describe changes which occur in these three intermediate filament proteins and the networks they form during fibre cell differentiation and maturation. The vimentin network was present in both epithelial cells and some fibre cells. Fibre cells were vimentin positive up to a specific point 2-3 mm in from the lens capsule where the vimentin signal was drastically reduced. The CP49/filensin network was not present in the undifferentiated epithelial cells but emerged in the differentiating fibre cells. This latter network exhibited a principally plasma membrane localization in younger fibre cells but became more cytoplasmic in older fibre cells. This change also occurred at a distinct point in fibre cell differentiation, much earlier than the observed loss of the vimentin network. The subcellular changes in the distributions of these cytoskeletal networks were correlated to the loss of the fibre cell nucleus, another feature of fibre cell differentiation. No correlation was found to changes in the vimentin network but nuclear loss did coincide with changes in the CP49/filensin network. Concomitant with nuclear pyknosis, there were also changes in the nuclear lamina as well as infringement of the nuclear compartment by CP49, as shown by confocal microscopy. This study demonstrates vimentin and the CP49/filensin network to be independent in the lens but both networks undergo dramatic changes in subcellular distribution during the differentiation/maturation of the fibre cell. Only changes in the CP49/filensin network can be correlated to nuclear loss. Thus in the lens, unlike mammalian erythropoiesis which is also characterized by nuclear loss, the vimentin network does not appear linked to nuclear retention.

Animals↗
PubMed2006

Sequential expression of type IV collagen networks: testis as a model and relevance to spermatogenesis.

The six alpha chains of type IV collagen are organized into three networks: alpha1/alpha2, alpha3/alpha4/alpha5, and alpha1/alpha2/alpha5/alpha6. A shift from the alpha1/alpha2 to the alpha3/alpha4/alpha5 network occurs in the developing glomerular basement membrane, but how the alpha1/alpha2/alpha5/alpha6 network fits into this sequence is less clear, because the three networks do not colocalize. Here, we studied the seminiferous tubule basement membrane of normal canine testis where all three networks do colocalize: the alpha1/alpha2 network is expressed from birth, the alpha1/alpha2/alpha5/alpha6 network by 5-6 weeks of age, and the alpha3/alpha4/alpha5 network by 2 months of age. A canine model of Alport syndrome allowed study of the absence of alpha3/alpha4/alpha5 and alpha1/alpha2/alpha5/alpha6 networks in testis. In Alport dogs, the seminiferous tubule basement membrane was thinner than in controls. Spermatogenesis began at the same time as with normal dogs; however, the number of mature sperm was significantly reduced in Alport dogs. Thus, it would appear that alpha3/alpha4/alpha5 and alpha1/alpha2/alpha5/alpha6 networks are not essential for onset of spermatogenesis, but long-term function may be compromised by the loss of one or both networks. This situation is analogous to the glomerular basement membrane in Alport syndrome. In conclusion, testis can serve as a model system to study the sequence of type IV collagen network expression.

Animals↗
PubMed2005

A managed clinical network for cardiac services: set-up, operation and impact on patient care.

PURPOSE: To investigate the set up and operation of a Managed Clinical Network for cardiac services and assess its impact on patient care. METHODS: This single case study used process evaluation with observational before and after comparison of indicators of quality of care and costs. The study was conducted in Dumfries and Galloway, Scotland and used a three-level framework. Process evaluation of the network set-up and operation through a documentary review of minutes; guidelines and protocols; transcripts of fourteen semi-structured interviews with health service personnel including senior managers, general practitioners, nurses, cardiologists and members of the public. Outcome evaluation of the impact of the network through interrupted time series analysis of clinical data of 202 patients aged less than 76 years admitted to hospital with a confirmed myocardial infarction one-year pre and one-year post, the establishment of the network. The main outcome measures were differences between indicators of quality of care targeted by network protocols. Economic evaluation of the transaction costs of the set-up and operation of the network and the resource costs of the clinical care of the 202 myocardial infarction patients from the time of hospital admission to 6 months post discharge through interrupted time series analysis. The outcome measure was different in National Health Service resource use. RESULTS: Despite early difficulties, the network was successful in bringing together clinicians, patients and managers to redesign services, exhibiting most features of good network management. The role of the energetic lead clinician was crucial, but the network took time to develop and 'bed down'. Its primary "modus operand" was the development of a myocardial infarction pathway and associated protocols. Of sixteen clinical care indicators, two improved significantly following the launch of the network and nine showed improvements, which were not statistically significant. There was no difference in resource use. DISCUSSION AND CONCLUSIONS: The Managed Clinical Network made a difference to ways of working, particularly in breaching traditional boundaries and involving the public, and made modest changes in patient care. However, it required a two-year "set-up" period. Managed clinical networks are complex initiatives with an increasing profile in health care policy. This study suggests that they require energetic leadership and improvements are likely to be slow and incremental.

Journal Article↗
PubMedDate not supplied

Informal networks: the company behind the chart.

A glance at an organizational chart can show who's the boss and who reports to whom. But this formal chart won't reveal which people confer on technical matters or discuss office politics over lunch. Much of the real work in any company gets done through this informal organization with its complex networks of relationships that cross functions and divisions. According to consultants David Krackhardt and Jeffrey Hanson, managers can harness the true power in their companies by diagramming three types of networks: the advice network, which reveals the people to whom others turn to get work done; the trust network, which uncovers who shares delicate information; and the communication network, which shows who talks about work-related matters. Using employee questionnaires, managers can generate network maps that will get to the root of many organizational problems. When a task force in a computer company, for example, was not achieving its goals, the CEO turned to network maps to find out why. He discovered that the task force leader was central in the advice network but marginal in the trust network. Task force members did not believe he would look out for their interests, so the CEO used the trust map to find someone to share responsibility for the group. And when a bank manager saw in the network map that there was little communication between tellers and supervisors, he looked for ways to foster interaction among employees of all levels. As companies continue to flatten and rely on teams, managers must rely less on their authority and more on understanding these informal networks. Managers who can use maps to identify, leverage, and revamp informal networks will have the key to success.

Communication↗
PubMed2001

Long-lasting reconfiguration of two interacting networks by a cooperation of presynaptic and postsynaptic plasticity.

The functional reconfiguration of central neuronal networks, a phenomenon by which neurons change their participation in network operation, is important for organizing adaptive behaviors. Such reconfiguration can be expressed in a long-lasting manner (hours, days) after a training paradigm. The present study shows that such a long-lasting network reconfiguration requires a cooperation of both presynaptic and postsynaptic modifications in a neuronal interaction between two functionally distinct networks. In isolated preparations of the lobster stomatogastric nervous system, the single ventral dilator (VD) neuron can switch its functional participation from one discrete network (the pyloric network) to another (the cardiac sac network). This switching capability can be long-lasting and can be induced by a sensitizing procedure. A persistent change that was associated with this neuronal switching was found in each of the two networks. First, the intrinsic membrane properties of the VD neuron that allow it to participate spontaneously in the pyloric network are altered. Second, bursting activity is strengthened in the inferior ventricular neurons that both drive cardiac sac network activity and monosynaptically excite the VD neuron in phase with this network activity. Importantly, these changes in intrinsic properties of both presynaptic and postsynaptic neurons are required to allow the VD neuron switching, because expression of either the presynaptic or the postsynaptic change alone did not permit VD neuron switching to occur. These results suggest that a cooperative modification of a discrete network interaction is able to persistently switch the output pattern of a motor neuron as a result of a sensitizing paradigm.

Action Potentials↗
PubMed1988

[Reactions of the neuronal networks with various mechanisms for the termination of activity to external de- and hyperpolarization exposures].

Responses of the stochastically organized uniform neuronal networks as well as responses of networks with pre- and postsynaptic inhibition to external de- and hyperpolarizing effects of different intensity and temporal structure were compared by means of the mathematical simulation model. In the networks with pre- and postsynaptic inhibition in comparison with uniform neuronal networks a region of long-term depolarizing effects with possible monitoring of the activity of neuronal networks parameters is enlarged. The effect of short-term de- and hyperpolarizing influences in neuronal networks depends on the neuronal network activity level oscillations. Depolarizing effects may shorten the activity of neuronal networks, while hyperpolarizing influences may prolong the activity. An effect of reducing the activity of neuronal networks due to depolarizing influences is more noticeable in the networks with pre- and postsynaptic inhibition. Coming from the results obtained a conclusion is made that the presence of additional negative feedback circuits in a form of presynaptic or postsynaptic inhibition networks contributes to control improvement of the mechanism, which terminates the network activity.

Animals↗
PubMed1984

Social networks and social support of primigravida mothers and fathers.

Most researchers have examined the effects of stress and social support on pregnancy outcomes without identifying the relationship between social support and social network factors. While the type and amount of support have been shown to be related to pregnancy outcomes, the sources of that support and the influence of network structure on a person's supportive resources have not been defined. Network factors, in fact, may predict perceived support or may explain more of the variance in pregnancy outcomes than social support does alone. The objectives of this study were to describe the social networks of primigravida women and their husbands; to determine if there are any differences in social networks based on gender, education, or income; and to examine the relationships among network characteristics, demographic characteristics, and perceived availability of support from network members. The 54 couples who composed the sample for this study were recruited through local physicians who provided the names of all clients who were primigravidas, living with the father of the child, and residing within 25 miles of Ann Arbor, Michigan. During the third trimester of pregnancy, couples were interviewed in their homes, and each parent completed a Social Network Inventory (SNI). The SNI obtained information about the size of the network, role relationships, frequency of contact, percent of uniplex relationships, and degree of overlap with spouse's social network. In addition, parents were provided with definitions of each of House's (1981) four types of social support and asked to indicate which forms of support they received from each network member. Both individual variables (age and educational level) and network structure variables (size, percent kin, percent females, frequency, and density) were significantly associated with the amount of perceived social support. For each type of support, the independent variables associated with support were different for men and women.

Adult↗
PubMed1997

Networking computers.

This decade the role of the personal computer has shifted dramatically from a desktop device designed to increase individual productivity and efficiency to an instrument of communication linking people and machines in different places with one another. A computer in one city can communicate with another that may be thousands of miles away. Networking is how this is accomplished. Just like the voice network used by the telephone, computer networks transmit data and other information via modems over these same telephone lines. A network can be created over both short and long distances. Networks can be established within a hospital or medical building or over many hospitals or buildings covering many geographic areas. Those confined to one location are called LANs, local area networks. Those that link computers in one building to those at other locations are known as WANs, or wide area networks. The ultimate wide area network is the one we've all been hearing so much about these days--the Internet, and its World Wide Web. Setting up a network is a process that requires careful planning and commitment. To avoid potential pitfalls and to make certain the network you establish meets your needs today and several years down the road, several steps need to be followed. This article reviews the initial steps involved in getting ready to network.

Computer Communication Networks↗
PubMed2004

Inhibition modifies the effects of slow calcium-activated potassium channels on epileptiform activity in a neuronal network model.

Generation of epileptiform activity typically results from a change in the balance between network excitation and inhibition. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties can produce increased network excitation. The slow Ca(2+)-activated K(+) currents (sI(AHP)) are important modulators of neuronal firing rate and excitability and have important established and potential roles in epileptogenesis. While the effects of changes in sI(AHP) on individual neuronal excitability are readily studied and well established, the effects of such changes on network behavior are less well known. The experiments here utilize a defined small network model of multicompartment pyramidal cells and an inhibitory interneuron to study the effects of changes in sI(AHP) on network behavior. The benefits of this model system include the ability to observe activity in all cells in a network and the effects of interactions of multiple simultaneous influences. In the model with no inhibitory interneuron, increasing sI(AHP) results in progressively decreasing burst activity. Adding an inhibitory interneuron changes the observed effects; at modest inhibitory strengths, increasing sI(AHP) in all network neurons actually results in increased network bursting (except at very high values). The duration of the burst activity is influenced by the length of delay in a feedback loop, with longer loops resulting in more prolonged bursting. These observations illustrate that the study of potential antiepileptogenic membrane effects must be extended to realistic networks. Network inhibition can dramatically alter the observations seen in pure excitatory networks.

Action Potentials↗
PubMed1997

Coherency and connectivity in oscillating neural networks: linear partialization analysis.

This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works.

Computer Simulation↗
PubMed2006

Pattern classification and recognition of invertebrate functional groups using self-organizing neural networks.

Self-organizing neural networks can be used to mimic non-linear systems. The main objective of this study is to make pattern classification and recognition on sampling information using two self-organizing neural network models. Invertebrate functional groups sampled in the irrigated rice field were classified and recognized using one-dimensional self-organizing map and self-organizing competitive learning neural networks. Comparisons between neural network models, distance (similarity) measures, and number of neurons were conducted. The results showed that self-organizing map and self-organizing competitive learning neural network models were effective in pattern classification and recognition of sampling information. Overall the performance of one-dimensional self-organizing map neural network was better than self-organizing competitive learning neural network. The number of neurons could determine the number of classes in the classification. Different neural network models with various distance (similarity) measures yielded similar classifications. Some differences, dependent upon the specific network structure, would be found. The pattern of an unrecognized functional group was recognized with the self-organizing neural network. A relative consistent classification indicated that the following invertebrate functional groups, terrestrial blood sucker; terrestrial flyer; tourist (nonpredatory species with no known functional role other than as prey in ecosystem); gall former; collector (gather, deposit feeder); predator and parasitoid; leaf miner; idiobiont (acarine ectoparasitoid), were classified into the same group, and the following invertebrate functional groups, external plant feeder; terrestrial crawler, walker, jumper or hunter; neustonic (water surface) swimmer (semi-aquatic), were classified into another group. It was concluded that reliable conclusions could be drawn from comparisons of different neural network models that use different distance (similarity) measures. Results with the larger consistency will be more reliable.

Animals↗
PubMed2006

Functional and evolutionary inference in gene networks: does topology matter?

The relationship between the topology of a biological network and its functional or evolutionary properties has attracted much recent interest. It has been suggested that most, if not all, biological networks are 'scale free.' That is, their connections follow power-law distributions, such that there are very few nodes with very many connections and vice versa. The number of target genes of known transcriptional regulators in the yeast, Saccharomyces cerevisiae, appears to follow such a distribution, as do other networks, such as the yeast network of protein-protein interactions. These findings have inspired attempts to draw biological inferences from general properties associated with scale-free network topology. One often cited general property is that, when compromised, highly connected nodes will tend to have a larger effect on network function than sparsely connected nodes. For example, more highly connected proteins are more likely to be lethal when knocked out. However, the correlation between lethality and connectivity is relatively weak, and some highly connected proteins can be removed without noticeable phenotypic effect. Similarly, network topology only weakly predicts the response of gene expression to environmental perturbations. Evolutionary simulations of gene-regulatory networks, presented here, suggest that such weak or non-existent correlations are to be expected, and are likely not due to inadequacy of experimental data. We argue that 'top-down' inferences of biological properties based on simple measures of network topology are of limited utility, and we present simulation results suggesting that much more detailed information about a gene's location in a regulatory network, as well as dynamic gene-expression data, are needed to make more meaningful functional and evolutionary predictions. Specifically, we find in our simulations that: (1) the relationship between a gene's connectivity and its fitness effect upon knockout depends on its equilibrium expression level; (2) correlation between connectivity and genetic variation is virtually non-existent, yet upon independent evolution of networks with identical topologies, some nodes exhibit consistently low or high polymorphism; and (3) certain genes show low polymorphism yet high divergence among independent evolutionary runs. This latter pattern is generally taken as a signature of positive selection, but in our simulations its cause is often neutral coevolution of regulatory inputs to the same gene.

Algorithms↗
PubMed2004

Effects of neural network feedback to physicians on admit/discharge decision for emergency department patients with chest pain.

STUDY OBJECTIVE: Neural networks can risk-stratify emergency department (ED) patients with potential acute coronary syndromes with a high specificity, potentially facilitating ED discharge of patients to home. We hypothesized that the use of "real-time" neural networks would decrease the admission rate for ED chest pain patients. METHODS: We conducted a before-and-after trial. Consecutive ED patients with chest pain were evaluated before and after implementation of a neural network in an urban university ED. Data included 40 variables used in neural networks for acute myocardial infarction and acute coronary syndrome. Data were obtained in real time, and neural network outputs were provided to the treating physician while patients were in the ED. On hospital discharge, attending physicians received feedback, including neural network output, their initial clinical impression, cardiac test results, and final diagnosis. The main outcome was the actual admit/discharge decision made before versus after the implementation of the neural network. RESULTS: Before implementation, 4,492 patients were enrolled; after implementation, 432 patients were enrolled. Implementation of the neural network did not decrease the hospital admission rate (before: 62.7% [95% confidence interval (CI) 61.3% to 64.1%] versus after: 66.6% [95% CI 62.2% to 71.0%]). Additionally, the ICU admission rates were not different (11.4% [95% CI 10.5% to 12.3%] versus 9.3% [95% CI 6.6% to 12.0%]). Physician query found that the neural network changed management in only 2 cases (<1%). CONCLUSION: The use of real-time neural network feedback did not influence the admission decision for ED patients with chest pain, most likely because the neural network output was delayed until the return of cardiac markers, and the disposition decision had already been made by that time.

Adult↗
PubMed2006

Operational principles of neurocognitive networks.

Large-scale neural networks are thought to be an essential substrate for the implementation of cognitive function by the brain. If so, then a thorough understanding of cognition is not possible without knowledge of how the large-scale neural networks of cognition (neurocognitive networks) operate. Of necessity, such understanding requires insight into structural, functional, and dynamical aspects of network operation, the intimate interweaving of which may be responsible for the intricacies of cognition. Knowledge of anatomical structure is basic to understanding how neurocognitive networks operate. Phylogenetically and ontogenetically determined patterns of synaptic connectivity form a structural network of brain areas, allowing communication between widely distributed collections of areas. The function of neurocognitive networks depends on selective activation of anatomically linked cortical and subcortical areas in a wide variety of configurations. Large-scale functional networks provide the cooperative processing which gives expression to cognitive function. The dynamics of neurocognitive network function relates to the evolving patterns of interacting brain areas that express cognitive function in real time. This article considers the proposition that a basic similarity of the structural, functional, and dynamical features of all neurocognitive networks in the brain causes them to function according to common operational principles. The formation of neural context through the coordinated mutual constraint of multiple interacting cortical areas, is considered as a guiding principle underlying all cognitive functions. Increasing knowledge of the operational principles of neurocognitive networks is likely to promote the advancement of cognitive theories, and to seed strategies for the enhancement of cognitive abilities.

Animals↗
PubMed2005

[A descriptive national survey of 166 Alzheimer health networks].

OBJECTIVE: Assess and describe the organization, operation, and aims of Alzheimer health networks in France. METHODS: Questionnaire sent by post or handed to physicians in France identified as involved in management of Alzheimer patients by Novartis Pharma sales representatives. RESULTS: 166 networks managing Alzheimer's disease (2/3 primarily gerontological and 1/3 specializing specifically in Alzheimer's). In 61.9% of the cases, the physician supervising the network was a hospital staff physician, often a geriatrician (48%). The other member physicians were essentially general practitioners. Several paramedics and social workers also participated. Most networks were organized as not-for-profit organizations. Financial support most often came from the relevant ministries and the health insurance funds. The number of active cases handled by the networks could not be globally assessed. The operating tools for the networks included membership charters, management guidelines and protocols, and shared medical files, but fewer than 30% of the networks used any one of these. The networks had as their primary objectives training and information, patient follow-up and gerontological coordination. These aims were consistent with the goals they felt that had come closest to attaining, i.e., improving the quality and organization of care, sharing information with and training other health professionals, and providing information to the public. Barely one third of the networks had developed an assessment procedure. Among the obstacles to network operations were the participants' lack of availability, the absence of collaboration between professionals, and financial problems. CONCLUSION: Despite the disparity in the quality and exhaustiveness of the data collected, our survey confirmed the diversity and dynamism, but also the lack of formal structure and the difficulties confronted by the Alzheimer networks in France.

Allied Health Personnel↗
PubMed2001

Upper bound of the expected training error of neural network regression for a Gaussian noise sequence.

In neural network regression problems, often referred to as additive noise models, NIC (Network Information Criterion) has been proposed as a general model selection criterion to determine the optimal network size with high generalization performance. Although NIC has been derived using asymptotic expansion, it has been pointed out that this technique cannot be applied under the assumption that a target function is in a family of assumed networks and the family is not minimal for representing the target true function, i.e. the overrealizable case, in which NIC reduces to the well-known AIC (Akaike Information Criterion) and others depending on a loss function. Because NIC is the unbiased estimator of generalization error based on training error, it is required to derive the expectations of errors for neural networks for such cases. This paper gives upper bounds of the expectations of training errors with respect to the distribution of training data, which we call the expected training error, for some types of networks under the squared error loss. In the overrealizable case, because the errors are determined by fitting properties of networks to noise components, including in data, the target set of data is taken to be a Gaussian noise sequence. For radial basis function networks and 3-layered neural networks with bell shaped activation function in the hidden layer, the expected training error is bounded above by sigma2* - 2nsigma2*logT/T, where sigma2* is the variance of noise, n is the number of basis functions or the number of hidden units and T is the number of data. Furthermore, for 3-layered neural networks with sigmoidal activation function in the hidden layer, we obtained the upper bound of sigma2* - O(log T/T) when n > 2. If the number of data is large enough, these bounds of the expected training error are smaller than sigma2* - N(n)sigma2*/T as evaluated in NIC, where N(n) is the number of all network parameters.

Analysis of Variance↗