To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between compression and pattern detection; by compressing a description of a random walker as a proxy for real flow on a network, we find regularities in the network that induce this system-wide flow. Finding the shortest multilevel description of the random walker therefore gives us the best hierarchical clustering of the network — the optimal number of levels and modular partition at each level — with respect to the dynamics on the network. With a novel search algorithm, we extract and illustrate the rich multilevel organization of several large social and biological networks. For example, from the global air traffic network we uncover countries and continents, and from the pattern of scientific communication we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. In general, we find shallow hierarchical structures in globally interconnected systems, such as neural networks, and rich multilevel organizations in systems with highly separated regions, such as road networks. Ever since Aristotle, organization and classification have been cornerstones of science. In network science Several network clustering algorithms generate hierarchical trees, but few make more than a single cut through the dendrogram. To extract multiple levels of the network structure In many real-world networks, directed and weighted links represent the constraints that the structure of a network places on dynamical processes taking place on this network. Networks thus often represent literal or metaphorical flows: people surfing the web, passengers traveling between airports, ideas spreading between scientists, funds passing between banks, and so on. This flow through a system makes its components interdependent to varying extents. The objective of our hierarchical clustering approach, therefore, is to reveal the multiple levels of interdependences between the nodes of a network with a single method. That is, a method that does not require multiple external resolution parameters, but rather inherently reveals the natural multiple levels of the system.map equationhierarchical map equation, which provides a natural answer to three questions: Into how many hierarchical levels is a given network organized? How many modules are present at each level? And which nodes are members of which modules? Here we focus on hard partitions and flow of random walkers; we postpone the natural extension of this approach to overlapping partitions and generalized flows to a subsequent paper. We begin by briefly reviewing the map equation, and then introduce the hierarchical map equation, of which our earlier two-level map equationIn this paper, we generalize the flow-based and information theoretic clustering method called the We have recently introduced the map equation to simplify and highlight important structures with respect to the dynamics on networks. This approach uses a random walk as a proxy for the real flow www.mapequation.org.The map equation is designed to capitalize on the modular structure of a network; the description length of the dynamics on the network can be compressed if the network has localized regions in which small groups of nodes have long persistence times. Compression is achieved by using multiple module codebooks with reused short codewords for different nodes in the network. To make the compressed description unambiguous, an index codebook distinguishes which module codebook is active. Specifically, for a module partition When driven by a strong search algorithm, the map equation provides an efficient tool for revealing the modular structure of networks To reveal pattern at multiple levels, we must generalize the coding structure upon which the two-level map equation is based. Broadly, in the hierarchical map equation we release the constraint of a single index codebook and allow for an arbitrary number of hierarchically nested index codebooks that specify movements between modules, submodules, subsubmodules, and so on, down to the finest modular level. Formally, for a hierarchical map The hierarchical map equation can reveal rich multilevel organization in real-world networks. The journal citation network traces more than nine million citations among nearly 8,000 journals in the sciences and social sciences. From the pattern of citations, we reveal more than 100 scientific fields organized in four major disciplines: life sciences, physical sciences, ecology and earth sciences, and social sciences. The physical sciences are in turn organized into physics and chemistry, with 35 subfields, and mathematics, with 24 subfields see .In the global air traffic network, two cities are considered connected if a regularly scheduled commercial passenger flight travels between them. From the network of 3,883 cities connected by 14,142 links, the algorithm uncovers an overall organization of cities grouped in countries and countries grouped in continents. For example, the largest module comprises European and African cities arranged into 55 submodules; the second largest module comprises North and South American cities organized into 75 submodules. These submodules represent the Eastern US cities, the Western US cities, Mexican cities, and so on.For the familiar networks of science and global air traffic, the organization revealed by the hierarchical map equation is intuitive and anticipated. But for the human disease network that connects diseases if they share common genes Beyond these three examples, many real-world networks have rich hierarchical structures. To illustrate, we have used the generalized map equation to partition twelve networks, ranging in size from hundreds to millions of nodes. In The network with the highest compression gain — i.e., the network with the greatest degree of nested hierarchical structure — is the California road network. The geographical constraints of the road network prevent shortcuts between different and remote parts of the network. As a result, the organization is distinct down to the very many small bottom modules. The web graphs have the next greatest compression gain. They are as deep as the road network, but without physical constraints, different parts of the web are presumably more interconnected. The lowest-level are on average larger, and the flow between different large-scale regions reduces the compression gain.C. Elegans brain network In the other extreme in Using the fundamental mathematics of information theory to exploit the duality between compression and pattern detection, we have shown how to reveal the multilevel organization of networks. Combined with powerful visualizations, the hierarchical map equation provides a useful tool to comprehend the hierarchical organization of large multiscale social and biological systems. Here we have focused on hard partitions and the flow of random walkers, but in a subsequent paper we will demonstrate the natural extension of the map equation to overlapping partitions and generalized flows. In short, we can capitalize on overlapping structures by modifying the code structure and releasing the constraint that a node can only belong to one module codebook. Because the codelength only depends on the rates of node visits and module transitions, the map equation framework is agnostic to the origin of the flow. Therefore, we can comprehend the organization in real systems for which a random walker is not a good proxy for flow through the system, by using a different model of flow or by directly measuring the real flow.Here we provide a detailed description of the mathematics of the hierarchical map equation and outline the stochastic and recursive algorithm we have developed to search for the hierarchical partition of a network that minimizes the hierarchical map equation. We also describe how we quantify the performance of our method with the relative mutual information of module and submodule assignments between the benchmark networks and the hierarchical clustering generated by the algorithm.http://www.tp.umu.se/~rosvall/code.html. Below we explain how we have implemented these differences.The hierarchical partitioning algorithm builds on the fast stochastic search algorithm presented in ref. To exclude random teleportation steps from the description length of directed networks, we first calculate the ergodic node visit frequencies For a given hierarchical network partition, the hierarchical map equation measures the per-step average minimal information necessary to track a random walker's movements along links on a network. Sometimes the random walker stays within the same finest-level submodule, and sometimes she moves up and down one or more levels in the hierarchy. At the coarsest level, the description length measures the information necessary to determine which coarsest-level module the random walker enters, weighted by how often such movements happen. The relative rate of codeword use is Adding the contribution from every module at all levels gives the total description length, which is quantified by the hierarchical map equation. For a hierarchical map The hierarchical map equation measures the per-step average code length necessary to describe a random walker's link movements on a network, given a hierarchical network partition, but the challenge is to find the partition that minimizes the description length. Into how many hierarchical levels should a given network be partitioned? How many modules should each level have? And which nodes should be members of which modules?We have generalized our search algorithm for the two-level map equation to recursively search for multilevel solutions. The recursive search operates on a module at any level; this can be all the nodes in the entire network, or a few nodes at the finest level. For a given module, the algorithm first generates submodules if this gives a shorter description length. If not, the recursive search does not go further down this branch. But if adding submodules gives a shorter description length, the algorithm tests if movements within the module can be further compressed by additional index codebooks. Further compression can be achieved both by adding one or more coarser codebooks to compress movements between submodules or by adding one or more finer index codebooks to compress movements within submodules. To test for all combinations, the algorithm calls itself recursively, both operating on the network formed by the submodules and on the networks formed by the nodes within every submodule. In this way, the algorithm successively increases and decreases the depth of different branches of the multilevel code structure in its search for the optimal hierarchical partitioning. For every split of a module into submodules, we use the search algorithm detailed in ref. Any greedy (fast but inaccurate) or Monte Carlo-based (accurate but slow) approach can be used to minimize the map equation. To provide a good balance between the two extremes, we developed a fast stochastic and recursive search algorithm, implemented it in C++, and made it available online both for directed and undirected weighted networks The core of the algorithm follows closely the method presented in ref. With this algorithm, a fairly good clustering of the network can be found in a very short time. Let us call this the core algorithm and see how it can be improved. The nodes assigned to the same module are forced to move jointly when the network is rebuilt. As a result, what was an optimal move early in the algorithm might have the opposite effect later in the algorithm. Because two or more modules that merge together and form one single module when the network is rebuilt can never be separated again in this algorithm, the accuracy can be improved by breaking the modules of the final state of the core algorithm in either of the two following ways:Submodule movements. First, each cluster is treated as a network on its own and the main algorithm is applied to this network. This procedure generates one or more submodules for each module. Then all submodules are moved back to their respective modules of the previous step. At this stage, with the same partition as in the previous step but with each submodule being freely movable between the modules, the main algorithm is re-applied.Single-node movements. First, each node is re-assigned to be the sole member of its own module, in order to allow for single-node movements. Then all nodes are moved back to their respective modules of the previous step. At this stage, with the same partition as in the previous step but with each single node being freely movable between the modules, the main algorithm is re-applied.In practice, we repeat the two extensions to the core algorithm in sequence and as long as the clustering is improved. Moreover, we apply the submodule movements recursively. That is, to find the submodules to be moved, the algorithm first splits the submodules into subsubmodules, subsubsubmodules, and so on until no further splits are possible. Finally, because the algorithm is stochastic and fast, we can restart the algorithm from scratch every time the clustering cannot be improved further and the algorithm stops. The implementation is straightforward and, by repeating the search more than once, 100 times or more if possible, the final partition is less likely to correspond to a local minimum. For each iteration, we record the clustering if the description length is shorter than the previous shortest description length. In practice, for networks with on the order of 10,000 nodes and 1,000,000 directed and weighted links, each iteration takes a few seconds on a modern laptop.http://sites.google.com/site/santofortunato/inthepress2. But before detailing the performance test, we follow the reasoning in ref. To test the performance of our algorithm, we used the benchmark paradigm developed by Lancichinetti and Fortunato From a topological point of view, a three-level hierarchical structure is well defined ifTo quantify the performance of our method, we use the relative mutual information To calculate the relative mutual information, we label every node by its module number. In this way, picking a random node and reading off its module number corresponds to sampling from the discrete random variable Finally, the normalized mutual information We used scale-free networks (exponent -2) with 10,000 nodes, average degree 20, and maximum degree 100, and let the module sizes vary between 400 and 4,000 nodes and the submodule sizes between 10 and 100 nodes, both with a scale-free size distribution (exponent -1).


In recent years it has become apparent that STM and WM interact and overlap with other cognitive processes, including attention (the selection of a subset of information for further processing) and long-term memory (LTM—the encoding and retention of an effectively unlimited amount of information for a much longer period of time). Broadly speaking, there have been two classes of memory models: M Cowan, . In this Baddeley and Hitch  suggesting the existence of different states of representation in STM. For example, Oberauer , 2005 haAnd what about the fate of the uncued memory items? A recent study examined behavioral accuracy for probes to memory items (in this example the memory items were colored circles) that were not prioritized by a retrocue during the first portion of the trial , and whether or not there is a qualitative distinction between states in STM outside the FoA and the remainder of LTM. We will return to these questions near the end of this review, to consider whether the neuroimaging findings that are the focus of this review might help adjudicate between these different theoretical propositions.To summarize, state-based models posit that STM performance is accomplished via the activation of LTM representations, with information that is “in mind” being held in a FoA, and recently attended items having a level of activation that is greater than the basal level of information in LTM. Two important points where these models diverge is on the capacity of the FoA  would test subjects’ memory performance for an item held inside the FoA, whereas probes matching earlier stimuli (“-2” and “-3” items) would test their memory performance for items held outside the FoA . They found that the blood-oxygen-level-dependent (BOLD) response in the anterior inferior temporal cortex was greater for probes matching the -1 item than for probes matching the -2 and -3 items. They also found increased activation of the medial temporal lobe (MTL) and left mid-ventrolateral prefrontal cortex (vlPFC) for probes matching the -2 and -3 items, compared to probes matching the -1 item. In a more fine-grained distinction, they found enhanced functional connectivity between inferior temporal cortex and both right vlPFC and left posterior parietal cortex for probes matching -1 items vs. probes matching -2 items. This difference was interpreted as a neural dissociation between the retrieval of items inside vs. outside the FoA in STM. Later work from the same group replicated and extended this result by expanding the list of items to be remembered on each trial from 3 to 6 items , the state of direct access (the -2 and -3 items), and the activated portion of LTM (the -4 and -5 items). Their results highlighted brain regions whose probe-evoked activity differed between these different probe types  retrieval from WM as well as LTM requires MTL activity, suggesting a common store; (2) MTL activity may be a better metric of memory strength than of LTM access, per se. Intriguingly, no brain regions showed increased probe-evoked activation for the early list items compared with the -2, -3 and -4 items. Most notably, they did not replicate the Nee and Jonides  the reorienting of attention to the information being probed; and (2) the decision process required to respond accurately to the probe. We will now discuss a second category of neuroimaging studies, those designed to measure the state of activation of mnemonic representations during the memory delay, when the neural signal would presumably be less susceptible to contamination by other cognitive processes.From this summary, it is clear that the pattern of findings in the “probe-based” literature is inconclusive with regard to the theoretical models that motivated them. Additionally, we believe that this type of design suffers from shortcomings that limit, after stimulus presentation, would require attentional allocation to items retained in STM . The analysis of electroencephalography (EEG) data recorded while subjects performed this task revealed that the cue-evoked event-related potentials (ERPs) in both conditions revealed a common marker of attentional allocation: a negative deflection (the N1 component) in voltage recordings from posterior electrodes, greater in magnitude in the electrodes contralateral to the attended spatial location than in ipsilateral electrodes. In comparing the retrocue and precue trials, an ERP difference extending from frontal to posterior electrodes was observed between 200 and 400 ms after the presentation of the cue. This was interpreted as reflecting the engagement of additional frontal cortical regions when the target of attentional allocation was an internal representation vs. an external stimulus. Subsequent fMRI studies confirmed this result by finding enhanced activity in dorsolateral prefrontal cortex and parietal cortex for retrocues vs. precues .The neuroimaging studies reviewed to this point attempted to infer the existence (or non-existence) of various representational states in memory, or their relation to perceptual representations, based on differences in BOLD signal magnitude or location. The premise of this reasoning is that if the activation state of a neural representation varied as a result of an experimental manipulation, the corresponding level of fMRI signal intensity would vary in a congruent manner. However, recent advances in our thinking about the multivariate nature of neuroimaging data sets has brought about a renewed appreciation for the fact that this “signal intensity-based” reasoning also supports only indirect inference with regard to assaying active neural representations . An approach that is maximally sensitive to the information contained in patterns of neural activity should provide a more direct measure of neural representations . Classifier evidence reflects the correspondence of the new brain data with the distinct patterns of brain data on which the classifier was trained; thus, it can be construed as an estimate of the presence of the pattern of neural activity specific to the category of interest. In the initial delay period, before any cues were presented, classifier evidence for the categories of the two items presented on each trial was significantly higher than the evidence for the non-present category . After the appearance of the first retrocue, evidence for the AMI’s category remained high, but evidence for the UMI’s category dropped to baseline  by the feature values  for the UMI following the retrocue. By approximately 1.25 s after the onset of the retrocue, evidence for the UMI was indistinguishable from baseline. This provides a neural counterpart to behavioral evidence suggesting that approximately 1 s is needed between the retrocue and the memory probe in order to observe the RT benefit of a retrocue . At this time, it is unclear if the sensitivity to distraction in patients with MTL damage should be construed as relating to a deficit in attention, binding, or both. One way to resolve this controversy would be to use a retrocuing task in a study of MTL lesion patients; a selective impairment in memory for UMIs relative to healthy controls would suggest a role for MTL in STM for items outside the FoA.The previous example of a patient with anterograde amnesia brings up an issue very germane for discussions of STM and LTM: what is the role of MTL in STM? The literature addressing this topic is large and evolving, but it seems clear that the long-standing notion that the MTL is only involved in LTM is an over-simplification. Especially notable is that distraction during a short retention interval can interfere with the performance of patients with MTL lesions on STM tasks . A second potential limitation of MVPA is the possibility that the patterns of neural activity measured by fMRI and EEG are epiphenomenal, and do not directly assay the neural representations that are important in the guidance of behavior. Though this is an important scenario to keep in mind, we consider it to be unlikely, especially because of the results we have discussed that show correlations between patterns of neural activity in sensory cortex and task performance , information selected by the FoA typically becomes the content of consciousness (see, e.g., Table 1 in Koch and Tsuchiya, The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The aim of this study was to determine the - largely unexplored - extent of systematic variation in the work disability assessment by Dutch insurance physicians (IPs) of employees on long-term sick leave, and to ascertain whether this variation was associated with the individual characteristics and opinions of IPs.2) for the three outcomes. A higher ICC reflects stronger systematic variation.In March 2008 we conducted a survey among IPs on the basis of the 'Attitude - Social norm - self-Efficacy' (ASE) model. We used the ensuing data to form latent variables for the ASE constructs. We then linked the background variables and the measured constructs for IPs (n = 199) working at regional offices (n = 27) to the work disability assessments of clients  and their characteristics. These assessments were carried out between July 2003 and April 2008. We performed multilevel regression analysis on three important assessment outcomes: No Sustainable Capacity or Restrictions for Working Hours , Functional Incapacity Score  and Maximum Work Disability Class . We calculated Intra Class Correlations (ICCs) at IP level and office level and explained variances (R2 was 11% for No Sustainable Capacity or Restrictions for Working Hours, 19% for Functional Incapacity Score and 37% for Maximum Work Disability Class.The ICCs at IP level were approximately 6% for No Sustainable Capacity or Restrictions for Working Hours and Maximum Work Disability Class and 12% for Functional Incapacity Score. Background IP variables and the measured ASE constructs for physicians contributed very little to the variation - at most 1%. The ICCs at office level ranged from 0% to around 1%. The ROur study uncovered small to moderate systematic variations in the outcome of disability assessments in the Netherlands. However, the individual characteristics and opinions of insurance physicians have very little impact on these variations. Our findings provided no indications of other reasons for these variations. They may be related to different work routines or to different views on the workload of a 'normal' employee. If so, they could be reduced by well-developed and comprehensively implemented guidelines. Therefore, further research is needed. Taking decisions in complex situations by professionals  implies that similar decisions may lead to variation in outcome between professionals. This is a universal given and physicians are no exception. The problem of so called 'inter-doctor variation' goes back a long way and was even highlighted by Montaigne 1595), the famous French essayist 595, the . VariousIn the Netherlands, insurance physicians work for private insurance companies or in the social insurance sector. In this study we investigate inter-doctor variation in disability assessments of long-term sick-listed employees by insurance physicians working in the social insurance sector. The actual assessment process, carried out by an insurance physician and a labour expert, is described in more detail in other studies -10, Broe, Broe10,In the Netherlands, if you are partially or fully incapable of working after two years of illness, you may be eligible to receive a benefit under the Work and Income Act (WIA). The WIA succeeded the Disability Insurance Act (WAO) in January 2006. The Adapted Re-assessment Act (HERBO) was introduced in August 2004 for the reassessment of WAO benefits clients on the basis of new, stricter criteria that put the emphasis on the client's residual functional capacities. The WAO and WIA differ in the time of assessment: the WAO provides for assessments after one year of sick-leave, whereas the WIA provides for assessments after two years. Insurance physicians have to judge a client's 'claim' to compensation for loss of work capacity. They base their decision on the information in the dossier, on information from the client and other parties, and on additional medical examinations. The insurance physician carries out this assessment within a statutory framework, supplemented with regulations and guidelines and - more recently - diagnosis-specific protocols for measuring the functional capacity of employees on long-term sick leave.The findings about the residual (post morbid) functional abilities of a client serve as input for the labour expert (LE) in determining with the Claim Assessment and Monitoring System, CAMS , to whicIn order to assess a clients' work limitations the insurance physician starts with the functional limitations experienced by the client. These are tested for plausibility and internal and external consistency on the basis of the medical history and the actual ability of the client to perform. The insurance physician bases his assessment on an interview and possibly a physical examination. He can obtain additional information by ordering additional tests or by contacting the GP, specialist or other healthcare provider, or the occupational physician (OP) who assessed the first two years of disability. For clients with severe pathology and impairments and with no chance on recovery, the insurance physician may assess full disability on medical ground: no sustainable capacity left. For all other clients, the client's capacity for work is determined by reference to an instrument known as Functional Ability List (FAL). As an instrument the FAL comes within the statutory framework of disability assessments in the Netherlands. On this list the physician enters the client's scores for limitations and abilities. The FAL consists of 106 items, categorised into six sections: personal functioning, social functioning, adjusting to the physical environment, dynamic movements, static posture, and working hours. In about 75% of the cases the insurance physician assesses the functional capacity of the client by applying the Functional Abilities List (FAL) ,11. The In the Netherlands disability assessment instruments have been the subject of a number of studies -15. ThesIn 2004 the Dutch Council for Health Care Research (CHR), a government body, drew attention to the need to research inter-doctor variation in disability assessments performed by insurance physicians in the Netherlands [In a previous study  we develA) What is the variation in relevant outcome measures of disability assessments at insurance physician level (IP level) and at regional office level?B) How strong is the association between the client background variables and the outcome measures?C) Which background variables, opinions and considerations of the insurance physicians themselves are associated with the outcome measures of disability assessments?D) How strong is the association of these outcome measures with IP level and office level, respectively?We collected information about social insurance physicians and their clients from two sources. The first source is a one-off survey in March 2008 to measure the background variables, opinions, and considerations of insurance physicians. The questions in the survey about opinions and considerations of insurance physicians were based on the 'Attitude - Social norm - self-Efficacy' model (ASE model) , an exteThe target group consisted of insurance physicians actively employed by the Employee Insurance Authority in May 2008 who performed assessments of long-term sick-listed employees in 2007 or in preceding years, within three comparable statutory regimes for long-term work disability: WAO; HERBO and WIA. Physicians who were not working for the Dutch Employee Insurance Authority in March 2008 and physicians who performed assessments only for other regimes  were excluded, because these regimes cover other populations and use other assessment criteria to determine disability. Our estimate was that the target group consisted of 450 insurance physicians. Two hundred and thirty-one insurance physicians (approximately 51% of the target group) responded to the survey, of whom 200 gave informed consent to link their survey answers with the client database. For further details on the study population of insurance physicians we refer to Steenbeek et al .We created a total client group from the three above-mentioned regimes so that the assessments could be analysed together. The inclusion criteria were: a) the client data could be linked with the insurance physician data, and b) the assessment period for the three regimes, i.e. from July 2003 to March 2005 for the WAO regime, from November 2004 to December 2006 for the HERBO regime, and from January 2006 to April 2008 for the WIA regime. All the clients were aged between 15 and 65 at the time of the assessment and suffered from one or more of the diseases or disorders in Version 10 of the International Code of Diseases . The surThe following data at client level on the results of disability assessments by insurance physicians were extracted from the CAMS-database a) no sustainable functional capacities (i.e. the client has zero working capacities left now and will not recover in the future); b) restrictions in working hours; c) functional capacities per FAL item; and d) work disability class. From the extracted data we constructed three outcome measures Table . 1) 'No The client background variables are summarized in Table The other background variables - standard earnings, standard working hours, educational level, and the severity of the three distinguished incapacities  social insurance system;• Social Norm: the insurance physician performed more autonomously, less influenced or uninfluenced by the social environment ;• Self-Efficacy: the insurance physician has more confidence in his/her own ability to control the interaction with the client during the assessment interview;• Barriers: the insurance physician experiences more barriers arising from work pressure, emotional workload, less scope for decision-making, higher levels of burnout, poorer cooperation in the office, less incentives from management and relatively more 'difficult' clients;• Knowledge: the insurance physician has sufficient information about the medical status of the client and about the rehabilitation efforts of the employer and the client;• Intention: the insurance physician attaches more importance to: the promotion of recovery, resumption of work, self-reflection and re-integration, the relevance of capability, illness, disorders and handicaps in the assessment and, most of all, proper checks for the consistency of information on the daily activities and home situation of the client. To some extent this paints the professional attitude that one would expect from an insurance physician;• Behaviour concerning the assessment process (Behaviour: process): the insurance physician has more confidence in his/her own vision of the job. A higher score suggests an insurance physician who is eager, takes control and is prepared to strike a compromise with the client;• Behaviour concerning the assessment content (Behaviour: assessment): the insurance physician adheres more to rules and professional standards. A higher score is typical of an insurance physician who sticks to the guidelines, does not consider the specific situation of the client, thinks as he goes along, but still believes that he engages with the client.We performed a non-response analysis for the insurance physicians and the clients. We compared relevant background variables of the insurance physicians in the study population with the available characteristics of all the insurance physicians at the Employee Insurance Authority. We also analysed the difference between the physicians whose survey results could and could not be linked with the database.We compared the data on the clients in our analysis with the data of all the clients in the database across the same assessment periods for the three regimes. We used frequencies for all variables, crosstabs and Chi-squared statistics for categorical variables, and means and t-tests for continuous variables, using SPSS 15.0.Using crosstabs and Chi-squares, we analysed the outcome measures univariately across insurance physicians and offices. We calculated the  mean, the standard deviation, the minimum and maximum and variation coefficient (standard deviation divided by the mean) across insurance physicians and offices by extracting the row percentages of the interesting categories in the categorical outcome measures from the crosstabs tables. For the univariate, descriptive analysis only, we divided the (approximately Poisson distributed) Functional Incapacity Scores (0 up to 6) into three parts: (nearly) no incapacity , moderate incapacity scores  and high incapacity scores . We produced these descriptives with SPSS 15.0 (crosstabs tables and Chi-square statistics) to derive the row percentages and used MS Office Excel 2003 to calculate their central tendency and dispersion.We performed multilevel analysis with MLwin version 2.02  for the We used logistic regression to analyse the two dichotomous outcome measures  and Poisson regression to analyse the outcome measure approximating a Poisson distribution (FIS). Because not all client background variables were available for all the outcome measures of clients, these outcome measures were analysed with different sets of client background variables. We analysed NSCE with Gender, Age, Sector of Occupation, Diagnosis, Objectification of Complaints and Statutory Regime as independent client background variables. The outcome measure (FIS) for the group of clients with a FAL (about 77%) was analysed with the fore-mentioned client background variables plus Standard Earnings, Standard Working Hours and Education Level. The MWDC outcome measure was analysed for the same 77% of clients and with the same set of independent client background variables plus Mental Incapacities, Physical Incapacities and Autonomous Incapacities.We estimated all the multivariate models in MLwin with Restricted Maximum Likelihood (RIGLS), the 'naive' models with first-order maximized quasi-likelihood (MQL) and the multilevel models with second-order penalized quasi-likelihood (PQL). The significance of coefficients was determined with Wald statistics. We chose P ≤ 0.10 as the level of significance because we did not want to miss interesting associations.The multilevel analysis for each outcome measure consisted of four steps . FirstlyWe expected Attitude, Intention and Behaviour: assessment to relate negatively to the outcome measures, and Behaviour: process, which showed a weak negative relationship with Behaviour: assessment , to relaTo determine the associations of the outcome measures at insurance physician level and office level, we calculated intra-class correlations (ICCs), which are commonly used in research to determine the extent of systematic variations between elements at a higher level -31. In tAn ICC is defined as the variance in the outcome measures (at client level) between physicians (or offices) divided by the total variance (the sum of the 'between' and the 'within' variance). The greater the 'between' variance is, the smaller the 'within' variance and the greater the ICC. An ICC that edges towards one, means that the 'between' variance is almost equal to the total variance. In our study this would indicate that the assessment outcomes are determined at insurance physician level (or office level). Conversely, an ICC that edges towards zero means that the 'within' variance is almost equal to the total variance. In our study this would indicate no association at insurance physician level (or office level) with the assessment outcomes of the clients. Additional file To gain an indication of the contribution of the client background variables to the total explained variance of the outcome measures we calculated the difference between the total explained variance on the one hand and the ICCs for IP level and office level on the other for the various models.Usually, in 'real life' cross-sectional studies among physicians, the ICC is no higher than 0.20 . This isBecause the necessary data of the target population (N = approximately 450) to do a full non-response analysis were not available, Steenbeek et al.  checked This raises the question whether the 32 insurance physicians who did not give us informed consent to link their survey data with the database (including one physician for whom the link failed) differed from the group of 199 insurance physicians. There was a significant relationship between these groups in terms of: a) most of the clients were assessed for the WAO ; b) most of the clients came from the temporary work sector ; and c) most of the clients came from public sectors other than healthcare and education . As far as age and the eight ASE variables were concerned, the analysed group of 199 physicians experienced fewer Barriers (P = 0.003), had higher self-Efficacy (P = 0.027) and scored higher for sufficient Knowledge (P = 0.035) than the group of 32 physicians. The variances for the continuous variables did not differ between the two groups.In our analysis of the non-response clients we compared the data of the clients of the 199 IPs with the data of all the clients over the same period. Only minor differences emerged between the variables of the 83,755 clients in our analysis as shown in Table The outcome measures for clients are listed in Table At physician level and office level  with the outcome measures. No association was found at IP level for gender (for MWDC), other diseases (for NSCE and FIS), strong physical incapacities, moderate autonomous incapacities and standard earnings (for MWDC) and standard working hours (for FIS and MWDC). At office level, only one random coefficient for the constant turned out to be weakly significant , indicating that there was a small systematic difference for this outcome measure between offices. None of the fixed coefficients for the independent insurance physician variables was associated with office level, indicating that there were no systematic differences in the outcome measures between offices, because of these insurance physician variables.We found only a few, weak associations between the outcome measures and the independent insurance physician variables . The ICCs ranged between 6.5% and 11.8%. The highest ICC at IP level was for Functional Incapacity Score (FIS). The contribution of the insurance physician background variables and the ASE variables to the ICCs at physician level was very small, around 1%  for the association between each of the three outcome measures on the one hand and insurance physician level and office level on the other. These ICCs are shown in Table 2) was highest (37%) for Maximum Work Disability Class (MWDC). The contribution of the client background variables to the explained variance of this outcome measure was nearly 31%. The three client background (incapacity) variables in the model were strongly associated with MWDC: Without these variables the explained variance of MWDC worked out at around 14% with a contribution of around 8% by the client background variables (not in Table At office level only an ICC for No Sustainable Capacities Extended (NSCE), though rather small, was to some extent meaningful. For the other two outcome measures, Functional Incapacity Score (FIS) and Maximum Work Disability Class (MWDC) the ICCs at office level were zero. The explained variance . The same result was found for the univariate variation at office level.Secondly, the strength of association between the client background variables and the outcome measures, i.e. the explained variance, was 10% in the case of No Sustainable Capacity Extended (NSCE) and 6% in the case of Functional Disability Score (FIS). This contribution was highest - 31% - for Maximum Work Disability Class (MWDC). The three client background incapacity variables had very strong positive associations with Maximum Work Disability Class (MWDC).Thirdly, the insurance physician background variables that were associated with the outcome measures are: the IP's age interacting with the client's age (weakly), previous employment as a curative physician and length of career as an insurance physician. Only four ASE variables were associated with the outcome measures: a positive Attitude was associated with lower scores for No Sustainable Capacities Extended (NSCE), higher self-Efficacy was weakly associated with fewer MWDC assessments, while a higher score for Knowledge, i.e. possessing sufficient information about the client, and a higher score for Behaviour: assessment, i.e. more adherence to rules and professional standards, was associated with more MWDC assessments. The contribution of the insurance physician background variables and the ASE variables to the ICCs at IP level were very small, at around 1%.At last, on the basis of the previously mentioned ICC evaluation criteria, the following conclusions may be drawn: none of the ICCs for the outcome measures at insurance physician level can be qualified as high; only the ICC for Functional Incapacity Score (FIS) is moderate, i.e. around 12%; the ICCs at office level are very low, only the ICC for No Sustainable Capacities Extended (NSCE) is meaningful at 1.6%.One of the strengths of this study is that the insurance physicians N = 199) are considered representative of all the insurance physicians at the Employee Insurance Authority. It should still be noted, however, that some differences emerged between the opinions of this group and those of the insurance physicians (N = 32) with no link to the client's database. The variances in the continuous variables did not, however, differ between these groups. Furthermore, only small differences emerged between the clients  in our study and the total number of clients . It is therefore unlikely that these differences will have a substantial effect on the estimation results of the multilevel analyses. Another strength is that the data covered a large number of clients and could be regarded as reliable since they came from an official database of the Employee Insurance Authority. The outcome measures that we used are relevant to the work of the insurance physicians at the Employee Insurance Authority and have deep relevance for Dutch society given the public expenditure on disability benefits. A third strength lies in the linkage between the client's data and the survey data of insurance physicians, and the reliability and validity of the ASE variables, which were constructed on the basis of measurement models and a structural equation 9 are con. FinallyThere are also some weaknesses in our study. The main weakness is the cross-sectional design, which prevents us from drawing conclusions about causal relationships. Secondly, we do not know whether the scores for the ASE variables based on the survey data of May 2008 are stable over time and valid for the preceding years. Another possible weakness may lie in the fact that the eight ASE variables are factor scores at such a highly condensed level, i.e. second-order factor scores of 48 additive scales and dimension variables resulting from first-order factor analysis and homogeneous analysis, that the relationship with the outcome measures might become very weak. We do not, however, believe this to be the case, as additional multilevel analyses with models, including the original 48 scales and dimension variables instead of the eight ASE variables, delivered similar results to those of the eight ASE variables. Another weakness was that we did not have client data on co-morbidity and the severity of the disorders because these were either poorly registered or not registered at all in the database by the insurance physicians. Such data could have influenced the results and accounted for lower explained variances, especially in the models which did not include the three incapacity variables.A final weakness lies in the fact that we assigned each insurance physician to the office where he/she assessed the most clients, which might cause an overestimation of the ICC on the office level. However, because of the very low resulting ICCs for the office level, in our opinion this overestimation is negligible.Some associations were found between the background variables and ASE variables of the insurance physicians and the outcome measures , but may still be qualified as moderate. This ICC may be relatively high because of the absence of guidelines or protocols on how to quantify restrictions on working hours and the severity of incapacities. This absence, in itself, is hardly surprising, given that there is little or no evidence that certain diseases lead to certain disabilities with specific degrees of severity. Dutch social insurance physicians even have difficulty reaching consensus on the level of disability arising from a major depression . ConversThe ICCs at office level are either low or negligible, which means that regional managers did not influence the assessment results in any other way than they are instructed to do in centralized directives from the Board of the Dutch Employee Insurance Authority. Our results show that the apparent, univariate differences between offices can to some extent be explained by differences at client and insurance physician level.Even though the ICCs at IP level are evaluated as low to moderate, they still form the largest part of the total explained variance for most of the outcome measures and thus suggest that insurance physician level is the prime factor in the apparent differences between insurance physicians. We refute this argument because it implies that if the explained variances were increased by, for example, implementing health variables in the model for these outcome measures, the ICCs at IP level would be higher as well. The results for Maximum Work Disability Class compared with those of Functional Incapacity Score show that this is not the case. It could also be argued that the ICCs at IP level are low because of the very large differences in the assessment results for the same kind of clients by the same insurance physicians. Again, we refute this theory: the results showed a very strong and consistent relationship between the three incapacity variables and Maximum Work Disability Class. This argument is also rendered invalid by research on the reliability of the FAL by Spanjer -14,16, wIn our study we found an average ICC of 12% at insurance physician level for Functional Incapacity Score: systematic variations between the overall incapacity assessments of clients with all types of disorders, which have to be attributed to differences between insurance physicians. This ICC of 12% reflects a systematic difference in a minority of the assessment outcomes with the FAL. This is in accordance with the absolute agreement found in the referred studies by Spanjer for the majority of the assessments.What is the relevance of our findings on systematic inter-doctor variations? Because the background variables and the ASE variables of the insurance physicians account for only about 1.0%-point of the ICC of 12% for FIS, the systematic variations in assessments with the FAL must be due to other factors related to insurance physicians. One plausible explanation is that different insurance physicians have different work routines, i.e. the way insurance physicians routinely conduct their  examinations of clients' health condition, which may result in different outcomes. Another plausible explanation is that insurance physicians may have different visions, consciously or unconsciously, of the workload of a 'normal' employee, which may result in different assessments of the incapacities and limitations. Or, the IPs may have different insights because of differences in the amount and accuracy of actual information from the client and employer. This includes information about the clients' social circumstances (e.g. caring responsibilities) and how the IP values this information in his assessment. IPs may differ in their expectations of what an employee should be able to cope with at work.If these explanations are valid, the systematic variations may be narrowed down by well-developed and comprehensively implemented guidelines from the Employee Insurance Authority on how to assess the severity of disabilities . At presThe individual characteristics and opinions of insurance physicians have very little influence on the outcome of disability assessments in the Netherlands. That said, our study still revealed systematic variations, which can be qualified as 'normal', i.e. equal to those between physicians in primary and secondary care. Our findings provided no indication of the reasons for these variations. They may be related to different work routines or to different views on the workload of a 'normal' employee. If so, they could be reduced by well-developed and comprehensively implemented guidelines, particularly on the assessment of working hour restrictions and the severity of the disability. Further research is needed to determine whether this is a valid proposal.The authors declare that they have no competing interests.AJMS, HM and RS designed the study. AJMS performed the statistical analysis and wrote the manuscript and RS revised the manuscript. HM, JRA, HK and JB commented on the manuscript. RS, HM, HK and JB coordinated the data collection. HK and HM coordinated the procedures for anonymizing and linking the data. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2458/11/864/prepubCalculating Intra Class Correlations (ICCs). Explanation how the ICCs were calculated.Click here for file


Broca's area has been suggested as the area responsible for the domain-general hierarchical processing of language and music. Although meaningful action shares a common hierarchical structure with language and music, the role of Broca's area in this domain remains controversial. To address the involvement of Broca's area in the processing action hierarchy, the activation of Broca's area was measured using near-infrared spectroscopy. Measurements were taken while participants watched silent movies that featured hand movements playing familiar and unfamiliar melodies. The unfamiliar melodies were reversed versions of the familiar melodies. Additionally, to investigate the effect of a motor experience on the activation of Broca's area, the participants were divided into well-trained and less-trained groups. The results showed that Broca's area in the well-trained participants demonstrated a significantly larger activation in response to the hand motion when an unfamiliar melody was played than when a familiar melody was played. However, Broca's area in the less-trained participants did not show a contrast between conditions despite identical abilities of the two participant groups to identify the melodies by watching key pressing actions. These results are consistent with previous findings that Broca's area exhibits increased activation in response to grammatically violated sentences and musically deviated chord progressions as well as the finding that this region does not represent the processing of grammatical structure in less-proficient foreign language speakers. Thus, the current study suggests that Broca's area represents action hierarchy and that sufficiently long motor training is necessary for it to become sensitive to motor syntax. Therefore, the notion that hierarchical processing in Broca's area is a common function shared between language and music may help to explain the role of Broca's area in action perception. Human language consists of a hierarchical structure in which phonemes are combined to form words, phrases and sentences up to the discourse level of speech structure according to several levels of rules. Uchiyama et al.  studied In the case of music, similarly to language, combinations of sequential and simultaneous notes make rhythms, melodies and harmonies to form an overall musical structure according to rules such as chord progressions. There is also a posterior-anterior functional gradient in the inferior frontal region in relation to the processing of musical hierarchy. For instance, the activation of BA 6/44 for rhythm discrimination and melody matching may reflect the processing of sequential sounds  can be combined into units of actions (such as reaching and grasping). These units of actions can be integrated into meaningful behavior (such as picking up a peanut). Despite evidence for the possible contribution of Broca's area in the hierarchical processing of observed skilled action , non-musicians watched silent videos of hands playing the piano while trying to identify the melodies . The NIRS results for familiar and unfamiliar melodies were compared to reveal the involvement of Broca's area in the hierarchical analysis of observed action. Additionally, the comparison of NIRS results between well-trained and less-trained participants was examined to determine the influence of skill in the observed action on the activation of Broca's area.All participants in the current study had sufficient knowledge about the familiar melodies preceding the experiments. Thus, tracking hand motions to identify the familiar melodies and even anticipating forthcoming action sequences may be easy. However, no participant had knowledge about the unfamiliar melodies. Thus, the participants had to pay extra attention to the hand motions to detect musical segments from stimulus movies and integrate them into whole melodies. Therefore, if a greater activation of Broca's area was found for unfamiliar than familiar melodies, it could be deduced that this area plays an essential role in the hierarchical processing of an observed action.Although NIRS cannot detect deep brain activity, this technique offers several advantages. NIRS detects changes in hemoglobin concentration associated with brain activation occurring beneath the optodes. Therefore, this technique enables the estimation of the activation source using fewer sensors than are required for EEG. Additionally, NIRS allows the participants to maintain a comfortable posture in a quiet room during measurement, while body movements of participants are strictly restricted during an fMRI session. Thus, NIRS is a suitable technique to measure activity in Broca's area and is advantageous, especially for the participants.The subjects were 20 healthy, right-handed adults aged 23–40 years. Handedness scores were determined using the Edinburgh handedness inventory  and “London Bridge is Falling Down” (L)  on the keyboard were filmed (640 × 480 pixels) Figure . StimuliThe unfamiliar stimuli contained spatial and temporal distributions of key-press durations of hand movement that were identical to those of the familiar stimuli. However, by reversing the temporal order, the sequential structure of hand motions (corresponding to note transitions) was rendered largely different between familiar and unfamiliar stimuli.An experimental session consisted of 12 trials. Each trial lasted 16 s, during which one of the four stimuli was presented. The length of the inter-trial interval was 25 s. All four movies were presented three times in a pseudorandom order, with each session beginning with a familiar stimulus. Every stimulus was presented once in four successive trials, and the same melody (M and L) and/or familiarity (familiar and unfamiliar) condition was repeated in no more than 3 consecutive trials. The participants were instructed to watch the movies carefully to identify the “melody” performed by the hand. The beginning of each stimulus movie was accompanied by a tone pip. The participants were asked to open their eyes gently when they heard the tone and close their eyes gently when the stimulus movie disappeared. Thus, the individuals' eyes were closed during the rest period. The entire experiment lasted for ~30 min.Prior to the beginning of the recording session, the participants practiced for 8 trials  with experimental stimuli to confirm that they understood the instructions.Cortical activity was continuously recorded throughout the experiment. Relative changes in oxy-hemoglobin (oxy-Hb) concentrations were measured using the NIRS system . The sampling rate was set to 10 Hz. Nine optodes (in a lattice pattern forming 12 channels) were placed on both hemispheres. Because the main region of interest was Broca's area, a single recording channel was determined as a point between the optode nearest to F7 of the international 10–20 system and its posteriorly adjacent optode. Thus, NIRS results presumably reflected activity from Broca's area since F7 on the scalp has been reported to project onto the cortical surface of the anterior portion of the inferior frontal cortex (BA 45/47)  was calculated for each condition. The averaged oxy-Hb values obtained during the familiar and unfamiliar conditions were then submitted to a paired One may assume that the degree of involvement of Broca's area to action hierarchy is influenced by the experience. Therefore, the relationship between this involvement of Broca's area and the duration of piano training was assessed. First, subtraction of the averaged oxy-Hb value in the familiar condition from that in the unfamiliar condition was individually calculated as an index that shows the sensitivity to action hierarchy. Then, the correlation between such contrast and the duration of piano training was evaluated using a Spearman's rank correlation test. The significance level was set to 5%.Figure t-test, t(9) = 3.167, p = 0.011]. Contrary to the well-trained group, the less-trained group (right) showed no significant difference in signal intensities between conditions  . Thus, the involvement of Broca's area in the hierarchical processing of observed action was observed in the well-trained participants.The activation of Broca's area within the peristimulus period is shown in Figure rho(18) = 0.593, p = 0.006]. When a correlation analysis was applied to individual groups, however, no significant correlation was found both in the well-trained group  = 0.654, p = 0.040) or the less-trained group  = 0.092, p = 0.800).The relationship between the degree of such involvement of Broca's area and the duration of piano training were then assessed. A correlation analysis of the entire population revealed that the between-condition difference in mean signal intensity strongly correlated with the duration of piano training [Figure The primary goal of the present study was to determine the role of Broca's area in the hierarchical processing of observed action. To address this issue, well-trained and less-trained participants were exposed to silent hand motions that played familiar and unfamiliar melodies. A key finding was that well-trained participants showed increased activation in Broca's area in response to hand motions associated with unfamiliar rather than familiar melodies. Thus, the current data indicate that this region plays an essential role in the hierarchical processing of an observed action. Previous fMRI and magnetic stimulation studies that showed that Broca's area is involved in hierarchical sequence of action planning  than unfamiliar movements (see Rizzolatti and Craighero, Alternatively, considering the shared function of Broca's area in a wide range of functional domains must be helpful to understand the role of this area in MNS. Musso et al.  indicateGiven that the acquisition of hierarchical structures is an essential factor for Broca's area to be active, the vPM activation in Calvo-Merino et al.  may be eIn conclusion, Broca's area was shown to be necessary for the hierarchical processing of observed action. Therefore, the notion that hierarchical processing in Broca's area is a common function shared between the language and music domains may help to explain the role of Broca's area in action perception. In support of these findings, previous studies have reported that the effect of expertise in one domain leads to the improvements in tasks of untrained domains such as enhanced linguistic performance after musical training (Moreno et al., The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two “hits”, and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common. The ability of stem cells to divide asymmetrically to produce one stem and one non-stem daughter cell is often considered to be one of the defining characteristics of stemness. On the other hand, there is ample evidence suggesting that adult stem cell can and do divide symmetrically Two basic models of stem cell divisions are discussed in the literature, see in vitro comes from the work of Yatabe et al who tracked methylation patterns in the dividing cells of the colon crypts Uncovering division patterns of stem cells has been subject of intense research in the last fifteen years. Some of the first quantification of the division strategies An important advance in quantification of symmetric vs antisymmetric divisions became possible with the invention of inducible genetic labeling These new findings reveal that contrary to the previous thinking, adult tissue stem cells are often lost (e.g. by differentiation) and replaced in a stochastic manner. This notion challenges the traditional concept of the stem cell as an immortal, slow-cycling, asymmetrically dividing cell In paper In the present paper, we explore an alternative hypothesis, which gives an additional “reason” for the tissue architecture favoring symmetric divisions. As a starting point, we note that in both symmetric and asymmetric division types, a dysregulation may lead to the loss of homeostatic control and an unchecked growth of cells. A disruption in the control of proliferation/differentiation decisions can tip the balance and lead to abnormal stem cell expansion Here, we examine the symmetric and asymmetric divisions in the context of producing mutations. Many cancerous transformations start off by an inactivation of a tumor-suppressor gene In this paper, we use both numerical simulations and analytical methods to study symmetric and asymmetric stem cell divisions in the context of mutation production. Other theoreticians have explored stem cell dynamics by means of deterministic stem cell modeling and stochastic numerical simulations In the present paper, we concentrate on the optimization problem of tissue architecture in the context of delaying double-hit mutant production, and focus specifically on symmetric and asymmetric stem cell divisions. We consider a stochastic model of double-hit mutant generation, and ask several questions related to evolutionary dynamics of mutations. What type of divisions is optimal? What cell types contribute the most to double-hit mutant generation? What is the optimal fraction of stem cells that delays carcinogenesis?We consider a two-compartment, agent-based model of stem cells and transit-amplifying (TA) cells. The stem cells are capable of both symmetric and asymmetric divisions see . The rel see , where  ells see . The totWe assume that the non-stem cells can die, and that all cell types have a chance to divide. Each time a division happens, there is a probability, The generation of two-hit mutants is normally considered to be a rate-limiting step in cancer initiation. Once such a mutant is produced, it may break down homeostatic control and result in a wave of clonal expansion, followed by further transformations. It is this first step, the creation of a double-hit mutant, that we focus on in this paper. We investigate how the timing of such a mutant production depends on the tissue architecture, and specifically, on the symmetry of stem cell divisions.In order to gain analytical insights, a slightly simplified stochastic process was considered see the  Section While the detailed temporal dynamics of double-mutant production is given in the Predictions of formula (1), as well as the more precise An important question is how the fraction of symmetric divisions  model compared with the conventional, homogeneous model that has been extensively studied Let us consider an optimization problem for the tissue design, with the goal to delay the production of double-hit mutants. What is the optimal fraction of stem cells that the population should maintain? Analysis of the tunneling rates for a hierarchical model with purely symmetric divisions suggests that the optimal fraction of stem cells depends on the fitness of the one-hit mutants. If the one-hit mutants are disadvantageous . Since cancer delay does not provide an important selection mechanism in the context of Drosophila, we can argue that this could help explain the observed differences.The mathematical result obtained here is that symmetrically dividing cells appear to delay double-hit mutant production compared to an equivalent system with asymmetrically dividing stem cells. What is the intuition behind this finding? Double-mutants are generated by means of mutations that happen in singly-mutated cells. To understand this process, let us focus on the dynamics of single mutants. In particular, we concentrate on singly-mutated stem cells, because the fates of single mutations in TA cells are identical in the two models. What happens to a singly-mutated stem cell under the different division patterns?As noted by Interestingly, the above argument can be made in a similar manner for disadvantageous, neutral, or advantageous mutants. In any of those cases, an asymmetrically dividing mutant stem cell remains in the population indefinitely. In the model with symmetric divisions, whenever a mutant stem cell is chosen for division, its probability to proliferate is similar to its probability to differentiate (in order to keep the homeostasis), and this the dynamics of each lineage is independent of its fitness  contributes more to the double-mutant production? It turns out that as long as the fraction of stem cells is smaller than a threshold , non-stem cells contribute equally or more to the production of double-mutants. This threshold fraction depends on (1) the mutation rate and (2) the fitness of intermediate, one-hit mutants. For example, if the intermediate mutants are neutral and the mutation rate is The arguments presented above clarify some aspects of the long-standing debate about the origins of cancer, see also Ref. The question discussed above is purely mathematical, and deals with the simple possibility to acquire two hits in the TA compartment. A related biological question is whether mutations occurring in the TA compartment can lead to further carcinogenic transformations, which brings us to the cancer stem cell hypothesis In the light of this latter hypothesis, let us analyze the process of double-hit mutant production that occurs via mutations in stem cells only. Will our results change if only stem cell mutations can lead to carcinogenic transformation? To accommodate this assumption in our model, we must only use the first term in in vivo, see e.g. The only scenario where the asymmetrically dividing cells can produce double-hit mutants slower than symmetrically dividing cells is provided by the immortal DNA strand hypothesis Our theoretical results on the rate of double-hit mutant formation provide a generalization of a number of previous papers that studied the process of stochastic tunneling. The concept of stochastic tunneling was introduced in Refs. This paper considers the inactivation of tumor suppressor genes. An inactivation of the first copy of the tumor suppressor gene does not typically result in the cell breaking out of the homeostatic control. The stem cell-TA cell system continues to function almost normally . The overall population remains approximately constant and the cellular turnover continues. A very different picture is observed in the case of oncogene activation. Oncogene activation is normally assumed to confer a significant fitness advantage to the mutated cells, which may lead to a wave of clonal expansion incompatible with homeostasis. In this case, the analysis is quite different because it must describe a population expansion following the oncogene activation.In order to make the current model useful for describing oncogenes, we can talk about the timing of an oncogene activating mutation under the different assumptions on the symmetry of stem cell divisions. The time distribution of acquiring the first mutant does not depend on whether stem cells divide symmetrically or asymmetrically. The dynamics of the mutant cells however depends on several factors, such as (1) whether wild-type stem cells divide symmetrically or asymmetrically, and (2) how the mutation modifies the growth properties of the cells. If we assume that the cell with an activated oncogene continues to divide in the same fashion as the wild type cell but with a higher frequency, then the following result is observed: (i) under symmetric stem cell divisions, the mutant clone will quickly invade the stem cell population; (ii) under asymmetric divisions, each one-hit mutant will remain in the population, creating a disproportionately large number of mutant TA cells.The theory developed in this paper is based on a model, which is in some sense an idealization or reality. We assume that stem cells can divide symmetrically and asymmetrically, and calculate which mixture of the two types of divisions minimizes the risk of acquiring double-hit mutants. Under most scenarios, symmetric divisions appear to be the optimal strategy in the context of delaying double-hit mutant generation. Therefore we propose that the reported prevalence of symmetric divisions in certain adult mammalian stem cell systems could have an evolutionary explanation.We would like to emphasize some of the important simplifications used in the present model. We do not focus specifically on numerous complex aspects of stem cell regulation and functioning. We do not study the mechanisms by which stem cells can switch between asymmetric and symmetric modes of division, and do not extend this model to disease states where the control of stem cell divisions is defective. These are some of important future directions.In the present paper we considered a two-compartment (stem/TA) model where all non-stem cells were treated as a single type. Our numerical explorations suggest that the addition of more compartments does not change the message of the paper, that is, in the presence of more cell types, symmetric divisions continue to minimize the rate of double-mutant production. Further, the effect of the stem cell niche was modeled in a very basic manner, by assuming the existence of a stem cell compartment and a relatively tight regulation of differentiation vs proliferation decisions. Future directions include the addition of a more detailed description of spatial interactions, and the inclusion of other cellular processes such as de-differentiation.A stochastic numerical simulation was set up according to the following generalized Moran  process. The population consists of four types of cells: stem cells  have a probability to divide. A cell is chosen for division based on its fitness. The fitness of mutated cells is given by If a wild-type TA cell divides, it creates another wild-type TA cell with probability Divisions of stem cells can be either symmetric  is chosen to divide, according to its fitness, with mutants having fitness The process described above is slightly different from the numerical agent-based algorithm outlined used in numerical simulations. In the generalized Moran process described here, the numbers of stem cells We hLet us first solve The linear growth stage, where The saturation stage, where The constant form see .Let us assume that If If Finally, if Let us assume that If If Let us assume that Let us assume that Calculations for regimes (1C) and (2C) are performed in a similar manner, see In all the previous calculations, we assumed that upon a stem cell division, with probability


This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. Leaf springs are widely used in the automotive industry as primary components in suspension systems for heavy vehicles because they possess advantages such as a simple structure, excellent guiding effects, convenience in maintenance, low cost, and prone to axle location. Leaf spring designs are mainly based on simplified equations as well as trial-and-error methods. Simplified equation models are limited to three-link mechanism assumptions and linear beam theory. According to beam deflection theory, the deflection of a beam is based on the dimensional, cross-sectional profile of the current beam. The thickness of the cross-sectional profile of a parabolic leaf spring contributes to the stiffness in the vertical direction. The higher vertical stiffness of the leaf spring provides vehicles additional load-carrying capabilities. Leaf springs could be categorized into two types: multileaf and parabolic leaf. From a geometric perspective, a parabolic leaf spring has a constant width but decreasing thickness from the center of its line of encasement in a parabolic profile, whereas a multileaf spring maintains a constant thickness along its length . ParabolLeaf springs absorb and store energy and then release it. The characteristics of a spring suspension are chiefly influenced by the spring vertical stiffness and the static deflection of the spring. The ride frequency and the load-carrying capabilities of the leaf spring vehicle are affected by the vertical stiffness of the installed leaf springs. The vertical stiffness of a leaf spring is defined as the change in load per unit deflection in the vertical direction. Most leaf springs are designed to operate with respect to the vertical loading of the vehicle. However, leaf springs are practically loaded not only by vertical forces but also by horizontal forces and torques in the longitudinal directions. The center of a spring is elastically constrained against wind-up or rotation torque along a longitudinal vertical plane because of its wind-up stiffness. Leaf spring wind-up usually occurs while the vehicle brakes and accelerates. When a car suddenly starts or stops, front-down or rear-down postures impose a rotational torque on the spring, referred to as a wind-up torque . In addiSeveral studies have been conducted on leaf spring analysis such as deflection and stress analysis by using the finite element method (FEM) –6. The vα-HHT is used as a default time integrator [The most implemented algorithms in dynamic FE analysis (FEA) are the implicit and the explicit schemes. In implicit dynamic simulation, an extension of the Newmark method known as tegrator . Mousseategrator . This aptegrator , 16. An tegrator . The exptegrator . The simtegrator . The simtegrator .The design of a parabolic leaf spring in a bus presents a challenge to engineers given very complex and limited considerations. Road conditions and the driving behavior of the drivers subject the leaf springs to varying loading conditions, at times severely damaging the leaf springs. Currently, leaf spring designs focus solely on the load-carrying capabilities or relative vertical stiffness. As mentioned in other previous studies, the design of the leaf spring with vertical stiffness only is insufficient when catastrophic failures have the possibility of occurrence. However, the experimental methods verifying the stress under those varying loading modes are too costly and complex to perform. This paper aims to present the analysis of the stress level of the parabolic leaf springs under different loading conditions by computer-aided engineering. The failure modes of the leaf springs normally occur under harsh braking or suspension rolling while striking a pothole. The braking condition of the bus is associated with the leaf spring wind-up, whereas pothole striking is related to the suspension roll. To promote bus safety under such conditions, newly designed parabolic leaf springs are evaluated in simulations for their performance. The new leaf spring designs are expected to provide enhanced roll resistance, improved load-carrying capability, and reduced occurrence of potential failure.The standard simulation setup for any commercial FEA software is shown in M, C, and K represent the mass, viscous damping, and stiffness matrices. u denote the displacement, velocity, and acceleration vectors, respectively. F is the external force vector. In the general Newmark method, the state vector is computed as follows:β and γ are the specified coefficients that govern the stability, accuracy, and numerical dissipation of the integration method [FE procedures need to be well developed to perform a complex FE nonlinear analysis. Selection of the appropriate solving method is significant. A conditionally stable explicit integration scheme derived from the Newmark scheme from the RADIOSS solver has been introduced . In dynamic analysis, the equation of motion for discrete structural models is expressed as follows:n method . A condiThe explicit central difference integration scheme can be derived from the relationships. The central difference scheme is used when explicit analysis is selected. The time step must be smaller than the critical time step to ensure the stability of the solution. Newmark nonlinear analysis efficiently captures energy decay and exhibits a satisfactory long-term performance after being tested .β is the relaxation value and T is the period to be damped. Thus, a viscous stress tensor is added to the stress tensor. In an explicit code, the application of the dashpot force modifies the velocity equation without relaxationTo reduce the dynamic effects, dynamic relaxation is used in the explicit scheme. A diagonal damping matrix proportional to the mass matrix is added to the dynamic equationWhen this option is activated, the running time of the whole simulation is increased. However, the damping period for the system is controlled within acceptable limits.y-axis for the front eye, whereas the rear eye was constrained in the Y, Z translation and the X, Z rotation. The boundary conditions are complied with [X-Z translation and the Y rotation. The vertical push boundary condition setup is shown in y axis for the front eye, whereas the rear eye was constrained in the Y-Z translation and the X-Z rotation. After maximum vertical loading is applied, a longitudinal force was created and applied at the center of the parabolic leaf springs [Three different parabolic leaf spring designs were analyzed in this study. Each design was simulated with different loading cases. Therefore, different simulation boundary condition setups for the vertical push, wind-up, and roll suitable to the load case were conducted accordingly. First, the boundary conditions for the vertical push were performed with free rotation around the ied with . The cen springs . The winY axis for the front eye, whereas the rear eye is attached to the shackle, and the shackle can rotate in the y-axis only. The front module of conventional buses considered in this study employed an antiroll bar to enhance the roll stiffness of the vehicle. The antiroll bar can be idealized as a torsional stiffener connected between the sprung and the unsprung masses. When the roll bar undergoes a relative rotation between the two masses, a restoring moment, MΦ, is generated, which is then related to its roll stiffness kΦ [For the suspension roll study, loads are applied to push the suspension to a curb position. A moment is subsequently applied to the suspension by increasing the vertical load on the left side and decreasing the load on the right side . The leaness kΦ . The park for parabolic leaf springs is indicated [Some parabolic leaf springs are designed to endure vertical load, whereas others are also designed to sustain wind-up loads. The vertical rate of the spring is calculated based on the beam deflection theory. The formula for the vertical rate ndicated  as folloE is the spring material elastic modulus, to is the thickness at center of the spring, wo is the width at the center of the spring, l is the length of cantilever, and Cv is the vertical rate factor. Besides that, lateral rate of the parabolic leaf spring is also taken into design considerations. The wind-up stiffness, ω is predicted through the vertical stiffness of the leaf spring as shown in equation [where equation  as folloIs, is computed from both the masters, Km, and slaves segment, Ks. The interface stiffness relationship between the master and slave is defined in equationIn geometric nonlinear analysis, components will undergo large deformations. The nonlinearities always come from contact or materials. A general purpose contact is introduced in Radioss which is FE commercial software. The interface stiffness, μ [Friction formulation is also being introduced in this contact interface. The most well-known friction law is the Coulomb friction law. This formulation provides accurate results with just one input parameter which is Coulomb friction coefficient, μ .Three parabolic leaf spring designs were prepared and simulated for validation purpose. One of the front parabolic leaf springs was obtained from the original bus model as benchmark for the analysis. The original parabolic leaf spring was named as “Baseline” in the simulation case. The profile design of “Baseline” is shown in y axis can lead to periodic deformations, where the axle accepts a torque higher than the friction limit for a short time and then slips when the inertial force disappears. Vibration and loss of braking efficiency or traction then occur [When a car suddenly starts or stops, front-down or rear-down posture occurs, imposing a rotational torque or “wind-up torque” on the leaf spring . Leaf spen occur . Therefoθ is measured based on the rotation of the solid axle in the y-axis connecting the left and the right parabolic leaf springs. The roll moment versus the roll angle curve for Baseline, Iteration 1, and Iteration 2 is plotted in Ms is the vehicle sprung mass, hroll is the height of the center of gravity of the vehicle body above the roll axis, and kΦ is the total roll stiffness of suspension and tires [kf is the front suspension roll stiffness, kd is the device roll stiffness such as antiroll bar, and kr is the rear suspension roll stiffness. The suspension front, rear roll stiffness, and the contribution of the antiroll bar constitute the amount of the vehicle body roll; thus, an increase in any of them reduces the vehicle body roll. The vehicle body roll reduces the stabilizing moment because of insufficient roll stiffness, leading to vehicle instability. Therefore, the parabolic leaf springs in Iteration 2 exhibit the highest suspension roll stiffness compared with those in Iteration 1 and the Baseline, thereby providing the vehicle the highest roll stability.For the suspension roll study, a 1.5 g gravitational force is applied to the left side, and the load on the right side is decreased to 0.5 g of the gravitational force. In this case, the same antiroll bar, axle, and linkages are implemented to ensure consistency in the simulation. To determine suspension roll stiffness, the roll angle of the suspension is measured, as shown in nd tires . Accordiotted in Φ=MshrollExternal loads applied to a component, particularly springs that undergo repeated cyclic loading, produce stress. In real-life settings, stresses would not be uniaxial, biaxial, and/or even multiaxial for most cases. Alternatively, an equivalent stress can be calculated from multiaxial stresses. The von Mises stress is a widely known equivalent stress, which is implemented for stress analysis of the leaf spring in this study. The stress levels of machine components are often monitored and controlled within the limit of the material that can sustain stress to prevent component failure. The von Mises stress contours of the Baseline, Iteration 1, and Iteration 2 of parabolic leaf springs under vertical and wind-up load cases are illustrated in In a vertical load case, Iteration 2 exhibits higher vertical stiffness compared with both Iteration 1 and the Baseline. In addition, Iteration 2 possesses a higher resistance to longitudinal loading compared with Iteration 1 and the Baseline during wind-up loading. The roll stiffness of Iteration 2 is also slightly greater than those of Iteration 1 and the Baseline. The stress level of Iteration 2 is lower than those of Iteration 1 and the Baseline even in the case of vertical and roll loads, as listed in An explicit dynamic nonlinear geometric scheme was adopted to simulate the vertical push, wind-up, and roll load cases of the parabolic leaf spring of a bus. An FE-based procedure dealing with the evaluation and assessment of the parabolic leaf spring of the bus was presented. Modeling details for an accurate calculation of the spring are discussed. New parabolic leaf spring designs are included in the analysis to obtain an improved bus load-carrying capability, braking resistance, and roll resistance, which were determined through the analysis of vertical stiffness, wind-up stiffness, and roll stiffness. In addition to the vertical, wind-up, and roll stiffness provided by the parabolic leaf springs, the stress level of the spring component itself is plotted and monitored to ensure falling within the controlled limit. Hence, no failures are expected when the new parabolic leaf spring designs are implemented in the vehicle. In this analysis, the designed parabolic leaf spring with higher vertical stiffness leads to higher wind-up and roll stiffness. The new parabolic leaf spring design with the highest vertical stiffness should possess higher load-carrying capability, braking instability resistance, and roll stability compared with the others. The stress level observed for the new leaf spring designs under these circumstances is lower compared with the original design. The chances of failure are reduced, and vehicle safety is enhanced under a braking or pothole strike condition. Vehicle safety is increased because of the increase in suspension reliability.