Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

The TAP approach to intensive and extensive connectivity systems

The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.

Graphical modelling for brain connectivity via partial coherence

Spectral and coherence methodologies are ubiquitous for the analysis of multiple time series. Partial coherence analysis may be used to try to determine graphical models for brain functional connectivity. The outcome of such an analysis may be considerably influenced by factors such as the degree of spectral smoothing, line and interference removal, matrix inversion stabilization and the suppression of effects caused by side-lobe leakage, the combination of results from different epochs and people, and multiple hypothesis testing. This paper examines each of these steps in turn and provides a possible path which produces relatively ‘clean’ connectivity plots. In particular we show how spectral matrix diagonal up-weighting can simultaneously stabilize spectral matrix inversion and reduce effects caused by side-lobe leakage, and use the stepdown multiple hypothesis test procedure to help formulate an interaction strength.

The lateral and ventromedial prefrontal cortex work as a dynamic integrated system:evidence from FMRI connectivity analysis

Recent functional magnetic resonance imaging (fMRI) investigations of the interaction between cognition and reward processing have found that the lateral prefrontal cortex (PFC) areas are preferentially activated to both increasing cognitive demand and reward level. Conversely, ventromedial PFC (VMPFC) areas show decreased activation to the same conditions, indicating a possible reciprocal relationship between cognitive and emotional processing regions. We report an fMRI study of a rewarded working memory task, in which we further explore how the relationship between reward and cognitive processing is mediated. We not only assess the integrity of reciprocal neural connections between the lateral PFC and VMPFC brain regions in different experimental contexts but also test whether additional cortical and subcortical regions influence this relationship. Psychophysiological interaction analyses were used as a measure of functional connectivity in order to characterize the influence of both cognitive and motivational variables on connectivity between the lateral PFC and the VMPFC. Psychophysiological interactions revealed negative functional connectivity between the lateral PFC and the VMPFC in the context of high memory load, and high memory load in tandem with a highly motivating context, but not in the context of reward alone. Physiophysiological interactions further indicated that the dorsal anterior cingulate and the caudate nucleus modulate this pathway. These findings provide evidence for a dynamic interplay between lateral PFC and VMPFC regions and are consistent with an emotional gating role for the VMPFC during cognitively demanding tasks. Our findings also support neuropsychological theories of mood disorders, which have long emphasized a dysfunctional relationship between emotion/motivational and cognitive processes in depression.

Disordered connectivity in the autistic brain:challenges for the 'new psychophysiology'

In 2002, we published a paper [Brock, J., Brown, C., Boucher, J., Rippon, G., 2002. The temporal binding deficit hypothesis of autism. Development and Psychopathology 142, 209-224] highlighting the parallels between the psychological model of 'central coherence' in information processing [Frith, U., 1989. Autism: Explaining the Enigma. Blackwell, Oxford] and the neuroscience model of neural integration or 'temporal binding'. We proposed that autism is associated with abnormalities of information integration that is caused by a reduction in the connectivity between specialised local neural networks in the brain and possible overconnectivity within the isolated individual neural assemblies. The current paper updates this model, providing a summary of theoretical and empirical advances in research implicating disordered connectivity in autism. This is in the context of changes in the approach to the core psychological deficits in autism, of greater emphasis on 'interactive specialisation' and the resultant stress on early and/or low-level deficits and their cascading effects on the developing brain [Johnson, M.H., Halit, H., Grice, S.J., Karmiloff-Smith, A., 2002. Neuroimaging of typical and atypical development: a perspective from multiple levels of analysis. Development and Psychopathology 14, 521-536].We also highlight recent developments in the measurement and modelling of connectivity, particularly in the emerging ability to track the temporal dynamics of the brain using electroencephalography (EEG) and magnetoencephalography (MEG) and to investigate the signal characteristics of this activity. This advance could be particularly pertinent in testing an emerging model of effective connectivity based on the balance between excitatory and inhibitory cortical activity [Rubenstein, J.L., Merzenich M.M., 2003. Model of autism: increased ratio of excitation/inhibition in key neural systems. Genes, Brain and Behavior 2, 255-267; Brown, C., Gruber, T., Rippon, G., Brock, J., Boucher, J., 2005. Gamma abnormalities during perception of illusory figures in autism. Cortex 41, 364-376]. Finally, we note that the consequence of this convergence of research developments not only enables a greater understanding of autism but also has implications for prevention and remediation. © 2006.

Estimation of functional connectivity from electromagnetic signals and the amount of empirical data required

An increasing number of neuroimaging studies are concerned with the identification of interactions or statistical dependencies between brain areas. Dependencies between the activities of different brain regions can be quantified with functional connectivity measures such as the cross-correlation coefficient. An important factor limiting the accuracy of such measures is the amount of empirical data available. For event-related protocols, the amount of data also affects the temporal resolution of the analysis. We use analytical expressions to calculate the amount of empirical data needed to establish whether a certain level of dependency is significant when the time series are autocorrelated, as is the case for biological signals. These analytical results are then contrasted with estimates from simulations based on real data recorded with magnetoencephalography during a resting-state paradigm and during the presentation of visual stimuli. Results indicate that, for broadband signals, 50-100 s of data is required to detect a true underlying cross-correlations coefficient of 0.05. This corresponds to a resolution of a few hundred milliseconds for typical event-related recordings. The required time window increases for narrow band signals as frequency decreases. For instance, approximately 3 times as much data is necessary for signals in the alpha band. Important implications can be derived for the design and interpretation of experiments to characterize weak interactions, which are potentially important for brain processing.

Abnormal amygdala-prefrontal effective connectivity to happy faces differentiates bipolar from major depression

Background - Bipolar disorder is frequently misdiagnosed as major depressive disorder, delaying appropriate treatment and worsening outcome for many bipolar individuals. Emotion dysregulation is a core feature of bipolar disorder. Measures of dysfunction in neural systems supporting emotion regulation might therefore help discriminate bipolar from major depressive disorder. Methods - Thirty-one depressed individuals—15 bipolar depressed (BD) and 16 major depressed (MDD), DSM-IV diagnostic criteria, ages 18–55 years, matched for age, age of illness onset, illness duration, and depression severity—and 16 age- and gender-matched healthy control subjects performed two event-related paradigms: labeling the emotional intensity of happy and sad faces, respectively. We employed dynamic causal modeling to examine significant among-group alterations in effective connectivity (EC) between right- and left-sided neural regions supporting emotion regulation: amygdala and orbitomedial prefrontal cortex (OMPFC). Results - During classification of happy faces, we found profound and asymmetrical differences in EC between the OMPFC and amygdala. Left-sided differences involved top-down connections and discriminated between depressed and control subjects. Furthermore, greater medication load was associated with an amelioration of this abnormal top-down EC. Conversely, on the right side the abnormality was in bottom-up EC that was specific to bipolar disorder. These effects replicated when we considered only female subjects. Conclusions - Abnormal, left-sided, top-down OMPFC–amygdala and right-sided, bottom-up, amygdala–OMPFC EC during happy labeling distinguish BD and MDD, suggesting different pathophysiological mechanisms associated with the two types of depression.

Abnormal left and right amygdala-orbitofrontal cortical functional connectivity to emotional faces:state versus trait vulnerability markers of depression in bipolar disorder

Background - Amygdala-orbitofrontal cortical (OFC) functional connectivity (FC) to emotional stimuli and relationships with white matter remain little examined in bipolar disorder individuals (BD). Methods - Thirty-one BD (type I; n = 17 remitted; n = 14 depressed) and 24 age- and gender-ratio-matched healthy individuals (HC) viewed neutral, mild, and intense happy or sad emotional faces in two experiments. The FC was computed as linear and nonlinear dependence measures between amygdala and OFC time series. Effects of group, laterality, and emotion intensity upon amygdala-OFC FC and amygdala-OFC FC white matter fractional anisotropy (FA) relationships were examined. Results - The BD versus HC showed significantly greater right amygdala-OFC FC (p = .001) in the sad experiment and significantly reduced bilateral amygdala-OFC FC (p = .007) in the happy experiment. Depressed but not remitted female BD versus female HC showed significantly greater left amygdala-OFC FC (p = .001) to all faces in the sad experiment and reduced bilateral amygdala-OFC FC to intense happy faces (p = .01). There was a significant nonlinear relationship (p = .001) between left amygdala-OFC FC to sad faces and FA in HC. In BD, antidepressants were associated with significantly reduced left amygdala-OFC FC to mild sad faces (p = .001). Conclusions - In BD, abnormally elevated right amygdala-OFC FC to sad stimuli might represent a trait vulnerability for depression, whereas abnormally elevated left amygdala-OFC FC to sad stimuli and abnormally reduced amygdala-OFC FC to intense happy stimuli might represent a depression state marker. Abnormal FC measures might normalize with antidepressant medications in BD. Nonlinear amygdala-OFC FC–FA relationships in BD and HC require further study.

Disconnected brains:what is the role of fMRI in connectivity research?

In this paper we consider how functional Magnetic Resonance Imaging (fMRI) has been used to study cortical connectivity in autism and autistic spectrum disorders (ASD). We discuss those studies that have contributed to the evidence supporting a model of disordered cortical connectivity in autism and (ASD), with a focusing emphasis on the application to research into the underconnectivity model. We note that the analytical techniques employed are limited and do not allow interpretation in terms of effective, or directional connectivity, nor do they provide information about the temporal or spectral characteristics of the functional networks being studied. We highlight how currently the features of neural generators that are being assessed by functional connectivity in fMRI are unclear. In addition, we note the importance in clinical studies of considering the consequences of task choice for the nature of the imaging data that can be collected and also of individual differences in participant state and trait characteristics for the accurate interpretation of imaging data. We discuss how alternative techniques such as EEG/MEG may address the limitations of fMRI in assessing brain connectivity, and additionally consider the potential of multimodal approaches. We conclude that fMRI has made significant contributions towards our understanding of the brain in terms of neural systems but that the conclusions drawn from its application in the sphere of autism research need to be approached with caution. It is important in research of this kind that we are aware of the need to examine the methodological and analytical techniques closely when applying findings in clinical populations, not only when they are used to support the development of theoretical models but also to inform diagnostic or treatment decisions.

Differential patterns of activity and functional connectivity in emotion processing neural circuitry to angry and happy faces in adolescents with and without suicide attempt

Background - Neural substrates of emotion dysregulation in adolescent suicide attempters remain unexamined. Method - We used functional magnetic resonance imaging to measure neural activity to neutral, mild or intense (i.e. 0%, 50% or 100% intensity) emotion face morphs in two separate emotion-processing runs (angry and happy) in three adolescent groups: (1) history of suicide attempt and depression (ATT, n = 14); (2) history of depression alone (NAT, n = 15); and (3) healthy controls (HC, n = 15). Post-hoc analyses were conducted on interactions from 3 group × 3 condition (intensities) whole-brain analyses (p < 0.05, corrected) for each emotion run. Results - To 50% intensity angry faces, ATT showed significantly greater activity than NAT in anterior cingulate gyral–dorsolateral prefrontal cortical attentional control circuitry, primary sensory and temporal cortices; and significantly greater activity than HC in the primary sensory cortex, while NAT had significantly lower activity than HC in the anterior cingulate gyrus and ventromedial prefrontal cortex. To neutral faces during the angry emotion-processing run, ATT had significantly lower activity than NAT in the fusiform gyrus. ATT also showed significantly lower activity than HC to 100% intensity happy faces in the primary sensory cortex, and to neutral faces in the happy run in the anterior cingulate and left medial frontal gyri (all p < 0.006,corrected). Psychophysiological interaction analyses revealed significantly reduced anterior cingulate gyral–insula functional connectivity to 50% intensity angry faces in ATT v. NAT or HC. Conclusions - Elevated activity in attention control circuitry, and reduced anterior cingulate gyral–insula functional connectivity, to 50% intensity angry faces in ATT than other groups suggest that ATT may show inefficient recruitment of attentional control neural circuitry when regulating attention to mild intensity angry faces, which may represent a potential biological marker for suicide risk.

Brain connectivity in positive and negative syndrome schizophrenia

If, as is widely believed, schizophrenia is characterized by abnormalities of brain functional connectivity, then it seems reasonable to expect that different subtypes of schizophrenia could be discriminated in the same way. However, evidence for differences in functional connectivity between the subtypes of schizophrenia is largely lacking and, where it exists, it could be accounted for by clinical differences between the patients (e.g. medication) or by the limitations of the measures used. In this study, we measured EEG functional connectivity in unmedicated male patients diagnosed with either positive or negative syndrome schizophrenia and compared them with age and sex matched healthy controls. Using new methodology (Medkour et al., 2009) based on partial coherence, brain connectivity plots were constructed for positive and negative syndrome patients and controls. Reliable differences in the pattern of functional connectivity were found with both syndromes showing not only an absence of some of the connections that were seen in controls but also the presence of connections that the controls did not show. Comparing connectivity graphs using the Hamming distance, the negative-syndrome patients were found to be more distant from the controls than were the positive syndrome patients. Bootstrap distributions of these distances were created which showed a significant difference in the mean distances that was consistent with the observation that negative-syndrome diagnosis is associated with a more severe form of schizophrenia. We conclude that schizophrenia is characterized by widespread changes in functional connectivity with negative syndrome patients showing a more extreme pattern of abnormality than positive syndrome patients.

Multiple frequency functional connectivity in the hand somatosensory network:an EEG study

Objective: To investigate the dynamics of communication within the primary somatosensory neuronal network. Methods: Multichannel EEG responses evoked by median nerve stimulation were recorded from six healthy participants. We investigated the directional connectivity of the evoked responses by assessing the Partial Directed Coherence (PDC) among five neuronal nodes (brainstem, thalamus and three in the primary sensorimotor cortex), which had been identified by using the Functional Source Separation (FSS) algorithm. We analyzed directional connectivity separately in the low (1-200. Hz, LF) and high (450-750. Hz, HF) frequency ranges. Results: LF forward connectivity showed peaks at 16, 20, 30 and 50. ms post-stimulus. An estimate of the strength of connectivity was modulated by feedback involving cortical and subcortical nodes. In HF, forward connectivity showed peaks at 20, 30 and 50. ms, with no apparent feedback-related strength changes. Conclusions: In this first non-invasive study in humans, we documented directional connectivity across subcortical and cortical somatosensory pathway, discriminating transmission properties within LF and HF ranges. Significance: The combined use of FSS and PDC in a simple protocol such as median nerve stimulation sheds light on how high and low frequency components of the somatosensory evoked response are functionally interrelated in sustaining somatosensory perception in healthy individuals. Thus, these components may potentially be explored as biomarkers of pathological conditions. © 2012 International Federation of Clinical Neurophysiology.

Right orbitofrontal corticolimbic and left corticocortical white matter connectivity differentiate bipolar and unipolar depression

Objectives - The absence of pathophysiologically relevant diagnostic markers of bipolar disorder (BD) leads to its frequent misdiagnosis as unipolar depression (UD). We aimed to determine whether whole brain white matter connectivity differentiated BD from UD depression. Methods - We employed a three-way analysis of covariance, covarying for age, to examine whole brain fractional anisotropy (FA), and corresponding longitudinal and radial diffusivity, in currently depressed adults: 15 with BD-type I (mean age 36.3 years, SD 12.0 years), 16 with recurrent UD (mean age 32.3 years, SD 10.0 years), and 24 healthy control adults (HC) (mean age 29.5 years, SD 9.43 years). Depressed groups did not differ in depression severity, age of illness onset, and illness duration. Results - There was a main effect of group in left superior and inferior longitudinal fasciculi (SLF and ILF) (all F = 9.8; p = .05, corrected). Whole brain post hoc analyses (all t = 4.2; p = .05, corrected) revealed decreased FA in left SLF in BD, versus UD adults in inferior temporal cortex and, versus HC, in primary sensory cortex (associated with increased radial and decreased longitudinal diffusivity, respectively); and decreased FA in left ILF in UD adults versus HC. A main effect of group in right uncinate fasciculus (in orbitofrontal cortex) just failed to meet significance in all participants but was present in women. Post hoc analyses revealed decreased right uncinate fasciculus FA in all and in women, BD versus HC. Conclusions - White matter FA in left occipitotemporal and primary sensory regions supporting visuospatial and sensory processing differentiates BD from UD depression. Abnormally reduced FA in right fronto-temporal regions supporting mood regulation, might underlie predisposition to depression in BD. These measures might help differentiate pathophysiologic processes of BD versus UD depression.

Abnormally increased effective connectivity between parahippocampal gyrus and ventromedial prefrontal regions during emotion labeling in bipolar disorder

Emotional liability and mood dysregulation characterize bipolar disorder (BD), yet no study has examined effective connectivity between parahippocampal gyrus and prefrontal cortical regions in ventromedial and dorsal/lateral neural systems subserving mood regulation in BD. Participants comprised 46 individuals (age range: 18-56 years): 21 with a DSM-IV diagnosis of BD, type I currently remitted; and 25 age- and gender-matched healthy controls (HC). Participants performed an event-related functional magnetic resonance imaging paradigm, viewing mild and intense happy and neutral faces. We employed dynamic causal modeling (DCM) to identify significant alterations in effective connectivity between BD and HC. Bayes model selection was used to determine the best model. The right parahippocampal gyrus (PHG) and right subgenual cingulate gyrus (sgCG) were included as representative regions of the ventromedial neural system. The right dorsolateral prefrontal cortex (DLPFC) region was included as representative of the dorsal/lateral neural system. Right PHG-sgCG effective connectivity was significantly greater in BD than HC, reflecting more rapid, forward PHG-sgCG signaling in BD than HC. There was no between-group difference in sgCG-DLPFC effective connectivity. In BD, abnormally increased right PHG-sgCG effective connectivity and reduced right PHG activity to emotional stimuli suggest a dysfunctional ventromedial neural system implicated in early stimulus appraisal, encoding and automatic regulation of emotion that may represent a pathophysiological functional neural mechanism for mood dysregulation in BD.