Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Astrocytes refine cortical connectivity at dendritic spines.

During cortical synaptic development, thalamic axons must establish synaptic connections despite the presence of the more abundant intracortical projections. How thalamocortical synapses are formed and maintained in this competitive environment is unknown. Here, we show that astrocyte-secreted protein hevin is required for normal thalamocortical synaptic connectivity in the mouse cortex. Absence of hevin results in a profound, long-lasting reduction in thalamocortical synapses accompanied by a transient increase in intracortical excitatory connections. Three-dimensional reconstructions of cortical neurons from serial section electron microscopy (ssEM) revealed that, during early postnatal development, dendritic spines often receive multiple excitatory inputs. Immuno-EM and confocal analyses revealed that majority of the spines with multiple excitatory contacts (SMECs) receive simultaneous thalamic and cortical inputs. Proportion of SMECs diminishes as the brain develops, but SMECs remain abundant in Hevin-null mice. These findings reveal that, through secretion of hevin, astrocytes control an important developmental synaptic refinement process at dendritic spines.

Preschool anxiety disorders predict different patterns of amygdala-prefrontal connectivity at school-age.

OBJECTIVE: In this prospective, longitudinal study of young children, we examined whether a history of preschool generalized anxiety, separation anxiety, and/or social phobia is associated with amygdala-prefrontal dysregulation at school-age. As an exploratory analysis, we investigated whether distinct anxiety disorders differ in the patterns of this amygdala-prefrontal dysregulation. METHODS: Participants were children taking part in a 5-year study of early childhood brain development and anxiety disorders. Preschool symptoms of generalized anxiety, separation anxiety, and social phobia were assessed with the Preschool Age Psychiatric Assessment (PAPA) in the first wave of the study when the children were between 2 and 5 years old. The PAPA was repeated at age 6. We conducted functional MRIs when the children were 5.5 to 9.5 year old to assess neural responses to viewing of angry and fearful faces. RESULTS: A history of preschool social phobia predicted less school-age functional connectivity between the amygdala and the ventral prefrontal cortices to angry faces. Preschool generalized anxiety predicted less functional connectivity between the amygdala and dorsal prefrontal cortices in response to fearful faces. Finally, a history of preschool separation anxiety predicted less school-age functional connectivity between the amygdala and the ventral prefrontal cortices to angry faces and greater school-age functional connectivity between the amygdala and dorsal prefrontal cortices to angry faces. CONCLUSIONS: Our results suggest that there are enduring neurobiological effects associated with a history of preschool anxiety, which occur over-and-above the effect of subsequent emotional symptoms. Our results also provide preliminary evidence for the neurobiological differentiation of specific preschool anxiety disorders.

Cross-hemispheric collaboration and segregation associated with task difficulty as revealed by structural and functional connectivity.

Although it is known that brain regions in one hemisphere may interact very closely with their corresponding contralateral regions (collaboration) or operate relatively independent of them (segregation), the specific brain regions (where) and conditions (how) associated with collaboration or segregation are largely unknown. We investigated these issues using a split field-matching task in which participants matched the meaning of words or the visual features of faces presented to the same (unilateral) or to different (bilateral) visual fields. Matching difficulty was manipulated by varying the semantic similarity of words or the visual similarity of faces. We assessed the white matter using the fractional anisotropy (FA) measure provided by diffusion tensor imaging (DTI) and cross-hemispheric communication in terms of fMRI-based connectivity between homotopic pairs of cortical regions. For both perceptual and semantic matching, bilateral trials became faster than unilateral trials as difficulty increased (bilateral processing advantage, BPA). The study yielded three novel findings. First, whereas FA in anterior corpus callosum (genu) correlated with word-matching BPA, FA in posterior corpus callosum (splenium-occipital) correlated with face-matching BPA. Second, as matching difficulty intensified, cross-hemispheric functional connectivity (CFC) increased in domain-general frontopolar cortex (for both word and face matching) but decreased in domain-specific ventral temporal lobe regions (temporal pole for word matching and fusiform gyrus for face matching). Last, a mediation analysis linking DTI and fMRI data showed that CFC mediated the effect of callosal FA on BPA. These findings clarify the mechanisms by which the hemispheres interact to perform complex cognitive tasks.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.