Anticipatory activation in the amygdala and anterior cingulate in generalized anxiety disorder and prediction of treatment response

OBJECTIVE: The anticipation of adverse outcomes, or worry, is a cardinal symptom of generalized anxiety disorder. Prior work with healthy subjects has shown that anticipating aversive events recruits a network of brain regions, including the amygdala and anterior cingulate cortex. This study tested whether patients with generalized anxiety disorder have alterations in anticipatory amygdala function and whether anticipatory activity in the anterior cingulate cortex predicts treatment response. METHOD: Functional magnetic resonance imaging (fMRI) was employed with 14 generalized anxiety disorder patients and 12 healthy comparison subjects matched for age, sex, and education. The event-related fMRI paradigm was composed of one warning cue that preceded aversive pictures and a second cue that preceded neutral pictures. Following the fMRI session, patients received 8 weeks of treatment with extended-release venlafaxine. RESULTS: Patients with generalized anxiety disorder showed greater anticipatory activity than healthy comparison subjects in the bilateral dorsal amygdala preceding both aversive and neutral pictures. Building on prior reports of pretreatment anterior cingulate cortex activity predicting treatment response, anticipatory activity in that area was associated with clinical outcome 8 weeks later following treatment with venlafaxine. Higher levels of pretreatment anterior cingulate cortex activity in anticipation of both aversive and neutral pictures were associated with greater reductions in anxiety and worry symptoms. CONCLUSIONS: These findings of heightened and indiscriminate amygdala responses to anticipatory signals in generalized anxiety disorder and of anterior cingulate cortex associations with treatment response provide neurobiological support for the role of anticipatory processes in the pathophysiology of generalized anxiety disorder.

A geometric approach to generalized Stokes conjectures

We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.

Entropy versus APE production: on the buoyancy power input in the oceans energy cycle

This letter argues that the current controversy about whether Wbuoyancy, the power input due to the surface buoyancy fluxes, is large or small in the oceans stems from two distinct and incompatible views on how Wbuoyancy relates to the volume-integrated work of expansion/contraction B. The current prevailing view is that Wbuoyancy should be identified with the net value of B, which current theories estimate to be small. The alternative view, defended here, is that only the positive part of B, i.e., the one converting internal energy into mechanical energy, should enter the definition of Wbuoyancy, since the negative part of B is associated with the non-viscous dissipation of mechanical energy. Two indirect methods suggest that by contrast, the positive part of B is potentially large.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Entropy application to improve construction finance decisions

In financial decision-making processes, the adopted weights of the objective functions have significant impacts on the final decision outcome. However, conventional rating and weighting methods exhibit difficulty in deriving appropriate weights for complex decision-making problems with imprecise information. Entropy is a quantitative measure of uncertainty and has been useful in exploring weights of attributes in decision making. A fuzzy and entropy-based mathematical approach is employed to solve the weighting problem of the objective functions in an overall cash-flow model. The multiproject being undertaken by a medium-size construction firm in Hong Kong was used as a real case study to demonstrate the application of entropy. Its application in multiproject cash flow situations is demonstrated. The results indicate that the overall before-tax profit was HK$ 0.11 millions lower after the introduction of appropriate weights. In addition, the best time to invest in new projects arising from positive cash flow was identified to be two working months earlier than the nonweight system.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Multiscale evolving complex network model of functional connectivity in neuronal cultures

Cultures of cortical neurons grown on multielectrode arrays exhibit spontaneous, robust and recurrent patterns of highly synchronous activity called bursts. These bursts play a crucial role in the development and topological selforganization of neuronal networks. Thus, understanding the evolution of synchrony within these bursts could give insight into network growth and the functional processes involved in learning and memory. Functional connectivity networks can be constructed by observing patterns of synchrony that evolve during bursts. To capture this evolution, a modelling approach is adopted using a framework of emergent evolving complex networks and, through taking advantage of the multiple time scales of the system, aims to show the importance of sequential and ordered synchronization in network function.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.