Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.

A family study of co-morbidity between generalized social phobia and generalized anxiety disorder in a non-clinic sample

Background: High rates of co-morbidity between Generalized Social Phobia (GSP) and Generalized Anxiety Disorder (GAD) have been documented. The reason for this is unclear. Family studies are one means of clarifying the nature of co-morbidity between two disorders. Methods: Six models of co-morbidity between GSP and GAD were investigated in a family aggregation study of 403 first-degree relatives of non-clinical probands: 37 with GSP, 22 with GAD, 15 with co-morbid GSP/GAD, and 41 controls with no history of GSP or GAD. Psychiatric data were collected for probands and relatives. Mixed methods (direct and family history interviews) were utilised. Results: Primary contrasts (against controls) found an increased rate of pure GSP in the relatives of both GSP probands and co-morbid GSP/GAD probands, and found relatives of co-morbid GSP/GAD probands to have an increased rate of both pure GAD and comorbid GSP/GAD. Secondary contrasts found (i) increased GSP in the relatives of GSP only probands compared to the relatives of GAD only probands; and (ii) increased GAD in the relatives of co-morbid GSP/GAD probands compared to the relatives of GSP only probands. Limitations: The study did not directly interview all relatives, although the reliability of family history data was assessed. The study was based on an all-female proband sample. The implications of both these limitations are discussed. Conclusions: The results were most consistent with a co-morbidity model indicating independent familial transmission of GSP and GAD. This has clinical implications for the treatment of patients with both disorders. (C) 2006 Elsevier B.V. All fights reserved.

Identification of nonlinear systems using generalized kernel models

Nonlinear system identification is considered using a generalized kernel regression model. Unlike the standard kernel model, which employs a fixed common variance for all the kernel regressors, each kernel regressor in the generalized kernel model has an individually tuned diagonal covariance matrix that is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. An efficient construction algorithm based on orthogonal forward regression with leave-one-out (LOO) test statistic and local regularization (LR) is then used to select a parsimonious generalized kernel regression model from the resulting full regression matrix. The proposed modeling algorithm is fully automatic and the user is not required to specify any criterion to terminate the construction procedure. Experimental results involving two real data sets demonstrate the effectiveness of the proposed nonlinear system identification approach.

Generalized matching networks and their properties

In this paper, we introduce two kinds of graphs: the generalized matching networks (GMNs) and the recursive generalized matching networks (RGMNs). The former generalize the hypercube-like networks (HLNs), while the latter include the generalized cubes and the star graphs. We prove that a GMN on a family of k-connected building graphs is -connected. We then prove that a GMN on a family of Hamiltonian-connected building graphs having at least three vertices each is Hamiltonian-connected. Our conclusions generalize some previously known results.

Minimum neighborhood in a generalized cube

Generalized cubes are a subclass of hypercube-like networks, which include some hypercube variants as special cases. Let theta(G)(k) denote the minimum number of nodes adjacent to a set of k vertices of a graph G. In this paper, we prove theta(G)(k) >= -1/2k(2) + (2n - 3/2)k - (n(2) - 2) for each n-dimensional generalized cube and each integer k satisfying n + 2 <= k <= 2n. Our result is an extension of a result presented by Fan and Lin [J. Fan, X. Lin, The t/k-diagnosability of the BC graphs, IEEE Trans. Comput. 54 (2) (2005) 176-184]. (c) 2005 Elsevier B.V. All rights reserved.

Generalized honeycomb torus is Hamiltonian

Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases. Existence of Hamiltonian cycle is a basic requirement for interconnection networks since it helps map a "token ring" parallel algorithm onto the associated network in an efficient way. Cho and Hsu [Inform. Process. Lett. 86 (4) (2003) 185-190] speculated that every generalized honeycomb torus is Hamiltonian. In this paper, we have proved this conjecture. (C) 2004 Elsevier B.V. All rights reserved.

A lower bound on the size of k-neighborhood in generalized cubes

The determination of the minimum size of a k-neighborhood (i.e., a neighborhood of a set of k nodes) in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems. The generalized cubes include the hypercube and most hypercube variants as special cases. In this paper, we present a lower bound on the size of a k-neighborhood in n-dimensional generalized cubes, where 2n + 1 <= k <= 3n - 2. This lower bound is tight in that it is met by the n-dimensional hypercube. Our result is an extension of two previously known results. (c) 2005 Elsevier Inc. All rights reserved.

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3(P) sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2(q)3(P) sequences.

Thermodynamics of climate change: generalized sensitivities

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks.

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.