Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Social media and political change: The case of the 2011 revolutions in Tunisia and Egypt

Throughout the past decade, social media have come on the scene of various popular revolts. Their role as tools of information and coordination of social movements, from the Iranian Green Movement in 2009 to the Arab uprisings in 2011, has been widely debated. In most cases, online activism through blogs, Facebook, Twitter or other forms of social media has allowed citizens to be part of a social networking exercise and to engage in a public sphere that would have otherwise been unreachable to them due to severe repression. In Tunisia and Egypt, social media helped protests start and expand thanks to their ability to coordinate and disseminate information quickly. The new information and communication tools were an influential factor in accelerating the revolutionary processes across the Arab world, albeit they cannot be seen as neither the spur nor the drivers of any revolution.

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Emotional attention as a modulatory system of perception

Report for the scientific sojourn carried out at the University Medical Center, Swiss, from 2010 to 2012. Abundant evidence suggests that negative emotional stimuli are prioritized in the perceptual systems, eliciting enhanced neural responses in early sensory regions as compared with neutral information. This facilitated detection is generally paralleled by larger neural responses in early sensory areas, relative to the processing of neutral information. In this sense, the amygdala and other limbic regions, such as the orbitofrontal cortex, may play a critical role by sending modulatory projections onto the sensory cortices via direct or indirect feedback.The present project aimed at investigating two important issues regarding these mechanisms of emotional attention, by means of functional magnetic resonance imaging. In Study I, we examined the modulatory effects of visual emotion signals on the processing of task-irrelevant visual, auditory, and somatosensory input, that is, the intramodal and crossmodal effects of emotional attention. We observed that brain responses to auditory and tactile stimulation were enhanced during the processing of visual emotional stimuli, as compared to neutral, in bilateral primary auditory and somatosensory cortices, respectively. However, brain responses to visual task-irrelevant stimulation were diminished in left primary and secondary visual cortices in the same conditions. The results also suggested the existence of a multimodal network associated with emotional attention, presumably involving mediofrontal, temporal and orbitofrontal regions Finally, Study II examined the different brain responses along the low-level visual pathways and limbic regions, as a function of the number of retinal spikes during visual emotional processing. The experiment used stimuli resulting from an algorithm that simulates how the visual system perceives a visual input after a given number of retinal spikes. The results validated the visual model in human subjects and suggested differential emotional responses in the amygdala and visual regions as a function of spike-levels. A list of publications resulting from work in the host laboratory is included in the report.

Emotional attention as a modulatory system of perception

Report for the scientific sojourn carried out at the University Medical Center, Swiss, from 2010 to 2012. Abundant evidence suggests that negative emotional stimuli are prioritized in the perceptual systems, eliciting enhanced neural responses in early sensory regions as compared with neutral information. This facilitated detection is generally paralleled by larger neural responses in early sensory areas, relative to the processing of neutral information. In this sense, the amygdala and other limbic regions, such as the orbitofrontal cortex, may play a critical role by sending modulatory projections onto the sensory cortices via direct or indirect feedback.The present project aimed at investigating two important issues regarding these mechanisms of emotional attention, by means of functional magnetic resonance imaging. In Study I, we examined the modulatory effects of visual emotion signals on the processing of task-irrelevant visual, auditory, and somatosensory input, that is, the intramodal and crossmodal effects of emotional attention. We observed that brain responses to auditory and tactile stimulation were enhanced during the processing of visual emotional stimuli, as compared to neutral, in bilateral primary auditory and somatosensory cortices, respectively. However, brain responses to visual task-irrelevant stimulation were diminished in left primary and secondary visual cortices in the same conditions. The results also suggested the existence of a multimodal network associated with emotional attention, presumably involving mediofrontal, temporal and orbitofrontal regions Finally, Study II examined the different brain responses along the low-level visual pathways and limbic regions, as a function of the number of retinal spikes during visual emotional processing. The experiment used stimuli resulting from an algorithm that simulates how the visual system perceives a visual input after a given number of retinal spikes. The results validated the visual model in human subjects and suggested differential emotional responses in the amygdala and visual regions as a function of spike-levels. A list of publications resulting from work in the host laboratory is included in the report.

Dynamic estimation of three-dimensional cerebrovascular deformation from rotational angiography

Purpose: The objective of this study is to investigate the feasibility of detecting and quantifying 3D cerebrovascular wall motion from a single 3D rotational x-ray angiography (3DRA) acquisition within a clinically acceptable time and computing from the estimated motion field for the further biomechanical modeling of the cerebrovascular wall. Methods: The whole motion cycle of the cerebral vasculature is modeled using a 4D B-spline transformation, which is estimated from a 4D to 2D + t image registration framework. The registration is performed by optimizing a single similarity metric between the entire 2D + t measured projection sequence and the corresponding forward projections of the deformed volume at their exact time instants. The joint use of two acceleration strategies, together with their implementation on graphics processing units, is also proposed so as to reach computation times close to clinical requirements. For further characterizing vessel wall properties, an approximation of the wall thickness changes is obtained through a strain calculation. Results: Evaluation on in silico and in vitro pulsating phantom aneurysms demonstrated an accurate estimation of wall motion curves. In general, the error was below 10% of the maximum pulsation, even in the situation when substantial inhomogeneous intensity pattern was present. Experiments on in vivo data provided realistic aneurysm and vessel wall motion estimates, whereas in regions where motion was neither visible nor anatomically possible, no motion was detected. The use of the acceleration strategies enabled completing the estimation process for one entire cycle in 5-10 min without degrading the overall performance. The strain map extracted from our motion estimation provided a realistic deformation measure of the vessel wall. Conclusions: The authors' technique has demonstrated that it can provide accurate and robust 4D estimates of cerebrovascular wall motion within a clinically acceptable time, although it has to be applied to a larger patient population prior to possible wide application to routine endovascular procedures. In particular, for the first time, this feasibility study has shown that in vivo cerebrovascular motion can be obtained intraprocedurally from a 3DRA acquisition. Results have also shown the potential of performing strain analysis using this imaging modality, thus making possible for the future modeling of biomechanical properties of the vascular wall.

Morphodynamic analysis of cerebral aneurysm pulsation from time-resolved rotational angiography

This paper presents a technique to estimate and model patient-specific pulsatility of cerebral aneurysms over onecardiac cycle, using 3D rotational X-ray angiography (3DRA) acquisitions. Aneurysm pulsation is modeled as a time varying-spline tensor field representing the deformation applied to a reference volume image, thus producing the instantaneousmorphology at each time point in the cardiac cycle. The estimated deformation is obtained by matching multiple simulated projections of the deforming volume to their corresponding original projections. A weighting scheme is introduced to account for the relevance of each original projection for the selected time point. The wide coverage of the projections, together with the weighting scheme, ensures motion consistency in all directions. The technique has been tested on digital and physical phantoms that are realistic and clinically relevant in terms of geometry, pulsation and imaging conditions. Results from digital phantomexperiments demonstrate that the proposed technique is able to recover subvoxel pulsation with an error lower than 10% of the maximum pulsation in most cases. The experiments with the physical phantom allowed demonstrating the feasibility of pulsation estimation as well as identifying different pulsation regions under clinical conditions.

The Standard Biplot

Biplots are graphical displays of data matrices based on the decomposition of a matrix as the product of two matrices. Elements of these two matrices are used as coordinates for the rows and columns of the data matrix, with an interpretation of the joint presentation that relies on the properties of the scalar product. Because the decomposition is not unique, there are several alternative ways to scale the row and column points of the biplot, which can cause confusion amongst users, especially when software packages are not united in their approach to this issue. We propose a new scaling of the solution, called the standard biplot, which applies equally well to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. The standard biplot also handles data matrices with widely different levels of inherent variance. Two concepts taken from correspondence analysis are important to this idea: the weighting of row and column points, and the contributions made by the points to the solution. In the standard biplot one set of points, usually the rows of the data matrix, optimally represent the positions of the cases or sample units, which are weighted and usually standardized in some way unless the matrix contains values that are comparable in their raw form. The other set of points, usually the columns, is represented in accordance with their contributions to the low-dimensional solution. As for any biplot, the projections of the row points onto vectors defined by the column points approximate the centred and (optionally) standardized data. The method is illustrated with several examples to demonstrate how the standard biplot copes in different situations to give a joint map which needs only one common scale on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot readable. The proposal also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important.

Fiat Money, Intrinsic Properties, and Government Transaction Policy

Why do people coordinate on the use of valueless pieces of paper as generally accepted money? A possible answer is that these objects have intrinsic properties that make them better candidates to be used as media of exchange. Another answer stresses the fact that unconvertible fiat money will not easily appear unless there is a centralized institution that favors its use. The main objective of the paper is to analyze these questions. In order to do this, we take a model of commodity money in which fiat money does not play any significant role and modify it to examine under which circumstances fiat money might come to circulate as medium of exchange. Some of the results obtained from the model differ in a rather substantial way from previous related literature.

The evolution of conventions under incomplete information

We formulate an evolutionary learning process in the spirit ofYoung (1993a) for games of incomplete information. The process involves trembles. For many games, if the amount of trembling is small, play will be in accordance with the games' (semi-strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Further, often play will most of the time be in accordance with exactly one Bayesian equilibrium. This gives a selection among the Bayesian equilibria. For two specific games of economic interest wecharacterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as Chicken. The second is an incomplete information bilateral monopoly, which is also an extension to incompleteinformation of Nash's demand game, or a simple version ofthe so-called sealed bid double auction. For both gamesselection by evolutionary learning is in favor of Bayesianequilibria where some types of players fail to coordinate, such that the outcome is inefficient.

Optimal second-degree price discrimination and arbitrage: On the role of asymetric information among buyers

The traditional theory of monopolistic screening tackles individualself-selection but does not address the possibility that buyers couldform a coalition to coordinate their purchases and to reallocate thegoods. In this paper, we design the optimal sale mechanism which takesinto account both individual and coalition incentive compatibilityfocusing on the role of asymmetric information among buyers. We showthat when a coalition of buyers is formed under asymmetric information,the monopolist can do as well as when there is no coalition. Although inthe optimal sale mechanism marginal rates of substitution are notequalized across buyers (hence there exists room for arbitrage), theyfail to realize the gains from arbitrage because of the transaction costsin coalition formation generated by asymmetric information.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Fiat money, intrinsic properties and government transaction policy

Why do people coordinate on the use of valueless piecesof paper as generally accepted money? A possible answeris that these objects have intrinsic properties that make them better candidates to be used as media of exchange. Another answer stresses the fact that unconvertible fiat money will not easily appear unless there is a centralized institution that favors its use.The main objective of the paper is to analyze these questions. In order to do this, we take a model of commodity money in which fiat money does not play any significant role and modify it to examine under which circumstances fiat money might come to circulate as medium of exchange. Some of the results obtained from the model differ in a rather substantial way from previous related literature.

Extremal climatic states simulated by a 2-dimensional model Part II: Different climatic scenarios

Different climatic simulations have been obtained by using a 2-Dim horizontal energy balancemodel (EBM), which has been constrained to satisfy several extremal principles on dissipationand convection. Moreover, 2 different versions of the model with fixed and variable cloud-coverhave been used. The assumption of an extremal type of behaviour for the climatic system canacquire additional support depending on the similarities found with measured data for pastconditions as well as with usual projections for possible future scenarios