Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Sharp LpL^p-LqL^q estimates for generalized kk-plane transforms

In this paper, optimal $L^p-L^q$ estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the $k$-plane transform. An important advance over previous work is that full $L^p-L^q$ estimates are obtained by methods which have traditionally yielded only restricted weak-type estimates. In the process, one is lead to make coercivity estimates for certain functionals on $L^p$ for $p < 1$.Comment: 23 pages; 1 figur

Hypothetical and Real Choice Differentially Activate Common Valuation Areas

Hypothetical reports of intended behavior are commonly used to draw conclusions about real choices. A fundamental question in decision neuroscience is whether the same type of valuation and choice computations are performed in hypothetical and real decisions. We investigated this question using functional magnetic resonance imaging while human subjects made real and hypothetical choices about purchases of consumer goods. We found that activity in common areas of the orbitofrontal cortex and the ventral striatum correlated with behavioral measures of the stimulus value of the goods in both types of decision. Furthermore, we found that activity in these regions was stronger in response to the stimulus value signals in the real choice condition. The findings suggest that the difference between real and hypothetical choice is primarily attributable to variations in the value computations of the medial orbitofrontal cortex and the ventral striatum, and not attributable to the use of different valuation systems, or to the computation of stronger stimulus value signals in the hypothetical condition

Operators for transforming kernels into quasi-local kernels that improve SVM accuracy

Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with di®erent characteristics and application domains, achieve very good results supported by statistical significance

Complexity transitions in global algorithms for sparse linear systems over finite fields

We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to changes in performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary to the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.Comment: 23 pages, 8 figure

Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown. New Method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP. Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data. Comparison with Existing Method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not. Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.Comment: 18 pages, 14 figure

NON-PARAMETRIC STATISTICAL APPROACH TO CORRECT SATELLITE RAINFALL DATA IN NEAR-REAL-TIME FOR RAIN BASED FLOOD NOWCASTING

Floods resulting from intense rainfall are one of the most disastrous hazards in many regions of the world since they contribute greatly to personal injury and to property damage mainly as a result of their ability to strike with little warning. The possibility to give an alert about a flooding situation at least a few hours before helps greatly to reduce the damage. Therefore, scores of flood forecasting systems have been developed during the past few years mainly at country level and regional level. Flood forecasting systems based only on traditional methods such as return period of flooding situations or extreme rainfall events have failed on most occasions to forecast flooding situations accurately because of changes on territory in recent years by extensive infrastructure development, increased frequency of extreme rainfall events over recent decades, etc. Nowadays, flood nowcasting systems or early warning systems which run on real- time precipitation data are becoming more popular as they give reliable forecasts compared to traditional flood forecasting systems. However, these kinds of systems are often limited to developed countries as they need well distributed gauging station networks or sophisticated surface-based radar systems to collect real-time precipitation data. In most of the developing countries and in some developed countries also, precipitation data from available sparse gauging stations are inadequate for developing representative aerial samples needed by such systems. As satellites are able to provide a global coverage with a continuous temporal availability, currently the possibility of using satellite-based rainfall estimates in flood nowcasting systems is being highly investigated. To contribute to the world's requirement for flood early warning systems, ITHACA developed a global scale flood nowcasting system that runs on near-real-time satellite rainfall estimates. The system was developed in cooperation with United Nations World Food Programme (WFP), to support the preparedness phase of the WFP like humanitarian assistance agencies, mainly in less developed countries. The concept behind this early warning system is identifying critical rainfall events for each hydrological basin on the earth with past rainfall data and using them to identify floodable rainfall events with real time rainfall data. The individuation of critical rainfall events was done with a hydrological analysis using 3B42 rainfall data which is the most accurate product of Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) dataset. These critical events have been stored in a database and when a rainfall event is found in real-time which is similar or exceeds the event in the database an alert is issued for the basin area. The most accurate product of TMPA (3B42) is derived by applying bias adjustments to real time rainfall estimates using rain gauge data, thus it is available for end-users 10-15 days after each calendar month. The real time product of TMPA (3B42RT) is released approximately 9 hours after real-time and lacks of such kind of bias adjustments using rain gauge data as rain gauge data are not available in real time. Therefore, to have reliable alerts it is very important to reduce the uncertainty of 3B42RT product before using it in the early warning system. For this purpose, a statistical approach was proposed to make near real- time bias adjustments for the near real time product of TMPA (3B42RT). In this approach the relationship between the bias adjusted rainfall data product (3B42) and the real-time rainfall data product (3B42RT) was analyzed on the basis of drainage basins for the period from January 2003 to December 2007, and correction factors were developed for each basin worldwide to perform near real-time bias adjusted product estimation from the real-time rainfall data product (3B42RT). The accuracy of the product was analyzed by comparing with gauge rainfall data from Bangladesh and it was found that the uncertainty of the product is less even than the most accurate product of TMPA dataset (3B42