Relationship between neural and hemodynamic signals during spontaneous activity studied with temporal kernel CCA

Functional magnetic resonance imaging (fMRI) based on the so-called blood oxygen level-dependent (BOLD) contrast is a powerful tool for studying brain function not only locally but also on the large scale. Most studies assume a simple relationship between neural and BOLD activity, in spite of the fact that it is important to elucidate how the “when” and “what” components of neural activity are correlated to the “where” of fMRI data. Here we conducted simultaneous recordings of neural and BOLD signal fluctuations in primary visual (V1) cortex of anesthetized monkeys. We explored the neurovascular relationship during periods of spontaneous activity by using temporal kernel canonical correlation analysis (tkCCA). tkCCA is a multivariate method that can take into account any features in the signals that univariate analysis cannot. The method detects filters in voxel space (for fMRI data) and in frequency–time space (for neural data) that maximize the neurovascular correlation without any assumption of a hemodynamic response function (HRF). Our results showed a positive neurovascular coupling with a lag of 4–5 s and a larger contribution from local field potentials (LFPs) in the γ range than from low-frequency LFPs or spiking activity. The method also detected a higher correlation around the recording site in the concurrent spatial map, even though the pattern covered most of the occipital part of V1. These results are consistent with those of previous studies and represent the first multivariate analysis of intracranial electrophysiology and high-resolution fMRI.     

Scale-dependent Planck mass and Higgs VEV from holography and functional renormalization

We compute the scale-dependence of the Planck mass and of the vacuum expectation value of the Higgs field using two very different renormalization group methods: a “holographic” procedure based on Einstein?s equations in five dimensions with matter confined to a 3-brane, and a “functional” procedure in four dimensions based on a Wilsonian momentum cutoff. Both calculations lead to very similar results, suggesting that the coupled theory approaches a non-trivial fixed point in the ultraviolet.     

Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a “relativity group” which is a one-parameter family of deformations of the standard Galilei group to the Newton–Hooke group which is a Wigner–?nönü contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn’s theorem and related results. Larmor’s theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the “Eisenhart” or “lightlike” lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdi?ka–Eardley–Nappi–Witten pp-wave solution of Einstein–Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi–Jackiw group.     

How random is a random vector?

Over 80 years ago Samuel Wilks proposed that the “generalized variance” of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the “Wilks standard deviation” –the square root of the generalized variance–is indeed the standard deviation of a random vector. We further establish that the “uncorrelation index” –a derivative of the Wilks standard deviation–is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: “randomness measures” and “independence indices” of random vectors. In turn, these general notions give rise to “randomness diagrams”—tangible planar visualizations that answer the question: How random is a random vector? The notion of “independence indices” yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.     

Preoperative localization of the sensorimotor area using independent component analysis of resting-state fMRI

Analysis of resting-state functional magnetic resonance imaging (fMRI) data is based on detecting low-frequency signal fluctuations in functionally connected brain areas. These synchronous fluctuations in resting-state networks have been observed in several studies with healthy subjects. In this study, we explored if independent component analysis (ICA) can be used to localize the sensorimotor area from resting-state fMRI data in patients with brain tumors. Finger-tapping activation task and resting-state blood-oxygenation-level-dependent fMRI data were acquired from 8 patients with brain tumors and 10 healthy volunteers. Sensorimotor task independent components (IC_task) were used to verify resting-state independent components (IC_rest) individually. In addition, sensorimotor IC_rests were compared between the groups and no significant differences were detected in volume, spatial correlation or temporal correlation. These results show that it is possible to localize a sensorimotor area from resting-state data using ICA in patients with brain tumors. This offers a complementary method for assessing the sensorimotor area in subjects with brain tumors who have difficulties in performing motor paradigms.     

Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.     

In contrast to BOLD: signal enhancement by extravascular water protons as an alternative mechanism of endogenous fMRI signal change

Despite the popularity and widespread application of functional magnetic resonance imaging (fMRI) in recent years, the physiological bases of signal change are not yet fully understood. Blood oxygen level-dependant (BOLD) contrast — attributed to local changes in blood flow and oxygenation, and therefore magnetic susceptibility — has become the most prevalent means of functional neuroimaging. However, at short echo times, spin-echo sequences show considerable deviations from the BOLD model, implying a second, non-BOLD component of signal change. This has been dubbed “signal enhancement by extravascular water protons” (SEEP) and is proposed to result from proton-density changes associated with cellular swelling. Given that such changes are independent of magnetic susceptibility, SEEP may offer new and improved opportunities for carrying out fMRI in regions with close proximity to air–tissue and/or bone–tissue interfaces (e.g., the prefrontal cortex and spinal cord), as well as regions close to large blood vessels, which may not be ideally suited for BOLD imaging. However, because of the interdisciplinary nature of the literature, there has yet to be a thorough synthesis, tying together the various and sometimes disparate aspects of SEEP theory. As such, we aim to provide a concise yet comprehensive overview of SEEP, including recent and compelling evidence for its validity, its current applications and its future relevance to the rapidly expanding field of functional neuroimaging. Before presenting the evidence for a non-BOLD component of endogenous functional contrast, and to enable a more critical review for the nonexpert reader, we begin by reviewing the fundamental principles underlying BOLD theory.     

A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging

Granger causality model (GCM) derived from multivariate vector autoregressive models of data has been employed to identify effective connectivity in the human brain with functional magnetic resonance imaging (fMRI) and to reveal complex temporal and spatial dynamics underlying a variety of cognitive processes. In the most recent fMRI effective connectivity measures, pair-wise GCM has commonly been applied based on single-voxel values or average values from special brain areas at the group level. Although a few novel conditional GCM methods have been proposed to quantify the connections between brain areas, our study is the first to propose a viable standardized approach for group analysis of fMRI data with GCM. To compare the effectiveness of our approach with traditional pair-wise GCM models, we applied a well-established conditional GCM to preselected time series of brain regions resulting from general linear model (GLM) and group spatial kernel independent component analysis of an fMRI data set in the temporal domain. Data sets consisting of one task-related and one resting-state fMRI were used to investigate connections among brain areas with the conditional GCM method. With the GLM-detected brain activation regions in the emotion-related cortex during the block design paradigm, the conditional GCM method was proposed to study the causality of the habituation between the left amygdala and pregenual cingulate cortex during emotion processing. For the resting-state data set, it is possible to calculate not only the effective connectivity between networks but also the heterogeneity within a single network. Our results have further shown a particular interacting pattern of default mode network that can be characterized as both afferent and efferent influences on the medial prefrontal cortex and posterior cingulate cortex. These results suggest that the conditional GCM approach based on a linear multivariate vector autoregressive model can achieve greater accuracy in detecting network connectivity than the widely used pair-wise GCM, and this group analysis methodology can be quite useful to extend the information obtainable in fMRI.     

Regional homogeneity of resting-state fMRI contributes to both neurovascular and task activation variations

The task induced blood oxygenation level dependent signal changes observed using functional magnetic resonance imaging (fMRI) are critically dependent on the relationship between neuronal activity and hemodynamic response. Therefore, understanding the nature of neurovascular coupling is important when interpreting fMRI signal changes evoked via task. In this study, we used regional homogeneity (ReHo), a measure of local synchronization of the BOLD time series, to investigate whether the similarities of one voxel with the surrounding voxels are a property of neurovascular coupling. FMRI scans were obtained from fourteen subjects during bilateral finger tapping (FTAP), digit–symbol substitution (DSST) and periodic breath holding (BH) paradigm. A resting-state scan was also obtained for each of the subjects for 4 min using identical imaging parameters. Inter-voxel correlation analyses were conducted between the resting-state ReHo, resting-state amplitude of low frequency fluctuations (ALFF), BH responses and task activations within the masks related to task activations. There was a reliable mean voxel-wise spatial correlation between ReHo and other neurovascular variables (BH responses and ALFF). We observed a moderate correlation between ReHo and task activations (FTAP: r = 0.32; DSST: r = 0.22) within the task positive network and a small yet reliable correlation within the default mode network (DSST: r = − 0.08). Subsequently, a linear regression was used to estimate the contribution of ReHo, ALFF and BH responses to the task activated voxels. The unique contribution of ReHo was minimal. The results suggest that regional synchrony of the BOLD activity is a property that can explain the variance of neurovascular coupling and task activations; but its contribution to task activations can be accounted for by other neurovascular factors such as the ALFF.     

Un-graviton corrections to the Schwarzschild black hole

We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation   of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension dU$d_U$.     

Overwriting information: Correlations,physical costs,and environment models

In this sequel to our previous study of the entropic and energetic costs of information erasure [N.G. Anderson, Phys. Lett. A 372 (2008) 5552], we consider direct overwriting of classical information encoded in a quantum-mechanical memory system interacting with a heat bath. Lower bounds on physical costs of overwriting – in both “single-shot” and “sequential” overwriting scenarios – are obtained from globally unitary quantum dynamics and entropic inequalities alone, all within a referential approach that grounds information content in correlations between physical system states. A heterogeneous environment model, required for consistent treatment of sequential overwriting, is introduced and used to establish and relate bounds for various cases.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Supermodels for early LHC

We investigate which new physics signatures could be discovered in the first year of the LHC, beyond the expected sensitivity of the Tevatron data by the end of 2010. We construct “supermodels”, for which the LHC sensitivity even with only 10 pb⁻¹ useful luminosity is greater than that of the Tevatron with 10 fb⁻¹. The simplest supermodels involve s  -channel resonances in the quark–antiquark and especially in the quark–quark channels. We concentrate on easily visible final states with small standard model backgrounds, and find that there are simple searches, besides those for Z^′$Z^{\prime }$ states, which could discover new physics in early LHC data. Many of these are well-suited to test searches for “more conventional” models, often discussed for multi-fb⁻¹ data sets.     

Is BTZ a separate superselection sector of CTMG?

We exhibit exact solutions of (positive) matter coupled to original “wrong G-sign” cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate “superselection” sector, one that unlike in GR, is not reachable by physical sources.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Introducing a Green–Volterra series formalism to solve weakly nonlinear boundary problems: Application to Kirchhoff's string

This paper introduces a formalism which extends that of “Green's function” and that of “the Volterra series”. These formalisms are typically used to solve, respectively, linear inhomogeneous space–time differential equations in physics and weakly nonlinear time-differential input-to-output systems in automatic control. While Green's function is a space–time integral kernel which fully characterizes a linear problem, the Volterra series expansions involve a sequence of multi-variate time integral kernels (of convolution type for time-invariant systems). The extension proposed here consists in combining the two approaches, by introducing a series expansion based on multi-variate space–time integral kernels. This series allows the representation of the space–time solution of weakly nonlinear boundary problems excited by an “input” which depends on space and time.     

Separating 4D multi-task fMRI data of multiple subjects by independent component analysis with projection

Independent component analysis (ICA) is a widely accepted method to extract brain networks underlying cognitive processes from functional magnetic resonance imaging (fMRI) data. However, the application of ICA to multi-task fMRI data is limited due to the potential non-independency between task-related components. The ICA with projection (ICAp) method proposed by our group (Hum Brain Mapp 2009;30:417–31) is demonstrated to be able to solve the interactions among task-related components for single subject fMRI data. However, it still must be determined if ICAp is capable of processing multi-task fMRI data over a group of subjects. Moreover, it is unclear whether ICAp can be reliably applied to event-related (ER) fMRI data. In this study, we combined the projection method with the temporal concatenation method reported by Calhoun (Hum Brain Mapp 2008;29:828–38), referred to as group ICAp, to perform the group analysis of multi-task fMRI data. Both a human fMRI rest data-based simulation and real fMRI experiments, of block design and ER design, verified the feasibility and reliability of group ICAp, as well as demonstrated that ICAp had the strength to separate 4D multi-task fMRI data into multiple brain networks engaged in each cognitive task and to adequately find the commonalities and differences among multiple tasks.     

Comparison of the performance of different tools for fast simulation of ultrasound data

Simulation of ultrasound data is often performed for developing new ultrasound data processing techniques. The spatial impulse response method (as implemented in FieldII) has typically been used as the gold standard due to its excellent accuracy in the linear domain. When scatterer numbers become significant and when 3D volumetric data sets need to be computed, calculation time can become an issue however. In order to solve this problem, two alternative methods have recently been proposed both of which are based on the principle of convolving a set of point scatterers with a point spread function. “FUSK” operates in the frequency domain while “COLE” runs in the spatio-temporal domain. The aim of this study was to directly contrast both methodologies in terms of accuracy and processing speed using FieldII as a reference.