Photoacoustic Tomography in a Rectangular Reflecting Cavity

Almost all known image reconstruction algorithms for photoacoustic and thermoacoustic tomography assume that the acoustic waves leave the region of interest after a finite time. This assumption is reasonable if the reflections from the detectors and surrounding surfaces can be neglected or filtered out (for example, by time-gating). However, when the object is surrounded by acoustically hard detector arrays, and/or by additional acoustic mirrors, the acoustic waves will undergo multiple reflections. (In the absence of absorption they would bounce around in such a reverberant cavity forever). This disallows the use of the existing free-space reconstruction techniques. This paper proposes a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations.Comment: 21 pages, 6 figure

A fully automatic CAD-CTC system based on curvature analysis for standard and low-dose CT data

Computed tomography colonography (CTC) is a rapidly evolving noninvasive medical investigation that is viewed by radiologists as a potential screening technique for the detection of colorectal polyps. Due to the technical advances in CT system design, the volume of data required to be processed by radiologists has increased significantly, and as a consequence the manual analysis of this information has become an increasingly time consuming process whose results can be affected by inter- and intrauser variability. The aim of this paper is to detail the implementation of a fully integrated CAD-CTC system that is able to robustly identify the clinically significant polyps in the CT data. The CAD-CTC system described in this paper is a multistage implementation whose main system components are: 1) automatic colon segmentation; 2) candidate surface extraction; 3) feature extraction; and 4) classification. Our CAD-CTC system performs at 100% sensitivity for polyps larger than 10 mm, 92% sensitivity for polyps in the range 5 to 10 mm, and 57.14% sensitivity for polyps smaller than 5 mm with an average of 3.38 false positives per dataset. The developed system has been evaluated on synthetic and real patient CT data acquired with standard and low-dose radiation levels

On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?

Although it has been believed that the models with generalised Chaplygin gas do not contain singularities, in a previous work we have studied how a big freeze could take place in some kinds of phantom generalised Chaplygin gas. In the present work, we study some types of generalised Chaplygin gas in order to show how different sorts of singularities could appears in such models, in the future or in the past. We point out that: (i) singularities may not be originated from the phantom nature of the fluid, and (ii) if initially the tension of the brane in a brane-world Chaplygin model is large enough then an infrared cut off appears in the past.Comment: 19 pages, 6 figures. Discussion expanded and references added. Version to appear in the International Journal of Modern Physics

A probabilistic approach to reducing the algebraic complexity of computing Delaunay triangulations

Computing Delaunay triangulations in $\mathbb{R}^d$ involves evaluating the so-called in\_sphere predicate that determines if a point $x$ lies inside, on or outside the sphere circumscribing $d+1$ points $p_0,\ldots ,p_d$. This predicate reduces to evaluating the sign of a multivariate polynomial of degree $d+2$ in the coordinates of the points $x, \, p_0,\, \ldots,\, p_d$. Despite much progress on exact geometric computing, the fact that the degree of the polynomial increases with $d$ makes the evaluation of the sign of such a polynomial problematic except in very low dimensions. In this paper, we propose a new approach that is based on the witness complex, a weak form of the Delaunay complex introduced by Carlsson and de Silva. The witness complex $\mathrm{Wit} (L,W)$ is defined from two sets $L$ and $W$ in some metric space $X$: a finite set of points $L$ on which the complex is built, and a set $W$ of witnesses that serves as an approximation of $X$. A fundamental result of de Silva states that $\mathrm{Wit}(L,W)=\mathrm{Del} (L)$ if $W=X=\mathbb{R}^d$. In this paper, we give conditions on $L$ that ensure that the witness complex and the Delaunay triangulation coincide when $W$ is a finite set, and we introduce a new perturbation scheme to compute a perturbed set $L'$ close to $L$ such that $\mathrm{Del} (L')= \mathrm{wit} (L', W)$. Our perturbation algorithm is a geometric application of the Moser-Tardos constructive proof of the Lov\'asz local lemma. The only numerical operations we use are (squared) distance comparisons (i.e., predicates of degree 2). The time-complexity of the algorithm is sublinear in $|W|$. Interestingly, although the algorithm does not compute any measure of simplex quality, a lower bound on the thickness of the output simplices can be guaranteed.Comment: 24 page

The holographic induced gravity model with a Ricci dark energy: smoothing the little rip and big rip through Gauss-Bonnet effects?

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infra-red cutoff can describe the late-time acceleration of the universe. In addition, we show that the dimensionless holographic parameter is very important in characterising the DGP branches, and in determining the behaviour of the Ricci dark energy as well as the asymptotic behaviour of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantom-like behaviour with no big rip if the holographic parameter is strictly larger than 1/2. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.Comment: 11 pages, 8 figures. RevTex4-1. Comments and references added. Version accepted in PR

Functional and structural brain differences associated with mirror-touch synaesthesia

Observing touch is known to activate regions of the somatosensory cortex but the interpretation of this finding is controversial (e.g. does it reflect the simulated action of touching or the simulated reception of touch?). For most people, observing touch is not linked to reported experiences of feeling touch but in some people it is (mirror-touch synaesthetes). We conducted an fMRI study in which participants (mirror-touch synaesthetes, controls) watched movies of stimuli (face, dummy, object) being touched or approached. In addition we examined whether mirror touch synaesthesia is associated with local changes of grey and white matter volume in the brain using VBM (voxel-based morphometry). Both synaesthetes and controls activated the somatosensory system (primary and secondary somatosensory cortices, SI and SII) when viewing touch, and the same regions were activated (by a separate localiser) when feeling touch — i.e. there is a mirror system for touch. However, when comparing the two groups, we found evidence that SII seems to play a particular important role in mirror-touch synaesthesia: in synaesthetes, but not in controls, posterior SII was active for watching touch to a face (in addition to SI and posterior temporal lobe); activity in SII correlated with subjective intensity measures of mirror-touch synaesthesia (taken outside the scanner), and we observed an increase in grey matter volume within the SII of the synaesthetes' brains. In addition, the synaesthetes showed hypo-activity when watching touch to a dummy in posterior SII. We conclude that the secondary somatosensory cortex has a key role in this form of synaesthesia