Euler Integration of Gaussian Random Fields and Persistent Homology

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.Comment: 21 pages, 1 figur

Binary Adaptive Semi-Global Matching Based on Image Edges

Image-based modeling and rendering is currently one of the most challenging topics in Computer Vision and Photogrammetry. The key issue here is building a set of dense correspondence points between two images, namely dense matching or stereo matching. Among all dense matching algorithms, Semi-Global Matching (SGM) is arguably one of the most promising algorithms for real-time stereo vision. Compared with global matching algorithms, SGM aggregates matching cost from several (eight or sixteen) directions rather than only the epipolar line using Dynamic Programming (DP). Thus, SGM eliminates the classical “streaking problem” and greatly improves its accuracy and efficiency. In this paper, we aim at further improvement of SGM accuracy without increasing the computational cost. We propose setting the penalty parameters adaptively according to image edges extracted by edge detectors. We have carried out experiments on the standard Middlebury stereo dataset and evaluated the performance of our modified method with the ground truth. The results have shown a noticeable accuracy improvement compared with the results using fixed penalty parameters while the runtime computational cost was not increased

Automatic balancing device Patent

Automatic balancing device for use on frictionless supported attitude-controlled test platform

Infrared scanner Patent

Infrared scanning system for maintaining spacecraft orientation with earth referenc

On the Validity and Applicability of Models of Negative Capacitance and Implications for MOS Applications

The observation of room temperature sub-60 mV/dec subthreshold slope (SS) in MOSFETs with ferroelectric (FE) layers in the gate stacks or in series with the gate has attracted much attention. Recently, we modeled this effect in the framework of a FE polarization switching model. However, there is a large amount of literature attributing this effect to a stabilization of quasi-static (QS) negative capacitance (NC) in the FE. The technological implications of a stabilized non-switching (NS) QSNC model vs a FE switching model are vastly different; the latter precluding applications to sub-60 mV/dec SS scaled CMOS due to speed limitations and power dissipated in switching. In this letter, we provide a thorough analysis assessing the foundations of models of QSNC, identifying which specific assumptions (ansatz) may be unlikely or unphysical, and analyzing their applicability. We show that it is not reasonable to expect QSNC for two separate capacitors connected in series (with a metal plate between dielectric (DE) and FE layers). We propose a model clarifying under which conditions a QS "apparent NC" for a FE layer in a FE-DE bi-layer stack may be observed, quantifying the requirements of strong interface polarization coupling in addition to capacitance matching. In this regime, our model suggests the FE layer does not behave as a NC layer, simply, the coupling leads to both the DE and FE behaving as high-k DE with similar permittivities. This may be useful for scaled EOT devices but does not lead to sub-60 mV/dec SS.Comment: Version published in Appl. Phys. Let

O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles

We present an analytical derivation of the winding number counting topological defects created by an O(N) symmetry-breaking quantum quench in N spatial dimensions. Our approach is universal in the sense that we do not employ any approximations apart from the large-$N$ limit. The final result is nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in 1/N, and we obtain far less topological defects than quasiparticle excitations, in sharp distinction to previous, low-dimensional investigations.Comment: 6 pages of RevTex4-1, 1 figure; to be published in Physical Review

Intra- and Extra-articular Features of Temporomandibular Joint Ankylosis in the Cat (Felis catus).

Temporomandibular joint (TMJ) ankylosis is an uncommon clinical entity in human and veterinary medicine. However, the condition is severely debilitating and is life-limiting if not treated. This study sought to characterize the intra- and extra-articular features of naturally occurring TMJ ankylosis in cats. TMJs from client-owned cats (n = 5) that underwent bilateral TMJ gap arthroplasty were examined and compared with TMJs from healthy, age-matched feline cadavers (n = 2) by cone-beam computed tomography (CBCT), micro-computed tomography (μCT) and histologically. Features of bilateral intra- and extra-articular ankylosis compounded by degenerative joint lesions were identified radiographically and histologically in all affected cats. Features of TMJ 'true' ankylosis included variable intracapsular fibro-osseous bridging, degeneration of the disc and the articular surfaces, narrowing of the joint space and flattening of the condylar process of the mandible. Extra-articular features of TMJ ankylosis included periarticular bone formation and fibro-osseous bridging between the mandible, zygomatic arch and coronoid process. In addition, subchondral bone loss or sclerosis, irregular and altered joint contours and irregularly increased density of the medullary bone characterized the degenerative changes of the osseous components of the TMJ. Complex radiological and histological features of both ankylosis and pseudoankylosis were identified that clinically manifested in complete inability to open the mouth

Topology of the three-qubit space of entanglement types

The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states, and hence describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R^6, which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.Comment: 9 pages, 3 figures, v2 adds a referenc

Differences in client and therapist views of the working alliance in drug treatment

Background - There is growing evidence that the therapeutic alliance is one of the most consistent predictors of retention and outcomes in drug treatment. Recent psychotherapy research has indicated that there is a lack of agreement between client, therapist and observer ratings of the therapeutic alliance; however, the clinical implications of this lack of consensus have not been explored. Aims - The aims of the study are to (1) explore the extent to which, in drug treatment, clients and counsellors agree in their perceptions of their alliance, and (2) investigate whether the degree of disagreement between clients and counsellors is related to retention in treatment. Methods - The study recruited 187 clients starting residential rehabilitation treatment for drug misuse in three UK services. Client and counsellor ratings of the therapeutic alliance (using the WAI-S) were obtained during weeks 1-12. Retention was in this study defined as remaining in treatment for at least 12 weeks. Results - Client and counsellor ratings of the alliance were only weakly related (correlations ranging from r = 0.07 to 0.42) and tended to become more dissimilar over the first 12 weeks in treatment. However, whether or not clients and counsellors agreed on the quality of their relationship did not influence whether clients were retained in treatment. Conclusions - The low consensus between client and counsellor views of the alliance found in this and other studies highlights the need for drug counsellors to attend closely to their clients' perceptions of the alliance and to seek regular feedback from clients regarding their feelings about their therapeutic relationship

Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities

We study structure, eigenvalue spectra and diffusion dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue equal 2 of the Laplacian. We corroborate the results with simulations of the random walk on several types of networks. Our results for the distribution of return-time of the walk to the origin (autocorrelator) agree well with recent analytical solution for trees, and it appear to be independent on their mesoscopic and global structure. For the cyclic graphs we find new results with twice larger stretching exponent of the tail of the distribution, which is virtually independent on the size of cycles. The modularity and clustering contribute to a power-law decay at short return times