Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late

Gesture Recognition in Robotic Surgery: a Review

OBJECTIVE: Surgical activity recognition is a fundamental step in computer-assisted interventions. This paper reviews the state-of-the-art in methods for automatic recognition of fine-grained gestures in robotic surgery focusing on recent data-driven approaches and outlines the open questions and future research directions. METHODS: An article search was performed on 5 bibliographic databases with combinations of the following search terms: robotic, robot-assisted, JIGSAWS, surgery, surgical, gesture, fine-grained, surgeme, action, trajectory, segmentation, recognition, parsing. Selected articles were classified based on the level of supervision required for training and divided into different groups representing major frameworks for time series analysis and data modelling. RESULTS: A total of 52 articles were reviewed. The research field is showing rapid expansion, with the majority of articles published in the last 4 years. Deep-learning-based temporal models with discriminative feature extraction and multi-modal data integration have demonstrated promising results on small surgical datasets. Currently, unsupervised methods perform significantly less well than the supervised approaches. CONCLUSION: The development of large and diverse open-source datasets of annotated demonstrations is essential for development and validation of robust solutions for surgical gesture recognition. While new strategies for discriminative feature extraction and knowledge transfer, or unsupervised and semi-supervised approaches, can mitigate the need for data and labels, they have not yet been demonstrated to achieve comparable performance. Important future research directions include detection and forecast of gesture-specific errors and anomalies. SIGNIFICANCE: This paper is a comprehensive and structured analysis of surgical gesture recognition methods aiming to summarize the status of this rapidly evolving field

Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case

In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.Comment: 37 pages, 4 figures. Presentation improved, typos corrected. Published in Journal Of Statistical Mechanic

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Constraint-Based Monitoring of Hyperproperties

Verifying hyperproperties at runtime is a challenging problem as hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other. It is necessary to store previously seen traces, because every new incoming trace needs to be compatible with every run of the system observed so far. Furthermore, the new incoming trace poses requirements on future traces. In our monitoring approach, we focus on those requirements by rewriting a hyperproperty in the temporal logic HyperLTL to a Boolean constraint system. A hyperproperty is then violated by multiple runs of the system if the constraint system becomes unsatisfiable. We compare our implementation, which utilizes either BDDs or a SAT solver to store and evaluate constraints, to the automata-based monitoring tool RVHyper

Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

Hamiltonians separable in cartesian coordinates and third-order integrals of motion

We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy

Development, Validation, and Modelling of Image Guidance Systems for Surgery

Image guidance systems for surgery enable the surgeon to make use of information from various sources during surgery. Such systems have the potential to improve outcomes for patients by allowing the surgeon to easily assimilate prior knowledge from pre-operative clinical scans as well as novel intra-operative imaging techniques. A key challenge is how to filter and process this information to allow it to be presented in an accurate, timely, and intuitive manner. Badly designed or poorly understood image guidance systems risk distracting the surgeon with irrelevant or incorrect information, leading to patient harm. The aim of my research is to develop tools to better quantify the performance of surgical image guidance systems, and measure how the system performance affects patient outcomes. I will present the results of my work developing the “SmartLiver”[1] image guidance system for minimally invasive liver surgery. I will follow this with a proposal for a generalised model of image guidance systems as multi input control systems