Multivariate Residues and Maximal Unitarity

We extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number of fermions and scalars in the adjoint representation. Deca-cuts realized by replacement of real slice integration contours by higher-dimensional tori encircling the global poles are used to factorize the planar triple box onto a product of trees. We apply computational algebraic geometry and multivariate complex analysis to derive unique projectors for all master integral coefficients and obtain compact analytic formulae in terms of tree-level data.Comment: 34 pages, 3 figure

An Image Understanding System for Detecting Indoor Features

The capability of identifying physical structures of an unknown environment is very important for vision based robot navigation and scene understanding. Among physical structures in indoor environments, corridor lines and doors are important visual landmarks for robot navigation since they show the topological structure in an indoor environment and establish connections among the different places or regions in the indoor environment. Furthermore, they provide clues for understanding the image. In this thesis, I present two algorithms to detect the vanishing point, corridor lines, and doors respectively using a single digital video camera. In both algorithms, we utilize a hypothesis generation and verification method to detect corridor and door structures using low level linear features. The proposed method consists of low, intermediate, and high level processing stages which correspond to the extraction of low level features, the formation of hypotheses, and verification of the hypotheses via seeking evidence actively. In particular, we extend this single-pass framework by employing a feedback strategy for more robust hypothesis generation and verification. We demonstrate the robustness of the proposed methods on a large number of real video images in a variety of corridor environments, with image acquisitions under different illumination and reflection conditions, with different moving speeds, and with different viewpoints of the camera. Experimental results performed on the corridor line detection algorithm validate that the method can detect corridor line locations in the presence of many spurious line features about one second. Experimental results carried on the door detection algorithm show that the system can detect visually important doors in an image with a very high accuracy rate when a robot navigates along a corridor environment

Distributed scene reconstruction from multiple mobile platforms

Recent research on mobile robotics has produced new designs that provide house-hold robots with omnidirectional motion. The image sensor embedded in these devices motivates the application of 3D vision techniques on them for navigation and mapping purposes. In addition to this, distributed cheapsensing systems acting as unitary entity have recently been discovered as an efficient alternative to expensive mobile equipment. In this work we present an implementation of a visual reconstruction method, structure from motion (SfM), on a low-budget, omnidirectional mobile platform, and extend this method to distributed 3D scene reconstruction with several instances of such a platform. Our approach overcomes the challenges yielded by the plaform. The unprecedented levels of noise produced by the image compression typical of the platform is processed by our feature filtering methods, which ensure suitable feature matching populations for epipolar geometry estimation by means of a strict quality-based feature selection. The robust pose estimation algorithms implemented, along with a novel feature tracking system, enable our incremental SfM approach to novelly deal with ill-conditioned inter-image configurations provoked by the omnidirectional motion. The feature tracking system developed efficiently manages the feature scarcity produced by noise and outputs quality feature tracks, which allow robust 3D mapping of a given scene even if - due to noise - their length is shorter than what it is usually assumed for performing stable 3D reconstructions. The distributed reconstruction from multiple instances of SfM is attained by applying loop-closing techniques. Our multiple reconstruction system merges individual 3D structures and resolves the global scale problem with minimal overlaps, whereas in the literature 3D mapping is obtained by overlapping stretches of sequences. The performance of this system is demonstrated in the 2-session case. The management of noise, the stability against ill-configurations and the robustness of our SfM system is validated on a number of experiments and compared with state-of-the-art approaches. Possible future research areas are also discussed

Robust pre-processing techniques for non-ideal iris images

The human iris has been demonstrated to be a very accurate, non-invasive and easy-to-use biometric for personal identification. Most of the current state-of-the-art iris recognition systems require the iris acquisition to be ideal. A lot of constraints are hence put on the user and the acquisition process.;Our aim in this research is to relax these conditions and to develop a pre-processing algorithm, which can be used in conjunction with any matching algorithm to handle the so-called non-ideal iris images. In this thesis we present a few robust techniques to process the non-ideal iris images so as to give a segmented iris image to the matching algorithm. The motivation behind this work is to reduce the false reject rates of the current recognition systems and to reduce the intra-class variability. A new technique for estimating and compensating the angle in non-frontal iris images is presented. We have also developed a novel segmentation algorithm, which uses an ellipse-fitting approach for localizing the pupil. A fast and simple limbus boundary segmentation algorithm is also presented

Measurement-Induced Phase Transitions in the Dynamics of Entanglement

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$ for each degree of freedom, we show that the system has two dynamical phases: `entangling' and `disentangling'. The former occurs for $p$ smaller than a critical rate $p_c$, and is characterized by volume-law entanglement in the steady-state and `ballistic' entanglement growth after a quench. By contrast, for $p > p_c$ the system can sustain only area-law entanglement. At $p = p_c$ the steady state is scale-invariant and, in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth R\'{e}nyi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher R\'{e}nyi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains, and show that the phenomenology of the two phases is similar to that of the toy model, but with distinct `quantum' critical exponents, which we calculate numerically in $1+1$D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.Comment: 17+4 pages, 16 figures; updated discussion and results for mutual information; graphics error fixe

Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters