Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are correcte

Artificial Intelligence in Material Engineering: A review on applications of AI in Material Engineering

Recently, there has been extensive use of artificial Intelligence (AI) in the field of material engineering. This can be attributed to the development of high performance computing and thereby feasibility to test deep learning models with large parameters. In this article we tried to review some of the latest developments in the applications of AI in material engineering.Comment: V

Design of a 3D-printed soft robotic hand with distributed tactile sensing for multi-grasp object identification

Tactile object identification is essential in environments where vision is occluded or when intrinsic object properties such as weight or stiffness need to be discriminated between. The robotic approach to this task has traditionally been to use rigid-bodied robots equipped with complex control schemes to explore different objects. However, whilst varying degrees of success have been demonstrated, these approaches are limited in their generalisability due to the complexity of the control schemes required to facilitate safe interactions with diverse objects. In this regard, Soft Robotics has garnered increased attention in the past decade due to the ability to exploit Morphological Computation through the agent's body to simplify the task by conforming naturally to the geometry of objects being explored. This exists as a paradigm shift in the design of robots since Soft Robotics seeks to take inspiration from biological solutions and embody adaptability in order to interact with the environment rather than relying on centralised computation. In this thesis, we formulate, simplify, and solve an object identification task using Soft Robotic principles. We design an anthropomorphic hand that has human-like range of motion and compliance in the actuation and sensing. The range of motion is validated through the Feix GRASP taxonomy and the Kapandji Thumb Opposition test. The hand is monolithically fabricated using multi-material 3D printing to enable the exploitation of different material properties within the same body and limit variability between samples. The hand's compliance facilitates adaptable grasping of a wide range of objects and features integrated distributed tactile sensing. We emulate the human approach of integrating information from multiple contacts and grasps of objects to discriminate between them. Two bespoke neural networks are designed to extract patterns from both the tactile data and the relationships between grasps to facilitate high classification accuracy

Bootstrapping Scattering Amplitudes in Effective Field Theories

The modern approach to scattering amplitudes has provided a plethora of techniques that allow us to circumvent Lagrangians and Feynman rules. The bootstrap of amplitudes in quantum field theories allows us to study the landscape of effective field theories. In this dissertation, we apply the amplitudes bootstrap to address a series of questions: 1) We exploit Goldstone soft theorems and supersymmetry to study EFTs that result from spontaneous symmetry-breaking and their supersymmetrizations. 2) Using methods of generalized unitarity, we construct a certain class of all-multiplicity 1-loop amplitudes in Born-Infeld theory. 3) These 1-loop results coupled with an assumption of tree-like factorization allow us to show that electromagnetic duality may be non-anomalous at 1-loop in Born-Infeld theory. 4) We introduce a novel formalism to double-copy scattering amplitudes with massive states along with spectral conditions that ensure that the resulting double-copy is local.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168100/1/shrpar_1.pd

Video Sequence Alignment

The task of aligning multiple audio visual sequences with similar contents needs careful synchronisation in both spatial and temporal domains. It is a challenging task due to a broad range of contents variations, background clutter, occlusions, and other factors. This thesis is concerned with aligning video contents by characterising the spatial and temporal information embedded in the high-dimensional space. To that end a three- stage framework is developed, involving space-time representation of video clips with local linear coding, followed by their alignment in the manifold embedded space. The first two stages present a video representation techniques based on local feature extraction and linear coding methods. Firstly, the scale invariant feature transform (SIFT) is extended to extract interest points not only from the spatial plane but also from the planes along the space-time axis. Locality constrained coding is then incorporated to project each descriptor into a local coordinate system produced by a pooling technique. Human action classification benchmarks are adopted to evaluate these two stages, comparing their performance against existing techniques. The results shows that space-time extension of SIFT with a linear coding scheme outperforms most of the state-of-the-art approaches on the action classification task owing to its ability to represent complex events in video sequences. The final stage presents a manifold learning algorithm with spatio-temporal constraints to embed a video clip in a lower dimensional space while preserving the intrinsic geometry of the data. The similarities observed between frame sequences are captured by defining two types of correlation graphs: an intra-correlation graph within a single video sequence and an inter-correlation graph between two sequences. A video retrieval and ranking tasks are designed to evaluate the manifold learning stage. The experimental outcome shows that the approach outperforms the conventional techniques in defining similar video contents and capture the spatio-temporal correlations between them

Ab initio machine learning in chemical compound space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first principles based virtual sampling of this space, for example in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest sub-sets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an {\em ab initio} view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics

Subjecthood and argument structure

This book reconsiders the role of order and structure in syntax, focusing on fundamental issues such as word order and grammatical functions. The first group of papers in the collection asks what word order can tell us about syntactic structure, using evidence from V2, object shift, word order gaps and different kinds of movement. The second group of papers all address the issue of subjecthood in some way, and examine how certain subject properties vary across languages: expression of subjects, expletive subjects, quirky and locative subjects. All of the papers address in some way the tension between modelling what can vary across languages whilst improving our understanding of what might be universal to human language