First-class features

Magdeburg, Univ., Fak. für Informatik, Diss., 2011von Sagar Sunkl

The Vampire and the FOOL

This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency

First-Class Subtypes

First class type equalities, in the form of generalized algebraic data types (GADTs), are commonly found in functional programs. However, first-class representations of other relations between types, such as subtyping, are not yet directly supported in most functional programming languages. We present several encodings of first-class subtypes using existing features of the OCaml language (made more convenient by the proposed modular implicits extension), show that any such encodings are interconvertible, and illustrate the utility of the encodings with several examples.Comment: In Proceedings ML 2017, arXiv:1905.0590

Quantum canonical tensor model and an exact wave function

Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints has structure functions, and provides an algebraically consistent way of discretizing the Dirac first-class constraint algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt scheme of quantization of the canonical tensor model; the ordering of operators in the constraints is determined without ambiguity by imposing Hermiticity and covariance on the constraints, and the commutation algebra of constraints takes essentially the same from as the classical Poisson algebra, i.e. is first-class. Thus one could consistently obtain, at least locally in the configuration space, wave functions of "universe" by solving the partial differential equations representing the constraints, i.e. the Wheeler-DeWitt equations for the quantum canonical tensor model. The unique wave function for the simplest non-trivial case is exactly and globally obtained. Although this case is far from being realistic, the wave function has a few physically interesting features; it shows that locality is favored, and that there exists a locus of configurations with features of beginning of universe.Comment: 17 pages. Section 2 expanded to include fuzzy-space interpretation, and other minor change

Subset Feature Learning for Fine-Grained Category Classification

Fine-grained categorisation has been a challenging problem due to small inter-class variation, large intra-class variation and low number of training images. We propose a learning system which first clusters visually similar classes and then learns deep convolutional neural network features specific to each subset. Experiments on the popular fine-grained Caltech-UCSD bird dataset show that the proposed method outperforms recent fine-grained categorisation methods under the most difficult setting: no bounding boxes are presented at test time. It achieves a mean accuracy of 77.5%, compared to the previous best performance of 73.2%. We also show that progressive transfer learning allows us to first learn domain-generic features (for bird classification) which can then be adapted to specific set of bird classes, yielding improvements in accuracy

Model-based learning of local image features for unsupervised texture segmentation

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images

Flow Equations for Non-BPS Extremal Black Holes

We exploit some common features of black hole and domain wall solutions of (super)gravity theories coupled to scalar fields and construct a class of stable extremal black holes that are non-BPS, but still can be described by first-order differential equations. These are driven by a "superpotential'', which replaces the central charge Z in the usual black hole potential. We provide a general procedure for finding this class and deriving the associated "superpotential''. We also identify some other cases which do not belong to this class, but show a similar behaviour.Comment: LaTeX, 21 pages, 2 figures. v2: reference added, JHEP versio

Patient-adapted and inter-patient ecg classification using neural network and gradient boosting

Heart disease diagnosis is an important non-invasive technique. Therefore, there exists an effort to increase the accuracy of arrhythmia classification based on ECG signals. In this work, we present a novel approach of heart arrhythmia detection. The model consists of two parts. The first part extracts important features from raw ECG signal using Auto-Encoder Neural Network. Extracted features obtained by Auto-Encoder represent an input for the second part of the model, the Gradient Boosting and Feedforward Neural Network classifiers. For comparison purposes, we evaluated our approach by using MIT-BIH ECG database and also following recommendations of the Association for the Advancement of Medical Instrumentation (AAMI) for ECG class labeling. We divided our experiment into two scenarios. The first scenario represents the classification task for the patient-adapted paradigm and the second one was dedicated to the inter-patient paradigm. We compared the measured results to the state-of-the-art methods and it shows that our method outperforms the state-of-the art methods in the Ventricular Ectopic (VEB) class for both paradigms and Supraventricular Ectopic (SVEB) class in the inter-patient paradigm.Web of Science28325424

On the BRST Quantization of the Massless Bosonic Particle in Twistor-Like Formulation

We study some features of bosonic particle path-integral quantization in a twistor-like approach by use of the BRST-BFV quantization prescription. In the course of the Hamiltonian analysis we observe links between various formulations of the twistor-like particle by performing a conversion of the Hamiltonian constraints of one formulation to another. A particular feature of the conversion procedure applied to turn the second-class constraints into the first-class constraints is that the simplest Lorentz-covariant way to do this is to convert a full mixed set of the initial first- and second-class constraints rather than explicitly extracting and converting only the second-class constraints. Another novel feature of the conversion procedure applied below is that in the case of the D=4 and D=6 twistor-like particle the number of new auxiliary Lorentz-covariant coordinates, which one introduces to get a system of first-class constraints in an extended phase space, exceeds the number of independent second-class constraints of the original dynamical system. We calculate the twistor-like particle propagator in D=3, 4 and 6 space-time dimensions and show, that it coincides with that of a conventional massless bosonic particle.Comment: LaTeX file, 17 page

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the corrections to many misprints of v1 and also the ones of the published version. The conceptual and technical parts of the paper are not altere