Warped products and Spaces of Constant Curvature

We will obtain the warped product decompositions of spaces of constant curvature (with arbitrary signature) in their natural models as subsets of pseudo-Euclidean space. This generalizes the corresponding result by S. Nolker to arbitrary signatures, and has a similar level of detail. Although our derivation is complete in some sense, none is proven. Motivated by applications, we will give more information for the spaces with Euclidean and Lorentzian signatures. This is an expository article which is intended to be used as a reference. So we also give a review of the theory of circles and spheres in pseudo-Riemannian manifolds

Concircular tensors in Spaces of Constant Curvature: With Applications to Orthogonal Separation of The Hamilton-Jacobi Equation

We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic Hamilton-Jacobi equation are called separable. Specifically for spaces of constant curvature, we obtain canonical forms of concircular tensors modulo the action of the isometry group, we obtain the separable coordinates induced by irreducible concircular tensors, and we obtain warped products adapted to reducible concircular tensors. Using these results, we show how to enumerate the isometrically inequivalent orthogonal separable coordinates, construct the transformation from separable to Cartesian coordinates, and execute the Benenti-Eisenhart-Kalnins-Miller (BEKM) separation algorithm for separating natural Hamilton-Jacobi equations.Comment: Removed preamble and references to unpublished articles. Also made some minor changes in the bod

Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature

We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tensor, hereafter called a concircular tensor. First, we show how to extend original results given by Benenti to intrinsically characterize all (orthogonal) separable coordinates in spaces of constant curvature using concircular tensors. This results in the construction of a special class of separable coordinates known as Kalnins-Eisenhart-Miller coordinates. Then we present the Benenti-Eisenhart-Kalnins-Miller separation algorithm, which uses concircular tensors to intrinsically search for Kalnins-Eisenhart-Miller coordinates which separate a given natural Hamilton-Jacobi equation. As a new application of the theory, we show how to obtain the separable coordinate systems in the two dimensional spaces of constant curvature, Minkowski and (Anti-)de Sitter space. We also apply the Benenti-Eisenhart-Kalnins-Miller separation algorithm to study the separability of the three dimensional Calogero-Moser and Morosi-Tondo systems

Noise Flooding for Detecting Audio Adversarial Examples Against Automatic Speech Recognition

Neural models enjoy widespread use across a variety of tasks and have grown to become crucial components of many industrial systems. Despite their effectiveness and extensive popularity, they are not without their exploitable flaws. Initially applied to computer vision systems, the generation of adversarial examples is a process in which seemingly imperceptible perturbations are made to an image, with the purpose of inducing a deep learning based classifier to misclassify the image. Due to recent trends in speech processing, this has become a noticeable issue in speech recognition models. In late 2017, an attack was shown to be quite effective against the Speech Commands classification model. Limited-vocabulary speech classifiers, such as the Speech Commands model, are used quite frequently in a variety of applications, particularly in managing automated attendants in telephony contexts. As such, adversarial examples produced by this attack could have real-world consequences. While previous work in defending against these adversarial examples has investigated using audio preprocessing to reduce or distort adversarial noise, this work explores the idea of flooding particular frequency bands of an audio signal with random noise in order to detect adversarial examples. This technique of flooding, which does not require retraining or modifying the model, is inspired by work done in computer vision and builds on the idea that speech classifiers are relatively robust to natural noise. A combined defense incorporating 5 different frequency bands for flooding the signal with noise outperformed other existing defenses in the audio space, detecting adversarial examples with 91.8% precision and 93.5% recall.Comment: Orally presented at the 18th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT) in Louisville, Kentucky, USA, December 2018. 5 pages, 2 figure

Kasabach-Merritt syndrome arising from an Enteroatmospheric Fistula

Kasabach-Merritt syndrome (KMS) is a rare, life-threatening condition that is characterized by profound thrombocytopenia, hypofibrinogenemia, elevated partial thromboplastin time, and may also be associated with microangiopathic hemolytic anemia. It is well established that this phenomenon is notably associated with the vascular tumors kaposiform hemangioendothelioma and tufted angioma; however, recent literature has suggested its presence in the settings of various vascular malformations (i.e. without neoplastic proliferation of endothelial cells). This report focuses on a patient in the first year of life, who experienced a chronic, consumptive coagulopathy in the setting of a highly vascular enteroatmospheric fistula. Sharing many features with the aforementioned syndrome, this anomaly suggests a novel association of the Kasabach-Merritt phenomenon with a unique vascular malformation. Although potentially lethal, Kasabach-Merritt syndrome can resolve with appropriate diagnosis and management; uncovering new associations can help to improve recognition and treatment in future cases