Local energy decay for scalar fields on time dependent non-trapping backgrounds

We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a “two point” local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a certain nonresonance property at zero frequency. The second result, which also requires the almost symmetry condition, is to establish an exponential trichotomy in the energy space via finite dimensional time dependent stable and unstable sub-spaces, with an infinite dimensional complement on which solutions disperse via the usual local energy decay estimate

Using spallation neutron sources for defense research

Advanced characterization techniques and accelerated simulation are the cornerstones of the Energy Department`s science-based program to maintain confidence in the safety, reliability, and performance of the US nuclear deterrent in an era of no nuclear testing. Neutrons and protons provided by an accelerator-based facility have an important role to play in this program, impacting several of the key stockpile stewardship and management issues identified by the Department of Defense. Many of the techniques used for defense research at a spallation source have been used for many years for the basic research community, and to a lesser extent by industrial scientists. By providing access to a broad spectrum of researchers with different backgrounds, a spallation source such as the Los Alamos Neutron Science Center is able to promote synergistic interaction between defense, basic and industrial researchers. This broadens the scientific basis of the stockpile stewardship program in the short term and will provide spin-off to industrial and basic research in the longer term

Analyzing CNN Based Behavioural Malware Detection Techniques on Cloud IaaS

Cloud Infrastructure as a Service (IaaS) is vulnerable to malware due to its exposure to external adversaries, making it a lucrative attack vector for malicious actors. A datacenter infected with malware can cause data loss and/or major disruptions to service for its users. This paper analyzes and compares various Convolutional Neural Networks (CNNs) for online detection of malware in cloud IaaS. The detection is performed based on behavioural data using process level performance metrics including cpu usage, memory usage, disk usage etc. We have used the state of the art DenseNets and ResNets in effectively detecting malware in online cloud system. CNN are designed to extract features from data gathered from a live malware running on a real cloud environment. Experiments are performed on OpenStack (a cloud IaaS software) testbed designed to replicate a typical 3-tier web architecture. Comparative analysis is performed for different metrics for different CNN models used in this research

Generalized and weighted Strichartz estimates

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.Comment: Final version, to appear in the Communications on Pure and Applied Analysis. 33 pages. 2 more references adde

Free Versus Constrained Evolution of the 2+1 Equivariant Wave Map

We compare the numerical solutions of the 2+1 equivariant Wave Map problem computed with the symplectic, constraint respecting Rattle algorithm and the well known fourth order Runge-Kutta method. We show the advantages of the Rattle algorithm for constrained system compared to the free evolution with the Runge-Kutta method. We also present an expression, which represents the energy loss due to constraint violation. Taking this expression into account we can achieve energy conservation for the Runge-Kutta scheme, which is better than with the Rattle method. Using the symplectic scheme with constraint enforcement we can reproduce previous calculations of the equivariant case without imposing the symmetry explicitly, thereby confirming that the critical behaviour is stable.Comment: 16 pages, 8 figures. Formula for the scaling function on p. 13 corrected and two typos eliminated; otherwise agrees with the published pape

A Multi-commodity network flow model for cloud service environments

Next-generation systems, such as the big data cloud, have to cope with several challenges, e.g., move of excessive amount of data at a dictated speed, and thus, require the investigation of concepts additional to security in order to ensure their orderly function. Resilience is such a concept, which when ensured by systems or networks they are able to provide and maintain an acceptable level of service in the face of various faults and challenges. In this paper, we investigate the multi-commodity flows problem, as a task within our D 2 R 2 +DR resilience strategy, and in the context of big data cloud systems. Specifically, proximal gradient optimization is proposed for determining optimal computation flows since such algorithms are highly attractive for solving big data problems. Many such problems can be formulated as the global consensus optimization ones, and can be solved in a distributed manner by the alternating direction method of multipliers (ADMM) algorithm. Numerical evaluation of the proposed model is carried out in the context of specific deployments of a situation-aware information infrastructure

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place

On the relation between mathematical and numerical relativity

The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions between numerical and mathematical methods is general relativity.Comment: 12 page

Energy dispersed large data wave maps in 2+1 dimensions

In this article we consider large data Wave-Maps from $\mathbb{R}^{2+1}$ into a compact Riemannian manifold $(\mathcal{M},g)$, and we prove that regularity and dispersive bounds persist as long as a certain type of bulk (non-dispersive) concentration is absent. In a companion article we use these results in order to establish a full regularity theory for large data Wave-Maps.Comment: 89 page