Detecting Singular Data for Better Analysis of Emotional Tweets

Smart Data ◽  
2019 ◽  
pp. 259-272
Author(s):  
Kiichi Tago ◽  
Kenichi Ito ◽  
Qun Jin
Keyword(s):  
Singular Data

NVESTIGATION OF THE EFFICIENCY OF DISTRIBUTED INFORMATION SYSTEMS BASED ON THE PROCESSING OF LARGE AMOUNTS OF DATA

2019 ◽  
Author(s):  
Mykhajlo Klymash ◽  
Olena Hordiichuk — Bublivska ◽  
Ihor Tchaikovskyi ◽  
Oksana Urikova
Keyword(s):  
Distributed Systems ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Data Decomposition ◽  
Distributed Information ◽  
Software Model ◽  
Computing Performance ◽  
Mapreduce Model ◽  
Singular Data

In this article investigated the features of processing large arrays of information for distributed systems. A method of singular data decomposition is used to reduce the amount of data processed, eliminating redundancy. Dependencies of com­putational efficiency on distributed systems were obtained using the MPI messa­ging protocol and MapReduce node interaction software model. Were analyzed the effici­ency of the application of each technology for the processing of different sizes of data: Non — distributed systems are inefficient for large volumes of information due to low computing performance. It is proposed to use distributed systems that use the method of singular data decomposition, which will reduce the amount of information processed. The study of systems using the MPI protocol and MapReduce model obtained the dependence of the duration calculations time on the number of processes, which testify to the expediency of using distributed computing when processing large data sets. It is also found that distributed systems using MapReduce model work much more efficiently than MPI, especially with large amounts of data. MPI makes it possible to perform calculations more efficiently for small amounts of information. When increased the data sets, advisable to use the Map Reduce model.

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

scholarly journals Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

2020 ◽  
Vol 20 (2) ◽  
pp. 373-384
Author(s):  
Quoc-Hung Nguyen ◽  
Nguyen Cong Phuc
Keyword(s):  
Elliptic Operator ◽  
Bounded Domain ◽  
Existence Of Solutions ◽  
Type Equation ◽  
Linear Range ◽  
Measure Data ◽  
Regularity Conditions ◽  
Compactly Supported ◽  
Singular Data ◽  
Quasilinear Elliptic

AbstractWe characterize the existence of solutions to the quasilinear Riccati-type equation\left\{\begin{aligned} \displaystyle-\operatorname{div}\mathcal{A}(x,\nabla u)% &\displaystyle=|\nabla u|^{q}+\sigma&&\displaystyle\phantom{}\text{in }\Omega,% \\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{on }\partial% \Omega,\end{aligned}\right.with a distributional or measure datum σ. Here {\operatorname{div}\mathcal{A}(x,\nabla u)} is a quasilinear elliptic operator modeled after the p-Laplacian ({p>1}), and Ω is a bounded domain whose boundary is sufficiently flat (in the sense of Reifenberg). For distributional data, we assume that {p>1} and {q>p}. For measure data, we assume that they are compactly supported in Ω, {p>\frac{3n-2}{2n-1}}, and q is in the sub-linear range {p-1<q<1}. We also assume more regularity conditions on {\mathcal{A}} and on {\partial\Omega\Omega} in this case.

Some uniqueness results for singular elliptic problems

2015 ◽  
Vol 26 (03) ◽  
pp. 1550026 ◽  
Author(s):  
L. Caso ◽  
R. D'Ambrosio
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Open Subset ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Singular Data

We prove some uniqueness results for Dirichlet problems for second-order linear elliptic partial differential equations in non-divergence form with singular data in suitable weighted Sobolev spaces, on an open subset Ω of ℝn, n ≥ 2, not necessarily bounded or regular.

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

A Lane–Emden system with singular data

2011 ◽  
Vol 141 (6) ◽  
pp. 1279-1294 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Singular Data

We study the elliptic system −Δu = δ(x)−avp in Ω, −Δv = δ(x)−buq in Ω, subject to homogeneous Dirichlet boundary conditions. Here, Ω ⊂ ℝN, N ≥ 1, is a smooth and bounded domain, δ(x) = dist(x, ∂Ω), a, b ≥ 0 and p, q ∈ ℝ satisfy pq > −1. The existence, non-existence and uniqueness of solutions are investigated in terms of a, b, p and q.

scholarly journals ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA

2009 ◽  
Vol 11 (03) ◽  
pp. 395-411 ◽  
Author(s):  
LEI ZHANG
Keyword(s):  
Elliptic Equations ◽  
Type Equation ◽  
Global Solutions ◽  
Order Elliptic Equation ◽  
Liouville Type ◽  
Exponential Nonlinearity ◽  
Second Order Elliptic Equation ◽  
Singular Data ◽  
Sharp Error ◽  
Uniformly Bounded

We consider a sequence of blowup solutions of a two-dimensional, second-order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci–Chen–Lin–Tarantello, it is proved that the profile of the solutions differs from global solutions of a Liouville-type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.

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