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Article
Open AccessQuasinormal modes in noncommutative Schwarzschild black holes: a spectral analysis
We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, ...
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Article
Correction to: Modeling the potential genesis of tsunamis from below an accretionary prism and their potential impact: a case study along the eastern boundary of the Caribbean Plate
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Article
Modeling the potential genesis of tsunamis from below an accretionary prism and their potential impact: a case study along the eastern boundary of the Caribbean Plate
The Lesser Antilles subduction zone marks the convergence between the Caribbean Plate and the oceanic Atlantic part of the America Plate. A specificity of this subduction is the development of a huge accretion...
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Article
On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries
There is studied the integrability of a generalized Gurevich-Zybin dynamical system based on the differential-algebraic and geometrically motivated gradient-holonomic approaches. There is constructed the corre...
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Chapter
Applications of Dimensionality Reduction to the Diagnosis of Energy Systems
This Chapter presents a few examples of applications of dimensionality reduction for the analysis of data towards the diagnosis of energy systems. These systems encompass smart-buildings (Sect. 8.1), photovolt...
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Chapter
Conclusions
Dimensionality Reduction (DR) enables analysts to perform visual exploration of high dimensional data by providing a low-dimensional representation. On its own, it allows, for instance, to identify at a glance...
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Chapter
Intrinsic Dimensionality
High dimensional data are subject to the curse of dimensionality defined in Sect. 2.1, which hinders their analysis. Yet, in practice, data may be assumed to live in a manifold whose dimensionality is lower th...
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Chapter
Map Interpretation
Map interpretation encompasses several tools enhancing the map with additional information. Some allow to study the link between axes of the data and embedding space, as detailed Sect. 4.1, while other perform...
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Chapter
Stress Functions for Supervised Dimensionality Reduction
In the general case, Dimensionality Reduction (DR) is an unsupervised task. Indeed, it does not necessitate data annotations, as opposed to classification for which the desired output must be provided for a tr...
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Chapter
Data Science Context
This chapter positions Dimensionality Reduction (DR) in the broader context of data science, considering both its use as an automated pre-processing tool extracting variable (manifold learning) for other autom...
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Chapter
Map Evaluation
The purpose of map evaluation is to assess the overall quality of a map. Most often, this quality is quantified by scalar indicators allowing to compare several maps. This may be used to select the best of sev...
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Chapter
Stress Functions for Unsupervised Dimensionality Reduction
Dimensionality Reduction (DR) represents a set of points {ξ i} in a high dimensional metric data space D $$\mathcal...
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Chapter
Optimization, Acceleration and Out of Sample Extensions
This chapter details the challenges involved for the optimization of the stress functions presented in the previous chapters, as well as the solutions effectively used (Sect. 7.1). It then addresses the issue ...
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Article
Alphabets, rewriting trails and periodic representations in algebraic bases
For \(\beta > 1\) β > 1 ...
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Article
Comparison of ground deformation due to movement of a fault for different types of crack surface
An analytical solution of deformation of a homogeneous, isotropic elastic layer of uniform thickness overlying a homogeneous, isotropic viscoelastic half-space of Burger medium due to movement of an infinite f...
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Chapter
Poisson and Symplectic Structures, Hamiltonian Action, Momentum and Reduction
This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisła–2019, Poland and written down by the second author. As the title suggests, the mater...
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Article
Horizontal displacement effect in tsunami wave generation in the western Makran region
The current silent status of the western segment of the Makran Subduction Zone (MSZ), also known as the western Makran, is an opportunity to examine different aspects of a tsunami hazard for this region. In this ...
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Article
On the comparison of three numerical methods applied to building simulation: Finite-differences, RC circuit approximation and a spectral method
Predictions of physical phenomena in buildings are carried out by using physical models formulated as a mathematical problem and solved by means of numerical methods, aiming at evaluating, for instance, the bu...
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Chapter and Conference Paper
A Computational Simulation of Steady Natural Convection in an H-Form Cavity
The simulation of natural convection problem based on the Galerkin finite-element method, with the penalty finite-element formulation of the momentum balance equation, is exploited for accurate solutions of eq...
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Chapter and Conference Paper
Dispersive Effects During Long Wave Run-up on a Plane Beach
Dispersive effects during long wave run-up on a plane beach are studied. We take advantage of experimental data collection of different wave types (single pulses, sinusoidal waves, bi-harmonic waves, and frequ...
