13,863 research outputs found
Integrated Generative Adversarial Networks and Deep Convolutional Neural Networks for Image Data Classification A Case Study for COVID-19
Convolutional Neural Networks (CNNs) have garnered significant utilisation within automated image classification systems. CNNs possess the ability to leverage the spatial and temporal correlations inherent in a dataset. This study delves into the use of cutting-edge deep learning for precise image data classification, focusing on overcoming the difficulties brought on by the COVID-19 pandemic. In order to improve the accuracy and robustness of COVID-19 image classification, the study introduces a novel methodology that combines the strength of Deep Convolutional Neural Networks (DCNNs) and Generative Adversarial Networks (GANs). This proposed study helps to mitigate the lack of labelled coronavirus (COVID-19) images, which has been a standard limitation in related research, and improves the model’s ability to distinguish between COVID-19-related patterns and healthy lung images. The study uses a thorough case study and uses a sizable dataset of chest X-ray images covering COVID-19 cases, other respiratory conditions, and healthy lung conditions. The integrated model outperforms conventional DCNN-based techniques in terms of classification accuracy after being trained on this dataset. To address the issues of an unbalanced dataset, GAN will produce synthetic pictures and extract deep features from every image. A thorough understanding of the model’s performance in real-world scenarios is also provided by the study’s meticulous evaluation of the model’s performance using a variety of metrics, including accuracy, precision, recall, and F1-score
Advances in machine learning algorithms for financial risk management
In this thesis, three novel machine learning techniques are introduced to address distinct
yet interrelated challenges involved in financial risk management tasks. These approaches
collectively offer a comprehensive strategy, beginning with the precise classification of credit
risks, advancing through the nuanced forecasting of financial asset volatility, and ending
with the strategic optimisation of financial asset portfolios.
Firstly, a Hybrid Dual-Resampling and Cost-Sensitive technique has been proposed to combat the prevalent issue of class imbalance in financial datasets, particularly in credit risk
assessment. The key process involves the creation of heuristically balanced datasets to effectively address the problem. It uses a resampling technique based on Gaussian mixture
modelling to generate a synthetic minority class from the minority class data and concurrently uses k-means clustering on the majority class. Feature selection is then performed
using the Extra Tree Ensemble technique. Subsequently, a cost-sensitive logistic regression
model is then applied to predict the probability of default using the heuristically balanced
datasets. The results underscore the effectiveness of our proposed technique, with superior
performance observed in comparison to other imbalanced preprocessing approaches. This
advancement in credit risk classification lays a solid foundation for understanding individual
financial behaviours, a crucial first step in the broader context of financial risk management.
Building on this foundation, the thesis then explores the forecasting of financial asset volatility, a critical aspect of understanding market dynamics. A novel model that combines a
Triple Discriminator Generative Adversarial Network with a continuous wavelet transform
is proposed. The proposed model has the ability to decompose volatility time series into
signal-like and noise-like frequency components, to allow the separate detection and monitoring of non-stationary volatility data. The network comprises of a wavelet transform
component consisting of continuous wavelet transforms and inverse wavelet transform components, an auto-encoder component made up of encoder and decoder networks, and a
Generative Adversarial Network consisting of triple Discriminator and Generator networks.
The proposed Generative Adversarial Network employs an ensemble of unsupervised loss derived from the Generative Adversarial Network component during training, supervised
loss and reconstruction loss as part of its framework. Data from nine financial assets are
employed to demonstrate the effectiveness of the proposed model. This approach not only
enhances our understanding of market fluctuations but also bridges the gap between individual credit risk assessment and macro-level market analysis.
Finally the thesis ends with a novel proposal of a novel technique or Portfolio optimisation. This involves the use of a model-free reinforcement learning strategy for portfolio
optimisation using historical Low, High, and Close prices of assets as input with weights of
assets as output. A deep Capsules Network is employed to simulate the investment strategy, which involves the reallocation of the different assets to maximise the expected return
on investment based on deep reinforcement learning. To provide more learning stability in
an online training process, a Markov Differential Sharpe Ratio reward function has been
proposed as the reinforcement learning objective function. Additionally, a Multi-Memory
Weight Reservoir has also been introduced to facilitate the learning process and optimisation of computed asset weights, helping to sequentially re-balance the portfolio throughout
a specified trading period. The use of the insights gained from volatility forecasting into
this strategy shows the interconnected nature of the financial markets. Comparative experiments with other models demonstrated that our proposed technique is capable of achieving
superior results based on risk-adjusted reward performance measures.
In a nut-shell, this thesis not only addresses individual challenges in financial risk management but it also incorporates them into a comprehensive framework; from enhancing the
accuracy of credit risk classification, through the improvement and understanding of market
volatility, to optimisation of investment strategies. These methodologies collectively show
the potential of the use of machine learning to improve financial risk management
Essential spectrum for dissipative Maxwell equations in domains with cylindrical ends
We consider the Maxwell equations with anisotropic coefficients and non-trivial conductivity in a domain with finitely many cylindrical ends. We assume that the conductivity vanishes at infinity and that the permittivity and permeability tensors converge to non-constant matrices at infinity, which coincide with a positive real multiple of the identity matrix in each of the cylindrical ends. We establish that the essential spectrum of Maxwell system can be decomposed as the union of the essential spectrum of a bounded multiplication operator acting on gradient fields, and the union of the essential spectra of the Maxwell systems obtained by freezing the coefficients to their different limiting values along the several different cylindrical ends of the domain
On the Global Topology of Moduli Spaces of Riemannian Metrics with Holonomy
We discuss aspects of the global topology of moduli spaces of hyperkähler metrics.
If the second Betti number is larger than , we show that each connected component of these moduli spaces is not contractible. Moreover, in certain cases, we show that the components are simply connected and determine the second rational homotopy group. By that, we prove that the rank of the second homotopy group is bounded from below by the number of orbits of MBM-classes in the integral cohomology. \\
An explicit description of the moduli space of these hyperkähler metrics in terms of Torelli theorems will be given. We also provide such a description for the moduli space of Einstein metrics on the Enriques manifold. For the Enriques manifold, we also give an example of a desingularization process similar to the Kummer construction of Ricci-flat metrics on a Kummer surface.\\
We will use these theorems to provide topological statements for moduli spaces of Ricci-flat and Einstein metrics in any dimension larger than . For a compact simply connected manifold we show that the moduli space of Ricci flat metrics on splits homeomorphically into a product of the moduli space of Ricci flat metrics on and the moduli of sectional curvature flat metrics on the torus
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Non-Abelian homology and homotopy colimit of classifying spaces for a diagram of groups
The paper considers non-Abelian homology groups for a diagram of groups
introduced as homotopy groups of a simplicial replacement. It is proved that
the non-Abelian homology groups of the group diagram are isomorphic to the
homotopy groups of the homotopy colimit of the diagram of classifying spaces,
with a dimension shift of 1. As an application, a method is developed for
finding a nonzero homotopy group of least dimension for a homotopy colimit of
classifying spaces. For a group diagram over a free category with a zero
colimit, a criterion for the isomorphism of the first non-Abelian and first
Abelian homology groups is obtained. It is established that the non-Abelian
homology groups are isomorphic to the cotriple derived functors of the colimit
functor defined on the category of group diagrams.Comment: 32 page
Equivariant toric geometry and Euler-Maclaurin formulae
We consider equivariant versions of the motivic Chern and Hirzebruch
characteristic classes of a quasi-projective toric variety, and extend many
known results from non-equivariant to the equivariant setting. The
corresponding generalized equivariant Hirzebruch genus of a torus-invariant
Cartier divisor is also calculated. Further global formulae for equivariant
Hirzebruch classes are obtained in the simplicial context by using the Cox
construction and the equivariant Lefschetz-Riemann-Roch theorem. Alternative
proofs of all these results are given via localization at the torus fixed
points in equivariant - and homology theories. In localized equivariant
-theory, we prove a weighted version of a classical formula of Brion for a
full-dimensional lattice polytope. We also generalize to the context of motivic
Chern classes the Molien formula of Brion-Vergne. Similarly, we compute the
localized Hirzebruch class, extending results of Brylinski-Zhang for the
localized Todd class.
We also elaborate on the relation between the equivariant toric geometry via
the equivariant Hirzebruch-Riemann-Roch and Euler-Maclaurin type formulae for
full-dimensional simple lattice polytopes. Our results provide generalizations
to arbitrary coherent sheaf coefficients, and algebraic geometric proofs of
(weighted versions of) the Euler-Maclaurin formulae of Cappell-Shaneson,
Brion-Vergne, Guillemin, etc., via the equivariant Hirzebruch-Riemann-Roch
formalism. Our approach, based on motivic characteristic classes, allows us to
obtain such Euler-Maclaurin formulae also for (the interior of) a face, or for
the polytope with several facets removed. We also prove such results in the
weighted context, and for Minkovski summands of the given full-dimensional
lattice polytope. Some of these results are extended to local Euler-Maclaurin
formulas for the tangent cones at the vertices of the given lattice polytope.Comment: 93 pages, comments are very welcom
Carath\'eodory Theory and A Priori Estimates for Continuity Inclusions in the Space of Probability Measures
In this article, we extend the foundations of the theory of differential
inclusions in the space of probability measures with compact support, laid down
recently in one of our previous work, to the setting of general Wasserstein
spaces. Anchoring our analysis on novel estimates for solutions of continuity
equations, we propose a new existence result ``\`a la Peano'' for this class of
dynamics, under mere Carath\'eodory regularity assumptions. The latter is based
on a set-valued generalisation of the semi-discrete Euler scheme proposed by
Filippov to study ordinary differential equations with measurable right-hand
sides. We also bring substantial improvements to the earlier versions of the
Filippov theorem, compactness and relaxation properties of the solution sets of
continuity inclusions which are derived in the more restrictive
Cauchy-Lipschitz setting
First order conservation law framework for large strain explicit contact dynamics
This thesis presents a novel vertex-centred finite volume algorithm for explicit large strain solid contact dynamic problems where potential contact loci are known a priori. This methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures, consisting of the deformation gradient tensor, its co-factor and its determinant, in combination with their associated Rankine-Hugoniot jump conditions. These jump conditions are used to derive several dynamic contact models ensuring the preservation of hyperbolic characteristic structure across solution discontinuities at the contact interface, which is a significant advantage over standard quasi-static contact models where the influence of inertial effects at the contact interface is completely neglected. By taking advantage of this conservative formalism, both kinematic (velocity) and kinetic (traction) contact-impact conditions are explicitly enforced at the fluxes through the use of the appropriate jump conditions. Specifically, the kinetic contact condition was enforced, in the traditional manner, through the linear momentum equation, while the kinematic contact condition was easily enforced through the geometric conservation equations without requiring a computationally demanding iterative scheme. Additionally, a Total Variation Diminishing shock capturing technique can be suitably incorporated in order to improve dramatically the performance of the algorithm at the vicinity of shocks, importantly no ad-hoc regularisation procedure is required to accurately capture shock phenomena. Moreover, to guarantee stability from the spatial discretisation standpoint, global entropy production is demonstrated through the satisfaction of semi-discrete version of the classical Coleman-Noll procedure expressed in terms of the time rate of the Hamiltonian energy of the system. Finally, a series of numerical examples is presented in order to assess the performance and applicability of the proposed algorithm suitably implemented across MATLAB and a purpose built OpenFOAM solver
Stability and Instability of Equilibria in Age-Structured Diffusive Populations
The principle of linearized stability and instability is established for a
classical model describing the spatial movement of an age-structured population
with nonlinear vital rates. It is shown that the real parts of the eigenvalues
of the corresponding linearization at an equilibrium determine the latter's
stability or instability. The key ingredient of the proof is the eventual
compactness of the semigroup associated with the linearized problem, which is
derived by a perturbation argument. The results are illustrated with examples.Comment: 39 page
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