The Experts below are selected from a list of 304698 Experts worldwide ranked by ideXlab platform
Andres Ortiz Garcia - One of the best experts on this subject based on the ideXlab platform.
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reducing the key space of an image encryption scheme based on two round Diffusion Process
Computational Intelligence in Security for Information Systems, 2015Co-Authors: Alberto Peinado, Andres Ortiz GarciaAbstract:In this work, we analyze the security of the image encryption scheme proposed by Norouzi et al. (Multimedia Syst 20:45–64, 2014) [1]. The encryption scheme is based on a hash function and a two-round Diffusion Process applied to each 8 × 8 patches that compose the entire image. The analysis reveals the existence of a huge number of weak keys, allowing us to compute the effective key length, thus reducing the key space from 2512 to 2195 keys.
Alberto Peinado - One of the best experts on this subject based on the ideXlab platform.
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reducing the key space of an image encryption scheme based on two round Diffusion Process
Computational Intelligence in Security for Information Systems, 2015Co-Authors: Alberto Peinado, Andres Ortiz GarciaAbstract:In this work, we analyze the security of the image encryption scheme proposed by Norouzi et al. (Multimedia Syst 20:45–64, 2014) [1]. The encryption scheme is based on a hash function and a two-round Diffusion Process applied to each 8 × 8 patches that compose the entire image. The analysis reveals the existence of a huge number of weak keys, allowing us to compute the effective key length, thus reducing the key space from 2512 to 2195 keys.
Zhiyuan Zhen - One of the best experts on this subject based on the ideXlab platform.
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explicit control law of a coupled reaction Diffusion Process
Journal of The Franklin Institute-engineering and Applied Mathematics, 2017Co-Authors: Cuihua He, Zhiyuan ZhenAbstract:Abstract Stabilization of a coupled linear plant and reaction–Diffusion Process by boundary control was considered in a paper by Zhao and Xie. In this paper, backstepping transformation with a kernel function and a vector-valued function was introduced to design a control law. For the situation without heat resource in the reaction–Diffusion Process, the kernel function and the vector-valued function in the transformation had been obtained, and the explicit control law had been established. However, for the reaction–Diffusion Process with heat resource, the explicit solutions of the kernel function and the vector-valued function in the transformation have not been obtained. Thus, an explicit control law has not been established. In the present paper, the explicit solutions of the kernel function and the vector-valued function in the transformation are obtained through some mathematical skills and complicated computation, and the explicit control law has been established.
Abass Sagna - One of the best experts on this subject based on the ideXlab platform.
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Product Markovian Quantization of a Diffusion Process with Applications to Finance
Methodology and Computing in Applied Probability, 2019Co-Authors: Lucio Fiorin, Gilles Pagès, Abass SagnaAbstract:We introduce a new methodology for the quantization of the Euler scheme for a d -dimensional Diffusion Process. This method is based on a Markovian and componentwise product quantization and allows us, from a numerical point of view, to speak of fast online quantization in a dimension greater than one since the product quantization of the Euler scheme of the Diffusion Process and its companion weights and transition probabilities may be computed quite instantaneously. We show that the resulting quantization Process is a Markov chain, then we compute the associated weights and transition probabilities from (semi-) closed formulas. From the analytical point of view, we show that the induced quantization errors at the k -th discretization step is a cumulative of the marginal quantization error up to that time. Numerical experiments are performed for the pricing of a Basket call option in a correlated Black Scholes framework, for the pricing of a European call option in a Heston model and for the approximation of the solution of backward stochastic differential equations in order to show the performances of the method.
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Recursive marginal quantization of the Euler scheme of a Diffusion Process
2014Co-Authors: Gilles Pagès, Abass SagnaAbstract:We propose a new approach to quantize the marginals of the discrete Euler Diffusion Process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler Process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler Process and the proposed quantizations. We show in particular that at every discretization step $t_k$ of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times $t_0=0$ to time $t_k$. For numerics, we restrict our analysis to the one dimensional setting and show how to compute the optimal grids using a Newton-Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular Diffusion Processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method.
Longin Jan Latecki - One of the best experts on this subject based on the ideXlab platform.
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regularized Diffusion Process on bidirectional context for object retrieval
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019Co-Authors: Qi Tian, Longin Jan LateckiAbstract:Diffusion Process has advanced object retrieval greatly as it can capture the underlying manifold structure. Recent studies have experimentally demonstrated that tensor product Diffusion can better reveal the intrinsic relationship between objects than other variants. However, the principle remains unclear, i.e., what kind of manifold structure is captured. In this paper, we propose a new affinity learning algorithm called Regularized Diffusion Process (RDP). By deeply exploring the properties of RDP, our first yet basic contribution is providing a manifold-based explanation for tensor product Diffusion. A novel criterion measuring the smoothness of the manifold is defined, which simultaneously regularizes four vertices in the affinity graph. Inspired by this observation, we further contribute two variants towards two specific goals. While ARDP can learn similarities across heterogeneous domains, HRDP performs affinity learning on tensor product hypergraph, considering the relationships between objects are generally more complex than pairwise. Consequently, RDP, ARDP and HRDP constitute a generic tool for object retrieval in most commonly-used settings, no matter the input relationships between objects are derived from the same domain or not, and in pairwise formulation or not. Comprehensive experiments on 10 retrieval benchmarks, especially on large scale data, validate the effectiveness and generalization of our work.
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locally constrained Diffusion Process on locally densified distance spaces with applications to shape retrieval
Computer Vision and Pattern Recognition, 2009Co-Authors: Xingwei Yang, Suzan Koknartezel, Longin Jan LateckiAbstract:The matching and retrieval of 2D shapes is an important challenge in computer vision. A large number of shape similarity approaches have been developed, with the main focus being the comparison or matching of pairs of shapes. In these approaches, other shapes do not influence the similarity measure of a given pair of shapes. In the proposed approach, other shapes do influence the similarity measure of each pair of shapes, and we show that this influence is beneficial even in the unsupervised setting (without any prior knowledge of shape classes). The influence of other shapes is propagated as a Diffusion Process on a graph formed by a given set of shapes. However, the classical Diffusion Process does not perform well in shape space for two reasons: it is unstable in the presence of noise and the underlying local geometry is sparse. We introduce a locally constrained Diffusion Process which is more stable even if noise is present, and we densify the shape space by adding synthetic points we call 'ghost points'. We present experimental results that demonstrate very significant improvements over state-of-the-art shape matching algorithms. On the MPEG-7 data set, we obtained a bull's-eye retrieval score of 93.32%, which is the highest score ever reported in the literature.
