Search results for "linear"
showing 10 items of 7165 documents
Exact extension of the DIRECT algorithm to multiple objectives
2019
The direct algorithm has been recognized as an efficient global optimization method which has few requirements of regularity and has proven to be globally convergent in general cases. direct has been an inspiration or has been used as a component for many multiobjective optimization algorithms. We propose an exact and as genuine as possible extension of the direct method for multiple objectives, providing a proof of global convergence (i.e., a guarantee that in an infinite time the algorithm becomes everywhere dense). We test the efficiency of the algorithm on a nonlinear and nonconvex vector function. peerReviewed
Twister Tries
2015
Many commonly used data-mining techniques utilized across research fields perform poorly when used for large data sets. Sequential agglomerative hierarchical non-overlapping clustering is one technique for which the algorithms’ scaling properties prohibit clustering of a large amount of items. Besides the unfavorable time complexity of O(n 2 ), these algorithms have a space complexity of O(n 2 ), which can be reduced to O(n) if the time complexity is allowed to rise to O(n 2 log2 n). In this paper, we propose the use of locality-sensitive hashing combined with a novel data structure called twister tries to provide an approximate clustering for average linkage. Our approach requires only lin…
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Iterative Methods for Pricing American Options under the Bates Model
2013
We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…
Exploiting ongoing EEG with multilinear partial least squares during free-listening to music
2016
During real-world experiences, determining the stimulus-relevant brain activity is excitingly attractive and is very challenging, particularly in electroencephalography. Here, spectrograms of ongoing electroencephalogram (EEG) of one participant constructed a third-order tensor with three factors of time, frequency and space; and the stimulus data consisting of acoustical features derived from the naturalistic and continuous music formulated a matrix with two factors of time and the number of features. Thus, the multilinear partial least squares (PLS) conforming to the canonical polyadic (CP) model was performed on the tensor and the matrix for decomposing the ongoing EEG. Consequently, we …
IMEX schemes for pricing options under jump–diffusion models
2014
We propose families of IMEX time discretization schemes for the partial integro-differential equation derived for the pricing of options under a jump-diffusion process. The schemes include the families of IMEX-midpoint, IMEX-CNAB and IMEX-BDF2 schemes. Each family is defined by a convex combination parameter [email protected]?[0,1], which divides the zeroth-order term due to the jumps between the implicit and explicit parts in the time discretization. These IMEX schemes lead to tridiagonal systems, which can be solved extremely efficiently. The schemes are studied through Fourier stability analysis and numerical experiments. It is found that, under suitable assumptions and time step restric…
Fractal dynamics in chaotic quantum transport
2013
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis -- a widely used method in time series analysis -- and show its usefulness in the interpretation of the conductance curves. Comparison with a s…
Symmetry breaking in ligand-protected gold clusters probed by nonlinear optics
2016
The first hyperpolarizabilities of [Au25(SR)18](-1/0) and Au38(SR)24 clusters were determined by Hyper-Rayleigh Scattering. A strong dependence on the molecular symmetry was observed, and we explore two strategies to destroy the center of inversion in [Au25(SR)18](-1/0), protection by chiral ligands and alloying of the cluster with silver. This may open new avenues to applications of Au : SR clusters in second-order nonlinear optics.
Multi-hop D2D Communications with Network Coding : From A Performance Perspective
2019
Multi-hop device-to-device (D2D) communications play an important role in expanding D2D coverage. In this paper, we study a relay-based and network-coding-assisted (in particular, XOR coding) multi-hop D2D communication system. In the system, toward jointly considering the impact of interference and network traffic conditions on the quality of D2D communications, various channel fading models and traffic models are investigated, and the packet loss probability of D2D links is meticulously computed using these models. With the packet loss probability of D2D links, the general closed-form expressions of end-to-end packet loss probability (E2EPLP) of the system with the presence (or absence) o…