The discrete version of the bispectral problem

1998 ◽  
pp. 93-104
Author(s):  
Fernando Levstein ◽  
Laura Matusevich
Keyword(s):  
Discrete Version ◽  
Bispectral Problem

scholarly journals Optimal Selection of Conductors in Three-Phase Distribution Networks Using a Discrete Version of the Vortex Search Algorithm

Computation ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 80
Author(s):  
John Fernando Martínez-Gil ◽  
Nicolas Alejandro Moyano-García ◽  
Oscar Danilo Montoya ◽  
Jorge Alexander Alarcon-Villamil
Keyword(s):  
Objective Function ◽  
Power Flow ◽  
Phase Distribution ◽  
Search Algorithm ◽  
Distribution Networks ◽  
Discrete Version ◽  
Optimal Selection ◽  
Flow Method ◽  
Three Phase ◽  
Selection Of

In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ− and Y−connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.

scholarly journals Transient Dynamics in the Random Growth and Reset Model

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 306
Author(s):  
Tamás S. Biró ◽  
Lehel Csillag ◽  
Zoltán Néda
Keyword(s):  
Differential Equation ◽  
Mean Field ◽  
Equation System ◽  
Transient Dynamics ◽  
Type Model ◽  
Discrete Version ◽  
Differential Equation System ◽  
Practical Applications ◽  
Random Growth ◽  
Recursive Integration

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

scholarly journals On the analytic form of the discrete Kramer sampling theorem

2001 ◽  
Vol 25 (11) ◽  
pp. 709-715 ◽  
Author(s):  
Antonio G. García ◽  
Miguel A. Hernández-Medina ◽  
María J. Muñoz-Bouzo
Keyword(s):  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Sampling Theorem ◽  
Discrete Version ◽  
Moment Problems ◽  
Sturm Liouville ◽  
The Subject ◽  
Sampling Expansions

The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problems as well as polynomials of the second kind associated with them provide examples of Kramer analytic kernels.

Volatility discovery in cryptocurrency markets

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Thomas Dimpfl ◽  
Dalia Elshiaty
Keyword(s):  
Design Methodology ◽  
Stochastic Volatility Model ◽  
Discrete Version ◽  
Data Series ◽  
Content Type ◽  
Vector Autoregressive ◽  
Volatility Model ◽  
Information Shares ◽  
The Common ◽  
To Come

PurposeCryptocurrency markets are notoriously noisy, but not all markets might behave in the exact same way. Therefore, the aim of this paper is to investigate which one of the cryptocurrency markets contributes the most to the common volatility component inherent in the market.Design/methodology/approachThe paper extracts each of the cryptocurrency's markets' latent volatility using a stochastic volatility model and, subsequently, models their dynamics in a fractionally cointegrated vector autoregressive model. The authors use the refinement of Lien and Shrestha (2009, J. Futures Mark) to come up with unique Hasbrouck (1995, J. Finance) information shares.FindingsThe authors’ findings indicate that Bitfinex is the leading market for Bitcoin and Ripple, while Bitstamp dominates for Ethereum and Litecoin. Based on the dominant market for each cryptocurrency, the authors find that the volatility of Bitcoin explains most of the volatility among the different cryptocurrencies.Research limitations/implicationsThe authors’ findings are limited by the availability of the cryptocurrency data. Apart from Bitcoin, the data series for the other cryptocurrencies are not long enough to ensure the precision of the authors’ estimates.Originality/valueTo date, only price discovery in cryptocurrencies has been studied and identified. This paper extends the current literature into the realm of volatility discovery. In addition, the authors propose a discrete version for the evolution of a markets fundamental volatility, extending the work of Dias et al. (2018).

REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

2002 ◽  
Vol 09 (03) ◽  
pp. 275-285 ◽  
Author(s):  
M. XIE ◽  
O. GAUDOIN ◽  
C. BRACQUEMOND
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Monotonicity Property ◽  
Discrete Distributions ◽  
The Other ◽  
Continuous Case ◽  
Discrete Version ◽  
Series System ◽  
Failure Rate Function ◽  
Definition Of

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.

scholarly journals Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160798 ◽  
Author(s):  
Wenjun Cai ◽  
Huai Zhang ◽  
Yushun Wang
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Conservation Law ◽  
Heterogeneous Media ◽  
Numerical Dispersion ◽  
Discrete Version ◽  
Symplectic Method ◽  
Ode System ◽  
Strang Splitting

We propose a novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude. Through introducing the conformal multi-symplectic structure, the intrinsic dissipation law and the conformal symplectic conservation law are revealed for the damped acoustic wave equation. The proposed algorithm is exactly designed to preserve a discrete version of the conformal symplectic conservation law. More specifically, two subsystems in conjunction with the original damped wave equation are derived. One is actually the conservative Hamiltonian wave equation and the other is a dissipative linear ordinary differential equation (ODE) system. Standard symplectic method is devoted to the conservative system, whereas the analytical solution is obtained for the ODE system. An explicit conformal symplectic scheme is constructed by concatenating these two parts of solutions by the Strang splitting technique. Stability analysis and convergence tests are given thereafter. A benchmark model in homogeneous media is presented to demonstrate the effectiveness and advantage of our method in suppressing numerical dispersion and preserving the energy dissipation. Further numerical tests show that our proposed method can efficiently capture the dissipation in heterogeneous media.

scholarly journals A Discrete Particle Swarm Optimization Algorithm for Uncapacitated Facility Location Problem

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Ali R. Guner ◽  
Mehmet Sevkli
Keyword(s):  
Particle Swarm Optimization ◽  
Facility Location ◽  
Location Problem ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Facility Location Problem ◽  
Discrete Version ◽  
Discrete Particle Swarm Optimization ◽  
Swarm Optimization ◽  
Better Than

A discrete version of particle swarm optimization (DPSO) is employed to solve uncapacitated facility location (UFL) problem which is one of the most widely studied in combinatorial optimization. In addition, a hybrid version with a local search is defined to get more efficient results. The results are compared with a continuous particle swarm optimization (CPSO) algorithm and two other metaheuristics studies, namely, genetic algorithm (GA) and evolutionary simulated annealing (ESA). To make a reasonable comparison, we applied to same benchmark suites that are collected from OR-library. In conclusion, the results showed that DPSO algorithm is slightly better than CPSO algorithm and competitive with GA and ESA.

scholarly journals Specializing Word Embeddings (for Parsing) by Information Bottleneck (Extended Abstract)

2020 ◽  
Author(s):  
Xiang Lisa Li ◽  
Jason Eisner
Keyword(s):  
Dimensionality Reduction ◽  
Semantic Information ◽  
State Of The Art ◽  
Word Embedding ◽  
Discrete Version ◽  
Word Embeddings ◽  
Continuous Version ◽  
Continuous Vector ◽  
Information Bottleneck ◽  
Art Performance

Pre-trained word embeddings like ELMo and BERT contain rich syntactic and semantic information, resulting in state-of-the-art performance on various tasks. We propose a very fast variational information bottleneck (VIB) method to nonlinearly compress these embeddings, keeping only the information that helps a discriminative parser. We compress each word embedding to either a discrete tag or a continuous vector. In the discrete version, our automatically compressed tags form an alternative tag set: we show experimentally that our tags capture most of the information in traditional POS tag annotations, but our tag sequences can be parsed more accurately at the same level of tag granularity. In the continuous version, we show experimentally that moderately compressing the word embeddings by our method yields a more accurate parser in 8 of 9 languages, unlike simple dimensionality reduction.

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