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article

Tight Lower Bound on Differential Entropy for Mixed Gaussian Distributions

Abdelrahman Marconi, Ahmed H. Elghandour, Ashraf D. Elbayoumy, Amr Abdelaziz

Journal of Telecommunications and Information Technology > 2024 > nr 2 > 23--31

In this paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then,...

article

Properties of given and detected unbounded solutions to a class of chemotaxis models

Alessandro Columbu, Silvia Frassu, Giuseppe Viglialoro

Studies in Applied Mathematics > 151 > 4 > 1349 - 1379

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction–repulsion model, with nonlinear productions, diffusion, sensitivities, and logistic term, we detect Lebesgue spaces where given unbounded solutions also blow up in the corresponding norms of those spaces; subsequently, estimates for the blow‐up time are established. Finally, for...

article

Residual‐based a posteriori error estimates for nonconforming finite element approximation to parabolic interface problems

Tanushree Ray, Rajen Kumar Sinha

Numerical Methods for Partial Differential Equations > 39 > 4 > 2935 - 2962

In this paper, we derive a residual‐based a posteriori error estimates for nonconforming finite element approximation to parabolic interface problems. The present approach does not involve the Helmholtz decomposition while analyzing the reliability of the estimator. The constants involved in the estimators are independent of the jump of the diffusion coefficient across the interface, and the quasi‐monotonocity...

article

Lower Bound Uncertainty and Long‐Term Interest Rates

CHRISTIAN GRISSE

Journal of Money, Credit and Banking > 55 > 2-3 > 619 - 634

Nominal interest rates are constrained by an effective lower bound, but the level of the lower bound is uncertain. This paper uses a simple shadow rate term structure model to study how lower bound uncertainty affects long‐term interest rates. A decline in lower bound uncertainty, in the sense of a mean‐preserving contraction, is associated with a drop in expected short rates. The effect on the variance...

article

Accelerating exact nearest neighbor search in high dimensional Euclidean space via block vectors

Haowen Zhang, Yabo Dong, Duanqing Xu

International Journal of Intelligent Systems > 37 > 2 > 1697 - 1722

The nearest neighbor search is an essential operation for many computer vision, data mining, and machine learning problems. Since it is so widely used, the nearest neighbor search should be as fast as possible. This paper explores lower bound‐based approaches to speed up the exact nearest neighbor search in high dimensional Euclidean space. We compute the lower bound of Euclidean Distance by using...

article

Lower bound analysis of modified pseudo‐dynamic lateral earth pressures for retaining wall‐backfill system with depth‐varying damping using FEM‐Second order cone programming

Hessam Fathipour, Meghdad Payan, Reza Jamshidi Chenari, Kostas Senetakis

International Journal for Numerical and Analytical Methods in Geomechanics > 45 > 16 > 2371 - 2387

Realistic constitutive ground models are critical in the evaluation of soil‐structure interaction problems and the assessment of key design parameters in the seismic analysis of infrastructure systems. In the present study, the modified pseudo‐dynamic lateral earth pressures acting on retaining structure with granular backfill of depth‐varying damping ratio are evaluated adopting the lower bound limit...

article

On the Density of Spoof Odd Perfect Numbers

L. Tóth

Computational Methods in Science and Technology > 2021 > Vol. 27, No. 1 > 25--28

We study the set S of odd positive integers n with the property 2n/σ(n) − 1 = 1/x, for positive integer x, i.e., the set that relates to odd perfect and odd “spoof perfect” numbers. As a consequence, we find that if D = pq denotes a spoof odd perfect number other than Descartes’ example, with pseudo-prime factor p, then q > 1012. Furthermore, we find irregularities in the ending digits of integers...

article

Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies

Marcello Braglia, Davide Castellano, Liberatina Santillo, Dongping Song

International Transactions in Operational Research > 28 > 1 > 376 - 400

In this paper, we consider the periodic review joint replenishment problem under the class of cyclic policies. For each item, the demand in the protection interval is assumed stochastic. Moreover, a fraction of shortage is lost, while the other quota is backordered. We suppose that lead times and minor ordering costs are controllable. The problem concerns determining the cyclic replenishment policy,...

article

A Note of Caution on Shadow Rate Estimates

LEO KRIPPNER

Journal of Money, Credit and Banking > 52 > 4 > 951 - 962

Shadow short rate (SSR) estimates are generated regressors proposed as a proxy for policy interest rates during unconventional monetary policy (UMP) periods. However, using the Wu and Xia (2016) shadow/lower‐bound model, I show that SSR estimates can be sensitive to minor choices in their estimation. Used subsequently in a small macroeconomic model, those sensitivities lead to wide variations in the...

article

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Boonchai Ukritchon, Suraparb Keawsawasvong

International Journal for Numerical and Analytical Methods in Geomechanics > 44 > 5 > 596 - 632

The undrained bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clay is investigated by the lower bound (LB) finite element limit analysis (FELA) under two‐dimensional (2D) axisymmetric condition using second‐order cone programming, and the new solution of the problem is presented. Modified from the isotropic von Mises yield criterion, a cross‐anisotropic undrained strength...

article

Performance analysis of achievable sum‐rate for downlink massive MIMO systems

Hao Li, Zhigang Wang, Houjun Wang

International Journal of Communication Systems > 33 > 4 > n/a - n/a

Massive multiple‐input and multiple‐output (MIMO) has been recognized as a promising technology in the fifth‐generation wireless networks. Under perfect channel state information, we derive three tractable closed‐form expressions that corresponding to the lower bound, approximation, and upper bound on the achievable rate in a massive MIMO downlink system with maximum‐ratio transmission precoding....

article

Computable Error Estimates for Ground State Solution of Bose–Einstein Condensates

Hehu Xie, Manting Xie

Journal of Scientific Computing > 2019 > 81 > 2 > 1072-1087

In this paper, we propose a computable error estimate of the Gross–Pitaevskii equation for the ground state solution of the Bose–Einstein condensate by the general conforming finite element method on general meshes. Based on this error estimate, the asymptotically lower and upper bound for the smallest eigenvalue and ground state energy can be calculated. Several numerical examples are presented to...

article

New Lower Bounds to Wrap-around L₂-discrepancy for U-type Designs with Three-level

Zheng-hong Wang, Hong Qin

Acta Mathematicae Applicatae Sinica, English Series > 2019 > 35 > 3 > 513-520

The objective of this paper is to study the issue of uniformity on three-level U-type designs in terms of the wrap-around L₂-discrepancy. Based on the known formula, we present a new lower bound of wrap-around L₂-discrepancy for three-level U-type designs and compare it with those existing ones through figures, numerical simulation and illustrative examples.

article

Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams

Paweł Gawrychowski, Oleg Merkurev, Arseny M. Shur, Przemysław Uznański

Algorithmica > 2019 > 81 > 9 > 3630-3654

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a setting, one can still hope for a good approximation guarantee. Our contribution is twofold. First, we provide lower bounds on the space requirements for randomized approximation...

article

Probing Uncertainty Relations in Non-Commutative Space

Pritam Chattopadhyay, Ayan Mitra, Goutam Paul

International Journal of Theoretical Physics > 2019 > 58 > 8 > 2619-2631

In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg’s uncertainty relation. We also derive the reverse uncertainty relation for product and sum of uncertainties of two incompatible variables for one linear and another non-linear model of the harmonic oscillator. The non-linear model in non-commutating...

article

Similarity join on time series by utilizing a dynamic segmentation index

Jinhua Wang, Qiuhong Li, Zhongsheng Li, Peng Wang, more

Knowledge and Information Systems > 2019 > 61 > 3 > 1517-1546

Similarity join on time series databases is an essential operation for data analysis applications. Due to the curse of dimensionality, it is not suitable to use traditional index techniques, such as R-tree and kd-tree. In the paper, a dynamic segment index (i.e., DSTree) is utilized to reduce the huge comparison cost on the similarity join on time series databases. However, the DSTree is designed...

article

Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions

Ying-Yue Yang, Wen-Yang Sun, Wei-Nan Shi, Fei Ming, more

Frontiers of Physics > 2019 > 14 > 3 > 1-9

The dynamics of measurement’s uncertainty via entropy for a one-dimensional Heisenberg XYZ mode is examined in the presence of an inhomogeneous magnetic field and Dzyaloshinskii–Moriya (DM) interaction. It shows that the uncertainty of interest is intensively in connection with the filed’s temperature, the direction-oriented coupling strengths and the magnetic field. It turns out that the stronger...

article

Lifespan estimates via Neumann heat kernel

Xin Yang, Zhengfang Zhou

Zeitschrift für angewandte Mathematik und Physik > 2019 > 70 > 1 > 1-26

We study the lower bound of the lifespan $$T^{*}$$ T∗ for the heat equation $$u_t=\Delta u$$ ut=Δu in a bounded domain $$\Omega \subset \mathbb {R}^{n}(n\ge 2)$$ Ω⊂Rn(n≥2) with positive initial data $$u_{0}$$ u0 and a nonlinear radiation condition on partial boundary: the exterior normal derivative $$\partial u/\partial n=u^{q}$$ ∂u/∂n=uq on $$\Gamma _1\subseteq \partial \Omega $$ Γ1⊆∂Ω for...

article

Two-center of the Convex Hull of a Point Set : Dynamic Model, and Restricted Streaming Model

Sanjib Sadhu, Sasanka Roy, Soumen Nandi, Anil Maheshwari, more

Fundamenta Informaticae > 2019 > Vol. 164, nr 1 > 119--138

In this paper, we consider the dynamic version of covering the convex hull of a point set P in ℝ²by two congruent disks of minimum size. Here, the points can be added or deleted in the set P, and the objective is to maintain a data structure that, at any instant of time, can efficiently report two disks of minimum size whose union completely covers the boundary of the convex hull of the point set...

article

Designing Uniform Computer Sequential Experiments with Mixture Levels Using Lee Discrepancy

A. M. Elsawah

Journal of Systems Science and Complexity > 2019 > 32 > 2 > 681-708

Computer experiments are constructed to simulate the behavior of complex physical systems. Uniform designs have good performance in computer experiments from several aspects. In practical use, the experimenter needs to choose a small size uniform design at the beginning of an experiment due to a limit of time, budget, resources, and so on, and later conduct a follow up experiment to obtain precious...

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Search results

Tight Lower Bound on Differential Entropy for Mixed Gaussian Distributions

Properties of given and detected unbounded solutions to a class of chemotaxis models

Residual‐based a posteriori error estimates for nonconforming finite element approximation to parabolic interface problems

Lower Bound Uncertainty and Long‐Term Interest Rates

Accelerating exact nearest neighbor search in high dimensional Euclidean space via block vectors

Lower bound analysis of modified pseudo‐dynamic lateral earth pressures for retaining wall‐backfill system with depth‐varying damping using FEM‐Second order cone programming

On the Density of Spoof Odd Perfect Numbers

Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies

A Note of Caution on Shadow Rate Estimates

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Performance analysis of achievable sum‐rate for downlink massive MIMO systems

Computable Error Estimates for Ground State Solution of Bose–Einstein Condensates

New Lower Bounds to Wrap-around L₂-discrepancy for U-type Designs with Three-level

Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams

Probing Uncertainty Relations in Non-Commutative Space

Similarity join on time series by utilizing a dynamic segmentation index

Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions

Lifespan estimates via Neumann heat kernel

Two-center of the Convex Hull of a Point Set : Dynamic Model, and Restricted Streaming Model

Designing Uniform Computer Sequential Experiments with Mixture Levels Using Lee Discrepancy

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