scholarly journals Corrigendum: Concise and tight security analysis of the Bennett-Brassard 1984 protocol with finite key lengths (2012 New J. Phys.14 093014)

2021 ◽  
Author(s):  
Masahito Hayashi ◽  
Toyohiro Tsurumaru
Keyword(s):  
Asymptotic Expansion ◽  
Security Analysis ◽  
Second Order ◽  
Definition Of ◽  
The Sacrifice ◽  
Tight Security

Abstract The paper (2012 New J. Phys.14 093014) contains an error at the definition of $g_t(x)$ in Section 5.3 while $g_t(x)$ is used for the second order asymptotic expansion for the sacrifice bit. This corrigendum corrects this error and shows its derivation.

A property of the asymptotic series for a class of Titchmarsh–Weyl m-functions

1986 ◽  
Vol 102 (3-4) ◽  
pp. 253-257 ◽  
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Linear Differential Equation ◽  
Asymptotic Series ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
The Real ◽  
Linear Differential ◽  
Image Position

SynopsisIn an earlier paper [6] we showed that if q ϵ CN[0, ε) for some ε > 0, then the Titchmarsh–Weyl m(λ) function associated with the second order linear differential equationhas the asymptotic expansionas |A| →∞ in a sector of the form 0 < δ < arg λ < π – δ.We show that if the real valued function q admits the expansionin a neighbourhood of 0, then

scholarly journals A note on symmetries of diffusions within a martingale problem approach

2019 ◽  
Vol 19 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Francesco C. De Vecchi ◽  
Paola Morando ◽  
Stefania Ugolini
Keyword(s):  
Diffusion Processes ◽  
Martingale Problem ◽  
Second Order ◽  
Lie Symmetries ◽  
Definition Of

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.

A Large Scale Cross-Validation of Second-Order Personality Structure Defined by the 16PF

1986 ◽  
Vol 59 (2) ◽  
pp. 683-693 ◽  
Author(s):  
Samuel E. Krug ◽  
Edgar F. Johns
Keyword(s):  
Large Scale ◽  
Common Factor ◽  
Geographic Location ◽  
Second Order ◽  
Personality Factor ◽  
Personality Factor Questionnaire ◽  
Normal Males ◽  
Definition Of ◽  
High Degree ◽  
Factor Estimation

The second-order factors structure of the 16 Personality Factor Questionnaire (16PF) was cross-validated on a large sample ( N = 17,381) of normal males and females. Subjects were sampled across a broad range of ages, socioeconomic levels, education, geographic location, and ethnicity. The purposes of this investigation were (1) to provide a precise definition of 16PF second-order factor structure, (2) to shed additional light on the nature of two second-order factors that have been previously identified but described as “unstable” and “poorly reproduced,” and (3) to determine the extent to which common factor estimation formulas for men and women would prove satisfactory for applied work. The resulting solutions were congruent with previous studies and showed a high degree of simple structure. Support was provided for one, but not both, of the two additional second-order factors. Results also supported the use of simplified estimation formulas for applied use.

scholarly journals Simple and Effective Secure Group Communications in Dynamic Wireless Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1909 ◽  
Author(s):  
Hisham N. AlMajed ◽  
Ahmad S. AlMogren
Keyword(s):  
Network Performance ◽  
Security Analysis ◽  
Wireless Sensor ◽  
Group Key ◽  
Security Research ◽  
Group Members ◽  
Shared Key ◽  
Definition Of ◽  
First Time ◽  
Secure Group Communications

Wireless Sensor Network (WSN) is a growing area of research in terms of applications, life enhancement and security. Research interests vary from enhancing network performance and decreasing overhead computation to solving security flaws. Secure Group Communication (SGC) is gaining traction in the world of network security. Proposed solutions in this area focus on generating, sharing and distributing a group key among all group members in a timely manner to secure their communication and reduce the computation overhead. This method of security is called SGC-Shared Key. In this paper, we introduce a simple and effective way to secure the network through Hashed IDs (SGC-HIDs). In our proposed method, we distribute a shared key among the group of nodes in the network. Each node would have the ability to compute the group key each time it needs to. We provide a security analysis for our method as well as a performance evaluation. Moreover, to the best of our knowledge, we present for the first time a definition of joining or leaving attack. Furthermore, we describe several types of such an attack as well as the potential security impacts that occur when a network is being attacked.

The nature of discrete second-order self-similarity

2003 ◽  
Vol 35 (02) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa
Keyword(s):  
Fixed Points ◽  
Long Range ◽  
Power Laws ◽  
Complete Classification ◽  
Second Order ◽  
General Definition ◽  
Long Range Dependence ◽  
Self Similarity ◽  
New Treatment ◽  
Definition Of

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.

ASYMPTOTIC EXPANSION AND CONVERGENCE THEOREM OF CONTROL AND OBSERVATION ON THE BOUNDARY FOR SECOND-ORDER ELLIPTIC EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

2004 ◽  
Vol 14 (03) ◽  
pp. 417-437 ◽  
Author(s):  
LI-QUN CAO
Keyword(s):  
Asymptotic Expansion ◽  
Elliptic Equation ◽  
Asymptotic Expansions ◽  
Convergence Theorem ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Oscillating Coefficients ◽  
Highly Oscillatory ◽  
Second Order Elliptic Equation ◽  
The Neumann Problem

In this paper, we shall study systems governed by the Neumann problem of second-order elliptic equation with rapidly oscillating coefficients and with control and observations on the boundary. The multiscale asymptotic expansions of the solution for considering problem in the case without any constraints, and homogenized equation in the case with constraints will be given, their rigorous proofs will also be proposed.

scholarly journals On the Definition of the Cloud Water Content Fluctuations and Its Effects on the Computation of a Second-Order Liquid Water Correlation

2007 ◽  
Vol 64 (2) ◽  
pp. 665-669 ◽  
Author(s):  
E. Bouzereau ◽  
L. Musson-Genon ◽  
B. Carissimo
Keyword(s):  
Water Content ◽  
Liquid Water ◽  
Climate Models ◽  
Cloud Water ◽  
Second Order ◽  
Subgrid Scale ◽  
Eddy Flux ◽  
Cloud Models ◽  
Cloud Water Content ◽  
Definition Of

Abstract In subgrid-scale condensation schemes of cloud models, the majority of previous authors have relied on results presented in a paper by Bougeault. In the present paper, second-order liquid water correlations are restated that differ from the former paper but are coherent with the corrigendum of Mellor. These differences are explained here through two different underlying definitions of cloud water content fluctuations; they can be summarized by whether or not unsaturated air within a grid box contributes to the eddy flux of the cloud water content. Taking into account the issue mentioned above, the “buoyancy flux” is also derived. Although the full impact of these changes has not been evaluated here, it may become important for future global cloud-resolving climate models.

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