A closed-form upper-bound for the distribution of the weighted sum of rayleigh variates

2005 ◽  
Vol 9 (7) ◽  
pp. 589-591 ◽  
Author(s):  
G.K. Karagiannidis ◽  
T.A. Tsiftsis ◽  
N.C. Sagias
Keyword(s):  
Closed Form ◽  
Upper Bound ◽  
Weighted Sum

A MEAN–VARIANCE BOUND FOR A THREE-PIECE LINEAR FUNCTION

2007 ◽  
Vol 21 (4) ◽  
pp. 611-621 ◽  
Author(s):  
Karthik Natarajan ◽  
Zhou Linyi
Keyword(s):  
Convex Function ◽  
Closed Form ◽  
Linear Function ◽  
Upper Bound ◽  
Random Variable ◽  
Expected Value ◽  
Variance Bound ◽  
The Mean ◽  
Mean Variance

In this article, we derive a tight closed-form upper bound on the expected value of a three-piece linear convex function E[max(0, X, mX − z)] given the mean μ and the variance σ2 of the random variable X. The bound is an extension of the well-known mean–variance bound for E[max(0, X)]. An application of the bound to price the strangle option in finance is provided.

scholarly journals Revenue-Capped Efficient Auctions

2019 ◽  
Vol 18 (3) ◽  
pp. 1284-1320 ◽  
Author(s):  
Nozomu Muto ◽  
Yasuhiro Shirata ◽  
Takuro Yamashita
Keyword(s):  
Upper Bound ◽  
Private Information ◽  
Weighted Sum ◽  
Reserve Price ◽  
Total Surplus ◽  
Good For ◽  
Expected Revenue ◽  
Social Surplus

Abstract We study an auction that maximizes the expected social surplus under an upper-bound constraint on the seller’s expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when (i) the auction designer is “pro-buyer”, that is, he maximizes the weighted sum of the buyers’ and seller’s auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multiunit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, “bunching” is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least “at the top,” that is, “no distortion at the top” fails.

The Effective Thermal Conductivity of a Packing of Spheres

1990 ◽  
Vol 57 (3) ◽  
pp. 789-791 ◽  
Author(s):  
A. Jagota ◽  
C. Y. Hui
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Closed Form ◽  
Effective Thermal Conductivity ◽  
Granular Materials ◽  
Upper Bound ◽  
Random Packing ◽  
Fabric Tensor ◽  
Mean Temperature

The anisotropic effective thermal conductivity of a random packing of spheres is derived. The conductivity is closely related to the fabric tensor of the theory of granular materials. The derivation involves a mean temperature field assumption which is shown to render the model an upper bound. Closed-form expressions for the conductivity are obtained in the isotropic and axisymmetric cases.

On Buckling Loads of Timoshenko Columns with Elastically Supported Ends

2012 ◽  
Vol 446-449 ◽  
pp. 578-581
Author(s):  
Hua Zhang ◽  
Xiang Fang Li
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
Upper Bound ◽  
Intermediate State ◽  
Critical Loads ◽  
Compressive Force ◽  
Buckling Loads ◽  
Characteristic Equations ◽  
The Stability ◽  
Elastically Supported

The stability of Timoshenko columns with elastically supported ends under axially compressive force is analyzed. Characteristic equations are obtained according to an intermediate state between Haringx’s and Engesser’s models. For clamped-free, clamped-clamped, and pinned-pinned columns, buckling loads are given in closed form. The influences of elastic restraint stiffness on the critical loads are elucidated. Haringx’s and Engesser’s models are two extreme cases of the present. Critical buckling loads using Haringx’s model are upper bound, and those using Engesser’s model are lower bound.

scholarly journals Real-Time Inverse Kinematics of the Human Arm

1996 ◽  
Vol 5 (4) ◽  
pp. 393-401 ◽  
Author(s):  
Deepak Tolani ◽  
Norman I. Badler
Keyword(s):  
Closed Form ◽  
Real Time ◽  
Upper Bound ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Additional Constraint ◽  
Degree Of Freedom ◽  
Empirical Results ◽  
Human Arm ◽  
Real Time Applications

A simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions, Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.

scholarly journals Reacting to outbreaks at neighboring localities

2020 ◽  
Author(s):  
Ceyhun Eksin ◽  
Martial-Ndeffo Mbah ◽  
Joshua S. Weitz
Keyword(s):  
Lower Bound ◽  
Behavior Change ◽  
Upper Bound ◽  
High Mobility ◽  
Cumulative Number ◽  
Weighted Sum ◽  
Combined Effects ◽  
Critical Levels ◽  
Metapopulation Model ◽  
Outbreak Size

AbstractWe study the dynamics of epidemics in a networked metapopulation model. In each subpopulation, representing a locality, disease propagates according to a modified susceptible-exposed-infected-recovered (SEIR) dynamics. We assume that individuals reduce their number of contacts as a function of the weighted sum of cumulative number of cases within the locality and in neighboring localities. We also assume that susceptible and exposed (pre-symptomatic and infectious) individuals can travel between localities. To investigate the combined effects of mobility and contact reduction on disease progression within interconnected localities, we consider a scenario with two localities where disease originates in one and is exported to the neighboring locality via travel of undetected pre-symptomatic individuals. We establish a lower bound on the outbreak size at the origin as a function of the speed of spread. We associate the behavior change at the disease-importing locality due to the outbreak size at the origin with the level of preparedness of the locality. Using the lower bound on the outbreak size at the origin, we establish an upper bound on the outbreak size at the importing locality as a function of the speed of spread and the level of preparedness for low mobility regimes. We show the accuracy of the bounds in determining critical levels of preparedness that stop the disease from becoming endemic at neighboring localities. Finally, we show how the benefit of preparedness diminishes under high mobility rates. Our results highlight the importance of preparedness at localities where cases are beginning to rise, and demonstrate the benefits of increase in contact reduction by considering the outbreaks in neighboring localities with severe, rather than weak, outbreaks.

On Riesz means of the coefficients of the Rankin–Selberg series

1999 ◽  
Vol 127 (1) ◽  
pp. 117-131 ◽  
Author(s):  
ALEKSANDAR IVIĆ ◽  
KOHJI MATSUMOTO ◽  
YOSHIO TANIGAWA
Keyword(s):  
Asymptotic Formula ◽  
Upper Bound ◽  
Error Term ◽  
Weighted Sum ◽  
Mean Square ◽  
Riesz Means ◽  
The Mean ◽  
Voronoi Formula

We study Δ(x; ϕ), the error term in the asymptotic formula for [sum ]n[les ]xcn, where the cns are generated by the Rankin–Selberg series. Our main tools are Voronoï-type formulae. First we reduce the evaluation of Δ(x; ϕ) to that of Δ1(x; ϕ), the error term of the weighted sum [sum ]n[les ]x(x−n)cn. Then we prove an upper bound and a sharp mean square formula for Δ1(x; ϕ), by applying the Voronoï formula of Meurman's type. We also prove that an improvement of the error term in the mean square formula would imply an improvement of the upper bound of Δ(x; ϕ). Some other related topics are also discussed.

scholarly journals Predictive mathematical models for the number of individuals infected with COVID-19

2020 ◽  
Author(s):  
A.S. Fokas ◽  
N. Dikaios ◽  
G.A. Kastis
Keyword(s):  
Lower Bound ◽  
Mathematical Models ◽  
Closed Form ◽  
Upper Bound ◽  
Logistic Model ◽  
Simple Formula ◽  
Time Dependent ◽  
Sigmoidal Curve ◽  
Specific Virus ◽  
Number Of Individuals

AbstractWe model the time-evolution of the number N(t) of individuals reported to be infected in a given country with a specific virus, in terms of a Riccati equation. Although this equation is nonlinear and it contains time-dependent coefficients, it can be solved in closed form, yielding an expression for N(t) that depends on a function α(t). For the particular case that α(t) is constant, this expression reduces to the well-known logistic formula, giving rise to a sigmoidal curve suitable for modelling usual epidemics. However, for the case of the COVID-19 pandemic, the long series of available data shows that the use of this simple formula for predictions underestimates N(t); thus, the logistic formula only provides a lower bound of N(t). After experimenting with more than 50 different forms of α(t), we introduce two novel models that will be referred to as “rational” and “birational”. The parameters specifying these models (as well as those of the logistic model), are determined from the available data using an error-minimizing algorithm. The analysis of the applicability of the above models to the cases of China and South Korea suggest that they yield more accurate predictions, and importantly that they may provide an upper bound of the actual N(t). Results are presented for Italy, Spain, and France.

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