Optimal Convex Combination Bounds for Toader Mean

2018 ◽  
Vol 10 (3) ◽  
pp. 1-11
Author(s):  
Shao-yun Li ◽  
Hui-zuo Xu ◽  
Fang Jin
Keyword(s):  
Convex Combination ◽  
Toader Mean

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 151
Author(s):  
Michele Flammini ◽  
Gianpiero Monaco ◽  
Luca Moscardelli ◽  
Mordechai Shalom ◽  
Shmuel Zaks
Keyword(s):  
Cost Function ◽  
Optical Networks ◽  
Cost Minimization ◽  
Convex Combination ◽  
Optical Network ◽  
Switching Cost ◽  
Wavelength Assignment ◽  
Intermediate Node ◽  
Polynomial Time Approximation Algorithm ◽  
Path Topology

All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the problem under consideration is an optical network modeled by a graph G, a set of lightpaths modeled by paths on G, and an integer g termed the grooming factor. One has to assign a wavelength (modeled by a color) to every lightpath, so that every edge of the graph is used by at most g paths of the same color. A lightpath operating at some wavelength λ uses one Add/Drop multiplexer (ADM) at both endpoints and one Optical Add/Drop multiplexer (OADM) at every intermediate node, all operating at a wavelength of λ. Two lightpaths, both operating at the same wavelength λ, share the ADMs and OADMs in their common nodes. Therefore, the total switching cost due to the usage of ADMs and OADMs depends on the wavelength assignment. We consider networks of ring and path topology and a cost function that is a convex combination α·|OADMs|+(1−α)|ADMs| of the number of ADMs and the number of OADMs deployed in the network. We showed that the problem of minimizing this cost function is NP-complete for every convex combination, even in a path topology network with g=2. On the positive side, we present a polynomial-time approximation algorithm for the problem.

OPTIMAL REINSURANCE FROM THE VIEWPOINTS OF BOTH AN INSURER AND A REINSURER UNDER THE CVAR RISK MEASURE AND VAJDA CONDITION

2021 ◽  
pp. 1-29
Author(s):  
Yanhong Chen
Keyword(s):  
Loss Function ◽  
Value At Risk ◽  
Numerical Study ◽  
Risk Measure ◽  
Convex Combination ◽  
Weighting Factor ◽  
Loss Functions ◽  
Conditional Value At Risk ◽  
Optimal Reinsurance ◽  
The Impact

ABSTRACT In this paper, we study the optimal reinsurance contracts that minimize the convex combination of the Conditional Value-at-Risk (CVaR) of the insurer’s loss and the reinsurer’s loss over the class of ceded loss functions such that the retained loss function is increasing and the ceded loss function satisfies Vajda condition. Among a general class of reinsurance premium principles that satisfy the properties of risk loading and convex order preserving, the optimal solutions are obtained. Our results show that the optimal ceded loss functions are in the form of five interconnected segments for general reinsurance premium principles, and they can be further simplified to four interconnected segments if more properties are added to reinsurance premium principles. Finally, we derive optimal parameters for the expected value premium principle and give a numerical study to analyze the impact of the weighting factor on the optimal reinsurance.

VidCloud

2021 ◽  
Vol 5 (4) ◽  
pp. 1-32
Author(s):  
Abubakr O. Al-Abbasi ◽  
Vaneet Aggarwal
Keyword(s):  
Video Streaming ◽  
Distributed Storage ◽  
Convex Combination ◽  
Video Quality ◽  
Moment Generating Function ◽  
Content Delivery Network ◽  
Two Stage ◽  
Erasure Code ◽  
Probabilistic Scheduling ◽  
Parallel Streams

As video-streaming services have expanded and improved, cloud-based video has evolved into a necessary feature of any successful business for reaching internal and external audiences. In this article, video streaming over distributed storage is considered where the video segments are encoded using an erasure code for better reliability. We consider a representative system architecture for a realistic (typical) content delivery network (CDN). Given multiple parallel streams/link between each server and the edge router, we need to determine, for each client request, the subset of servers to stream the video, as well as one of the parallel streams from each chosen server. To have this scheduling, this article proposes a two-stage probabilistic scheduling. The selection of video quality is also chosen with a certain probability distribution that is optimized in our algorithm. With these parameters, the playback time of video segments is determined by characterizing the download time of each coded chunk for each video segment. Using the playback times, a bound on the moment generating function of the stall duration is used to bound the mean stall duration. Based on this, we formulate an optimization problem to jointly optimize the convex combination of mean stall duration and average video quality for all requests, where the two-stage probabilistic scheduling, video quality selection, bandwidth split among parallel streams, and auxiliary bound parameters can be chosen. This non-convex problem is solved using an efficient iterative algorithm. Based on the offline version of our proposed algorithm, an online policy is developed where servers selection, quality, bandwidth split, and parallel streams are selected in an online manner. Experimental results show significant improvement in QoE metrics for cloud-based video as compared to the considered baselines.

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