scholarly journals Cache-Aided General Linear Function Retrieval

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 25
Author(s):  
Kai Wan ◽  
Hua Sun ◽  
Mingyue Ji ◽  
Daniela Tuninetti ◽  
Giuseppe Caire
Keyword(s):  
Linear Function ◽  
Linear Functions ◽  
General Linear ◽  
Linear Combinations ◽  
Past Work ◽  
Single File ◽  
Caching Scheme ◽  
Retrieval Scheme ◽  
Data Points ◽  
Coded Caching

Coded Caching, proposed by Maddah-Ali and Niesen (MAN), has the potential to reduce network traffic by pre-storing content in the users’ local memories when the network is underutilized and transmitting coded multicast messages that simultaneously benefit many users at once during peak-hour times. This paper considers the linear function retrieval version of the original coded caching setting, where users are interested in retrieving a number of linear combinations of the data points stored at the server, as opposed to a single file. This extends the scope of the authors’ past work that only considered the class of linear functions that operate element-wise over the files. On observing that the existing cache-aided scalar linear function retrieval scheme does not work in the proposed setting, this paper designs a novel coded caching scheme that outperforms uncoded caching schemes that either use unicast transmissions or let each user recover all files in the library.

scholarly journals The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 372 ◽  
Author(s):  
Yi-Peng Wei ◽  
Batuhan Arasli ◽  
Karim Banawan ◽  
Sennur Ulukus
Keyword(s):  
Information Retrieval ◽  
Private Information ◽  
Data Center ◽  
Distributed Databases ◽  
Private Information Retrieval ◽  
Caching Scheme ◽  
Retrieval Scheme ◽  
Two Phases ◽  
Coded Caching ◽  
Retrieval Phase

We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the K files, where each file is of size L bits, and several databases with storage size constraint μ K L bits exist in the system. Each database independently chooses μ K L bits out of the total K L bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses N databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be D * = ∑ n = 1 N + 1 N n - 1 μ n - 1 ( 1 - μ ) N + 1 - n 1 + 1 n + ⋯ + 1 n K - 1 . We show that uniform and random caching scheme which is originally proposed for decentralized coded caching by Maddah-Ali and Niesen, along with Sun and Jafar retrieval scheme which is originally proposed for PIR from replicated databases surprisingly results in the lowest normalized download cost. This is the decentralized counterpart of the recent result of Attia, Kumar, and Tandon for the centralized case. The converse proof contains several ingredients such as interference lower bound, induction lemma, replacing queries and answering string random variables with the content of distributed databases, the nature of decentralized uncoded caching databases, and bit marginalization of joint caching distributions.

scholarly journals Investigation of eighth-grade students' understanding of the slope of the linear function

2012 ◽  
Vol 26 (42a) ◽  
pp. 139-162 ◽  
Author(s):  
Osman Birgin
Keyword(s):  
Linear Function ◽  
Analytical Techniques ◽  
Structured Interview ◽  
Linear Functions ◽  
Eighth Grade ◽  
The Black Sea ◽  
Algebraic Representation ◽  
Black Sea Region ◽  
Eighth Grade Students ◽  
Written Questions

This study aimed to investigate eighth-grade students' difficulties and misconceptions and their performance of translation between the different representation modes related to the slope of linear functions. The participants were 115 Turkish eighth-grade students in a city in the eastern part of the Black Sea region of Turkey. Data was collected with an instrument consisting of seven written questions and a semi-structured interview protocol conducted with six students. Students' responses to questions were categorized and scored. Quantitative data was analyzed using the SPSS 17.0 statistical packet program with cross tables and one-way ANOVA. Qualitative data obtained from interviews was analyzed using descriptive analytical techniques. It was found that students' performance in articulating the slope of the linear function using its algebraic representation form was higher than their performance in using transformation between graphical and algebraic representation forms. It was also determined that some of them had difficulties and misunderstood linear function equations, graphs, and slopes and could not comprehend the connection between slope and the x- and y-intercepts.

scholarly journals Placement Delivery Array Design for Coded Caching Scheme in D2D Networks

2019 ◽  
Vol 67 (5) ◽  
pp. 3388-3395 ◽  
Author(s):  
Jinyu Wang ◽  
Minquan Cheng ◽  
Qifa Yan ◽  
Xiaohu Tang
Keyword(s):  
Array Design ◽  
Caching Scheme ◽  
Coded Caching

Decentralized Coded Caching Scheme With Heterogeneous File Sizes

2020 ◽  
Vol 69 (1) ◽  
pp. 818-827
Author(s):  
Lei Zheng ◽  
Qingchun Chen ◽  
Qifa Yan ◽  
Xiaohu Tang
Keyword(s):  
Caching Scheme ◽  
Coded Caching

scholarly journals Probabilistic Analysis of Steady-State Temperature and Maximum Frequency of Multicore Processors considering Workload Variation

2016 ◽  
Vol 2016 ◽  
pp. 1-17
Author(s):  
Biying Zhang ◽  
Zhongchuan Fu ◽  
Hongsong Chen ◽  
Gang Cui
Keyword(s):  
Linear Function ◽  
Multicore Processors ◽  
Probabilistic Method ◽  
Linear Functions ◽  
Maximum Frequency ◽  
Dynamic Frequency Scaling ◽  
Probabilistic Distribution ◽  
Steady State Temperature ◽  
Instructions Per Cycle ◽  
Workload Variation

A probabilistic method is presented to analyze the temperature and the maximum frequency for multicore processors based on consideration of workload variation, in this paper. Firstly, at the microarchitecture level, dynamic powers are modeled as the linear function of IPCs (instructions per cycle), and leakage powers are approximated as the linear function of temperature. Secondly, the microarchitecture-level hotspot temperatures of both active cores and inactive cores are derived as the linear functions of IPCs. The normal probabilistic distribution of hotspot temperatures is derived based on the assumption that IPCs of all cores follow the same normal distribution. Thirdly and lastly, the probabilistic distribution of the set of discrete frequencies is determined. It can be seen from the experimental results that hotspot temperatures of multicore processors are not deterministic and have significant variations, and the number of active cores and running frequency simultaneously determine the probabilistic distribution of hotspot temperatures. The number of active cores not only results in different probabilistic distribution of frequencies, but also leads to different probabilities for triggering DFS (dynamic frequency scaling).

scholarly journals Filtration of parameters of the Heston model

2020 ◽  
pp. 48-55
Author(s):  
О.А. Кобилін ◽  
О.Є. Путятіна ◽  
М.В. Гарячий
Keyword(s):  
Linear Function ◽  
Financial Market ◽  
Stock Price ◽  
Linear Functions ◽  
Heston Model ◽  
Model Parameters ◽  
Filtration Problem ◽  
Practical Applications ◽  
Non Linear

In this article we consider the Heston model of the stock price behaviour. While the volatility of the model is the non-linear function of another stochastic unobservable function, that is why we consider linearizing all non-linear functions of the model. The aim is to make the Heston model simpler for practical applications, in particular for solving the filtration problem. The filtration problem for the models of the financial market consists of evaluating of unobservable model parameters, having got the stock price observations.

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