This paper develops a framework for studying the popularity dynamics of user-generated videos, presents a characterization of the popularity dynamics, and proposes a model that captures the key properties of these dynamics. We illustrate the biases that may be introduced in the analysis for some choices of the sampling technique used for collecting data; however, sampling from recently-uploaded videos provides a dataset that is seemingly unbiased. Using a dataset that tracks the views to a sample of recently-uploaded YouTube videos over the first eight months of their lifetime, we study the popularity dynamics. We find that the relative popularities of the videos within our dataset are highly non-stationary, owing primarily to large differences in the required time since upload until peak popularity is finally achieved, and secondly to popularity oscillation. We propose a model that can accurately capture the popularity dynamics of collections of recently-uploaded videos as they age, including key measures such as hot set churn statistics, and the evolution of the viewing rate and total views distributions over time.
Video sharing services that allow ordinary Web users to upload video clips of their choice and watch video clips uploaded by others have recently become very popular. This paper identifies invariants in video sharing workloads, through comparison of the workload characteristics of four popular video sharing services. Our traces contain meta-data on approximately 1.8 million videos which together have been viewed approximately 6 billion times. Using these traces, we study the similarities and differences in use of several Web 2.0 features such as ratings, comments, favorites, and propensity of uploading content. In general, we find that active contribution, such as video uploading and rating of videos, is much less prevalent than passive use. While uploaders in general are skewed with respect to the number of videos they upload, the fraction of multi-time uploaders is found to differ by a factor of two between two of the sites. The distributions of life-time measures of video popularity are found to have heavy-tailed forms that are similar across the four sites. Finally, we consider implications for system design of the identified invariants. To gain further insight into caching in video sharing systems, and the relevance to caching of life-time popularity measures, we gathered an additional data set tracking views to a set of approximately 1.3 million videos from one of the services, over a twelve week period. We find that life-time popularity measures have some relevance for large cache (hot set) sizes (i.e., a hot set defined according to one of these measures is indeed relatively "hot"), but that this relevance substantially decreases as cache size decreases, owing to churn in video popularity.
Video sharing services that allow ordinary Web users to upload video clips of their choice and watch video clips uploaded by others have recently become very popular. This paper identifies invariants in video sharing workloads, through comparison of the workload characteristics of four popular video sharing services. Our traces contain meta-data on approximately 1.8 million videos which together have been viewed approximately 6 billion times. Using these traces, we study the similarities and differences in use of several Web 2.0 features such as ratings, comments, favorites, and propensity of uploading content. In general, we find that active contribution, such as video uploading and rating of videos, is much less prevalent than passive use. While uploaders in general are skewed with respect to the number of videos they upload, the fraction of multi-time uploaders is found to differ by a factor of two between two of the sites. The distributions of life-time measures of video popularity are found to have heavy-tailed forms that are similar across the four sites. Finally, we consider implications for system design of the identified invariants. To gain further insight into caching in video sharing systems, and the relevance to caching of life-time popularity measures, we gathered an additional data set tracking views to a set of approximately 1.3 million videos from one of the services, over a twelve week period. We find that life-time popularity measures have some relevance for large cache (hot set) sizes (i.e., a hot set defined according to one of these measures is indeed relatively "hot"), but that this relevance substantially decreases as cache size decreases, owing to churn in video popularity.
Purpose of study: To introduce the concept of projective and involuntary variational inequality problems of order and respectively. To study the equivalence theorem between these problems. To study the projected dynamical system using self involutory variational inequality problems. Methodology: Improved extra gradient method is used. Main Finding: Using a self-solvable improved extra gradient method we solve the variational inequalities. The algorithm of the projected dynamical system is provided using the RK-4 method whose equilibrium point solves the involutory variational inequality problems. Application of this study: Runge-Kutta type method of order 2 and 4 is used for the initial value problem with the given projected dynamical system with the help of self involutory variational inequality problems. The originality of this study: The concept of self involutory variational inequality problems, projective and involuntary variational inequality problems of order and respectively are newly defined.
We study how to adapt to smoothly-varying (‘easy’) environments in well-known online learning problems where acquiring information is expensive. For the problem of label efficient prediction, which is a budgeted version of prediction with expert advice, we present an online algorithm whose regret depends optimally on the number of labels allowed and Q* (the quadratic variation of the losses of the best action in hindsight), along with a parameter-free counterpart whose regret depends optimally on Q (the quadratic variation of the losses of all the actions). These quantities can be significantly smaller than T (the total time horizon), yielding an improvement over existing, variation-independent results for the problem. We then extend our analysis to handle label efficient prediction with bandit (partial) feedback, i.e., label efficient bandits. Our work builds upon the framework of optimistic online mirror descent, and leverages second order corrections along with a carefully designed hybrid regularizer that encodes the constrained information structure of the problem. We then consider revealing action-partial monitoring games – a version of label efficient prediction with additive information costs – which in general are known to lie in the hard class of games having minimax regret of order T2/3. We provide a strategy with an O((Q*T)1/3 bound for revealing action games, along with one with a O((QT)1/3) bound for the full class of hard partial monitoring games, both being strict improvements over current bounds.
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