If a variable's probability distribution follows a power law with exponent λ, then the associated frequency distribution ϕ will follow a power law with exponent k = 1 + 1/λ (Adamic & Huberman, 2002 Hanel, Corominas-Murtra, Liu, & Thurner, 2017) since probabilities p(i) for these bins follow a power law with exponent λ = 1, our prediction is the frequency distribution ϕ ∆ will follow a power law with exponent k = 1 + 1/λ = 2. Since infection numbers in each bin in this distribution have occurred at least once, the probability of observing an infection i that falls into any one of these bins is approximated by the conditional probability p(i) ∼ i −λ with λ = 1. We provide formal proof of the security of the protocol assuming a common random coin. This allows providing impossibility results in some edge cases and in the asynchronous communication model. We propose a framework to analyse liveness and safety under different communication and adversary models. Paradigm at the node level and not at the validator level. Moreover, it enables the removal of the intermediary of miners and validators, allowing a pure two-step process that follows the The DAG structure and the underlying Reality-based UTXO Ledger allow parallel validation of transactions without the need for total ordering. Consensus is no longer found in the longest chain but on the heaviest DAG, where PoW is replaced by a stake- or reputation-based weight function. The Tangle naturally succeeds the blockchain as its next evolutionary step as it offers features suited to establish more efficient and scalable distributed ledger solutions. We introduce the theoretical foundations of the Tangle 2.0, a probabilistic leaderless consensus protocol based on a directed acyclic graph (DAG) called the Tangle. The proposed scheme outperforms the state-of-the-art schemes in terms of energy consumption by 55%,Īverage latency, and cache hit rate by a minimum of 35%. In this work, we propose a novel decentralized placement scheme named self-organized cooperative caching (SOCC) for mobile ICN to improve the overall network performance through efficient bandwidth utilization and less traffic overhead. ICN can mitigate traffic overhead and meet future Internet requirements. The concept of ICN is to entertain the request locally by neighbor nodes without accessing the source, which will help offload the network’s data traffic. A new internet paradigm known as Information Centric Networks (ICN) was introduced based on contentoriented addressing. The current internet cannot cope with such high data traffic due to its fixed infrastructure (host centric-network) degrading the network performance. Due to these overheads (high bandwidth consumption), the service providers fail to provide high-speed and low latency internet to users around the globe. These applications are used for uploading informational content such as images, videos, and voices, which results in exponential traffic overhead. The usage of social media applications such as Youtube, Facebook, and other applications is rapidly increasing with each passing day. Because of the convex nature of the optimization problem, the speedup is achieved without any degradation in classification accuracy. This comes in part from the reduced number of iterations that need to be performed due to starting closer to the solution, and in part from an implicit negative-mining effect that allows to ignore easy negatives in the CG step. We demonstrate a training speedup of up to 5×\documentclass on Amazon-670K dataset with 670,000 labels. For margin losses, such an initialization is achieved by selecting the initial vector such that it separates the mean of all positive (relevant for a label) instances from the mean of all negatives – two quantities that can be calculated quickly for the highly imbalanced binary problems occurring in XMC. We want to start in a region of weight space (a) with low loss value, (b) that is favourable for second-order optimization, and (c) where the conjugate-gradient (CG) calculations can be performed quickly. We discuss the problem of choosing the initial weights from the perspective of three goals. In this paper, we show that a simple, data dependent way of setting the initial vector can be used to substantially speed up the training of linear one-versus-all classifiers in extreme multi-label classification (XMC).
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