Related papers: Counting the Chain Records: The Product Case
The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the…
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a L\'evy flight on a line. After a brief survey of the theory of records for independent and…
We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and $d$-dimensional simplex.…
We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution rho. The running record equals the maximum of all elements in the sequence up…
In this paper we give an overview of recent results on (upper and lower) discrepancy estimates for (concrete) sequences in the unit-cube. In particular we also give an overview of discrepancy estimates for certain classes of hybrid…
We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…
Collecting traces from software running in the field is both useful and challenging. Traces may indeed help revealing unexpected usage scenarios, detecting and reproducing failures, and building behavioral models that reflect how the…
We consider the classic infinite occupancy scheme, where balls are thrown in boxes independently, with probability $p_j$ of hitting box $j$. Each time a box receives its first ball we speak of a record and, more generally, call an…
Low-count time series describe sparse or intermittent events, which are prevalent in large-scale online platforms that capture and monitor diverse data types. Several distinct challenges surface when modelling low-count time series,…
This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…
The need to analyze information from streams arises in a variety of applications. One of its fundamental research directions is to mine sequential patterns over data streams. Current studies mine series of items based on the presence of the…
In [7], we introduced the category of chain bundles with examples and established its significance. Here we shall describe certain categories which we call the category of chains in the chain bundle category and discuss some interesting…
Process mining provides ways to analyze business processes. Common process mining techniques consider the process as a whole. However, in real-life business processes, different behaviors exist that make the overall process too complex to…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…
The family of methods collectively known as classifier chains has become a popular approach to multi-label learning problems. This approach involves linking together off-the-shelf binary classifiers in a chain structure, such that class…
Breaking of an atomic chain under stress is a collective many-particle tunneling phenomenon. We study classical dynamics in imaginary time by using conformal mapping technique, and derive an analytic formula for the probability of breaking.…
In this uncertain world, data uncertainty is inherent in many applications and its importance is growing drastically due to the rapid development of modern technologies. Nowadays, researchers have paid more attention to mine patterns in…
We provide a vast class of counterexamples to the chain rule for the divergence of bounded vector fields in three space dimensions. Our convex integration approach allows us to produce renormalization defects of various kinds, which in a…
It is effective to improve the reliability and availability of large-scale cluster systems through the analysis of failures. Existed failure analysis methods understand and analyze failures from one or few dimension. The analysis results…
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…