Related papers: Counting the Chain Records: The Product Case
Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…
Multivariate data is often visualized using linear projections, produced by techniques such as principal component analysis, linear discriminant analysis, and projection pursuit. A problem with projections is that they obscure low and high…
We investigate the occurrence of bound states in the continuum (BIC's) in serial structures of quantum dots coupled to an external waveguide, when some characteristic length of the system is changed. By resorting to a multichannel…
A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in…
We consider the motion of a Brownian particle in $\mathbb{R}$, moving between a particle fixed at the origin and another moving deterministically away at slow speed $\epsilon>0$. The middle particle interacts with its neighbours via a…
We study finite probability theory through a category of finite probability schemes and probability-preserving maps, called \emph{bundles}. A bundle simultaneously records a quotient of a sample space, an algebra of random variables, and…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast…
A data store allows application processes to put and get data from a shared memory. In general, a data store cannot be modelled as a strictly sequential process. Applications observe non-sequential behaviours, called anomalies. The set of…
As the amount of linked data published on the web grows, attempts are being made to describe and measure it. However even basic statistics about a graph, such as its size, are difficult to express in a uniform and predictable way. In order…
Some data is linearly additive, other data is not. In this paper, I discuss types of data based on the boundedness of the data and their linearity. 1) Unbounded data can be linear. 2) One-side bounded data is usually log transformed to be…
Classifier chains are an effective technique for modeling label dependencies in multi-label classification. However, the method requires a fixed, static order of the labels. While in theory, any order is sufficient, in practice, this order…
Dynamical supersymmetry breaking is considered in models which admit descriptions in terms of electric, confined, or magnetic degrees of freedom in various limits. In this way, a variety of seemingly different theories which break…
Identifier names play a significant role in program comprehension activities, with high-quality names improving developer productivity and system quality. To correct poor-quality names, developers rename identifiers to reflect their…
Chunking data is obviously no new concept; however, I had never found any data structures that used chunking as the basis of their implementation. I figured that by using chunking alongside concurrency, I could create an extremely fast…
Process mining gains increasing popularity in business process analysis, also in heavy industry. It requires a specific data format called an event log, with the basic structure including a case identifier (case ID), activity (event) name,…
There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a…
We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound…