Related papers: Pseudometrics and preorders on sets of integer seq…
We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
We introduce the notion of coarse metric. Every coarse metric induces a coarse structure on the underlying set. Conversely, we observe that all coarse spaces come from a particular type of coarse metric in a unique way. In the case when the…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We establish that every second countable completely regularly preordered space (E,T,\leq) is quasi-pseudo-metrizable, in the sense that there is a quasi-pseudo-metric p on E for which the pseudo-metric p\veep^-1 induces T and the graph of…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
In the preprocessing framework for dealing with uncertain data, one is given a set of regions that one is allowed to preprocess to create some auxiliary structure such that when a realization of these regions is given, consisting of one…
Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest,…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We introduce a type of surgery on metric spaces. This surgery, in some sense, seeks to replace a subspace $S$ of a metric space $X$ with another metric space $T$ via a function $f : S \to T$. When $T$ is a discrete space, this amounts to…
In this paper we investigate the interplay between isolated suborders and closures. Isolated suborders are a special kind of suborders and can be used to diminish the number of elements of an ordered set by means of a quotient construction.…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…