Related papers: Parametrised second-order complexity theory with a…
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…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
Recently, Anshu et al. introduced "partially" smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
Parametricity is a property of the syntax of type theory implying, e.g., that there is only one function having the type of the polymorphic identity function. Parametricity is usually proven externally, and does not hold internally.…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
We introduce an asymmetric distance in the space of learning tasks, and a framework to compute their complexity. These concepts are foundational for the practice of transfer learning, whereby a parametric model is pre-trained for a task,…
Parameterization extends higher-order processes with the capability of abstraction (akin to that in lambda-calculus), and is known to be able to enhance the expressiveness. This paper focuses on the parameterization of names, i.e. a…
We give some connections between various functions defined on finitely presented groups (isoperimetric, isodiametric, Todd-Coxeter radius, filling length functions, etc.), and we study the relation between those functions and the…
Graphcodes were recently introduced as a technique to employ two-parameter persistence modules in machine learning tasks (Kerber and Russold, NeurIPS 2024). We show in this work that a compressed version of graphcodes yields a description…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we…
Common intervals of K permutations over the same set of n elements were firstly investigated by T. Uno and M.Yagiura (Algorithmica, 26:290:309, 2000), who proposed an efficient algorithm to find common intervals when K=2. Several particular…
The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…
System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
Common intervals have been defined as a modelisation of gene clusters in genomes represented either as permutations or as sequences. Whereas optimal algorithms for finding common intervals in permutations exist even for an arbitrary number…
We study an interval ordering problem introduced by D\"urr et al. [Discrete Appl. Math. 2012] which is motivated by applications in bioinformatics. The task is to order a given set of n intervals with the goal of minimizing a certain…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…