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Some notions in mathematics can be considered relative. Relative is a term used to denote when the variation in the position of an observer implies variation in properties or measures on the observed object. We know, from Skolem theorem,…
Concept learning constructs visual representations that are connected to linguistic semantics, which is fundamental to vision-language tasks. Although promising progress has been made, existing concept learners are still vulnerable to…
In this paper we describe the mathematical foundations of a new approach to semi-supervised Machine Learning. Using techniques of Symbolic Computation and Computer Algebra, we apply the concept of persistent homology to obtain a new…
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a…
Subwords are the most widely used output units in end-to-end speech recognition. They combine the best of two worlds by modeling the majority of frequent words directly and at the same time allow open vocabulary speech recognition by…
In this paper, new characterizations for functional observability, functional detectability, and structural functional observability (SFO) are developed, and based on them, the related optimal sensor placement problems are investigated. A…
A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based computations. Conversely, by the Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable relative to…
Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this…
Controllability and observability are important properties of a distributed paramater systems.The equivalence between the notion of exact observability and exact controllability holds in general. In this work, we define a new notion of…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
In the last years renewed investigation of operator precedence languages (OPL) led to discover important properties thereof: OPL are closed with respect to all major operations, are characterized, besides the original grammar family, in…
A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We present a novel unsupervised approach for multilingual sentiment analysis driven by compositional syntax-based rules. On the one hand, we exploit some of the main advantages of unsupervised algorithms: (1) the interpretability of their…
How to best integrate linguistic and perceptual processing in multi-modal tasks that involve language and vision is an important open problem. In this work, we argue that the common practice of using language in a top-down manner, to direct…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
Abductive reasoning aims to find plausible explanations for an event. This style of reasoning is critical for commonsense tasks where there are often multiple plausible explanations. Existing approaches for abductive reasoning in natural…
The downward closure of a language $L$ of words is the set of all (not necessarily contiguous) subwords of members of $L$. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a…
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the…