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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…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
Quantitative analysis of commonalities and differences between recorded music performances is an increasingly common task in computational musicology. A typical scenario involves manual annotation of different recordings of the same piece…
Prevalent efforts have been put in automatically inferring genres of musical items. Yet, the propose solutions often rely on simplifications and fail to address the diversity and subjectivity of music genres. Accounting for these has,…
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
It has long been hypothesized that perceptual ambiguities play an important role in aesthetic experience: a work with some ambiguity engages a viewer more than one that does not. However, current frameworks for testing this theory are…
Any measurement is intended to provide information on a system, namely knowledge about its state. However, we learn from quantum theory that it is generally impossible to extract information without disturbing the state of the system or its…
We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…
Omnimodal Notation Processing (ONP) represents a unique frontier for omnimodal AI due to the rigorous, multi-dimensional alignment required across auditory, visual, and symbolic domains. Current research remains fragmented, focusing on…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
Summarizing data samples by quantitative measures has a long history, with descriptive statistics being a case in point. However, as natural language processing methods flourish, there are still insufficient characteristic metrics to…
In quantum information theory, communication capacities are mostly given in terms of entropic formulas. Continuity of such entropic quantities are significant, as they ensure uniformity of measures against perturbations of quantum states.…
The use of persistent homology in applications is justified by the validity of certain stability results. At the core of such results is a notion of distance between the invariants that one associates with data sets. Here we introduce a…
The concept of compatibility originally emerged as a synonym for the commutativity of observables and later evolved into the notion of measurement compatibility. In any case, however, it has remained predominantly algebraic in nature, tied…
We propose a new measure of quantum entanglement. Our measure is defined in terms of conditional information transmission for a Quantum Bayesian Net. We show that our measure is identically equal to the Entanglement of Formation in the case…
Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography,…
Integrating datasets from different disciplines is hard because the data are often qualitatively different in meaning, scale, and reliability. When two datasets describe the same entities, many scientific questions can be phrased around…