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Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
We present EntropyDB, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum…
In this thesis, we study aspects of entanglement theory of quantum field theories from an algebraic point of view. The main motivation is to gain insights about the general structure of the entanglement in QFT, towards a definition of an…
Many information-theoretic quantities have corresponding representations in terms of sets. The prevailing signed measure space for characterising entropy, the $I$-measure of Yeung, is occasionally unable to discern between qualitatively…
Timbre allows us to distinguish between sounds even when they share the same pitch and loudness, playing an important role in music, instrument recognition, and speech. Traditional approaches, such as frequency analysis or machine learning,…
The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…
Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence,…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
A reliable and efficient representation of multivariate time series is crucial in various downstream machine learning tasks. In multivariate time series forecasting, each variable depends on its historical values and there are…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
In this paper we propose a data intensive approach for inferring sentence-internal temporal relations. Temporal inference is relevant for practical NLP applications which either extract or synthesize temporal information (e.g.,…
We investigate the concept of time-like entanglement entropy (tEE) within the framework of holography. We introduce a robust top-down prescription for computing tEE in higher-dimensional QFTs, both conformal and confining, eliminating the…
In this paper, we investigate entanglement for causally connected subregions $A$ and $B$ in quantum field theory and holography. Recent developments have established that a transition operator $T_{AB}$ can be well-defined for such…
In a temporal network, the presence and activity of nodes and links can change through time. To describe temporal networks we introduce the notion of temporal quantities. We define the addition and multiplication of temporal quantities in a…
Many studies record replicated time series epochs from different groups with the goal of using frequency domain properties to discriminate between the groups. In many applications, there exists variation in cyclical patterns from time…
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…
We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…
Understanding the emergence of the thermodynamic arrow of time in microscopic systems is of fundamental importance, particularly given that unitary evolution preserves time-reversal symmetry. While projective measurements introduce temporal…
In this paper we give a complementary view of some of the results on group systems by Forney and Trott. We find an encoder of a group system which has the form of a time convolution. We consider this to be a time domain encoder while the…