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Home-based physical therapies are effective if the prescribed exercises are correctly executed and patients adhere to these routines. This is specially important for older adults who can easily forget the guidelines from therapists. Inertial Measurement Units (IMUs) are commonly used for tracking exercise execution giving information of patients' motion data. In this work, we propose the use of Machine Learning techniques to recognize which exercise is being carried out and to assess if the recognized exercise is properly executed by using data from four IMUs placed on the person limbs. To the best of our knowledge, both tasks have never been addressed together as a unique complex task before. However, their combination is needed for the complete characterization of the performance of physical therapies. We evaluate the performance of six machine learning classifiers in three contexts: recognition and evaluation in a single classifier, recognition of correct exercises, excluding the wrongly performed exercises, and a two-stage approach that first recognizes the exercise and then evaluates it. We apply our proposal to a set of 8 exercises of the upper-and lower-limbs designed for maintaining elderly people health status. To do so, the motion of volunteers were monitored with 4 IMUs. We obtain accuracies of 88.4 \% and the 91.4 \% in the two initial scenarios. In the third one, the recognition provides an accuracy of 96.2 \%, whereas the exercise evaluation varies between 93.6 \% and 100.0 \%. This work proves the feasibility of IMUs for a complete monitoring of physical therapies in which we can get information of which exercise is being performed and its quality, as a basis for designing virtual coaches.

A crucial challenge for solving problems in conflict research is in leveraging the semi-supervised nature of the data that arise. Observed response data such as counts of battle deaths over time indicate latent processes of interest such as intensity and duration of conflicts, but defining and labeling instances of these unobserved processes requires nuance and imprecision. The availability of such labels, however, would make it possible to study the effect of intervention-related predictors - such as ceasefires - directly on conflict dynamics (e.g., latent intensity) rather than through an intermediate proxy like observed counts of battle deaths. Motivated by this problem and the new availability of the ETH-PRIO Civil Conflict Ceasefires data set, we propose a Bayesian autoregressive (AR) hidden Markov model (HMM) framework as a sufficiently flexible machine learning approach for semi-supervised regime labeling with uncertainty quantification. We motivate our approach by illustrating the way it can be used to study the role that ceasefires play in shaping conflict dynamics. This ceasefires data set is the first systematic and globally comprehensive data on ceasefires, and our work is the first to analyze this new data and to explore the effect of ceasefires on conflict dynamics in a comprehensive and cross-country manner.

In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information Geometry sense even when the generatrix is non-even or non-smooth. A novel formula is obtained for the computation of curvature in the case of exponential families: this formula implies some new flatness criteria in dimension 2. Finally, it is observed that many two parameter distributions, widely used in applications, are locally hyperbolic, which highlights the role of hyperbolic geometry in the study of commonly employed probability manifolds. These results have benefited from the use of explainable computational tools, which can substantially boost scientific productivity.

We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model. Recently, Bhattacharyya et al. (2021) obtained finite-sample guarantees for recovering tree-structured Bayesian networks, i.e., 1-polytrees. We extend their results by providing an efficient algorithm which learns $d$-polytrees in polynomial time and sample complexity for any bounded $d$ when the underlying undirected graph (skeleton) is known. We complement our algorithm with an information-theoretic sample complexity lower bound, showing that the dependence on the dimension and target accuracy parameters are nearly tight.

We study propositional proof systems with inference rules that formalize restricted versions of the ability to make assumptions that hold without loss of generality, commonly used informally to shorten proofs. Each system we study is built on resolution. They are called BC${}^-$, RAT${}^-$, SBC${}^-$, and GER${}^-$, denoting respectively blocked clauses, resolution asymmetric tautologies, set-blocked clauses, and generalized extended resolution - all "without new variables." They may be viewed as weak versions of extended resolution (ER) since they are defined by first generalizing the extension rule and then taking away the ability to introduce new variables. Except for SBC${}^-$, they are known to be strictly between resolution and extended resolution. Several separations between these systems were proved earlier by exploiting the fact that they effectively simulate ER. We answer the questions left open: We prove exponential lower bounds for SBC${}^-$ proofs of a binary encoding of the pigeonhole principle, which separates ER from SBC${}^-$. Using this new separation, we prove that both RAT${}^-$ and GER${}^-$ are exponentially separated from SBC${}^-$. This completes the picture of their relative strengths.

Comparisons of frequency distributions often invoke the concept of shift to describe directional changes in properties such as the mean. In the present study, we sought to define shift as a property in and of itself. Specifically, we define distributional shift (DS) as the concentration of frequencies away from the discrete class having the greatest value (e.g., the right-most bin of a histogram). We derive a measure of DS using the normalized sum of exponentiated cumulative frequencies. We then define relative distributional shift (RDS) as the difference in DS between two distributions, revealing the magnitude and direction by which one distribution is concentrated to lesser or greater discrete classes relative to another. We find that RDS is highly related to popular measures that, while based on the comparison of frequency distributions, do not explicitly consider shift. While RDS provides a useful complement to other comparative measures, DS allows shift to be quantified as a property of individual distributions, similar in concept to a statistical moment.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

Deterministic communication is required for applications of several industry verticals including manufacturing, automotive, financial, and health care, etc. These applications rely on reliable and time-synchronized delivery of information among the communicating devices. Therefore, large delay variations in packet delivery or inaccuracies in time synchronization cannot be tolerated. In particular, the industrial revolution on digitization, connectivity of digital and physical systems, and flexible production design require deterministic and time-synchronized communication. A network supporting deterministic communication guarantees data delivery in a specified time with high reliability. The IEEE 802.1 TSN task group is developing standards to provide deterministic communication through IEEE 802 networks. The IEEE 802.1AS standard defines time synchronization mechanism for accurate distribution of time among the communicating devices. The time synchronization accuracy depends on the accurate calculation of the residence time which is the time between the ingress and the egress ports of the bridge and includes the processing, queuing, transmission, and link latency of the timing information. This paper discusses time synchronization mechanisms supported in current wired and wireless integrated systems.

Power posteriors "robustify" standard Bayesian inference by raising the likelihood to a constant fractional power, effectively downweighting its influence in the calculation of the posterior. Power posteriors have been shown to be more robust to model misspecification than standard posteriors in many settings. Previous work has shown that power posteriors derived from low-dimensional, parametric locally asymptotically normal models are asymptotically normal (Bernstein-von Mises) even under model misspecification. We extend these results to show that the power posterior moments converge to those of the limiting normal distribution suggested by the Bernstein-von Mises theorem. We then use this result to show that the mean of the power posterior, a point estimator, is asymptotically equivalent to the maximum likelihood estimator.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.