We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}. Persistence spheres map an integrable measure $μ$ on the upper half-plane, including persistence diagrams (PDs) as counting measures, to a function $S(μ)\in C(\mathbb{S}^2)$, and the map is stable with respect to 1-Wasserstein partial transport distance $\mathrm{POT}_1$. Moreover, to the best of our knowledge, persistence spheres are the first explicit representation used in topological machine learning for which continuity of the inverse on the image is established at every compactly supported target. Recent bounded-cardinality bi-Lipschitz embedding results in partial transport spaces, despite being powerful, are not given by the kind of explicit summary map considered here. Our construction is rooted in convex geometry: for positive measures, the defining ReLU integral is the support function of the lift zonoid. Building on~\cite{pegoraro2025persistence}, we refine the definition to better match the $\mathrm{POT}_1$ deletion mechanism, encoding partial transport via a signed diagonal augmentation. In particular, for integrable $μ$, the uniform norm between $S(0)$ and $S(μ)$ depends only on the persistence of $μ$, without any need of ad-hoc re-weightings, reflecting optimal transport to the diagonal at persistence cost. This yields a parameter-free representation at the level of measures (up to numerical discretization), while accommodating future extensions where $μ$ is a smoothed measure derived from PDs (e.g., persistence intensity functions~\citep{wu2024estimation}). Across clustering, regression, and classification tasks involving functional data, time series, graphs, meshes, and point clouds, the updated persistence spheres are competitive and often improve upon persistence images, persistence landscapes, persistence splines, and sliced Wasserstein kernel baselines.

Developments in machine learning together with the increasing usage of sensor data challenge the reliance on deterministic logs, requiring new process mining solutions for uncertain, and in particular stochastically known, logs. In this work we formulate {trace recovery}, the task of generating a deterministic log from stochastically known logs that is as faithful to reality as possible. An effective trace recovery algorithm would be a powerful aid for maintaining credible process mining tools for uncertain settings. We propose an algorithmic framework for this task that recovers the best alignment between a stochastically known log and a process model, with three innovative features. Our algorithm, SKTR, 1) handles both Markovian and non-Markovian processes; 2) offers a quality-based balance between a process model and a log, depending on the available process information, sensor quality, and machine learning predictiveness power; and 3) offers a novel use of a synchronous product multigraph to create the log. An empirical analysis using five publicly available datasets, three of which use predictive models over standard video capturing benchmarks, shows an average relative accuracy improvement of more than 10 over a common baseline.

Motivated by the abundance of uncertain event data from multiple sources including physical devices and sensors, this paper presents the task of relating a stochastic process observation to a process model that can be rendered from a dataset. In contrast to previous research that suggested to transform a stochastically known event log into a less informative uncertain log with upper and lower bounds on activity frequencies, we consider the challenge of accommodating the probabilistic knowledge into conformance checking techniques. Based on a taxonomy that captures the spectrum of conformance checking cases under stochastic process observations, we present three types of challenging cases. The first includes conformance checking of a stochastically known log with respect to a given process model. The second case extends the first to classify a stochastically known log into one of several process models. The third case extends the two previous ones into settings in which process models are only stochastically known. The suggested problem captures the increasingly growing number of applications in which sensors provide probabilistic process information.

CHIBA, JAPAN--Technology has made its way into just about everything we have and everywhere we go, even the bathroom – and the bed, the work uniform, and many other unlikely places. No place is that clearer than in Japan at the CEATEC tech trade show just outside of Tokyo. You may not see all of these things in a store, home or office near you anytime soon – CEATEC's emphasis on research made it look a bit like a science fair compared to such larger gadget gatherings as CES in Las Vegas and IFA in Berlin. But Japan's longstanding status as a leading indicator of technology makes it likely that some of these things will wind up in your life. On this convention's first day, All Nippon Airways president and CEO Shinya Katanozaka talked up the airline's plans to let people skip flying by experiencing other places through robot avatars.