Answering complex queries in store fulfillment, such as ''What percentage of employee-assigned actions remain unresolved?'' or ''How many worklists for a specific product type were completed within a timeframe at each location?'' requires precise, multi-hop reasoning across datasets with varying granularities. This paper introduces an ontology-based knowledge graph (KG) approach integrated with a structured text-to-Cypher generation pipeline, enabling accurate retrieval for such queries. Benchmarking against a robust hybrid search baseline combining BM25 and semantic search, our method demonstrates superior performance in addressing multi-hop and cross-granularity questions. Leveraging a KG schema designed to capture intricate relationships (e.g. (OrderLineItem)-[:INVOLVES_ACTION]->(Action)-[:INVOLVES]->(BatchProcess)-[:IS_COMPLETED_AT]->(Location)), we reveal universal patterns for constructing and querying highly relational data. This work highlights the transformative potential of ontology-driven KGs to improve reasoning, data aggregation, and decision-making, with broader implications for any domain requiring structured, multi-relational data analysis.

The problem of matching not just two, but m different sets of objects to each other arises in a variety of contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, permutation synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods.

Hypothesis testing on signals defined on surfaces (such as the cortical surface) is a fundamental component of a variety of studies in Neuroscience. The goal here is to identify regions that exhibit changes as a function of the clinical condition under study. As the clinical questions of interest move towards identifying very early signs of diseases, the corresponding statistical differences at the group level invariably become weaker and increasingly hard to identify. Indeed, after a multiple comparisons correction is adopted (to account for correlated statistical tests over all surface points), very few regions may survive. In contrast to hypothesis tests on point-wise measurements, in this paper, we make the case for performing statistical analysis on multi-scale shape descriptors that characterize the local topological context of the signal around each surface vertex. Our descriptors are based on recent results from harmonic analysis, that show how wavelet theory extends to non-Euclidean settings (i.e., irregular weighted graphs). We provide strong evidence that these descriptors successfully pick up group-wise differences, where traditional methods either fail or yield unsatisfactory results. Other than this primary application, we show how the framework allows performing cortical surface smoothing in the native space without mappint to a unit sphere.

Alzheimer's disease (AD) research has recently witnessed a great deal of activity focused on developing new statistical learning tools for automated inference using imaging data. The workhorse for many of these techniques is the support vector machine (SVM) framework (or more generally kernel-based methods). Most of these require, as a first step, specification of a kernel matrix K between input examples (i.e., images). The inner product between images I(i) and I(j) in a feature space can generally be written in closed form and so it is convenient to treat K as "given." However, in certain neuroimaging applications such an assumption becomes problematic. As an example, it is rather challenging to provide a scalar measure of similarity between two instances of highly attributed data such as cortical thickness measures on cortical surfaces. Note that cortical thickness is known to be discriminative for neurological disorders, so leveraging such information in an inference framework, especially within a multi-modal method, is potentially advantageous. But despite being clinically meaningful, relatively few works have successfully exploited this measure for classification or regression. Motivated by these applications, our paper presents novel techniques to compute similarity matrices for such topologically-based attributed data. Our ideas leverage recent developments to characterize signals (e.g., cortical thickness) motivated by the persistence of their topological features, leading to a scheme for simple constructions of kernel matrices. As a proof of principle, on a dataset of 356 subjects from the Alzheimer's Disease Neuroimaging Initiative study, we report good performance on several statistical inference tasks without any feature selection, dimensionality reduction, or parameter tuning.