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This paper proposes the RePAIR dataset that represents a challenging benchmark to test modern computational and data driven methods for puzzle-solving and reassembly tasks. Our dataset has unique properties that are uncommon to current benchmarks for 2D and 3D puzzle solving. The fragments and fractures are realistic, caused by a collapse of a fresco during a World War II bombing at the Pompeii archaeological park. The fragments are also eroded and have missing pieces with irregular shapes and different dimensions, challenging further the reassembly algorithms. The dataset is multi-modal providing high resolution images with characteristic pictorial elements, detailed 3D scans of the fragments and meta-data annotated by the archaeologists. Ground truth has been generated through several years of unceasing fieldwork, including the excavation and cleaning of each fragment, followed by manual puzzle solving by archaeologists of a subset of approx. 1000 pieces among the 16000 available. After digitizing all the fragments in 3D, a benchmark was prepared to challenge current reassembly and puzzle-solving methods that often solve more simplistic synthetic scenarios. The tested baselines show that there clearly exists a gap to fill in solving this computationally complex problem., Comment: NeurIPS 2024, Track Datasets and Benchmarks, 10 pages

Mobile health (mHealth) apps have gained popularity over the past decade for patient health monitoring, yet their potential for timely intervention is underutilized due to limited integration with electronic health records (EHR) systems. Current EHR systems lack real-time monitoring capabilities for symptoms, medication adherence, physical and social functions, and community integration. Existing systems typically rely on static, in-clinic measures rather than dynamic, real-time patient data. This highlights the need for automated, scalable, and human-centered platforms to integrate patient-generated health data (PGHD) within EHR. Incorporating PGHD in a user-friendly format can enhance patient symptom surveillance, ultimately improving care management and post-surgical outcomes. To address this barrier, we have developed an mHealth platform, ROAMM-EHR, to capture real-time sensor data and Patient Reported Outcomes (PROs) using a smartwatch. The ROAMM-EHR platform can capture data from a consumer smartwatch, send captured data to a secure server, and display information within the Epic EHR system using a user-friendly interface, thus enabling healthcare providers to monitor post-surgical symptoms effectively., Comment: 8 pages, ACM MobiCom4AgeTech 2024

Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can effectively process and learn such structured information. However, learning effective information propagation patterns within DGNs remains a critical challenge that heavily influences the model capabilities, both in the static domain and in the temporal domain (where features and/or topology evolve). Given this challenge, this thesis investigates the dynamics of information propagation within DGNs for static and dynamic graphs, focusing on their design as dynamical systems. Throughout this work, we provide theoretical and empirical evidence to demonstrate the effectiveness of our proposed architectures in propagating and preserving long-term dependencies between nodes, and in learning complex spatio-temporal patterns from irregular and sparsely sampled dynamic graphs. In summary, this thesis provides a comprehensive exploration of the intersection between graphs, deep learning, and dynamical systems, offering insights and advancements for the field of graph representation learning and paving the way for more effective and versatile graph-based learning models., Comment: PhD thesis

We address the challenge of simulating unitary quantum dynamics in large systems using Neural Quantum States, focusing on overcoming the computational instabilities and high cost of existing methods. This work offers a comprehensive formalization of the projected time-dependent Variational Monte Carlo (p-tVMC) method by thoroughly analyzing its two essential components: stochastic infidelity minimization and discretization of the unitary evolution. We investigate neural infidelity minimization using natural gradient descent strategies, identifying the most stable stochastic estimators and introducing adaptive regularization strategies that eliminate the need for manual adjustment of the hyperparameter along the dynamics. We formalize the specific requirements that p-tVMC imposes on discretization schemes for them to be efficient, and introduce four high-order integration schemes combining Taylor expansions, Pad\'e approximants, and Trotter splitting to enhance accuracy and scalability. We benchmark our adaptive methods against a 2D Ising quench, matching state of the art techniques without manual tuning of hyperparameters. This work establishes p-tVMC as a highly promising framework for addressing complex quantum dynamics, offering a compelling alternative for researchers looking to push the boundaries of quantum simulations., Comment: 28 pages, 10 figures, 7 tables

In the rapidly evolving digital technology landscape, community-oriented wearable computing systems are emerging as a key tool for enhancing connectivity and interaction within communal spaces. This paper contributes to this burgeoning field by presenting the development and implementation of a proximity-based wearable computing testbed designed to forge stronger links within communities. The testbed exploits Ultra-Wideband (UWB) position sensors, 9-axis motion sensors, edge nodes, and a centralized server, forming a cohesive network that actively facilitates community interactions and engagements. By employing anchors and targets within the UWB sensors, the system achieves high precision in location and distance measurements, laying the groundwork for various proximity-based applications. Integrating 9-axis motion sensors and advanced edge nodes further underscores the system's versatility and robustness in wearable and edge computing. This paper delves into an in-depth exploration and evaluation of the proposed system's architecture, design, and implementation processes. It provides a comprehensive analysis of experimental results and discusses the system's potential impact on enhancing community networks, along with the future directions this technology could take.

Learning Continuous-Time Dynamic Graphs (C-TDGs) requires accurately modeling spatio-temporal information on streams of irregularly sampled events. While many methods have been proposed recently, we find that most message passing-, recurrent- or self-attention-based methods perform poorly on long-range tasks. These tasks require correlating information that occurred "far" away from the current event, either spatially (higher-order node information) or along the time dimension (events occurred in the past). To address long-range dependencies, we introduce Continuous-Time Graph Anti-Symmetric Network (CTAN). Grounded within the ordinary differential equations framework, our method is designed for efficient propagation of information. In this paper, we show how CTAN's (i) long-range modeling capabilities are substantiated by theoretical findings and how (ii) its empirical performance on synthetic long-range benchmarks and real-world benchmarks is superior to other methods. Our results motivate CTAN's ability to propagate long-range information in C-TDGs as well as the inclusion of long-range tasks as part of temporal graph models evaluation., Comment: Accepted at ICML 2024 (https://openreview.net/forum?id=gVg8V9isul)

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.

A common problem in Message-Passing Neural Networks is oversquashing -- the limited ability to facilitate effective information flow between distant nodes. Oversquashing is attributed to the exponential decay in information transmission as node distances increase. This paper introduces a novel perspective to address oversquashing, leveraging properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. Namely, we present SWAN, a uniquely parameterized model GNN with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by achieving these properties, SWAN offers an enhanced ability to transmit information over extended distances. Empirical evaluations on synthetic and real-world benchmarks that emphasize long-range interactions validate the theoretical understanding of SWAN, and its ability to mitigate oversquashing.

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous dynamics and sporadic observations. To address this limitation, we introduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework, which learns both the temporal and spatial dynamics from graph streams where the intervals between observations are not regularly spaced. We empirically validate the proposed approach on several graph benchmarks, showing that TG-ODE can achieve state-of-the-art performance in irregular graph stream tasks., Comment: Preprint. Accepted at IJCAI 2024

TorchGPE is a general-purpose Python package developed for solving the Gross-Pitaevskii equation (GPE). This solver is designed to integrate wave functions across a spectrum of linear and non-linear potentials. A distinctive aspect of TorchGPE is its modular approach, which allows the incorporation of arbitrary self-consistent and time-dependent potentials, e.g., those relevant in many-body cavity QED models. The package employs a symmetric split-step Fourier propagation method, effective in both real and imaginary time. In our work, we demonstrate a significant improvement in computational efficiency by leveraging GPU computing capabilities. With the integration of the latter technology, TorchGPE achieves a substantial speed-up with respect to conventional CPU-based methods, greatly expanding the scope and potential of research in this field.

Neural quantum state (NQS) ans\"atze have shown promise in variational Monte Carlo algorithms by their theoretical capability of representing any quantum state. However, the reason behind the practical improvement in their performance with an increase in the number of parameters is not fully understood. In this work, we systematically study the efficiency of a shallow neural network to represent the ground states in different phases of the spin-1 bilinear-biquadratic chain, as the number of parameters increases. We train our ansatz by a supervised learning procedure, minimizing the infidelity w.r.t. the exact ground state. We observe that the accuracy of our ansatz improves with the network width in most cases, and eventually saturates. We demonstrate that this can be explained by looking at the spectrum of the quantum geometric tensor (QGT), particularly its rank. By introducing an appropriate indicator, we establish that the QGT rank provides a useful diagnostic for the practical representation power of an NQS ansatz.

We introduce a novel, model-independent method for the efficient simulation of low-entropy systems, whose dynamics can be accurately described with a limited number of states. Our method leverages the time-dependent variational principle to efficiently integrate the Lindblad master equation, dynamically identifying and modifying the low-rank basis over which we decompose the system's evolution. By dynamically adapting the dimension of this basis, and thus the rank of the density matrix, our method maintains optimal representation of the system state, offering a substantial computational advantage over existing adaptive low-rank schemes in terms of both computational time and memory requirements. We demonstrate the efficacy of our method through extensive benchmarks on a variety of model systems, with a particular emphasis on multi-qubit bosonic codes, a promising candidate for fault-tolerant quantum hardware. Our results highlight the method's versatility and efficiency, making it applicable to a wide range of systems characterized by arbitrary degrees of entanglement and moderate entropy throughout their dynamics. We provide an implementation of the method as a Julia package, making it readily available to use., Comment: 19 pages, 11 figures

We continue our study, started in arXiv:2212.00705, of (self-)collisions of viscoelastic solids in an inertial regime. We show existence of weak solutions with a corresponding contact force measure in the case of solids with only Lipschitz-regular boundaries. This necessitates a careful study of different concepts of tangent and normal cones and the role these play both in the proofs and in the formulation of the problem itself. Consistent with our previous approach, we study contact without resorting to penalization, i.e. by only relying on a strict non-interpenetration condition. Additionally, we improve the strategies of our previous proof, eliminating the need for regularization terms across all levels of approximation., Comment: 24 pages

The traditional dietary recommendation systems are basically nutrition or health-aware where the human feelings on food are ignored. Human affects vary when it comes to food cravings, and not all foods are appealing in all moods. A questionnaire-based and preference-aware meal recommendation system can be a solution. However, automated recognition of social affects on different foods and planning the menu considering nutritional demand and social-affect has some significant benefits of the questionnaire-based and preference-aware meal recommendations. A patient with severe illness, a person in a coma, or patients with locked-in syndrome and amyotrophic lateral sclerosis (ALS) cannot express their meal preferences. Therefore, the proposed framework includes a social-affective computing module to recognize the affects of different meals where the person's affect is detected using electroencephalography signals. EEG allows to capture the brain signals and analyze them to anticipate affective toward a food. In this study, we have used a 14-channel wireless Emotive Epoc+ to measure affectivity for different food items. A hierarchical ensemble method is applied to predict affectivity upon multiple feature extraction methods and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) is used to generate a food list based on the predicted affectivity. In addition to the meal recommendation, an automated menu planning approach is also proposed considering a person's energy intake requirement, affectivity, and nutritional values of the different menus. The bin-packing algorithm is used for the personalized menu planning of breakfast, lunch, dinner, and snacks. The experimental findings reveal that the suggested affective computing, meal recommendation, and menu planning algorithms perform well across a variety of assessment parameters.

Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically, there is an urge of making DGNs suitable for predictive tasks on realworld systems of interconnected entities, which evolve over time. With the aim of fostering research in the domain of dynamic graphs, at first, we survey recent advantages in learning both temporal and spatial information, providing a comprehensive overview of the current state-of-the-art in the domain of representation learning for dynamic graphs. Secondly, we conduct a fair performance comparison among the most popular proposed approaches on node and edge-level tasks, leveraging rigorous model selection and assessment for all the methods, thus establishing a sound baseline for evaluating new architectures and approaches, Comment: Preprint version. Accepted at IEEE TNNLS (https://ieeexplore.ieee.org/document/10490120)

We introduce a criterion to characterize quantum chaos in driven-dissipative open quantum systems, based on the spectral decomposition of the Liouvillian and of quantum trajectories. The method generalizes the analysis of the statistical distribution of complex Liouvillian eigenvalues to the state of the system at an arbitrary given time. As a result, we can separately characterize chaos in the transient dynamics and in the steady state of the system. The method naturally introduces a selection of the relevant Liouvillian spectral components of the quantum state, thus lifting the requirement of additional selection criteria based on symmetry sectors or an energy cutoff. We apply the method to the study of quantum chaos in a boundary-driven-dissipative Bose-Hubbard chain. The system displays three phases, respectively characterized by integrability, transient chaos, and steady-state chaos. Most of the cases characterized by quantum chaos become integrable in the mean-field classical limit. The quantum trajectory analysis shows that quantum chaos in these cases originates exclusively from quantum fluctuations associated with the dissipation mechanism. It provides strong evidence for the existence of an emergent dissipative quantum chaos., Comment: 17 pages, 8 figures

Let $\mathbb{F}_q$ be the finite field with $q$ elements and consider the $n$-dimensional $\mathbb{F}_q$-vector space $V=\mathbb{F}_q^n\,$. In this paper we define a closure operator on the subgroup lattice of the group $G = \mathrm{PGL}(V)$. Let $\mu$ denote the M\"obius function of this lattice. The aim is to use this closure operator to characterize subgroups $H$ of $G$ for which $\mu(H,G)\neq 0$. Moreover, we establish a polynomial bound on the number $c(m)$ of closed subgroups $H$ of index $m$ in $G$ for which the lattice of $H$-invariant subspaces of $V$ is isomorphic to a product of chains. This bound depends only on $m$ and not on the choice of $n$ and $q$. It is achieved by considering a similar closure operator for the subgroup lattice of $\mathrm{GL}(V)$ and the same results proven for this group., Comment: 21 pages. Revised version; the exposition of the material has been improved compared to the first version (thanks to the suggestions of a reviewer)

The M\"obius function of the subgroup lattice of a finite group has been introduced by Hall and applied to investigate several questions. In this paper, we consider the M\"obius function defined on an order ideal related to the lattice of the subgroups of an irreducible subgroup $G$ of the general linear group $\mathrm{GL}(n,q)$ acting on the $n$-dimensional vector space $V=\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the finite field with $q$ elements. We find a relation between this function and the Euler characteristic of two simplicial complexes $\Delta_1$ and $\Delta_2$, the former raising from the lattice of the subspaces of $V$, the latter from the subgroup lattice of $G$., Comment: 10 pages. Revised version; the first version contained some inaccuracies that have been corrected

We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in the field. Our construction directly includes the physically correct, measure-valued contact forces and thus obeys conservation of momentum and an energy balance. In particular, we prove an independently useful compactness result for contact forces., Comment: 35 pages, with corrections