Search

In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a suitable stabilizing form, we develop a rigorous interpolation, stability, and convergence analysis obtaining optimal error estimates in the energy norm. Finally, we validate the theoretical findings through numerical experiments., Comment: 24 pages, 6 figures

Over the past decade, several urban visual analytics systems and tools have been proposed to tackle a host of challenges faced by cities, in areas as diverse as transportation, weather, and real estate. Many of these tools have been designed through collaborations with urban experts, aiming to distill intricate urban analysis workflows into interactive visualizations and interfaces. However, the design, implementation, and practical use of these tools still rely on siloed approaches, resulting in bespoke applications that are difficult to reproduce and extend. At the design level, these tools undervalue rich data workflows from urban experts, typically treating them only as data providers and evaluators. At the implementation level, they lack interoperability with other technical frameworks. At the practical use level, they tend to be narrowly focused on specific fields, inadvertently creating barriers to cross-domain collaboration. To address these gaps, we present Curio, a framework for collaborative urban visual analytics. Curio uses a dataflow model with multiple abstraction levels (code, grammar, GUI elements) to facilitate collaboration across the design and implementation of visual analytics components. The framework allows experts to intertwine data preprocessing, management, and visualization stages while tracking the provenance of code and visualizations. In collaboration with urban experts, we evaluate Curio through a diverse set of usage scenarios targeting urban accessibility, urban microclimate, and sunlight access. These scenarios use different types of data and domain methodologies to illustrate Curio's flexibility in tackling pressing societal challenges. Curio is available at https://urbantk.org/curio., Comment: Accepted at IEEE VIS 2024. Source code available at https://urbantk.org/curio

This study presents a transit routing, assignment, and simulation framework which is fully embedded in a multimodal, multi-agent transportation demand and supply modeling platform. POLARIS, a high-performance agent-based simulation platform, efficiently integrates advanced travel and freight demand modeling, dynamic traffic and transit assignment, and multimodal transportation simulation within a unified framework. We focus on POLARIS's transit routing, assignment, and simulation components, detailing its structural design and essential terminologies. We demonstrate how the model integrates upstream decision-making processes - activity generation, location and timing choices, and mode selection, particularly for transit-inclusive trips - followed by routing, assignment decisions, and the movement of travelers and vehicles within a multimodal network. This integration enables modeling of interactions among all agents, including travelers, vehicles, and transportation service providers. The study reviews literature on transportation system modeling tools, describes the transit modeling framework within POLARIS, and presents findings from large-scale analyses of various policy interventions. Results from numerical experiments reveal that measures such as congestion pricing, transit service improvements, first-mile-last-mile subsidies, increased e-commerce deliveries, and vehicle electrification significantly impact transit ridership, with some interactions between these levers exhibiting synergistic or canceling effects. The case study underscores the necessity of integrating transit modeling within a broader multimodal network simulation and decision-making context.

Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many approaches in literature on how to appropriately choose it as to increase the accuracy of interpolation while avoiding instability issues. However, finding the optimal shape parameter value in general remains a challenge. We present a novel approach to determine the shape parameter in RBFs: we introduce a data-driven method that controls the condition of the interpolation matrix to avoid numerically unstable interpolations, while keeping a very good accuracy. In addition, we formulate a fall-back procedure that enforces a strict upper bound on the condition number of the generated interpolation matrix. We present numerical test cases to assess the performance of the proposed methods in interpolation tasks and in a RBF based finite difference (RBF-FD) method, in one and two-space dimensions., Comment: 28 pages

We study the convergence analysis of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the discrete level.

The effect of thermal surface cleaning on the Gilbert damping, $\alpha$, of yttrium iron garnet (YIG), before capping with a metallic layer, has been investigated. Our results show that $\alpha$ is strongly effected by relatively mild annealing conditions (T = 300 C) when performed in a vacuum. This increase needs to be taken into account when obtaining the spin mixing conductance from spin pumping measurements. We measure an increase in $\alpha$ by a factor of 8 when the YIG is vacuum annealed at 300 C. No such changes in $\alpha$ are observed when annealed at the same temperature in 0.1 mbar of oxygen., Comment: 5 page, 4 figures

We explain the relation between the $r=1$ logistic map $x_{i+1}=rx_i(1-x_i)$, $x_i\in\mathbb R$, $i=0,1,\ldots$, $r>0$ and $x_0\geq0$, and the RG flow in the multiscale analysis of zero fixed point, asymptotic free QFT models as e.g. the ultraviolet (1+1)-dimensional Gross-Neveu model and QCD, and the infrared $\phi^4_4$. We obtain the asymptotics of the mapping, showing an inverse power decay to the fixed point $x^*=0$ Gaussian fixed point, with logarithmic-like corrections. This asymptotics is independent of the initial condition $x_0\in(0,1)$ (so, there is no constraint for $x_0$ to be small, as usual in QFT models), and only depends on the lowest orders in a polynomial perturbation. In asymptotic free QFT, this means that knowing the RG $\beta$ function expansion up to higher orders in the coupling does not improve our knowledge of the flow asymptotics. A comparison with an ODE with continuous time is made by analyzing stability of the solution with higher order monomial perturbations. We also obtain the asymptotics for $0

Messaging Layer security (MLS) and its underlying Continuous Group Key Agreement (CGKA) protocol allows a group of users to share a cryptographic secret in a dynamic manner, such that the secret is modified in member insertions and deletions. Although this flexibility makes MLS ideal for implementations in distributed environments, a number of issues need to be overcome. Particularly, the use of digital certificates for authentication in a group goes against the group members' privacy. In this work we provide an alternative method of authentication in which the solicitors, instead of revealing their identity, only need to prove possession of certain attributes, dynamically defined by the group, to become a member. Instead of digital certificates, we employ Attribute-Based Credentials accompanied with Selective Disclosure in order to reveal the minimum required amount of information and to prevent attackers from linking the activity of a user through multiple groups. We formally define a CGKA variant named Attribute-Authenticated Continuous Group Key Agreement (AA-CGKA) and provide security proofs for its properties of Requirement Integrity, Unforgeability and Unlinkability. We also provide guidelines for an integration of our construction in MLS., Comment: Submitted to IEEE Transactions on Dependable and Secure Computing This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. The schemes make use of suitable upwind and CIP stabilizations to handle the fluid and magnetic convective terms. The developed error estimates are uniform in both diffusion parameters and optimal with respect to the diffusive norm; furthermore, for the second (more complex) method we are able to show a quicker error reduction rate in convection dominated regimes. A set of numerical tests support our theoretical findings.

Federated Learning (FL) is an interesting strategy that enables the collaborative training of an AI model among different data owners without revealing their private datasets. Even so, FL has some privacy vulnerabilities that have been tried to be overcome by applying some techniques like Differential Privacy (DP), Homomorphic Encryption (HE), or Secure Multi-Party Computation (SMPC). However, these techniques have some important drawbacks that might narrow their range of application: problems to work with non-linear functions and to operate large matrix multiplications and high communication and computational costs to manage semi-honest nodes. In this context, we propose a solution to guarantee privacy in FL schemes that simultaneously solves the previously mentioned problems. Our proposal is based on the Berrut Approximated Coded Computing, a technique from the Coded Distributed Computing paradigm, adapted to a Secret Sharing configuration, to provide input privacy to FL in a scalable way. It can be applied for computing non-linear functions and treats the special case of distributed matrix multiplication, a key primitive at the core of many automated learning tasks. Because of these characteristics, it could be applied in a wide range of FL scenarios, since it is independent of the machine learning models or aggregation algorithms used in the FL scheme. We provide analysis of the achieved privacy and complexity of our solution and, due to the extensive numerical results performed, a good trade-off between privacy and precision can be observed.

We consider the wiretap channel, where the individual channel uses have memory or are influenced by an adversary. We analyze the explicit and computationally efficient construction of information-theoretically secure coding schemes which use the inverse of an extractor and an error-correcting code. These schemes are known to achieve secrecy capacity on a large class of memoryless wiretap channels. We show that this also holds for certain channel types with memory. In particular, they can achieve secrecy capacity on channels where an adversary can pick a sequence of ``states'' governing the channel's behavior, as long as, given every possible state, the channel is strongly symmetric., Comment: 25 pages

Simulating long-term hydrothermal bid-based markets considering strategic agents is a challenging task. The representation of strategic agents considering inter-temporal constraints within a stochastic framework brings additional complexity to the already difficult single-period bilevel, thus, non-convex, optimal bidding problem. Thus, we propose a simulation methodology that effectively addresses these challenges for large-scale hydrothermal power systems. We demonstrate the effectiveness of the framework through a case study with real data from the large-scale Brazilian power system. In the case studies, we show the effects of market concentration in power systems and how contracts can be used to mitigate them. In particular, we show how market power might affect the current setting in Brazil. The developed method can strongly benefit policy makers, market monitors, and market designers as simulations can be used to understand existing power systems and experiment with alternative designs.

In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous operator, is introduced and theoretically investigated. The proposed method has several appealing features, including the exact enforcement of the divergence free condition and the possibility of making use of fully general polygonal meshes. A complete well-posedness and convergence analysis of the proposed method is presented under mild assumptions on the non-linear laws, encompassing common examples such as the Carreau--Yasuda model. Numerical experiments validating the theoretical bounds as well as demonstrating the practical capabilities of the proposed formulation are presented.

The first Quantum Key Distribution (QKD) networks are currently being deployed, but the implementation cost is still prohibitive for most researchers. As such, there is a need for realistic QKD network simulators. The \textit{QKDNetSim} module for the network simulator NS-3 focuses on the representation of packets and the management of key material in a QKD network at the application layer. Although QKDNetSim's representation of a QKD network is insightful, some its components lack the depth that would allow the simulator to faithfully represent the behaviour of a real quantum network. In this work, we analyse QKDNetSim's architecture to identify its limitations, and we present an enhanced version of QKDNetSim in which some of its components have been modified to provide a more realistic simulation environment., Comment: 15 pages, 5 figures, preprint submitted to SoftwareX

We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and $p$-type diffusion, with Sobolev indices $p\in (1, \infty)$. The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local P\'eclet numbers. A set of numerical tests supports the theoretical derivations.

We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learning rate, a general formula for computing the difference between test risk curves of pure gradient and stochastic gradient flows. We apply the general theory to a simple model of weak features, which displays the double descent phenomenon, and explicitly compute the corrections brought about by the added stochastic term in the dynamics, as a function of time and model parameters. The analytical results are compared to simulations of discrete-time stochastic gradient descent and show good agreement., Comment: Accepted to ICML 2024

Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material properties. Traditionally, such datasets consist of inputs given as meshes with a large number of nodes representing the problem geometry (seen as graphs), and corresponding outputs obtained with a numerical solver. This means the supervised learning model must be able to handle large and sparse graphs with continuous node attributes. In this work, we focus on Gaussian process regression, for which we introduce the Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel. In contrast to existing graph kernels, the proposed SWWL kernel enjoys positive definiteness and a drastic complexity reduction, which makes it possible to process datasets that were previously impossible to handle. The new kernel is first validated on graph classification for molecular datasets, where the input graphs have a few tens of nodes. The efficiency of the SWWL kernel is then illustrated on graph regression in computational fluid dynamics and solid mechanics, where the input graphs are made up of tens of thousands of nodes.

Resistive switching is the fundamental process that triggers the sudden change of the electrical properties in solid-state devices under the action of intense electric fields. Despite its relevance for information processing, ultrafast electronics, neuromorphic devices, resistive memories and brain-inspired computation, the nature of the local stochastic fluctuations that drive the formation of metallic nuclei out of the insulating state has remained hidden. Here, using operando X-ray nano-imaging, we have captured the early-stages of resistive switching in a V2O3-based device under working conditions. V2O3 is a paradigmatic Mott material, which undergoes a first-order metal-to-insulator transition coupled to a lattice transformation that breaks the threefold rotational symmetry of the rhombohedral metal phase. We reveal a new class of volatile electronic switching triggered by nanoscale topological defects of the lattice order parameter of the insulating phase. Our results pave the way to the use of strain engineering approaches to manipulate topological defects and achieve the full control of the electronic Mott switching. The concept of topology-driven reversible electronic transition is of interest for a broad class of quantum materials, comprising transition metal oxides, chalcogenides and kagome metals, that exhibit first-order electronic transitions coupled to a symmetry-breaking order.

High-entropy random numbers are an essential part of cryptography, and Quantum Random Number Generators (QRNG) are an emergent technology that can provide high-quality keys for cryptographic algorithms but unfortunately are currently difficult to access. Existing Entropy-as-a-Service solutions require users to trust the central authority distributing the key material, which is not desirable in a high-privacy environment. In this paper, we present a novel key transmission protocol that allows users to obtain cryptographic material generated by a QRNG in such a way that the server is unable to identify which user is receiving each key. This is achieved with the inclusion of Zero Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARK), a cryptographic primitive that allow users to prove knowledge of some value without needing to reveal it. The security analysis of the protocol proves that it satisfies the properties of Anonymity, Unforgeability and Confidentiality, as defined in this document. We also provide an implementation of the protocol demonstrating its functionality and performance, using NFC as the transmission channel for the QRNG key., Comment: 36 pages, 6 figures. Submitted to Computer Networks

This work presents an unsupervised method for automatically constructing and expanding topic taxonomies using instruction-based fine-tuned LLMs (Large Language Models). We apply topic modeling and keyword extraction techniques to create initial topic taxonomies and LLMs to post-process the resulting terms and create a hierarchy. To expand an existing taxonomy with new terms, we use zero-shot prompting to find out where to add new nodes, which, to our knowledge, is the first work to present such an approach to taxonomy tasks. We use the resulting taxonomies to assign tags that characterize merchants from a retail bank dataset. To evaluate our work, we asked 12 volunteers to answer a two-part form in which we first assessed the quality of the taxonomies created and then the tags assigned to merchants based on that taxonomy. The evaluation revealed a coherence rate exceeding 90% for the chosen taxonomies. The taxonomies' expansion with LLMs also showed exciting results for parent node prediction, with an f1-score above 70% in our taxonomies.