We investigate elastic-plastic adhesive wear via a continuum variational phase-field approach. The model seamlessly captures the transition from perfectly brittle, over quasi-brittle to elastic-plastic wear regimes, as the ductility of the contacting material increases. Simulation results highlight the existence of a critical condition that morphological features and material ductility need to satisfy for the adhesive junction to detach a wear debris. We propose a new criterion to discriminate between non-critical and critical asperity contacts, where the former produce negligible wear while the latter lead to significant debris formation.
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We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove optimal according to some dimension. The first, based on the minimum-diameter averaging, requires $ n \geq 6f+1$, but achieves asymptotically the best-possible averaging constant up to a multiplicative constant. The second, based on reliable broadcast and coordinate-wise trimmed mean, achieves optimal Byzantine resilience, i.e., $n \geq 3f+1$. Each of these algorithms induces an optimal Byzantine collaborative learning protocol. In particular, our equivalence yields new impossibility theorems on what any collaborative learning algorithm can achieve in adversarial and heterogeneous environments.
The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction between incompressibility and smeared crack opening. Drawing on the stiffness-degradation idea in PFM, we resolved this contradiction through loosening incompressible constraint of the damaged phase without affecting the incompressibility of intact material. By modifying the perturbed Lagrangian approach, we derived a novel mixed formulation. In numerical aspects, the finite element discretization uses the classical Q1/P0 and high-order P2/P1 schemes, respectively. To ease the mesh distortion at large strains, an adaptive mesh deletion technology is also developed. The validity and robustness of the proposed mixed framework are corroborated by four representative numerical examples. By comparing the performance of Q1/P0 and P2/P1, we conclude that the Q1/P0 formulation is a better choice for finite strain fracture in nearly incompressible cases. Moreover, the numerical examples also show that the combination of the proposed framework and methodology has vast potential in simulating complex peeling and tearing problems
Biological as well as advanced artificial intelligences (AIs) need to decide which goals to pursue. We review nature's solution to the time allocation problem, which is based on a continuously readjusted categorical weighting mechanism we experience introspectively as emotions. One observes phylogenetically that the available number of emotional states increases hand in hand with the cognitive capabilities of animals and that raising levels of intelligence entail ever larger sets of behavioral options. Our ability to experience a multitude of potentially conflicting feelings is in this view not a leftover of a more primitive heritage, but a generic mechanism for attributing values to behavioral options that can not be specified at birth. In this view, emotions are essential for understanding the mind. For concreteness, we propose and discuss a framework which mimics emotions on a functional level. Based on time allocation via emotional stationarity (TAES), emotions are implemented as abstract criteria, such as satisfaction, challenge and boredom, which serve to evaluate activities that have been carried out. The resulting timeline of experienced emotions is compared with the `character' of the agent, which is defined in terms of a preferred distribution of emotional states. The long-term goal of the agent, to align experience with character, is achieved by optimizing the frequency for selecting individual tasks. Upon optimization, the statistics of emotion experience becomes stationary.
Blood pressure (BP) is one of the most influential bio-markers for cardiovascular diseases and stroke; therefore, it needs to be regularly monitored to diagnose and prevent any advent of medical complications. Current cuffless approaches to continuous BP monitoring, though non-invasive and unobtrusive, involve explicit feature engineering surrounding fingertip Photoplethysmogram (PPG) signals. To circumvent this, we present an end-to-end deep learning solution, BP-Net, that uses PPG waveform to estimate Systolic BP (SBP), Mean Average Pressure (MAP), and Diastolic BP (DBP) through intermediate continuous Arterial BP (ABP) waveform. Under the terms of the British Hypertension Society (BHS) standard, BP-Net achieves Grade A for DBP and MAP estimation and Grade B for SBP estimation. BP-Net also satisfies Advancement of Medical Instrumentation (AAMI) criteria for DBP and MAP estimation and achieves Mean Absolute Error (MAE) of 5.16 mmHg and 2.89 mmHg for SBP and DBP, respectively. Further, we establish the ubiquitous potential of our approach by deploying BP-Net on a Raspberry Pi 4 device and achieve 4.25 ms inference time for our model to translate the PPG waveform to ABP waveform.
Faster-than-Nyquist (FTN) signaling aided non-orthogonal multiple access (NOMA) is conceived and its achievable rate is quantified in the presence of random link delays of the different users. We reveal that exploiting the link delays may potentially lead to a signal-to-interference-plus-noise ratio (SINR) gain, while transmitting the data symbols at FTN rates has the potential of increasing the degree-of-freedom (DoF). We then unveil the fundamental trade-off between the SINR and DoF. In particular, at a sufficiently high symbol rate, the SINR gain vanishes while the DoF gain achieves its maximum, where the achievable rate is almost $(1+\beta)$ times higher than that of the conventional synchronous NOMA transmission in the high signal-to-noise ratio (SNR) regime, with $\beta$ being the roll-off factor of the signaling pulse. Our simulation results verify our analysis and demonstrate considerable rate improvements over the conventional power-domain NOMA scheme.
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The resulting regularized risk minimization problems admit exact convex relaxations of the type $L^1+$ (nonlocal) $\operatorname{TV}$, a form frequently studied in image analysis and graph-based learning. A rich geometric structure is revealed by this reformulation which in turn allows us to establish a series of properties of optimal solutions of the original problem, including the existence of minimal and maximal solutions (interpreted in a suitable sense), and the existence of regular solutions (also interpreted in a suitable sense). In addition, we highlight how the connection between adversarial training and perimeter minimization problems provides a novel, directly interpretable, statistical motivation for a family of regularized risk minimization problems involving perimeter/total variation. The majority of our theoretical results are independent of the distance used to define adversarial attacks.
Traffic flows in a distributed computing network require both transmission and processing, and can be interdicted by removing either communication or computation resources. We study the robustness of a distributed computing network under the failures of communication links and computation nodes. We define cut metrics that measure the connectivity, and show a non-zero gap between the maximum flow and the minimum cut. Moreover, we study a network flow interdiction problem that minimizes the maximum flow by removing communication and computation resources within a given budget. We develop mathematical programs to compute the optimal interdiction, and polynomial-time approximation algorithms that achieve near-optimal interdiction in simulation.
In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups.
A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace transform. The unique existence of the solution to the forward problem is obtained based on the inverse Laplace transform, and the uniqueness of the inverse problem is proved in the real-space of Laplace transform by the maximum principle, and numerical inversions with noisy data are presented to demonstrate a numerical stability of the inverse problem.
While many existing graph neural networks (GNNs) have been proven to perform $\ell_2$-based graph smoothing that enforces smoothness globally, in this work we aim to further enhance the local smoothness adaptivity of GNNs via $\ell_1$-based graph smoothing. As a result, we introduce a family of GNNs (Elastic GNNs) based on $\ell_1$ and $\ell_2$-based graph smoothing. In particular, we propose a novel and general message passing scheme into GNNs. This message passing algorithm is not only friendly to back-propagation training but also achieves the desired smoothing properties with a theoretical convergence guarantee. Experiments on semi-supervised learning tasks demonstrate that the proposed Elastic GNNs obtain better adaptivity on benchmark datasets and are significantly robust to graph adversarial attacks. The implementation of Elastic GNNs is available at \url{//github.com/lxiaorui/ElasticGNN}.
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