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In backbone networks, it is fundamental to quickly protect traffic against any unexpected event, such as failures or congestions, which may impact Quality of Service (QoS). Standard solutions based on Segment Routing (SR), such as Topology-Independent Loop-Free Alternate (TI-LFA), are used in practice to handle failures, but no distributed solutions exist for distributed and tactical congestion mitigation. A promising approach leveraging SR has been recently proposed to quickly steer traffic away from congested links over alternative paths. As the pre-computation of alternative paths plays a paramount role to efficiently mitigating congestions, we investigate the associated path computation problem aiming at maximizing the amount of traffic that can be rerouted as well as the resilience against any 1-link failure. In particular, we focus on two variants of this problem. First, we maximize the residual flow after all possible failures. We show that the problem is NP-Hard, and we solve it via a Benders decomposition algorithm. Then, to provide a practical and scalable solution, we solve a relaxed variant problem, that maximizes, instead of flow, the number of surviving alternative paths after all possible failures. We provide a polynomial algorithm. Through numerical experiments, we compare the two variants and show that they allow to increase the amount of rerouted traffic and the resiliency of the network after any 1-link failure.

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying the full-field heterogeneous elastic properties of soft materials using traditional computational and engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring the full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. Our improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples. This research has significant potential for advancing our understanding of micromechanical behaviors in biological materials, impacting future innovations in engineering and medicine.

Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which includes, when the equation is time-dependent, a time sampling. It was argued in the literature that the sampling need not be uniform but should overweight initial time instants, but no rigorous explanation was provided for these choice. In this paper we take some prototypical examples and, under standard hypothesis concerning the neural network convergence, we show that the optimal time sampling follows a truncated exponential distribution. In particular we explain when the time sampling is best to be uniform and when it should not be. The findings are illustrated with numerical examples on linear equation, Burgers' equation and the Lorenz system.

Interaction and cooperation with humans are overarching aspirations of artificial intelligence (AI) research. Recent studies demonstrate that AI agents trained with deep reinforcement learning are capable of collaborating with humans. These studies primarily evaluate human compatibility through "objective" metrics such as task performance, obscuring potential variation in the levels of trust and subjective preference that different agents garner. To better understand the factors shaping subjective preferences in human-agent cooperation, we train deep reinforcement learning agents in Coins, a two-player social dilemma. We recruit $N = 501$ participants for a human-agent cooperation study and measure their impressions of the agents they encounter. Participants' perceptions of warmth and competence predict their stated preferences for different agents, above and beyond objective performance metrics. Drawing inspiration from social science and biology research, we subsequently implement a new ``partner choice'' framework to elicit revealed preferences: after playing an episode with an agent, participants are asked whether they would like to play the next episode with the same agent or to play alone. As with stated preferences, social perception better predicts participants' revealed preferences than does objective performance. Given these results, we recommend human-agent interaction researchers routinely incorporate the measurement of social perception and subjective preferences into their studies.

Domain decomposition provides an effective way to tackle the dilemma of physics-informed neural networks (PINN) which struggle to accurately and efficiently solve partial differential equations (PDEs) in the whole domain, but the lack of efficient tools for dealing with the interfaces between two adjacent sub-domains heavily hinders the training effects, even leads to the discontinuity of the learned solutions. In this paper, we propose a symmetry group based domain decomposition strategy to enhance the PINN for solving the forward and inverse problems of the PDEs possessing a Lie symmetry group. Specifically, for the forward problem, we first deploy the symmetry group to generate the dividing-lines having known solution information which can be adjusted flexibly and are used to divide the whole training domain into a finite number of non-overlapping sub-domains, then utilize the PINN and the symmetry-enhanced PINN methods to learn the solutions in each sub-domain and finally stitch them to the overall solution of PDEs. For the inverse problem, we first utilize the symmetry group acting on the data of the initial and boundary conditions to generate labeled data in the interior domain of PDEs and then find the undetermined parameters as well as the solution by only training the neural networks in a sub-domain. Consequently, the proposed method can predict high-accuracy solutions of PDEs which are failed by the vanilla PINN in the whole domain and the extended physics-informed neural network in the same sub-domains. Numerical results of the Korteweg-de Vries equation with a translation symmetry and the nonlinear viscous fluid equation with a scaling symmetry show that the accuracies of the learned solutions are improved largely.

Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also improve the theoretical understanding of neural networks. Nevertheless, it seems limited when these networks are trained with cross-entropy loss, mainly because of the unboundedness of the target function. In this paper, we aim to fill this gap by analyzing the rate of the excess risk of a CNN classifier trained by cross-entropy loss. Under suitable assumptions on the smoothness and structure of the a posteriori probability, it is shown that these classifiers achieve a rate of convergence which is independent of the dimension of the image. These rates are in line with the practical observations about CNNs.

Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the remaining ones do not consider scenarios in which the ratio of the number of covariates to sample size is high. In this work, we compare the discrimination performance of lasso and maximum likelihood estimation in logistic regression using simulation studies and applications. Variable selection is done both by lasso and by stepwise when maximum likelihood estimation is used. We consider a wide range of values for the ratio of the number of covariates to sample size. The main conclusion of the work is that lasso has a better discrimination performance than maximum likelihood estimation when the ratio of the number of covariates to sample size is high.

We argue that the success of reservoir computing lies within the separation capacity of the reservoirs and show that the expected separation capacity of random linear reservoirs is fully characterised by the spectral decomposition of an associated generalised matrix of moments. Of particular interest are reservoirs with Gaussian matrices that are either symmetric or whose entries are all independent. In the symmetric case, we prove that the separation capacity always deteriorates with time; while for short inputs, separation with large reservoirs is best achieved when the entries of the matrix are scaled with a factor $\rho_T/\sqrt{N}$, where $N$ is the dimension of the reservoir and $\rho_T$ depends on the maximum length of the input time series. In the i.i.d. case, we establish that optimal separation with large reservoirs is consistently achieved when the entries of the reservoir matrix are scaled with the exact factor $1/\sqrt{N}$. We further give upper bounds on the quality of separation in function of the length of the time series. We complement this analysis with an investigation of the likelihood of this separation and the impact of the chosen architecture on separation consistency.

Twin nodes in a static network capture the idea of being substitutes for each other for maintaining paths of the same length anywhere in the network. In dynamic networks, we model twin nodes over a time-bounded interval, noted $(\Delta,d)$-twins, as follows. A periodic undirected time-varying graph $\mathcal G=(G_t)_{t\in\mathbb N}$ of period $p$ is an infinite sequence of static graphs where $G_t=G_{t+p}$ for every $t\in\mathbb N$. For $\Delta$ and $d$ two integers, two distinct nodes $u$ and $v$ in $\mathcal G$ are $(\Delta,d)$-twins if, starting at some instant, the outside neighbourhoods of $u$ and $v$ has non-empty intersection and differ by at most $d$ elements for $\Delta$ consecutive instants. In particular when $d=0$, $u$ and $v$ can act during the $\Delta$ instants as substitutes for each other in order to maintain journeys of the same length in time-varying graph $\mathcal G$. We propose a distributed deterministic algorithm enabling each node to enumerate its $(\Delta,d)$-twins in $2p$ rounds, using messages of size $O(\delta_\mathcal G\log n)$, where $n$ is the total number of nodes and $\delta_\mathcal G$ is the maximum degree of the graphs $G_t$'s. Moreover, using randomized techniques borrowed from distributed hash function sampling, we reduce the message size down to $O(\log n)$ w.h.p.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.