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We consider a model of two interdependent networks, where every node in one network depends on one or more supply nodes in the other network and a node fails if it loses all of its supply nodes. We develop algorithms to compute the failure probability of a path, and obtain the most reliable path between a pair of nodes in a network, under the condition that each supply node fails independently with a given probability. Our work generalizes the classical shared risk group model, by considering multiple risks associated with a node and letting a node fail if all the risks occur. Moreover, we study the diverse routing problem by considering two paths between a pair of nodes. We define two paths to be $d$-failure resilient if at least one path survives after removing $d$ or fewer supply nodes, which generalizes the concept of disjoint paths in a single network, and risk-disjoint paths in a classical shared risk group model. We compute the probability that both paths fail, and develop algorithms to compute the most reliable pair of paths.

More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more sophisticated methods than the crude way of concatenation is needed. In this letter, by placing the continuous-time Markov chain (CTMC) on the species set, I present a novel model for inferring the phylogeny, obtaining the network graph, or drawing the proximity conclusions. The rate of transition between states is calculated based on the binary character paths between each two species. This is the base for the pairwise distances between species. Next to its generic use, the formulation of the model allows the site-wise phylogenetic inference and a mathematically justified method of combining these information to form as big as the whole genome phylogenetic inference. Although based on the characters or traits, this model is inherently a distance method but its advantage to other methods of the same class is its ability to incorporate the information of all the other species in forming the pairwise distance between two them.

In this letter, we revisit the IEQ method and provide a new perspective on its ability to preserve the original energy dissipation laws. The invariant energy quadratization (IEQ) method has been widely used to design energy stable numerical schemes for phase-field or gradient flow models. Although there are many merits of the IEQ method, one major disadvantage is that the IEQ method usually respects a modified energy law, where the modified energy is expressed in the auxiliary variables. Still, the dissipation laws in terms of the original energy are not guaranteed. Using the widely-used Cahn-Hilliard equation as an example, we demonstrate that the Runge-Kutta IEQ method indeed can preserve the original energy dissipation laws for certain situations up to arbitrary high-order accuracy. Interested readers are highly encouraged to apply our idea to other phase-field equations or gradient flow models.

We propose a new method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an arbitrary point to start the calculation. This makes it possible to find solutions of the GLME at an arbitrary point with a cutoff of the matrix coefficient, which allows to avoid the occurrence of numerical instability and to perform calculations for soliton solutions spaced apart in the time domain. Using an example of two solitons, we demonstrate our method and its range of applicability. An example of eight solitons shows how the method can be applied to a more complex signal configuration.

We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity snapshots are used to generate a POD-Galerkin ROM which is subsequently exploited to generate the data, covering the whole parameter range, used in the training phase of the DL-ROM. A convolutional autoencoder is employed to map the system response onto a low-dimensional representation and, in parallel, to model the reduced nonlinear trial manifold. The system dynamics on the manifold is described by means of a deep feedforward neural network that is trained together with the autoencoder. The strategy is benchmarked against high fidelity solutions on a clamped-clamped beam and on a real micromirror with softening response and multiplicity of solutions. By comparing the different computational costs, we discuss the impressive gain in performance and show that the DL-ROM truly represents a real-time tool which can be profitably and efficiently employed in complex system-level simulation procedures for design and optimisation purposes.

In this letter, we investigate the performance of reconfigurable intelligent surface (RIS)-assisted communications, under the assumption of generalized Gaussian noise (GGN), over Rayleigh fading channels. Specifically, we consider an RIS, equipped with $N$ reflecting elements, and derive a novel closed-form expression for the symbol error rate (SER) of arbitrary modulation schemes. The usefulness of the derived new expression is that it can be used to capture the SER performance in the presence of special additive noise distributions such as Gamma, Laplacian, and Gaussian noise. These special cases are also considered and their associated asymptotic SER expressions are derived, and then employed to quantify the achievable diversity order of the system. The theoretical framework is corroborated by numerical results, which reveal that the shaping parameter of the GGN ($\alpha$) has a negligible effect on the diversity order of RIS-assisted systems, particularly for large $\alpha$ values. Accordingly, the maximum achievable diversity order is determined by $N$.

Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The underlying correlation matrix is thus of interest for both model specification and model validation. In this paper, we develop tests of the hypothesis that the entries of the Kendall rank correlation matrix are linear combinations of a smaller number of parameters. The asymptotic behavior of the proposed test statistics is investigated both when the dimension is fixed and when it grows with the sample size. We pay special attention to the restricted hypothesis of partial exchangeability, which contains full exchangeability as a special case. We show that under partial exchangeability, the test statistics and their large-sample distributions simplify, which leads to computational advantages and better performance of the tests. We propose various scalable numerical strategies for implementation of the proposed procedures, investigate their behavior through simulations and power calculations under local alternatives, and demonstrate their use on a real dataset of mean sea levels at various geographical locations.

Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.

Over the past decade, knowledge graphs became popular for capturing structured domain knowledge. Relational learning models enable the prediction of missing links inside knowledge graphs. More specifically, latent distance approaches model the relationships among entities via a distance between latent representations. Translating embedding models (e.g., TransE) are among the most popular latent distance approaches which use one distance function to learn multiple relation patterns. However, they are not capable of capturing symmetric relations. They also force relations with reflexive patterns to become symmetric and transitive. In order to improve distance based embedding, we propose multi-distance embeddings (MDE). Our solution is based on the idea that by learning independent embedding vectors for each entity and relation one can aggregate contrasting distance functions. Benefiting from MDE, we also develop supplementary distances resolving the above-mentioned limitations of TransE. We further propose an extended loss function for distance based embeddings and show that MDE and TransE are fully expressive using this loss function. Furthermore, we obtain a bound on the size of their embeddings for full expressivity. Our empirical results show that MDE significantly improves the translating embeddings and outperforms several state-of-the-art embedding models on benchmark datasets.

Recommender systems rely on large datasets of historical data and entail serious privacy risks. A server offering recommendations as a service to a client might leak more information than necessary regarding its recommendation model and training dataset. At the same time, the disclosure of the client's preferences to the server is also a matter of concern. Providing recommendations while preserving privacy in both senses is a difficult task, which often comes into conflict with the utility of the system in terms of its recommendation-accuracy and efficiency. Widely-purposed cryptographic primitives such as secure multi-party computation and homomorphic encryption offer strong security guarantees, but in conjunction with state-of-the-art recommender systems yield far-from-practical solutions. We precisely define the above notion of security and propose CryptoRec, a novel recommendations-as-a-service protocol, which encompasses a crypto-friendly recommender system. This model possesses two interesting properties: (1) It models user-item interactions in a user-free latent feature space in which it captures personalized user features by an aggregation of item features. This means that a server with a pre-trained model can provide recommendations for a client without having to re-train the model with the client's preferences. Nevertheless, re-training the model still improves accuracy. (2) It only uses addition and multiplication operations, making the model straightforwardly compatible with homomorphic encryption schemes.