QBF solvers implementing the QCDCL paradigm are powerful algorithms that successfully tackle many computationally complex applications. However, our theoretical understanding of the strength and limitations of these QCDCL solvers is very limited. In this paper we suggest to formally model QCDCL solvers as proof systems. We define different policies that can be used for decision heuristics and unit propagation and give rise to a number of sound and complete QBF proof systems (and hence new QCDCL algorithms). With respect to the standard policies used in practical QCDCL solving, we show that the corresponding QCDCL proof system is incomparable (via exponential separations) to Q-resolution, the classical QBF resolution system used in the literature. This is in stark contrast to the propositional setting where CDCL and resolution are known to be p-equivalent. This raises the question what formulas are hard for standard QCDCL, since Q-resolution lower bounds do not necessarily apply to QCDCL as we show here. In answer to this question we prove several lower bounds for QCDCL, including exponential lower bounds for a large class of random QBFs. We also introduce a strengthening of the decision heuristic used in classical QCDCL, which does not necessarily decide variables in order of the prefix, but still allows to learn asserting clauses. We show that with this decision policy, QCDCL can be exponentially faster on some formulas. We further exhibit a QCDCL proof system that is p-equivalent to Q-resolution. In comparison to classical QCDCL, this new QCDCL version adapts both decision and unit propagation policies.
In this letter, we investigate a novel quadrature spatial scattering modulation (QSSM) transmission technique based on millimeter wave (mmWave) systems, in which the transmitter generates two orthogonal beams targeting candidate scatterers in the channel to carry the real and imaginary parts of the conventional signal, respectively. Meanwhile, the maximum likelihood (ML) detector is adopted at the receiver to recover the received beams and signals. Based on the ML detector, we derive the closed-form average bit error probability (ABEP) expression of the QSSM scheme. Furthermore, we evaluate the asymptotic ABEP expression of the proposed scheme. Monte Carlo simulations verify the exactness and tightness of the derivation results. It is shown that the ABEP performance of QSSM is better than that of traditional spatial scattering modulation.
Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, this framework is only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.
Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length $n$ with the property that the real-valued sums of all distinct pairs of strings are distinct. In addition to this defining property, constant-weight binary $B_2$-sequences also satisfy the constraint that each string has a fixed, relatively small weight $\omega$ that scales linearly with $n$. The constant-weight constraint ensures low-cost synthesis and uniform processing of the data readout via tandem mass spectrometers. Our main results include upper bounds on the size of the codes formulated as entropy-optimization problems and constructive lower bounds based on Sidon sequences.
In this paper, we study the severity of cascading failures in supply chain networks defined by a node percolation process corresponding to product suppliers failing independently due to systemic shocks. We first show that the size of the cascades follows a power law in random directed acyclic graphs, whose topology encodes the natural ordering of products from simple raw materials to complex products. This motivates the need for a supply chain resilience metric, which we define as the maximum magnitude shock that the production network can withstand such that at least $(1 - \varepsilon)$-fraction of the products are produced with high probability as the size of the production network grows to infinity. Next, we study the resilience of many network architectures and classify them as resilient, where large cascading failures can be avoided almost surely, and as fragile, where large cascades are inevitable. In the next step, we give bounds on the expected size of cascading failures in a given production network graph as the solution to a linear program and show that extending the node percolation process to a joint percolation process that affects the nodes and the links of the production network becomes a special instance of the well-studied financial contagion model of Eisenberg and Noe. We show that under certain assumptions, the Katz centrality of each node can be used as a measure of their vulnerability and give general lower bounds as well as optimal interventions for improving resilience as a function of Katz centralities. Finally, to validate our theoretical results, we empirically calculate the resilience metric and study interventions in a variety of real-world networks.
5G and Beyond networks promise low-latency support for applications that need to deliver mission-critical data with strict deadlines. However, innovations on the physical and medium access layers are not sufficient. Additional considerations are needed to support applications under different network topologies, and while network setting and data paths change. Such support could be developed at the transport layer, ensuring end-to-end latency in a dynamic network and connectivity environment. In this paper, we present a partial reliability framework, which governs per-packet reliability through bespoke policies at the transport layer. The framework follows a no-ack and no-retransmit philosophy for unreliable transmission of packets, yet maintains cooperation with its reliable counterpart for arbitrary use of either transmission mode. This can then address latency and reliability fluctuations in a changing network environment, by smartly altering packet reliability. Our evaluations are conducted using mininet to simulate real-world network characteristics, while using a video streaming application as a real-time use-case. The results demonstrate the reduction of session packet volume and backlogged packets, with little to no effect on the freshness of the packet updates.
Numerical simulations with rigid particles, drops or vesicles constitute some examples that involve 3D objects with spherical topology. When the numerical method is based on boundary integral equations, the error in using a regular quadrature rule to approximate the layer potentials that appear in the formulation will increase rapidly as the evaluation point approaches the surface and the integrand becomes sharply peaked. To determine when the accuracy becomes insufficient, and a more costly special quadrature method should be used, error estimates are needed. In this paper we present quadrature error estimates for layer potentials evaluated near surfaces of genus 0, parametrized using a polar and an azimuthal angle, discretized by a combination of the Gauss-Legendre and the trapezoidal quadrature rules. The error estimates involve no unknown coefficients, but complex valued roots of a specified distance function. The evaluation of the error estimates in general requires a one dimensional local root-finding procedure, but for specific geometries we obtain analytical results. Based on these explicit solutions, we derive simplified error estimates for layer potentials evaluated near spheres; these simple formulas depend only on the distance from the surface, the radius of the sphere and the number of discretization points. The usefulness of these error estimates is illustrated with numerical examples.
Feature models are commonly used to specify the valid configurations of a product line. In industry, feature models are often complex due to a large number of features and constraints. Thus, a multitude of automated analyses have been proposed. Many of those rely on computing the number of valid configurations which typically depends on solving a #SAT problem, a computationally expensive operation. Further, most counting-based analyses require numerous #SAT computations on the same feature model. In particular, many analyses depend on multiple computations for evaluating the number of valid configurations that include certain features or conform to partial configurations. Instead of using expensive repetitive computations on highly similar formulas, we aim to improve the performance by reusing knowledge between these computations. In this work, we are the first to propose reusing d-DNNFs for performing efficient repetitive queries on features and partial configurations. Our empirical evaluation shows that our approach is up-to 8,300 times faster (99.99\% CPU-time saved) than the state of the art of repetitively invoking #SAT solvers. Applying our tool ddnnife reduces runtimes from days to minutes compared to using #SAT solvers.
Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information from its neighbors using a permutation-invariant aggregation function. Standard well-examined choices such as the mean or sum aggregation functions have limited capabilities, as they are not able to capture interactions among neighbors. In this work, we formalize these interactions using an information-theoretic framework that notably includes synergistic information. Driven by this definition, we introduce the Graph Ordering Attention (GOAT) layer, a novel GNN component that captures interactions between nodes in a neighborhood. This is achieved by learning local node orderings via an attention mechanism and processing the ordered representations using a recurrent neural network aggregator. This design allows us to make use of a permutation-sensitive aggregator while maintaining the permutation-equivariance of the proposed GOAT layer. The GOAT model demonstrates its increased performance in modeling graph metrics that capture complex information, such as the betweenness centrality and the effective size of a node. In practical use-cases, its superior modeling capability is confirmed through its success in several real-world node classification benchmarks.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. As the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Different from previous surveys, this survey paper reviews over forty representative transfer learning approaches from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.