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Due to their intrinsic capabilities on parallel signal processing, optical neural networks (ONNs) have attracted extensive interests recently as a potential alternative to electronic artificial neural networks (ANNs) with reduced power consumption and low latency. Preliminary confirmation of the parallelism in optical computing has been widely done by applying the technology of wavelength division multiplexing (WDM) in the linear transformation part of neural networks. However, inter-channel crosstalk has obstructed WDM technologies to be deployed in nonlinear activation in ONNs. Here, we propose a universal WDM structure called multiplexed neuron sets (MNS) which apply WDM technologies to optical neurons and enable ONNs to be further compressed. A corresponding back-propagation (BP) training algorithm is proposed to alleviate or even cancel the influence of inter-channel crosstalk on MNS-based WDM-ONNs. For simplicity, semiconductor optical amplifiers (SOAs) are employed as an example of MNS to construct a WDM-ONN trained with the new algorithm. The result shows that the combination of MNS and the corresponding BP training algorithm significantly downsize the system and improve the energy efficiency to tens of times while giving similar performance to traditional ONNs.

Cognitive Radio Network (CRN) provides effective capabilities for resource allocation with the valuable spectrum resources in the network. It provides the effective allocation of resources to the unlicensed users or Secondary Users (SUs) to access the spectrum those are unused by the licensed users or Primary Users (Pus). This paper develops an Optimal Relay Selection scheme with the spectrum-sharing scheme in CRN. The proposed Cross-Layer Spider Swarm Shifting is implemented in CRN for the optimal relay selection with Spider Swarm Optimization (SSO). The shortest path is estimated with the data shifting model for the data transmission path in the CRN. This study examines a cognitive relay network (CRN) with interference restrictions imposed by a mobile end user (MU). Half-duplex communication is used in the proposed system model between a single primary user (PU) and a single secondary user (SU). Between the SU source and SU destination, an amplify and forward (AF) relaying mechanism is also used. While other nodes (SU Source, SU relays, and PU) are supposed to be immobile in this scenario, the mobile end user (SU destination) is assumed to travel at high vehicle speeds. The suggested method achieves variety by placing a selection combiner at the SU destination and dynamically selecting the optimal relay for transmission based on the greatest signal-to-noise (SNR) ratio. The performance of the proposed Cross-Layer Spider Swarm Shifting model is compared with the Spectrum Sharing Optimization with QoS Guarantee (SSO-QG). The comparative analysis expressed that the proposed Cross-Layer Spider Swarm Shifting model delay is reduced by 15% compared with SSO-QG. Additionally, the proposed Cross-Layer Spider Swarm Shifting exhibits the improved network performance of ~25% higher throughput compared with SSO-QG.

We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid defined on a bounding box, with some of the centers outside the computational domain. The equation is discretized using collocation with oversampling, with collocation points inside the domain only, resulting in a rectangular linear system to be solved in a least squares sense. The goal of this paper is the efficient solution of that rectangular system. We show that the least squares problem splits into a regular part, which can be expedited with the FFT, and a low rank perturbation, which is treated separately with a direct solver. The rank of the perturbation is influenced by the irregular shape of the domain and by the weak enforcement of boundary conditions at points along the boundary. The solver extends the AZ algorithm which was previously proposed for function approximation involving frames and other overcomplete sets. The solver has near optimal log-linear complexity for univariate problems, and loses optimality for higher-dimensional problems but remains faster than a direct solver.

How can citizens address hate in online discourse? We analyze a large corpus of more than 130,000 discussions on Twitter over four years. With the help of human annotators, language models and machine learning classifiers, we identify different dimensions of discourse that might be related to the probability of hate speech in subsequent tweets. We use a matching approach and longitudinal statistical analyses to discern the effectiveness of different counter speech strategies on the micro-level (individual tweet pairs), meso-level (discussion trees) and macro-level (days) of discourse. We find that expressing simple opinions, not necessarily supported by facts, but without insults, relates to the least hate in subsequent discussions. Sarcasm can be helpful as well, in particular in the presence of organized extreme groups. Mentioning either outgroups or ingroups is typically related to a deterioration of discourse. A pronounced emotional tone, either negative such as anger or fear, or positive such as enthusiasm and pride, also leads to worse discourse quality. We obtain similar results for other measures of quality of discourse beyond hate speech, including toxicity, extremity of speech, and the presence of extreme speakers. Going beyond one-shot analyses on smaller samples of discourse, our findings have implications for the successful management of online commons through collective civic moderation.

Functional magnetic resonance imaging analytical workflows are highly flexible with no definite consensus on how to choose a pipeline. While methods have been developed to explore this analytical space, there is still a lack of understanding of the relationships between the different pipelines. We use community detection algorithms to explore the pipeline space and assess its stability across different contexts. We show that there are subsets of pipelines that give similar results, especially those sharing specific parameters (e.g. number of motion regressors, software packages, etc.), with relative stability across groups of participants. By visualizing the differences between these subsets, we describe the effect of pipeline parameters and derive general relationships in the analytical space.

Immortal time is a period of follow-up during which death or the study outcome cannot occur by design. Bias from immortal time has been increasingly recognized in epidemiologic studies. However, it remains unclear how immortal time arises and what the structures of bias from immortal time are. Here, we use an example "Do Nobel Prize winners live longer than less recognized scientists?" to illustrate that immortal time arises from using postbaseline information to define exposure or eligibility. We use time-varying directed acyclic graphs (DAGs) to present the structures of bias from immortal time as the key sources of bias, that is confounding and selection bias. We explain that excluding immortal time from the follow-up does not fully address the bias, and that the presence of competing risks can worsen the bias. We also discuss how the structures of bias from immortal time are shared by different study designs in pharmacoepidemiology and provide solutions, where possible, to address the bias.

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable that enters the state equation as a coefficient; pointwise constraints on the control variable are considered as well. We establish the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality conditions. Regularity estimates for optimal variables are also analyzed. We develop two finite element discretization strategies: a semidiscrete scheme in which the control variable is not discretized, and a fully discrete scheme in which the control variable is discretized with piecewise constant functions. For both schemes, we analyze the convergence properties of discretizations and derive error estimates.

Normal modal logics extending the logic K4.3 of linear transitive frames are known to lack the Craig interpolation property, except some logics of bounded depth such as S5. We turn this `negative' fact into a research question and pursue a non-uniform approach to Craig interpolation by investigating the following interpolant existence problem: decide whether there exists a Craig interpolant between two given formulas in any fixed logic above K4.3. Using a bisimulation-based characterisation of interpolant existence for descriptive frames, we show that this problem is decidable and coNP-complete for all finitely axiomatisable normal modal logics containing K4.3. It is thus not harder than entailment in these logics, which is in sharp contrast to other recent non-uniform interpolation results. We also extend our approach to Priorean temporal logics (with both past and future modalities) over the standard time flows-the integers, rationals, reals, and finite strict linear orders-none of which is blessed with the Craig interpolation property.

There are various applications, where companies need to decide to which individuals they should best allocate treatment. To support such decisions, uplift models are applied to predict treatment effects on an individual level. Based on the predicted treatment effects, individuals can be ranked and treatment allocation can be prioritized according to this ranking. An implicit assumption, which has not been doubted in the previous uplift modeling literature, is that this treatment prioritization approach tends to bring individuals with high treatment effects to the top and individuals with low treatment effects to the bottom of the ranking. In our research, we show that heteroskedastictity in the training data can cause a bias of the uplift model ranking: individuals with the highest treatment effects can get accumulated in large numbers at the bottom of the ranking. We explain theoretically how heteroskedasticity can bias the ranking of uplift models and show this process in a simulation and on real-world data. We argue that this problem of ranking bias due to heteroskedasticity might occur in many real-world applications and requires modification of the treatment prioritization to achieve an efficient treatment allocation.

Anderson acceleration (AA) is a technique for accelerating the convergence of an underlying fixed-point iteration. AA is widely used within computational science, with applications ranging from electronic structure calculation to the training of neural networks. Despite AA's widespread use, relatively little is understood about it theoretically. An important and unanswered question in this context is: To what extent can AA actually accelerate convergence of the underlying fixed-point iteration? While simple enough to state, this question appears rather difficult to answer. For example, it is unanswered even in the simplest (non-trivial) case where the underlying fixed-point iteration consists of applying a two-dimensional affine function. In this note we consider a restarted variant of AA applied to solve symmetric linear systems with restart window of size one. Several results are derived from the analytical solution of a nonlinear eigenvalue problem characterizing residual propagation of the AA iteration. This includes a complete characterization of the method to solve $2 \times 2$ linear systems, rigorously quantifying how the asymptotic convergence factor depends on the initial iterate, and quantifying by how much AA accelerates the underlying fixed-point iteration. We also prove that even if the underlying fixed-point iteration diverges, the associated AA iteration may still converge.