The M/M/ N

This paper considers the M/M/N repairable queuing system. The customers' arrival is a Poisson process. The servers are subject to breakdown according to Poisson processes with different rates in idle time and busy time, respectively. The breakdown servers are repaired by repairmen, and the repair time is an exponential distribution. Using probability generating function and transform method, we obtain the steady-state probabilities of the system states, the steady-state availability of the servers, and the mean queueing length of the model

Certifying the Fairness of KNN in the Presence of Dataset Bias

We propose a method for certifying the fairness of the classification result of a widely used supervised learning algorithm, the k-nearest neighbors (KNN), under the assumption that the training data may have historical bias caused by systematic mislabeling of samples from a protected minority group. To the best of our knowledge, this is the first certification method for KNN based on three variants of the fairness definition: individual fairness, $\epsilon$-fairness, and label-flipping fairness. We first define the fairness certification problem for KNN and then propose sound approximations of the complex arithmetic computations used in the state-of-the-art KNN algorithm. This is meant to lift the computation results from the concrete domain to an abstract domain, to reduce the computational cost. We show effectiveness of this abstract interpretation based technique through experimental evaluation on six datasets widely used in the fairness research literature. We also show that the method is accurate enough to obtain fairness certifications for a large number of test inputs, despite the presence of historical bias in the datasets

Open-world Semi-supervised Generalized Relation Discovery Aligned in a Real-world Setting

Open-world Relation Extraction (OpenRE) has recently garnered significant attention. However, existing approaches tend to oversimplify the problem by assuming that all unlabeled texts belong to novel classes, thereby limiting the practicality of these methods. We argue that the OpenRE setting should be more aligned with the characteristics of real-world data. Specifically, we propose two key improvements: (a) unlabeled data should encompass known and novel classes, including hard-negative instances; and (b) the set of novel classes should represent long-tail relation types. Furthermore, we observe that popular relations such as titles and locations can often be implicitly inferred through specific patterns, while long-tail relations tend to be explicitly expressed in sentences. Motivated by these insights, we present a novel method called KNoRD (Known and Novel Relation Discovery), which effectively classifies explicitly and implicitly expressed relations from known and novel classes within unlabeled data. Experimental evaluations on several Open-world RE benchmarks demonstrate that KNoRD consistently outperforms other existing methods, achieving significant performance gains.Comment: 10 pages, 6 figure

A BP Neural Network Model to Predict Reservior Parameters

This paper proposes an artificial neural network (ANN) method to calculate reservoir parameters. By improving the algorithm of BP neural network, convergence speed is enhanced and better result can be achieved. Practical applications prove that neural network technique is of significant importance for reservoir description