A separation logic for negative dependence

Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller (like the number of elements hashed into the other buckets). This is an example of negative dependence , a generalization of probabilistic independence that has recently found interesting applications in algorithm design and machine learning. Despite the usefulness of negative dependence for the analyses of probabilistic data structures, existing verification methods cannot establish this property for randomized programs. To fill this gap, we design LINA, a probabilistic separation logic for reasoning about negative dependence. Following recent works on probabilistic separation logic using separating conjunction to reason about the probabilistic independence of random variables, we use separating conjunction to reason about negative dependence. Our assertion logic features two separating conjunctions, one for independence and one for negative dependence. We generalize the logic of bunched implications (BI) to support multiple separating conjunctions, and provide a sound and complete proof system. Notably, the semantics for separating conjunction relies on a non-deterministic , rather than partial, operation for combining resources. By drawing on closure properties for negative dependence, our program logic supports a Frame-like rule for negative dependence and monotone operations. We demonstrate how LINA can verify probabilistic properties of hash-based data structures and balls-into-bins processes.

A Residual-Based Message Passing Algorithm for Constraint Satisfaction Problems

Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given a high priority in updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.

Computer Network Security Defense Model

With the rapid development of the Internet industry, hundreds of millions of online resources are also booming. In the information space with huge and complex resources, it is necessary to quickly help users find the resources they are interested in and save users time. At this stage, the content industry’s application of the recommendation model in the content distribution process has become the mainstream. The content recommendation model provides users with a highly efficient and highly satisfying reading experience, and solves the problem of information redundancy to a certain extent. Knowledge tag personalized dynamic recommendation technology is currently widely used in the field of e-commerce. The purpose of this article is to study the optimization of the knowledge tag personalized dynamic recommendation system based on artificial intelligence algorithms. This article first proposes a hybrid recommendation algorithm based on the comparison between content-based filtering and collaborative filtering algorithms. It mainly introduces user browsing behavior analysis and design, KNN-based item similarity algorithm design, and hybrid recommendation algorithm implementation. Finally, through algorithm simulation experiments, the effectiveness of the algorithm in this paper is verified, and the accuracy of the recommendation has been improved.

Optimal structure control for earthquake resistance

This work developed the optimal and active control algorithms applicable to structural control for earthquake resistance. [Lewis, F. L., Vrabie, D. and Syrmos, V. L. [2012] Optimal Control (John Wiley & Sons)] developed a rigorous and comprehensive procedure for the derivation of an optimal control strategy based on the calculus of variation. This work is an application of Lewis’ formulation to the control of a structure for earthquake resistance. We developed a computer software which can be used to generate a dynamic model to simulate a planar structure and to construct the control law. This model also includes the tendon driven actuators, sensors and true history of earthquake excitation. The control law has two parts: (I) the feedback control which depends on the estimate state variables (Kalman filter) and (II) the record of the realistic earthquake excitation. The optimal control problem eventually leads to a two-point boundary value problem whose solution hinges on the knowledge of the entire history of the earthquake excitation. We employ true records of earthquake excitation as input. This approach enables one to solve the Riccati equations rigorously. Then, from the simulation results, one may study the relations between the control algorithm design and the characteristics (frequency, amplitude and duration) of earthquake excitation.

Extended Fractional Singular Kalman Filter

Effective and accurate state estimation is a staple of modern modeling. On the other hand, nonlinear fractional-order singular (FOS) systems are an attractive modeling tool as well since they can provide accurate descriptions of systems with complex dynamics. Consequently, developing accurate state estimation methods for such systems is highly relevant since it provides vital information about the system including related memory effects and long interconnection properties with constraint elements. However, missing features in transforming structures such as violation of constraints in non-singular versions of such systems may affect the performance of the estimation result. This paper proposes the state estimation algorithm design for the original and non-transformed stochastic nonlinear FOS system. We introduce a deterministic data-fitting based framework which helps us to take steps directly towards Kalman filter (KF) derivation of the system, called extended fractional singular KF (EFSKF). Using stochastic reasoning, we demonstrate how to construct recursive form of the filter. Analysis of the filter shows how the proposed algorithm reduces to the nominal nonlinear filters when the system is in its usual state-space form making said algorithm highly flexible. Finally, simulation results verify that the estimation of nonlinear states can be accomplished with the proposed EFSKF algorithm with a reasonable performance.

Parallel Classification Algorithm Design of Human Resource Big Data Based on Spark Platform

In order to solve the problem of large data classification of human resources, a new parallel classification algorithm of large data of human resources based on the Spark platform is proposed in this study. According to the spark platform, it can complete the update and distance calculation of the human resource big data clustering center and design the big data clustering process. Based on this, the K-means clustering method is introduced to mine frequent itemsets of large data and optimize the aggregation degree of similar large data. A fuzzy genetic algorithm is used to identify the balance of big data. This study adopts the selective integration method to study the unbalanced human resource database classifier in the process of transmission, introduces the decision contour matrix to construct the anomaly support model of the set of unbalanced human resource data classifier, identifies the features of the big data of human resource in parallel, repairs the relevance of the big data of human resource, introduces the improved ant colony algorithm, and finally realizes the design of the parallel classification algorithm of the big data of human resource. The experimental results show that the proposed algorithm has a low time cost, good classification effect, and ideal parallel classification rule complexity.