相关论文: Balanced Binary Tree Schemes for Computing Zernike…

Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…

The series-parallel (active) redundancy allocation problem with mixed components (RAP) involves setting reliable objectives for components or subsystems to meet the resource consumption constraint, e.g., the total cost. RAP has been an…

Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open:…

Binary Balanced Tree RvNNs (BBT-RvNNs) enforce sequence composition according to a preset balanced binary tree structure. Thus, their non-linear recursion depth is just $\log_2 n$ ($n$ being the sequence length). Such logarithmic scaling…

Computing the partition function, $Z$, of an Ising model over a graph of $N$ \enquote{spins} is most likely exponential in $N$. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute…

The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…

This paper presents a novel approach to enhance the Binary-Addition-Tree algorithm (BAT) by integrating incremental learning techniques. BAT, known for its simplicity in development, implementation, and application, is a powerful implicit…

The sampling based motion planning algorithm known as Rapidly-exploring Random Trees (RRT) has gained the attention of many researchers due to their computational efficiency and effectiveness. Recently, a variant of RRT called RRT* has been…

Segmentation-based image coding methods provide high compression ratios when compared with traditional image coding approaches like the transform and sub band coding for low bit-rate compression applications. In this paper, a…

We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric…

Various networks are broadly and deeply applied in real-life applications. Reliability is the most important index for measuring the performance of all network types. Among the various algorithms, only implicit enumeration algorithms, such…

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…

In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…

Online 3D Bin Packing Problem (3D-BPP) has widespread applications in industrial automation. Existing methods usually solve the problem with limited resolution of spatial discretization, and/or cannot deal with complex practical constraints…

This paper proposes a novel binarized weight network (BT) for a resource-efficient neural structure. The proposed model estimates a binary representation of weights by taking into account the approximation error with an additional term.…

This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…

Many network applications are based on binary-state networks, where each component has one of two states: success or failure. Efficient algorithms to evaluate binary-state network reliability are continually being developed. Reliability…

The Zernike radial polynomials are a system of orthogonal polynomials over the unit interval with weight x. They are used as basis functions in optics to expand fields over the cross section of circular pupils. To calculate the roots of…

In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…

In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform…