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Combinatorial optimization problems such as Traveling Salesman Problem (TSP) have a wide range of real-world applications in transportation, logistics, manufacturing. It has always been a difficult problem to solve large-scale TSP problems quickly because of memory usage limitations. Recent research shows that the Transformer model is a promising approach. However, the Transformer has several severe problems that prevent it from quickly solving TSP combinatorial optimization problems, such as quadratic time complexity, especially quadratic space complexity, and the inherent limitations of the encoder and decoder itself. To address these issues, we developed a memory-efficient Transformer-based network model for TSP combinatorial optimization problems, termed Tspformer, with two distinctive characteristics: (1) a sampled scaled dot-product attention mechanism with O(Llog(L)) (L is the length of input sequences) time and space complexity, which is the most different between our work and other works. (2) due to the reduced space complexity, GPU/CPU memory usage is significantly reduced. Extensive experiments demonstrate that Tspformer significantly outperforms existing methods and provides a new solution to the TSP combinatorial optimization problems. Our Pytorch code will be publicly available on GitHub https://github.com/yhnju/tspFormer., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Human genome has structures of haplotype and haplotype block which provide valuable information on human evolutionary history and may lead to the development of more efficient strategies to identify genetic variants that increase susceptibility to complex diseases. Haplotype block can be divided into discrete blocks of limited haplotype diversity. In each block, a small fraction of ptag SNPsq can be used to distinguish a large fraction of the haplotypes. These tag SNPs can be potentially useful for construction of haplotype and haplotype block, and association studies in complex diseases. There are two general classes of methods to construct haplotype and haplotype blocks based on genotypes on large pedigrees and statistical algorithms respectively. The author evaluate several construction methods to assess the power of different association tests with a variety of disease models and block-partitioning criteria. The advantages, limitations and applications of each method and the application in the association studies are discussed equitably. With the completion of the HapMap and development of statistical algorithms for addressing haplotype reconstruction, ideas of construction of haplotype based on combination of mathematics, physics, and computer science etc will have profound impacts on population genetics, location and cloning for susceptible genes in complex diseases, and related domain with life science etc.

The traditional negative selection algorithm with a randomly generated hypersphere detector is unable to satisfy the development needs of continuous learning due to the inherent defects of the detector. This paper proposes a novel negative selection algorithm for hyper-rectangle detectors that overcomes the shortcomings of randomly generated hyper-sphere detectors and lays the foundation for a negative selection algorithm with continuous learning capability. It uses self-sample clusters of equal-sized hypercubes instead of self-samples for training. The hyper-rectangle detectors are generated by cutting the nonself-space along the boundary of the self-sample clusters. The state space is covered without overlapping each other by self-sample clusters and detectors. The anomaly detection performance of the proposed method was demonstrated using Iris data, vowel recognition data (Vowel), and Wisconsin Breast Cancer (BCW) data. The experimental results show that the proposed method outperforms other artificial immune algorithms and clustering algorithms under the same parameter conditions. [ABSTRACT FROM AUTHOR]

Negative selection algorithms play an important role in anomaly detection. Interface detectors are a special negative selection algorithm that completely eliminates outer holes, but there are detection blind areas. This paper proposes a negative selection algorithm with hypercube interface detectors for anomaly detection. It uses self-sample clusters to construct self-space, and boundary self-sample clusters to describe the interface detectors. It eliminates the detection blind area and improves the detection rate. To validate the performance of the proposed method, experiments were conducted using the iris dataset, the skin segmentation dataset, the Breast Cancer of Wisconsin (BCW) dataset, and the Waveform Database Generator (Version 2) dataset. Experimental results show that the proposed method in this paper has a higher detection rate, lower false alarm rate, and fewer detectors than other anomaly detection methods for the same parameters. • HI-detector breaks away from the hyperspherical detector used by traditional negative selection algorithms. • HI-detector consists of a cluster of multiple hypercube self-samples. • HI-detector completely eliminates duplicate coverage of holes and detectors. • HI-detector has only one parameter that needs to be set. [ABSTRACT FROM AUTHOR]

Real-time switched networks are becoming popular with the growing complexity of distributed embedded systems. There is a practical need to transmit noncritical data including diagnostic and supervising data for cost reduction. To meet hard real-time constraints, the time-triggered method is widely used due to its deterministic property, where both the reliability of the control data transmission and the tolerance of link failures are required. Conventional methods deploy redundant links and transmit frames over multiple disjoint paths. This paper presents a novel schedule method for the time-triggered network without simultaneous transmissions with multiple frames. The fault tolerance protocol is localized for critical data. We harness multiple effective optimization heuristics and strategies to ameliorate the existing schedule model and constraints. The experimental evaluation substantiates that our effective method can considerably improve the bandwidth for noncritical traffics with no link failures. [ABSTRACT FROM AUTHOR]

The infrared traffic image acquired by the intelligent traffic surveillance equipment has low contrast, little hierarchical differences in perceptions of image and the blurred vision effect. Therefore, infrared traffic image enhancement, being an indispensable key step, is applied to nearly all infrared imaging based traffic engineering applications. In this paper, we propose an infrared traffic image enhancement algorithm that is based on dark channel prior and gamma correction. In existing research dark channel prior, known as a famous image dehazing method, here is used to do infrared image enhancement for the first time. Initially, in the proposed algorithm, the original degraded infrared traffic image is transformed with dark channel prior as the initial enhanced result. A further adjustment based on the gamma curve is needed because initial enhanced result has lower brightness. Comprehensive validation experiments reveal that the proposed algorithm outperforms the current state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an approximate LU factorization algorithm is developed for nonsymmetric matrices based on the hierarchically semiseparable matrix techniques. It utilizes a technique involving orthogonal transformations and approximations to avoid the explicit computation of the Schur complement in each factorization step. A modified compression method is further developed for the case when some diagonal blocks have small singular values. The complexity of the methods proposed in this paper is analyzed and shown to be $$O(N^2k)$$ , where $$N$$ is the dimension of matrix and $$k$$ is the maximum off-diagonal (numerical) rank. Depending on the accuracy and efficiency requirements in the approximation, this factorization can be used either as a direct solver or a preconditioner. Numerical results from applications are included to show the efficiency of our method. [ABSTRACT FROM AUTHOR]

In this article, we propose an algorithm, nesta- lasso, for the lasso problem, i.e., an underdetermined linear least-squares problem with a 1-norm constraint on the solution. We prove under the assumption of the restricted isometry property ( rip) and a sparsity condition on the solution, that nesta- lasso is guaranteed to be almost always locally linearly convergent. As in the case of the algorithm nesta, proposed by Becker, Bobin, and Candès, we rely on Nesterov’s accelerated proximal gradient method, which takes $O(\sqrt {1/\varepsilon })$ iterations to come within $\varepsilon > 0$ of the optimal value. We introduce a modification to Nesterov’s method that regularly updates the prox-center in a provably optimal manner. The aforementioned linear convergence is in part due to this modification. In the second part of this article, we attempt to solve the basis pursuit denoising ( bpdn) problem (i.e., approximating the minimum 1-norm solution to an underdetermined least squares problem) by using nesta- lasso in conjunction with the Pareto root-finding method employed by van den Berg and Friedlander in their spgl1 solver. The resulting algorithm is called parnes. We provide numerical evidence to show that it is comparable to currently available solvers. [ABSTRACT FROM AUTHOR]

Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by structural designers. A method for equivalent static wind loads applicable to multi-responses is proposed in this paper. A modified loadresponse- correlation (LRC) method corresponding to a particular peak response is presented, and the similarity algorithm implemented for the group response is described. The main idea of the algorithm is that two responses can be put into one group if the value of one response is close to that of the other response, when the structure is subjected to equivalent static wind loads aiming at the other response. Based on the modified LRC, the grouping response method is put forward to construct equivalent static wind loading. This technique can simultaneously reproduce peak responses for some grouped responses. To verify its computational accuracy, the method is applied to an actual large-span roof structure. Calculation results show that when the similarity of responses in the same group is high, equivalent static wind loads with high accuracy and reasonable magnitude of equivalent static wind distribution can be achieved. [ABSTRACT FROM AUTHOR]

One of the key factors underlying the popularity of low-density parity-check (LDPC) code is its iterative decoding algorithm which is amenable to efficient analog and digital implementation. However, different applications of LDPC codes (e.g. wireless sensor networks) impose different sets of constraints which include speed, bit error rates (BER) and energy efficiency. Our previous work reported an algorithmic framework for designing margin propagation (MP) based LDPC decoders where the BER performance can be traded off with its energy efficiency. In this paper we present an analog current-mode implementation of an MP-based (32,8) LDPC decoder. The implementation uses only addition, subtraction and threshold operations and hence is independent of transistor biasing. Measured results from prototypes fabricated in a 0.5 \mum CMOS process verify the functionality of a (32,8) LDPC decoder and demonstrate the trade-off capability which is realized by adapting a system hyper-parameter. When configured as a min-sum LDPC decoder, the proposed implementation demonstrates superior BER performance compared to the state-of-the-art analog min-sum decoder at SNR greater than 3.5 dB. We show that an optimal configuration of the same MP-based decoder can also deliver up to 3 dB improvement in BER compared to the benchmark min-sum LDPC decoder. [ABSTRACT FROM AUTHOR]

Semiseparable matrices and many other rank-structured matrices have been widely used in developing new fast matrix algorithms. In this paper, we generalize the hierarchically semiseparable (HSS) matrix representations and propose some fast algorithms for HSS matrices. We represent HSS matrices in terms of general binary HSS trees and use simplified postordering notation for HSS forms. Fast HSS algorithms including new HSS structure generation and HSS form Cholesky factorization are developed. Moreover, we provide a new linear complexity explicit ULV factorization algorithm for symmetric positive definite HSS matrices with a low-rank property. The corresponding factors can be used to solve the HSS systems also in linear complexity. Numerical examples demonstrate the efficiency of the algorithms. All these algorithms have nice data locality. They are useful in developing fast-structured numerical methods for large discretized PDEs (such as elliptic equations), integral equations, eigenvalue problems, etc. Some applications are shown. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Interconnect planning is an important issue in VLSI designs. Routing congestion is an important problem during placement. This paper presents a novel approach to estimating the routing congestion on the hexagonal model with bounded-length detours. It is the first probabilistic estimation work on hexagonal topologies. A combinatorial estimation algorithm is presented. The experimental results demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The basic requirement for direction selectivity is a nonlinear interaction between two different inputs in space-time. In some models, the interaction is hypothesized to occur between excitation and inhibition of the shunting type in the neuron's dendritic tree. How can the required spatial specificity be acquired in an unsupervised manner? We here propose an activity-based, local learning model that can account for direction selectivity in visual cortex based on such a local veto operation and that depends on synaptically induced changes in intracellular calcium concentration. Our biophysical simulations suggest that a model cell with our learning algorithm can develop direction selectivity organically after unsupervised training. The learning rule is also applicable to a neuron with multiple-direction-selective subunits and to a pair of cells with oppositedirection selectivities and is stable under different starting conditions, delays, and velocities. [ABSTRACT FROM AUTHOR]

Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the normwise smallest perturbation that makes the given system uncontrollable. Many algorithms have been previously proposed to estimate this distance. Our new algorithms are the first that correctly estimate this distance at a cost polynomial in a dimension of the given system. We report results from some numerical experiments that demonstrate the reliability and effectiveness of these new algorithms. [ABSTRACT FROM AUTHOR]

We propose a new stochastic approximation (SA) algorithm for maximum-likelihood estimation (MLE) in the incomplete-data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E-step or M-step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins-Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long-standing problems in computing an MLE with incomplete data. We prove that in general O(n) simulation steps are required in computing the MLE with the SA algorithm and O( n log n) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, where n is the sample size of the observations. Examples include computing the MLE in the nonlinear error-in-variable model and nonlinear regression model with random effects. [ABSTRACT FROM AUTHOR]

Recently, Higham, Waldén, Karlson, and Sun have provided formulas for computing the best backward perturbation bounds for the linear least squares problem. In this paper we provide several backward perturbation bounds that are easier to compute and optimal up to a factor less than 2. We also show that any least squares algorithm that is stable in the sense of Stewart is necessarily a backward stable algorithm. Our results make it possible to measure numerically the amount of accuracy in any alleged solution of a least squares problem. [ABSTRACT FROM AUTHOR]

Summary: Graph matching problem appears frequently in the applications of computer vision and machine learning. In this work, based on the spectral matching with affine constraint (SMAC) formulation, we present a new formulation, named bounded SMAC (BSMAC), for the graph matching problem by adding an upper‐bound constraint on the solution norm. We demonstrate the existence of a unique solution with BSMAC, whereas SMAC needs not to have any meaningful solution in general. We develop an effective numerical method to solve the BSMAC formulation as an optimization problem. Numerical experiments are presented to verify feasibility and to show the performance of the proposed numerical method. [ABSTRACT FROM AUTHOR]

Abstract: The GPS carrier phase observations are widely used for the high precision static and kinematic positioning applications. However, GPS signals are seriously distorted when passing through walls and other obstructions. This paper focuses on this issue and outlines the research carried out to investigate the effects of some commonly used construction materials on the GPS signals. For the purpose of generating the multipath in a controlled manner, an experimental set-up is designed to test the effect of typical building surface materials (toughened glass, wood board, PVC board and ceramic tile) on positioning accuracy. The effects of signal attenuation on the accuracy of the positioning solution are explored by an improved particle filtering algorithm and some statistical methods, and reasons for these effects are further analyzed. The findings of the experimental results may be used to enhance the performance of GPS technology. [Copyright &y& Elsevier]