A Novel Value for the Parameter in the Dai-Liao-Type Conjugate Gradient Method

A new rule for calculating the parameter t involved in each iteration of the MHSDL (Dai-Liao) conjugate gradient (CG) method is presented. The new value of the parameter initiates a more efficient and robust variant of the Dai-Liao algorithm. Under proper conditions, theoretical analysis reveals that the proposed method in conjunction with backtracking line search is of global convergence. Numerical experiments are also presented, which confirm the influence of the new value of the parameter t on the behavior of the underlying CG optimization method. Numerical comparisons and the analysis of obtained results considering Dolan and Moré’s performance profile show better performances of the novel method with respect to all three analyzed characteristics: number of iterative steps, number of function evaluations, and CPU time.

Robustness Verification of Semantic Segmentation Neural Networks Using Relaxed Reachability

This paper introduces robustness verification for semantic segmentation neural networks (in short, semantic segmentation networks [SSNs]), building on and extending recent approaches for robustness verification of image classification neural networks. Despite recent progress in developing verification methods for specifications such as local adversarial robustness in deep neural networks (DNNs) in terms of scalability, precision, and applicability to different network architectures, layers, and activation functions, robustness verification of semantic segmentation has not yet been considered. We address this limitation by developing and applying new robustness analysis methods for several segmentation neural network architectures, specifically by addressing reachability analysis of up-sampling layers, such as transposed convolution and dilated convolution. We consider several definitions of robustness for segmentation, such as the percentage of pixels in the output that can be proven robust under different adversarial perturbations, and a robust variant of intersection-over-union (IoU), the typical performance evaluation measure for segmentation tasks. Our approach is based on a new relaxed reachability method, allowing users to select the percentage of a number of linear programming problems (LPs) to solve when constructing the reachable set, through a relaxation factor percentage. The approach is implemented within NNV, then applied and evaluated on segmentation datasets, such as a multi-digit variant of MNIST known as M2NIST. Thorough experiments show that by using transposed convolution for up-sampling and average-pooling for down-sampling, combined with minimizing the number of ReLU layers in the SSNs, we can obtain SSNs with not only high accuracy (IoU), but also that are more robust to adversarial attacks and amenable to verification. Additionally, using our new relaxed reachability method, we can significantly reduce the verification time for neural networks whose ReLU layers dominate the total analysis time, even in classification tasks.

SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.

SLALOM: A Simple and Rapid Method for Enzymatic Synthesis of CRISPR-Cas9 sgRNA Libraries

ABSTRACTCRISPR-Cas9 sgRNA libraries have transformed functional genetic screening and have enabled innovative CRISPR-based methods, such as the visualization of chromatin dynamics in living cells. These libraries have the potential to be applied to a vast number of biological systems and aid in the development of new technologies, but their synthesis is hindered by the cost, time requirements, and technical difficulty of current sgRNA library generation methods. Here, we describe SLALOM—a rapid enzymatic method for generating robust, variant-matched sgRNA libraries from any source of DNA in under 3 hours. This method utilizes a custom sgRNA scaffold sequence and a novel method for detaching oligonucleotides from solid supports using a strand displacing polymerase. Using this method, we have constructed libraries targeting the E. coli genome and the transcriptome of developing zebrafish hearts, demonstrating its potential to expand the reach of CRISPR technology and facilitate methods requiring custom sgRNA libraries.

A leader-follower single allocation hub location problem under fixed markups

This study examines a scenario in which two competitors, called a leader and a follower, sequentially create their hub and spoke networks to maximize their profits. It is assumed that a non-hub node can be allocated to at most one hub. The pricing is regulated with a fixed markup. Demand is split according to the logit model, and customers patronize their choice of route by a price. Two variants of this Stackelberg competition are addressed: deterministic and robust. In both cases, it was shown how to present the problem as a bi-level mixed-integer non-linear program. When it comes to the deterministic variant, a mixed-integer linear reformulation of the follower?s model is given. For the robust variant, it is shown how to reformulate the follower?s program as a mixed-integer conic-quadratic one. The benefits of these reformulations are that they allow the usage of state-of-the-art solvers in finding feasible solutions. As a solution approach for the leader, an alternating heuristic is proposed. Computational experiments are conducted on the set of Cinstances and thoroughly discussed, providing some managerial insights.

Real-Time Implementation of MAD-Based RFI Excision on FPGA

Radio Frequency Interference (RFI) excision in wideband radio telescope receivers is gaining significance due to increasing levels of manmade RFI and operation outside the protected radio astronomy bands. The effect of RFI on astronomical data can be significantly reduced through real-time excision. In this paper, Median Absolute Deviation (MAD) is used for excising signals corrupted by strong impulsive interference. MAD estimation requires recursive median calculation which is a computationally challenging problem for real-time excision. This challenge is addressed by implementation of a histogram-based technique for MAD computation. The architecture is developed and optimized for Field Programmable Gate Array (FPGA) implementation. The design of a more robust variant of MAD called Median-of-MAD (MoM) is described. The architecture of MAD and MoM techniques and subsequent optimization allows for four RFI excision blocks on a single Xilinx Virtex-5 FPGA. These techniques have been tested on the GMRT wideband backend (GWB) processing a maximum of 400[Formula: see text]MHz bandwidth and the results show significant improvement in the signal-to-noise ratio (SNR).