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2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-29
Author(s):  
Zi Wang ◽  
Aws Albarghouthi ◽  
Gautam Prakriya ◽  
Somesh Jha

To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation , primarily using the interval abstract domain. In this paper, we study the theoretical power and limits of the interval domain for neural-network verification. First, we introduce the interval universal approximation (IUA) theorem. IUA shows that neural networks not only can approximate any continuous function f (universal approximation) as we have known for decades, but we can find a neural network, using any well-behaved activation function, whose interval bounds are an arbitrarily close approximation of the set semantics of f (the result of applying f to a set of inputs). We call this notion of approximation interval approximation . Our theorem generalizes the recent result of Baader et al. from ReLUs to a rich class of activation functions that we call squashable functions . Additionally, the IUA theorem implies that we can always construct provably robust neural networks under ℓ ∞ -norm using almost any practical activation function. Second, we study the computational complexity of constructing neural networks that are amenable to precise interval analysis. This is a crucial question, as our constructive proof of IUA is exponential in the size of the approximation domain. We boil this question down to the problem of approximating the range of a neural network with squashable activation functions. We show that the range approximation problem (RA) is a Δ 2 -intermediate problem, which is strictly harder than NP -complete problems, assuming coNP ⊄ NP . As a result, IUA is an inherently hard problem : No matter what abstract domain or computational tools we consider to achieve interval approximation, there is no efficient construction of such a universal approximator. This implies that it is hard to construct a provably robust network, even if we have a robust network to start with.


2021 ◽  
Vol 22 (19) ◽  
pp. 10304
Author(s):  
Yang Xu ◽  
Ziqiang Zhu

Basic helix-loop-helix (bHLH) family transcription factor PHYTOCHROME INTERACTING FACTOR 4 (PIF4) is necessary for plant adaption to light or high ambient temperature. PIF4 directly associates with plenty of its target genes and modulates the global transcriptome to induce or reduce gene expression levels. However, PIF4 activity is tightly controlled by its interacting proteins. Until now, twenty-five individual proteins have been reported to physically interact with PIF4. These PIF4-interacting proteins act together with PIF4 and form a unique nexus for plant adaption to light or temperature change. In this review, we will discuss the different categories of PIF4-interacting proteins, including photoreceptors, circadian clock regulators, hormone signaling components, and transcription factors. These distinct PIF4-interacting proteins either integrate light and/or temperature cues with endogenous hormone signaling, or control PIF4 abundances and transcriptional activities. Taken together, PIF4 and PIF4-interacting proteins play major roles for exogenous and endogenous signal integrations, and therefore establish a robust network for plants to cope with their surrounding environmental alterations.


Author(s):  
Fernanda Dreux M. Fernandes ◽  
Leonardo Wanderley Lopes ◽  
Mara Behlau

Purpose The pandemic created new and urgent challenges to professionals in the field of communication sciences and disorders known as Phonoaudiology in Brazil. The Brazilian Association of Phonoaudiology has the second-largest group of professionals in this field. This article presents actions and projects of the scientific association taken to support clinical and teaching practices in Brazil to face of the challenges posed by the pandemic. In addition, broad strategies were implemented to address the current and future challenges to speech therapists in Brazil. Conclusions The Brazilian Association of Phonoaudiology heard the demands of the phonoaudiologists and reacted quickly using all available resources to face the unprecedented challenges imposed by the pandemic. Immediate and future challenges included being present in the life of the average phonoaudiologist, as a scientific and professional robust network, and enlarging the number of members to represent all of Brazil, a country with geographic, racial, linguistic, and economic complex diversity.


2021 ◽  
Vol 9 ◽  
Author(s):  
Xiangzhen Yan ◽  
Hanchao Yang ◽  
Zhongyuan Yu ◽  
Shuguang Zhang

This article proposes the use of a novel approach to portfolio optimization, referred to as “Fundamental Networks” (FN). FN is an effective and robust network-based fundamental-incorporated method, and can be served as an alternative to classical mean-variance framework models. As a proxy for a portfolio, a fundamental network is defined as a set of “interconnected” stocks, among which linkages are a measure of similarity of fundamental information and are referred to asset allocation directly. Two empirical models are provided in this paper as applications of Fundamental Networks. We find that Fundamental Networks efficient portfolios are in general more mean-variance efficient in out-of-sample performance than Markwotiz’s efficient portfolios. Specifically, portfolios set for profitability goals create excess return in a general/upward trending market; portfolios targeted for operating fitness perform better in a downward trending market, and can be considered as a defensive strategy in the event of a crisis.


2021 ◽  
Vol 12 ◽  
Author(s):  
Yonglei Jiang ◽  
Xing Chen ◽  
Gaokun Zhao ◽  
Jiahong Liu ◽  
Yan Xie ◽  
...  

“Cherry-red” tobacco is the superior variant of tobacco, appearing with the apperance of red dapples on cured leaves due to the demethylation of nicotine to nornicotine during maturation and curing. Fungi are known to have the capacity to convert nicotine to nornicotine. However, an endophytic fungal community of “cherry-red” tobacco has never been reported to our best knowledge. Here, we sampled mature leaves from both “cherry-red” and ordinary tobacco at lower, center, and upper plant sections, and we analyzed the ITS diversity using high-throughput sequencing. Results revealed a significantly different fungal community of foliar endophyte in “cherry-red” and ordinary tobacco. In comparison to the ordinary control, higher diversity and a co-occurrence network complex were found in “cherry-red” samples, especially in the center and upper leaves, where the red dapples mainly emerged. More taxa were enriched in the “cherry-red” than ordinary tobacco leaves at all plant sections. In particular, Aspergillus, some strains of which are reported capable of converting nicotine to nornicotine, was specifically enriched in upper “cherry-red” tobacco leaves, which showed most red dapples after curing. A less robust network structure was detected in the “cherry-red” tobacco compared to ordinary tobacco. The nearest taxon index (NTI) and β NTI indicated that the local community structuration of tobacco endophytic fungi mainly driven by deterministic process, while the community turnover among plant sections was stochastic. In conclusion, our study provides the earliest information of endophytic fungal community in “cherry-red” tobacco leaf, and the community diversity, composition, and network features are synchronously varied with the appearance of red dapples, which is suggestive of their relationship to the formation of “cherry-red” tobacco.


2021 ◽  
Vol 349 ◽  
pp. 129112
Author(s):  
Yang Jiang ◽  
Chen Zhang ◽  
Jinghe Yuan ◽  
Yayun Wu ◽  
Feng Li ◽  
...  

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