Bivariate functions with low cc-differential uniformity

Starting with the multiplication of elements in $\mathbb{F}_{q}^2$ which is consistent with that over $\mathbb{F}_{q^2}$, where $q$ is a prime power, via some identification of the two environments, we investigate the $c$-differential uniformity for bivariate functions $F(x,y)=(G(x,y),H(x,y))$. By carefully choosing the functions $G(x,y)$ and $H(x,y)$, we present several constructions of bivariate functions with low $c$-differential uniformity. Many P$c$N and AP$c$N functions can be produced from our constructions.Comment: Low $c$-differential uniformity, perfect and almost perfect $c$-nonlinearity, the bivariate functio

A HINT from Arithmetic: On Systematic Generalization of Perception, Syntax, and Semantics

Inspired by humans' remarkable ability to master arithmetic and generalize to unseen problems, we present a new dataset, HINT, to study machines' capability of learning generalizable concepts at three different levels: perception, syntax, and semantics. In particular, concepts in HINT, including both digits and operators, are required to learn in a weakly-supervised fashion: Only the final results of handwriting expressions are provided as supervision. Learning agents need to reckon how concepts are perceived from raw signals such as images (i.e., perception), how multiple concepts are structurally combined to form a valid expression (i.e., syntax), and how concepts are realized to afford various reasoning tasks (i.e., semantics). With a focus on systematic generalization, we carefully design a five-fold test set to evaluate both the interpolation and the extrapolation of learned concepts. To tackle this challenging problem, we propose a neural-symbolic system by integrating neural networks with grammar parsing and program synthesis, learned by a novel deduction--abduction strategy. In experiments, the proposed neural-symbolic system demonstrates strong generalization capability and significantly outperforms end-to-end neural methods like RNN and Transformer. The results also indicate the significance of recursive priors for extrapolation on syntax and semantics.Comment: Preliminary wor

Neural-Symbolic Recursive Machine for Systematic Generalization

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required

Uloga deplecije glutationa u aktivaciji Nrf2/ARE deltametrinom u štakorskim PC12-stanicama feokromocitoma

Transcription factor NF-E2-related factor 2 (Nrf2) is important for cell protection against chemical-induced oxidative stress. Previously, we have reported that in PC12 cells, Nrf2 can be triggered by deltamethrin (DM), a commonly used pyrethroid insecticide. Molecular mechanisms behind Nrf2 activation by DM are still unclear. Here we studied the effects of cell glutathione (GSH) depletion on Nrf2 activation by DM. We found that DM enhanced Nrf2 expression at the mRNA and protein levels and increased nuclear Nrf2 levels. Activation of Nrf2 was associated with activation of its downstream targets, such as heme oxygenase-1 (HO-1) and glutamate cysteine ligase catalytic subunit (GCLC). In contrast, DL-buthionine-[S,R]- sulfoximine (BSO), a known GSH-depleting agent, did not increase Nrf2 protein expression or cause its nuclear accumulation. However, pre-treatment with BSO triggered mRNA expression of HO-1 and GCLC. Furthermore, BSO pre-treatment suppressed DM-induced Nrf2 upregulation and activation and lowered mRNA expression of HO-1 and GCLC upon DM treatment. These data demonstrate that GSH depletion is not necessary for the activation of Nrf2/ARE by DM in PC12 cells, and that GCLC and HO-1 expression can increase through other signalling pathways.Transkripcijski čimbenik 2 povezan s NF-E2 (Nrf2) važan je za zaštitu stanice od oksidacijskog stresa uzrokovanog kemijskim spojevima. U prijašnjem smo istraživanju utvrdili da često rabljeni piretroidni insekticid deltametrin aktivira Nrf2 u štakorskim PC12-stanicama feokromocitoma. Još međutim nisu jasni molekularni mehanizmi te aktivacije. U ovome smo istraživanju željeli utvrditi ulogu deplecije staničnoga glutationa (GSH) u aktivaciji Nrf2 od strane DM-a. DM je pojačao ekspresiju Nrf2 u mRNA te povisio razinu proteina i razinu Nrf2 u jezgri. Aktivacija Nrf2 bila je povezana s nizvodnom aktivacijom hemoksigenaze 1 (HO-1) i katalitičke podjedinice glutamat cistein ligaze (GCLC). DL-butionin-[S,R]-sulfoksimin (BSO), za koji se zna da dovodi do deplecije GSH, nije međutim povećao ekspresiju Nrf2-proteina niti doveo do njegova nakupljanja u staničnoj jezgri. Prethodna primjena BSO aktivirala je međutim ekspresiju HO-1 i GCLC u mRNA. Usto je suprimirala djelovanje DM-a na aktivaciju i regulaciju Nrf2 te smanjila ekspresiju HO-1 i GCLC u mRNA nakon primjene DM-a. Ova saznanja govore da deplecija GSH nije nuždan mehanizam za aktivaciju Nrf2/ARE od strane DM-a u PC12-stanica te da do povećane ekspresije GCLC i HO-1 može doći drugim signalnim putovima