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Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing interest in the overlapping area between neural networks and more traditional statistical methods, which can help overcome those problems. In this article, a mathematical framework relating neural networks and polynomial regression is explored by building an explicit expression for the coefficients of a polynomial regression from the weights of a given neural network, using a Taylor expansion approach. This is achieved for single hidden layer neural networks in regression problems. The validity of the proposed method depends on different factors like the distribution of the synaptic potentials or the chosen activation function. The performance of this method is empirically tested via simulation of synthetic data generated from polynomials to train neural networks with different structures and hyperparameters, showing that almost identical predictions can be obtained when certain conditions are met. Lastly, when learning from polynomial generated data, the proposed method produces polynomials that approximate correctly the data locally. [ABSTRACT FROM AUTHOR]

Cancer metabolic reprogramming promotes resistance to therapies. In this study, we addressed the role of the Warburg effect in the resistance to photodynamic therapy (PDT) in skin squamous cell carcinoma (sSCC). Furthermore, we assessed the effect of metformin treatment, an antidiabetic type II drug that modulates metabolism, as adjuvant to PDT. For that, we have used two human SCC cell lines: SCC13 and A431, called parental (P) and from these cell lines we have generated the corresponding PDT resistant cells (10GT). Here, we show that 10GT cells induced metabolic reprogramming to an enhanced aerobic glycolysis and reduced activity of oxidative phosphorylation, which could influence the response to PDT. This result was also confirmed in P and 10GT SCC13 tumors developed in mice. The treatment with metformin caused a reduction in aerobic glycolysis and an increase in oxidative phosphorylation in 10GT sSCC cells. Finally, the combination of metformin with PDT improved the cytotoxic effects on P and 10GT cells. The combined treatment induced an increase in the protoporphyrin IX production, in the reactive oxygen species generation and in the AMPK expression and produced the inhibition of AKT/mTOR pathway. The greater efficacy of combined treatments was also seen in vivo , in xenografts of P and 10GT SCC13 cells. Altogether, our results reveal that PDT resistance implies, at least partially, a metabolic reprogramming towards aerobic glycolysis that is prevented by metformin treatment. Therefore, metformin may constitute an excellent adjuvant for PDT in sSCC. [Display omitted] • Cell resistant to Photodynamic therapy (PDT) is due to the metabolic reprogramming. • Metformin modulates energetic metabolism in PDT-resistant cells, sensitizing to PDT. • Metformin increases protoporphyrin IX and reactive oxygen species generation. • Metformin+PDT is proposed as potential therapy against skin squamous cell carcinoma. [ABSTRACT FROM AUTHOR]

Abstract In the excitement of the widely publicized new finds of Aurignacian art from Chauvet, from the Swabian Jura and from as far afield as Pestera Coliboaia in Romania, it has almost been forgotten that a rich corpus of Aurignacian wall painting, engraving and bas-relief sculpture had been recognized and studied before World War I in the Vézère Valley of SW France. Scientific knowledge of the chronological and cultural context of that early-discovered graphic record has been limited by the crude archaeological methods of that pioneering era, and the loss and dispersal of many of the works discovered. In 2011, we launched new excavations and a re-analysis of one of the key sites for such early discoveries, the collapsed rock shelter of Abri Blanchard. In 2012, we discovered in situ a limestone slab engraved with a complex composition combining an aurochs and dozens of aligned punctuations. This new find, recovered by modern methods and dated by molecular filtration and Hydroxyproline 14C, provides new information on the context and dating of Aurignacian graphic imagery in SW France and its relationship to that of other regions. The support is not a fragment of collapsed shelter ceiling and is situated in the midst of quotidian occupational debris. The image shows significant technical and thematic similarities to Chauvet that are reinforced by our reanalysis of engraved slabs from the older excavations at Blanchard. The aligned punctuations find their counterparts at Chauvet, in the south German sites and on several other objects from Blanchard and surrounding Aurignacian sites. In sum, we argue that dispersing Aurignacian groups show a broad commonality in graphic expression against which a certain number of more regionalized characteristics stand out, a pattern that fits well with social geography models that focus on the material construction of identity at regional, group and individual levels. [ABSTRACT FROM AUTHOR]