Global existence and blow-up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations

This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable, respectively. The well-known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here. The class of nonlocal nonlinear wave equations also covers a variety of well-known wave equations such as various forms of the Boussinesq equation. Local existence of solutions of the Cauchy problem with initial data in suitable Sobolev spaces is proven and the conditions for global existence and finite-time blow-up of solutions are established.Comment: 17 page

Interpreting multi-stable behaviour in input-driven recurrent neural networks

Recurrent neural networks (RNNs) are computational models inspired by the brain. Although RNNs stand out as state-of-the-art machine learning models to solve challenging tasks as speech recognition, handwriting recognition, language translation, and others, they are plagued by the so-called vanishing/exploding gradient issue. This prevents us from training RNNs with the aim of learning long term dependencies in sequential data. Moreover, a problem of interpretability affects these models, known as the ``black-box issue'' of RNNs. We attempt to open the black box by developing a mechanistic interpretation of errors occurring during the computation. We do this from a dynamical system theory perspective, specifically building on the notion of Excitable Network Attractors. Our methodology is effective at least for those tasks where a number of attractors and a switching pattern between them must be learned. RNNs can be seen as massively large nonlinear dynamical systems driven by external inputs. When it comes to analytically investigate RNNs, often in the literature the input-driven property is neglected or dropped in favour of tight constraints on the input driving the dynamics, which do not match the reality of RNN applications. Trying to bridge this gap, we framed RNNs dynamics driven by generic input sequences in the context of nonautonomous dynamical system theory. This brought us to enquire deeply into a fundamental principle established for RNNs known as the echo state property (ESP). In particular, we argue that input-driven RNNs can be reliable computational models even without satisfying the classical ESP formulation. We prove a sort of input-driven fixed point theorem and exploit it to (i) demonstrate the existence and uniqueness of a global attracting solution for strongly (in amplitude) input-driven RNNs, (ii) deduce the existence of multiple responses for certain input signals which can be reliably exploited for computational purposes, and (iii) study the stability of attracting solutions w.r.t. input sequences. Finally, we highlight the active role of the input in determining qualitative changes in the RNN dynamics, e.g. the number of stable responses, in contrast to commonly known qualitative changes due to variations of model parameters

The echo index and multistability in input-driven recurrent neural networks

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A recurrent neural network (RNN) possesses the echo state property (ESP) if, for a given input sequence, it “forgets” any internal states of the driven (nonautonomous) system and asymptotically follows a unique, possibly complex trajectory. The lack of ESP is conventionally understood as a lack of reliable behaviour in RNNs. Here, we show that RNNs can reliably perform computations under a more general principle that accounts only for their local behaviour in phase space. To this end, we formulate a generalisation of the ESP and introduce an echo index to characterise the number of simultaneously stable responses of a driven RNN. We show that it is possible for the echo index to change with inputs, highlighting a potential source of computational errors in RNNs due to characteristics of the inputs driving the dynamics.Engineering and Physical Sciences Research Council (EPSRC)Canada Research Chairs programNZ Marsden fun

8-Oxo-7,8-dihydro-2'-deoxyguanosine and other lesions along the coding strand of the exon 5 of the tumour suppressor gene P53 in a breast cancer case-control study.

The next-generation sequencing studies of breast cancer have reported that the tumour suppressor P53 (TP53) gene is mutated in more than 40% of the tumours. We studied the levels of oxidative lesions, including 8-oxo-7,8-dihydro-2′-deoxyguanosine (8-oxodG), along the coding strand of the exon 5 in breast cancer patients as well as in a reactive oxygen species (ROS)-attacked breast cancer cell line using the ligation-mediated polymerase chain reaction technique. We detected a significant ‘in vitro’ generation of 8-oxodG between the codons 163 and 175, corresponding to a TP53 region with high mutation prevalence, after treatment with xanthine plus xanthine oxidase, a ROS-generating system. Then, we evaluated the occurrence of oxidative lesions in the DNA-binding domain of the TP53 in the core needle biopsies of 113 of women undergoing breast investigation for diagnostic purpose. An increment of oxidative damage at the −G− residues into the codons 163 and 175 was found in the cancer cases as compared to the controls. We found significant associations with the pathological stage and the histological grade of tumours. As the major news of this study, this largest analysis of genomic footprinting of oxidative lesions at the TP53 sequence level to date provided a first roadmap describing the signatures of oxidative lesions in human breast cancer. Our results provide evidence that the generation of oxidative lesions at single nucleotide resolution is not an event highly stochastic, but causes a characteristic pattern of DNA lesions at the site of mutations in the TP53, suggesting causal relationship between oxidative DNA adducts and breast cancer

Antineoplastic effects of rosiglitazone and PPARγ transactivation in neuroblastoma cells

Neuroblastoma (NB) is the most common extracranial solid tumour in infants. Unfortunately, most children present with advanced disease and have a poor prognosis. In the present study, we evaluated the role of the peroxisome proliferator-activated receptor γ (PPARγ) agonist rosiglitazone (RGZ) in two NB cell lines (SK-N-AS and SH-SY5Y), which express PPARγ. Rosiglitazone decreased cell proliferation and viability to a greater extent in SK-N-AS than in SH-SY5Y. Furthermore, 20 μM RGZ significantly inhibited cell adhesion, invasiveness and apoptosis in SK-N-AS, but not in SH-SY5Y. Because of the different response of SK-N-AS and SH-SY5Y cells to RGZ, the function of PPARγ as a transcriptional activator was assessed. Noticeably, transient transcription experiments with a PPARγ responsive element showed that RGZ induced a three-fold increase of the reporter activity in SK-N-AS, whereas no effect was observed in SH-SY5Y. The different PPARγ activity may be likely due to the markedly lower amount of phopshorylated (i.e. inactive) protein observed in SK-N-AS. To our knowledge, this is the first demonstration that the differential response of NB cells to RGZ may be related to differences in PPARγ transactivation. This finding indicates that PPARγ activity may be useful to select those patients, for whom PPARγ agonists may have a beneficial therapeutic effect

Molecular Characterization of a Novel Intracellular ADP-Ribosyl Cyclase

Background. ADP-ribosyl cyclases are remarkable enzymes capable of catalyzing multiple reactions including the synthesis of the novel and potent intracellular calcium mobilizing messengers, cyclic ADP-ribose and NAADP. Not all ADP-ribosyl cyclases however have been characterized at the molecular level. Moreover, those that have are located predominately at the outer cell surface and thus away from their cytosolic substrates. Methodology/Principal Findings. Here we report the molecular cloning of a novel expanded family of ADP-ribosyl cyclases from the sea urchin, an extensively used model organism for the study of inositol trisphosphate-independent calcium mobilization. We provide evidence that one of the isoforms (SpARC1) is a soluble protein that is targeted exclusively to the endoplasmic reticulum lumen when heterologously expressed. Catalytic activity of the recombinant protein was readily demonstrable in crude cell homogenates, even under conditions where luminal continuity was maintained. Conclusions/Significance. Our data reveal a new intracellular location for ADP-ribosyl cyclases and suggest that production of calcium mobilizing messengers may be compartmentalized

Selective inhibitors of cardiac ADPR cyclase as novel anti-arrhythmic compounds

ADP-ribosyl cyclases (ADPRCs) catalyse the conversion of nicotinamide adenine dinucleotide to cyclic adenosine diphosphoribose (cADPR) which is a second messenger involved in Ca2+ mobilisation from intracellular stores. Via its interaction with the ryanodine receptor Ca2+ channel in the heart, cADPR may exert arrhythmogenic activity. To test this hypothesis, we have studied the effect of novel cardiac ADPRC inhibitors in vitro and in vivo in models of ventricular arrhythmias. Using a high-throughput screening approach on cardiac sarcoplasmic reticulum membranes isolated from pig and rat and nicotinamide hypoxanthine dinuleotide as a surrogate substrate, we have identified potent and selective inhibitors of an intracellular, membrane-bound cardiac ADPRC that are different from the two known mammalian ADPRCs, CD38 and CD157/Bst1. We show that two structurally distinct cardiac ADPRC inhibitors, SAN2589 and SAN4825, prevent the formation of spontaneous action potentials in guinea pig papillary muscle in vitro and that compound SAN4825 is active in vivo in delaying ventricular fibrillation and cardiac arrest in a guinea pig model of Ca2+ overload-induced arrhythmia. Inhibition of cardiac ADPRC prevents Ca2+ overload-induced spontaneous depolarizations and ventricular fibrillation and may thus provide a novel therapeutic principle for the treatment of cardiac arrhythmias