Formal and Empirical Studies of Counting Behaviour in ReLU RNNs

In recent years, the discussion about systematicity of neural network learning has gained renewed interest, in particular the formal analysis of neural network behaviour. In this paper, we investigate the capability of single-cell ReLU RNN models to demonstrate precise counting behaviour. Formally, we start by characterising the semi-Dyck-1 language and semi-Dyck-1 counter machine that can be implemented by a single Rectified Linear Unit (ReLU) cell. We define three Counter Indicator Conditions (CICs) on the weights of a ReLU cell and show that fulfilling these conditions is equivalent to accepting the semi-Dyck-1 language, i.e. to perform exact counting. Empirically, we study the ability of single-cell ReLU RNNs to learn to count by training and testing them on different datasets of Dyck-1 and semi-Dyck-1 strings. While networks that satisfy the CICs count exactly and thus correctly even on very long strings, the trained networks exhibit a wide range of results and never satisfy the CICs exactly. We investigate the effect of deviating from the CICs and find that configurations that fulfil the CICs are not at a minimum of the loss function in the most common setups. This is consistent with observations in previous research indicating that training ReLU networks for counting tasks often leads to poor results. We finally discuss implications of these results and possible avenues for improving network behaviour

Redox linked flavin sites in extracellular decaheme proteins involved in microbe-mineral electron transfer

Extracellular microbe-mineral electron transfer is a major driving force for the oxidation of organic carbon in many subsurface environments. Extracellular multi-heme cytochromes of the Shewenella genus play a major role in this process but the mechanism of electron exchange at the interface between cytochrome and acceptor is widely debated. The 1.8 Å x-ray crystal structure of the decaheme MtrC revealed a highly conserved CX8C disulfide that, when substituted for AX8A, severely compromised the ability of S. oneidensis to grow under aerobic conditions. Reductive cleavage of the disulfide in the presence of flavin mononucleotide (FMN) resulted in the reversible formation of a stable flavocytochrome. Similar results were also observed with other decaheme cytochromes, OmcA, MtrF and UndA. The data suggest that these decaheme cytochromes can transition between highly reactive flavocytochromes or less reactive cytochromes, and that this transition is controlled by a redox active disulfide that responds to the presence of oxygen

On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient

Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

Nile Basin Focal Project. Synthesis report

The Nile basin experiences wide spread poverty, lack of food and land and water degradation. Because poverty is linked to access to water for crop, fish and livestock based livelihoods, improving access to water and increasing agricultural water productivity can potentially contribute substantially to poverty reduction. The major goal of the Nile Basin Focal project is to identify high potential investments that reduce poverty yet reverse trends in land and water degradation. This is done through the implementation of six interlinked work packages allowing us to examine water availability, access, use, productivity, institutions and their linkages to poverty. Important in the Nile BFP is knowledge management and the uptake of results for ultimate impact

A Prokaryotic Membrane Sculpting BAR Domain Protein

Bin/Amphiphysin/RVS (BAR) domain proteins belong to a superfamily of coiled-coil proteins influencing membrane curvature in eukaryotes and are associated with vesicle biogenesis, vesicle-mediated protein trafficking, and intracellular signaling. Here we report the first prokaryotic BAR domain protein, BdpA, from Shewanella oneidensis MR-1, known to produce redox-active membrane vesicles and micrometer-scale outer membrane extensions (OMEs). BdpA is required for uniform size distribution of membrane vesicles and scaffolding OMEs into a consistent diameter and curvature. Cryogenic transmission electron microscopy reveals a strain lacking BdpA produces lobed, disordered OMEs rather than membrane tubes produced by the wild type strain. Overexpression of BdpA promotes OME formation during conditions where they are less common. Heterologous expression results in OME production in Marinobacter atlanticus and Escherichia coli. Based on the ability of BdpA to alter membrane curvature in vivo, we propose that BdpA and its homologs comprise a newly identified class of prokaryotic BAR (P-BAR) domains

Acinic cell carcinoma in pregnancy: a case report and review of the literature

<p>Abstract</p> <p>Introduction</p> <p>We report an observational study on the etiology and recurrence of acinic cell carcinoma of the parotid gland that seemed to be related to pregnancy. The medical literature has never reported such an association; therefore, our case report is probably the first to mention this observation.</p> <p>Case presentation</p> <p>This report is of a 25-year-old Arabic female patient from the United Arab Emirates, who, during her first pregnancy, developed acinic cell carcinoma of the right parotid gland that was managed with surgical excision in the form of superficial parotidectomy. During her second pregnancy, which occurred four years later, she had a recurrence of the same malignant neoplasm associated with ipsilateral malignant cervical lymphadenopathy. The patient was managed with total parotidectomy and neck dissection, as well as postoperative adjuvant radiotherapy. Our observation on this particular case of acinic cell carcinoma is that the initial onset of her neoplasm was during her first pregnancy, and the recurrence of the same malignant disease was during a subsequent pregnancy. This chronologic association raised our suspicion that there might be a possible etiologic effect of pregnancy or its associated hormonal or physiologic changes or both on the pathogenesis or etiology of acinic cell carcinoma.</p> <p>Conclusion</p> <p>Some association might exist between pregnancy and the pathogenesis or etiology of acinic cell carcinoma.</p