Ranking the importance of nuclear reactions for activation and transmutation events

Pathways-reduced analysis is one of the techniques used by the Fispact-II nuclear activation and transmutation software to study the sensitivity of the computed inventories to uncertainties in reaction cross-sections. Although deciding which pathways are most important is very helpful in for example determining which nuclear data would benefit from further refinement, pathways-reduced analysis need not necessarily define the most critical reaction, since one reaction may contribute to several different pathways. This work examines three different techniques for ranking reactions in their order of importance in determining the final inventory, comparing the pathways based metric (PBM), the direct method and one based on the Pearson correlation coefficient. Reasons why the PBM is to be preferred are presented.Comment: 30 pages, 10 figure

On the security of a new image encryption scheme based on chaotic map lattices

This paper reports a detailed cryptanalysis of a recently proposed encryption scheme based on the logistic map. Some problems are emphasized concerning the key space definition and the implementation of the cryptosystem using floating-point operations. It is also shown how it is possible to reduce considerably the key space through a ciphertext-only attack. Moreover, a timing attack allows the estimation of part of the key due to the existent relationship between this part of the key and the encryption/decryption time. As a result, the main features of the cryptosystem do not satisfy the demands of secure communications. Some hints are offered to improve the cryptosystem under study according to those requirements.Comment: 8 pages, 8 Figure

A depth camera-based system for estimating cyclist-bike projected frontal area

A major component of total resistive force in cycling is aerodynamic drag. For speeds greater than ~14 m/s aerodynamic drag accounts for approximately 90% of total resistive force (Debraux et al., 2009: International Journal of Sports Medicine, 30, 266-272). Together with the air density, the coefficient of drag and the velocity of the cyclist-bike, an important determinant of aerodynamic drag is projected frontal area. Several techniques have been used to estimate the projected frontal area of a cyclist-bike, including the weighing of photographs and image digitising (Debraux et al., 2009). These techniques are similar as they involve extracting the cyclist-bike from a two-dimensional (2D) image and using scaling information from a plane of known dimensions. With the weighing photographs method this is done physically using sensitive weighing scales whereas image processing software is used for the image digitising technique. Both techniques require the collection of a calibration plane, involve considerable post-processing and cannot be performed in real time. We have developed a depth camera-based system for estimating cyclist-bike projected frontal area which addresses these issues. The depth camera algorithm works by creating a metrically scaled, three-dimensional point cloud of the cyclist-bike. The point cloud is projected on to a 2D representation of the scene and the area of the point cloud is calculated using a technique similar to ‘voxelization’; points in the cloud occupy spaces in a fine grid – the sum of the occupied grid spaces gives total area. The aim of this study was to investigate the agreement between our new method and the image digitising technique.After institutional ethics approval, eight regular cyclists volunteered to participate and provided written informed consent. Participants wore their normal cycling clothing and their bicycle was mounted on a stationary indoor trainer. The bicycle was positioned against a white background to help with the image digitising method. Participants placed their feet on the pedals and held the cranks parallel to the floor. A digital camera (Canon EOS 400D, 10.1 megapixel) and Kinect depth camera (Microsoft, Redmond, WA, USA) were mounted on tripods at a height of 1.1 m and positioned 5 m and 2.2 m in front of the participant, respectively. Similar to Debraux et al. (2009), participants adopted two positions on the bike: 1. Upright – upright torso with hands close to the stem and 2. Drops Position – hands on the drops. Three repeat captures were performed in each position, with the participant relaxing between each capture. The digitising method was performed as described by Debraux et al. (2009). Agreement between methods was assessed using limits of agreement (LOA - Bland and Altman, 1986: Lancet, 1, 307-310). A two-way repeated measures analysis of variance (method by position) was used to assess the effect of cyclist position on the systematic difference between measurement methods.There was no interaction between cyclist position and measurement method (p = 0.201) indicating that the same effect of cyclist position was observed using both measurement techniques. A significant main effect for cyclist position (p = 0.017) indicated that projected frontal area was smaller with hands on the drops (upright: 0.485 m2, drops: 0.434 m2). There was also a significant main effect for measurement method (p < 0.001) indicating a significantly smaller estimation of projected frontal area using the Kinect (Kinect: 0.416 m2, Image: 0.503 m2). A predominantly systematic difference between methods was also suggested by the LOA analysis (upright: 0.086 ± 0.029 m2, drops: 0.090 ± 0.033 m2).The aim of this study was to assess the agreement between a common method of estimating cyclist-bike frontal area and a new depth camera-based technique. The new technique estimated systematically smaller projected frontal area than the image digitisation method but there was relatively little random variation and the same effect of cyclist position was observed with both techniques. Which technique gives the most accurate estimate of projected frontal area is not clear as the image digitisation technique - to which the new technique was compared - has associated errors e.g. identification of the cyclist-bike outline and out-of-plane errors. However, it was apparent during testing that the depth camera-based system often failed to identify parts of the bike and this is most likely the cause of the difference between techniques. Regardless, the results of this study suggest that the new technique can be used to assess changes in projected frontal area – as the cyclist changes position, for example. Further, the new technique offers the possibility of analysing changes in projected frontal area in real time – there is no requirement for calibration or post-processing

Deep learning: an introduction for applied mathematicians

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of state-of-the art software on a large scale image classification problem. We finish with references to the current literature

Information mobility in complex networks

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible

A new algorithm to diagnose atrial ectopic origin from multi lead ECG systems - insights from 3D virtual human atria and torso

Rapid atrial arrhythmias such as atrial fibrillation (AF) predispose to ventricular arrhythmias, sudden cardiac death and stroke. Identifying the origin of atrial ectopic activity from the electrocardiogram (ECG) can help to diagnose the early onset of AF in a cost-effective manner. The complex and rapid atrial electrical activity during AF makes it difficult to obtain detailed information on atrial activation using the standard 12-lead ECG alone. Compared to conventional 12-lead ECG, more detailed ECG lead configurations may provide further information about spatio-temporal dynamics of the body surface potential (BSP) during atrial excitation. We apply a recently developed 3D human atrial model to simulate electrical activity during normal sinus rhythm and ectopic pacing. The atrial model is placed into a newly developed torso model which considers the presence of the lungs, liver and spinal cord. A boundary element method is used to compute the BSP resulting from atrial excitation. Elements of the torso mesh corresponding to the locations of the placement of the electrodes in the standard 12-lead and a more detailed 64-lead ECG configuration were selected. The ectopic focal activity was simulated at various origins across all the different regions of the atria. Simulated BSP maps during normal atrial excitation (i.e. sinoatrial node excitation) were compared to those observed experimentally (obtained from the 64-lead ECG system), showing a strong agreement between the evolution in time of the simulated and experimental data in the P-wave morphology of the ECG and dipole evolution. An algorithm to obtain the location of the stimulus from a 64-lead ECG system was developed. The algorithm presented had a success rate of 93%, meaning that it correctly identified the origin of atrial focus in 75/80 simulations, and involved a general approach relevant to any multi-lead ECG system. This represents a significant improvement over previously developed algorithms

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Stereoselective palladium-catalyzed C(sp3)–H mono-arylation of piperidines and tetrahydropyrans with a C(4) directing group

A selective Pd-catalyzed C(3)–H cis-functionalization of piperidine and tetrahydropyran carboxylic acids is achieved using a C(4) aminoquinoline amide auxiliary. High mono- and cis-selectivity is attained by using mesityl carboxylic acid as an additive. Conditions are developed with significantly lower reaction temperatures (≤50 °C) than other reported heterocycle C(sp3)–H functionalization reactions, which is facilitated by a DoE optimization. A one-pot C–H functionalization-epimerization procedure provides the trans-3,4-disubstituted isomers directly. Divergent aminoquinoline removal is accomplished with the installation of carboxylic acid, alcohol, amide and nitrile functional groups. Overall fragment compounds suitable for screening are generated in 3-4 steps from readily-available heterocyclic carboxylic acids