Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at http://www.mines.edu/fs_home/whereman

Quantum-Classical Multiple Kernel Learning

As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the near future. Paired with kernel methods like support-vector machines, small and noisy quantum computers can evaluate classically-hard quantum kernels that capture unique notions of similarity in data. Taking inspiration from techniques in classical machine learning, this work investigates simulated quantum kernels in the context of multiple kernel learning (MKL). We consider pairwise combinations of several classical-classical, quantum-quantum, and quantum-classical kernels in an empirical investigation of their classification performance with support-vector machines. We also introduce a novel approach, which we call QCC-net (quantum-classical-convex neural network), for optimizing the weights of base kernels together with any kernel parameters. We show this approach to be effective for enhancing various performance metrics in an MKL setting. Looking at data with an increasing number of features (up to 13 dimensions), we find parameter training to be important for successfully weighting kernels in some combinations. Using the optimal kernel weights as indicators of relative utility, we find growing contributions from trainable quantum kernels in quantum-classical kernel combinations as the number of features increases. We observe the opposite trend for combinations containing simpler, non-parametric quantum kernels.Comment: 15 pages, Supplementary Information on page 15, 6 main figures, 1 supplementary figur

Multipath fading effect on terrestrial microwave LOS radio links

In this paper, the calculation of both the total received power with the effect of the ground reflection and the fade margin to find out the link availability for terrestrial microwave LOS (line-of-sight) radio links is proposed. The expressions are derived from clear-air, rainfall propagation mechanisms and multipath fading due to multipath arising from surface reflection along the defined microwave LOS radio link. We verify the mathematical model by using the ATDI ICS telecom software over sample microwave LOS radio links located in Turkey. © 2015 IEEE

Short-term propagation measurements and modeling for terrestrial line-of-sight links

This paper presents a propagation prediction technique to predict propagation mechanisms for fixed terrestrial line-of-sight (LOS) radio links, especially proposed for rural environments. We report the results of a short-term propagation measurement campaign carried out in the area of Ankara, Turkey. The field measurements were performed at the frequency of 2.536 GHz for a period of three months in summer 2015. It is observed that the difference between measurement data and predicted mean received power is smaller than the standard deviation value provided by Recommendation ITU-R P. 1546. © 2016 European Association of Antennas and Propagation

The effect of terrain roughness in the microwave line-of-sight multipath fading estimation based on Rec. ITU-R P.530-15

Multipath fading is an important constraint on the prediction of path loss for terrestrial line-of-sight microwave links. The International Telecommunication Union - Radiocommunication (ITU-R) Rec. P.530 [1] is one of the most widely used methods providing guidelines for the design of terrestrial line-of-sight links. The purpose of the study presented in this paper is to make an investigation of the effect of both terrain roughness and geoclimatic factor parameters in the path loss characteristics of microwave line-of-sight (LOS) propagation in NATO Band 3+ (1350-2690 MHz) and NATO Band 4 (4440-5000 MHz) frequency ranges. The two parameters led to significantly different results for the link availability due to multipath fading as a function of the fade margin. © 2014 IEEE

Assessment on the Use of High Capacity “Sn4_{4}P3_{3}”/NHC Composite Electrodes for Sodium-Ion Batteries with Ether and Carbonate Electrolytes

This work reports the facile synthesis of a Sn–P composite combined with nitrogen doped hard carbon (NHC) obtained by ball-milling and its use as electrode material for sodium ion batteries (SIBs). The “Sn$_{4}$P$_{3}$”/NHC electrode (with nominal composition “Sn$_{4}$P$_{3}$”:NHC = 75:25 wt%) when coupled with a diglyme-based electrolyte rather than the most commonly employed carbonate-based systems, exhibits a reversible capacity of 550 mAh g$_{electrode}$$^{−1}$ at 50 mA g$^{−1}$ and 440 mAh g$_{electrode}$$^{−1}$ over 500 cycles (83% capacity retention). Morphology and solid electrolyte interphase formation of cycled “Sn$_{4}$P$_{3}$”/NHC electrodes is studied via electron microscopy and X-ray photoelectron spectroscopy. The expansion of the electrode upon sodiation (300 mAh g$_{electrode}$$^{−1}$) is only about 12–14% as determined by in situ electrochemical dilatometry, giving a reasonable explanation for the excellent cycle life despite the conversion-type storage mechanism. In situ X-ray diffraction shows that the discharge product is Na$_{15}$Sn$_{4}$. The formation of mostly amorphous Na$_{3}$P is derived from the overall (electro)chemical reactions. Upon charge the formation of Sn is observed while amorphous P is derived, which are reversibly alloying with Na in the subsequent cycles. However, the formation of Sn$_{4}$P$_{3}$ can be certainly excluded

Estimation of ocular volume from axial length

BACKGROUND/AIMS: To determine which biometric parameters provide optimum predictive power for ocular volume. METHODS: Sixty-seven adult subjects were scanned with a Siemens 3-T MRI scanner. Mean spherical error (MSE) (D) was measured with a Shin-Nippon autorefractor and a Zeiss IOLMaster used to measure (mm) axial length (AL), anterior chamber depth (ACD) and corneal radius (CR). Total ocular volume (TOV) was calculated from T2-weighted MRIs (voxel size 1.0 mm(3)) using an automatic voxel counting and shading algorithm. Each MR slice was subsequently edited manually in the axial, sagittal and coronal plane, the latter enabling location of the posterior pole of the crystalline lens and partitioning of TOV into anterior (AV) and posterior volume (PV) regions. RESULTS: Mean values (±SD) for MSE (D), AL (mm), ACD (mm) and CR (mm) were -2.62±3.83, 24.51±1.47, 3.55±0.34 and 7.75±0.28, respectively. Mean values (±SD) for TOV, AV and PV (mm(3)) were 8168.21±1141.86, 1099.40±139.24 and 7068.82±1134.05, respectively. TOV showed significant correlation with MSE, AL, PV (all p<0.001), CR (p=0.043) and ACD (p=0.024). Bar CR, the correlations were shown to be wholly attributable to variation in PV. Multiple linear regression indicated that the combination of AL and CR provided optimum R(2) values of 79.4% for TOV. CONCLUSION: Clinically useful estimations of ocular volume can be obtained from measurement of AL and CR

Differential spatial repositioning of activated genes in Biomphalaria glabrata snails infected with Schistosoma mansoni

Copyright @ 2014 Arican-Goktas et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.Schistosomiasis is an infectious disease infecting mammals as the definitive host and fresh water snails as the intermediate host. Understanding the molecular and biochemical relationship between the causative schistosome parasite and its hosts will be key to understanding and ultimately treating and/or eradicating the disease. There is increasing evidence that pathogens that have co-evolved with their hosts can manipulate their hosts' behaviour at various levels to augment an infection. Bacteria, for example, can induce beneficial chromatin remodelling of the host genome. We have previously shown in vitro that Biomphalaria glabrata embryonic cells co-cultured with schistosome miracidia display genes changing their nuclear location and becoming up-regulated. This also happens in vivo in live intact snails, where early exposure to miracidia also elicits non-random repositioning of genes. We reveal differences in the nuclear repositioning between the response of parasite susceptible snails as compared to resistant snails and with normal or live, attenuated parasites. Interestingly, the stress response gene heat shock protein (Hsp) 70 is only repositioned and then up-regulated in susceptible snails with the normal parasite. This movement and change in gene expression seems to be controlled by the parasite. Other differences in the behaviour of genes support the view that some genes are responding to tissue damage, for example the ferritin genes move and are up-regulated whether the snails are either susceptible or resistant and upon exposure to either normal or attenuated parasite. This is the first time host genome reorganisation has been seen in a parasitic host and only the second time for any pathogen. We believe that the parasite elicits a spatio-epigenetic reorganisation of the host genome to induce favourable gene expression for itself and this might represent a fundamental mechanism present in the human host infected with schistosome cercariae as well as in other host-pathogen relationships.NIH and Sandler Borroughs Wellcome Travel Fellowshi

Evaluation of peripapillary choroidal and retinal nerve fiber layer thickness in eyes with tilted optic disc

Purpose: This study was performed to evaluate the retinal nerve fiber layer (RNFL) and peripapillary choroidal thickness in eyes with tilted optic disc in order to identify characteristic RNFL and peripapillary choroid patterns verified by optical coherence tomography (OCT). Methods: Twenty-nine eyes of 29 patients with tilted optic discs were studied with spectral-domain (SD)-OCT and compared with age and sex-matched control subjects in a prospective design. The imaging of RNFL was performed using circular scans of a diameter of 3.4 mm around the optic disc using OCT. For measurements of peripapillary choroidal thickness, the standar d protocol for RNFL assessment was performed. Results: SD-OCT indicated significantly lower superotemporal (p<0.001), superonasal (p=0.001), and global (p=0.005) RNFL thicknesses in the tilted disc group than those of the control group. Peripapillary choroid was significantly thicker at the site of the elevated rim of eyes with tilted disc (p<0.001). Conclusion: This study demonstrated a clinical characterization of the main tilted disc morphologies that may be helpful in differentiating a tilted disc from other altered disc morphologies. Further studies are recommended to study the comparison between glaucoma and tilted disc groups