Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles $S_rM$ of a Riemannian manifold $M,g$ of $\dim\geq 3$, assuming different variable radius functions $r$ and weighted Sasaki metrics induced by the conformal class of $g$. New examples are shown of manifolds with constant positive or with constant negative scalar curvature, which are not Einstein. Recalling results on the associated almost complex structure $I^G$ and symplectic structure ${\omega}^G$ on the manifold $TM$, generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds $TM$ and $S_rM$.Comment: 15 pages, to appear in Journal of Geometr

Convergence of vector bundles with metrics of Sasaki-type

If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-type with a uniform upper bound on rank, then a subsequence of the $E_i$ converges in the pointed Gromov-Hausdorff sense to a metric space, $E_\infty$. The projection maps $\pi_i$ converge to a limit submetry $\pi_\infty$ and the fibers converge to its fibers; the latter may no longer be vector spaces but are homeomorphic to $\R^k/G$, where $G$ is a closed subgroup of $O(k)$ ---called the {\em wane group}--- that depends on the basepoint and that is defined using the holonomy groups on the vector bundles. The norms $\mu_i=\|\cdot\|_i$ converges to a map $\mu_{\infty}$ compatible with the re-scaling in $\R^k/G$ and the $\R$-action on $E_i$ converges to an $\R-$action on $E_{\infty}$ compatible with the limiting norm. In the special case when the sequence of vector bundles has a uniform lower bound on holonomy radius (as in a sequence of collapsing flat tori to a circle), the limit fibers are vector spaces. Under the opposite extreme, e.g. when a single compact $n$-dimensional manifold is re-scaled to a point, the limit fiber is $\R^n/H$ where $H$ is the closure of the holonomy group of the compact manifold considered. An appropriate notion of parallelism is given to the limiting spaces by considering curves whose length is unchanged under the projection. The class of such curves is invariant under the $\R$-action and each such curve preserves norms. The existence of parallel translation along rectifiable curves with arbitrary initial conditions is also exhibited. Uniqueness is not true in general, but a necessary condition is given in terms of the aforementioned wane groups $G$.Comment: 44 pages, 1 figure, in V.2 added Theorem E and Section 4 on parallelism in the limit space

A novel efficient energy optimization in smart urban buildings based on optimal demand side management

Data availability: The data used for this research and prepatation of this article can be accessed from Brunel University of London repository at: https://doi.org/10.17633/rd.brunel.26049436.v1.Increasing electrical energy consumption during peak hours leads to increased electrical energy losses and the spread of environmental pollution. For this reason, demand-side management programs have been introduced to reduce consumption during peak hours. This study proposes an efficient energy optimization in Smart Urban Buildings (SUBs) based on Improved Sine Cosine Algorithm (ISCA) that uses the load-shifting technique for demand-side management as a way to improve the energy consumption patterns of a SUBs. The proposed system's goal is to optimize the energy of SUBs appliances in order to effectively regulate load demand, with the end result being a reduction in the peak to average ratio (PAR) and a consequent minimization of electricity costs. This is accomplished while also keeping user comfort as a priority. The proposed system is evaluated by comparing it with the Grasshopper Optimization Algorithm (GOA) and unscheduled cases. Without applying an optimization algorithm, the total electricity cost, carbon emission, PAR and waiting time are equal to 1703.576 ID, 34.16664 (kW), and 413.5864s respectively for RTP. While, after applying GOA, the total electricity cost, carbon emission, PAR and waiting time are improved to 1469.72 ID, 21.17 (kW), and 355.772s respectively for RTP. While, after applying the ISCA Improves the total electricity cost, PAR, and waiting time by 1206.748 ID, 16.5648 (kW), and 268.525384s respectively. Where after applying GOA, the total electricity cost, PAR, and waiting time are improved to 13.72 %, 38.00 %, and 13.97 % respectively. And after applying proposed method, the total electricity cost, PAR, and waiting time are improved to 29.16 %, 51.51 %, and 35.07 % respectively. According to the results, the created ISCA algorithm performed better than the unscheduled case and GOA scheduling situations in terms of the stated objectives and was advantageous to both utilities and consumers. Furthermore, this study has presented a novel two-stage stochastic model based on Moth-Flame Optimization Algorithm (MFOA) for the co-optimization of energy scheduling and capacity planning for systems of energy storage that would be incorporated to grid connected smart urban buildings.The research has been partially supported by the Faculty of Informatics and Management UHK excellence project “Methodological perspectives on modeling and simulation of hard and soft systems”

Imaging of esophageal lymph node metastases by desorption electrospray ionization mass spectrometry

Histopathological assessment of lymph node metastases (LNM) depends on subjective analysis of cellular morphology with inter-/intra-observer variability. In this study, LNM from esophageal adenocarcinoma was objectively detected using desorption electrospray ionization-mass spectrometry imaging (DESI-MSI). Ninety lymph nodes and their primary tumor biopsies from 11 esophago-gastrectomy specimens were examined and analyzed by DESI-MSI. Images from mass spectrometry and corresponding histology were co-registered and analyzed using multivariate statistical tools. The MSIs revealed consistent lipidomic profiles of individual tissue types found within lymph nodes. Spatial mapping of the profiles showed identical distribution patterns as per the tissue types in matched immunohistochemistry images. Lipidomic profile comparisons of LNM versus the primary tumor revealed a close association in contrast to benign lymph node tissue types. This similarity was used for the objective prediction of LNM in mass spectrometry images utilizing the average lipidomic profile of esophageal adenocarcinoma. The multivariate statistical algorithm developed for LNM identification demonstrated a sensitivity, specificity, positive predictive value and negative predictive value of 89.5, 100, 100 and 97.2 per-cent, respectively, when compared to gold-standard immunohistochemistry. DESI-MSI has the potential to be a diagnostic tool for peri-operative identification of LNM and compares favorably with techniques currently used by histopathology experts

Robust graphene-based molecular devices

One of the main challenges to upscale the fabrication of molecular devices is to achieve a mechanically stable device with reproducible and controllable electronic features that operates at room temperature1,2. This is crucial because structural and electronic fluctuations can lead to significant changes in the transport characteristics at the electrode-molecule interface3,4. In this study, we report on the realization of a mechanically and electronically robust graphene-based molecular junction. Robustness was achieved by separating the requirements for mechanical and electronic stability at the molecular level. Mechanical stability was obtained by anchoring molecules directly to the substrate, rather than to graphene electrodes, using a silanization reaction. Electronic stability was achieved by adjusting the π-π orbitals overlap of the conjugated head groups between neighbouring molecules. The molecular devices exhibited stable current-voltage (I-V) characteristics up to bias voltages of 2.0 V with reproducible transport features in the temperature range from 20 to 300 K

Characterisation of bioenergetic pathways and related regulators by multiple assays in human tumour cells

Background: Alterations in cellular metabolism are considered as hallmarks of cancers, however, to recognize these alterations and understand their mechanisms appropriate techniques are required. Our hypothesis was to determine whether dominant bioenergetic mechanism may be estimated by comparing the substrate utilisation with different methods to detect the labelled carbon incorporation and their application in tumour cells. Methods: To define the bioenergetic pathways different metabolic tests were applied: (a) measuring CO2 production from [1-14C]-glucose and [1-14C]-acetate; (b) studying the effect of glucose and acetate on adenylate energy charge; (c) analysing glycolytic and TCA cycle metabolites and the number of incorporated 13C atoms after [U-13C]-glucose/[2-13C]-acetate labelling. Based on [1-14C]-substrate oxidation two selected cell lines out of seven were analysed in details, in which the highest difference was detected at their substrate utilization. To elucidate the relevance of metabolic characterisation the expression of certain regulatory factors, bioenergetic enzymes, mammalian target of rapamycin (mTOR) complexes (C1/C2) and related targets as important elements at the crossroad of cellular signalling network were also investigated. Results: Both [U-13C]-glucose and [1-14C]-substrate labelling indicated high glycolytic capacity of tumour cells. However, the ratio of certain 13C-labelled metabolites showed detailed metabolic differences in the two selected cell lines in further characterisation. The detected differences of GAPDH, β-F1-ATP-ase expression and adenylate energy charge in HT-1080 and ZR-75.1 tumour cells also confirmed the altered metabolism. Moreover, the highly limited labelling of citrate by [2-13C]-acetate-representing a novel functional test in malignant cells-confirmed the defect of TCA cycle of HT-1080 in contrast to ZR-75.1 cells. Noteworthy, the impaired TCA cycle in HT-1080 cells were associated with high mTORC1 activity, negligible protein level and activity of mTORC2, high expression of interleukin-1β, interleukin-6 and heme oxygenase-1 which may contribute to the compensatory mechanism of TCA deficiency. Conclusions: The applied methods of energy substrate utilisation and other measurements represent simple assay system using 13C-acetate and glucose to recognize dominant bioenergetic pathways in tumour cells. These may offer a possibility to characterise metabolic subtypes of human tumours and provide guidelines to find biomarkers for prediction and development of new metabolism related targets in personalized therapy. © 2016 Jeney et al