Search Results (24)

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere. Full article

Spherical structures of dielectric and magnetic materials are studied intensively in basic research and employed widely in applications. The polarization, (P for dielectric and M for magnetic materials), is the parent physical vector of all relevant entities (e.g., moment, , and force, F), which determine the signals recorded by an experimental setup or diagnostic equipment and configure the motion in real space. Here, we use classical electromagnetism to study the polarization, , of spherical structures of linear and isotropic—however, not necessarily homogeneous—materials subjected to an external vector field, (E_ext for dielectric and H_ext for magnetic materials), dc (static), or even ac of low frequency (quasistatic limit). We tackle an integro-differential equation on the polarization, , able to provide closed-form solutions, determined solely from , on the basis of spherical harmonics, ${\mathrm{Y}}_l^m$. These generic equations can be used to calculate analytically the polarization, , directly from an external field, , of any form. The proof of concept is studied in homogeneous dielectric and magnetic spheres. Indeed, the polarization, , can be obtained by universal expressions, directly applicable for any form of the external field, . Notably, we obtain the relation between the extrinsic, , and intrinsic, , susceptibilities (${\chi }_{\mathrm{e}}^{\mathrm{e}\mathrm{x}\mathrm{t}}$ and ${\chi }_{\mathrm{e}}^{\mathrm{i}\mathrm{n}\mathrm{t}}$ for dielectric and ${\chi }_{\mathrm{m}}^{\mathrm{e}\mathrm{x}\mathrm{t}}$ and ${\chi }_{\mathrm{m}}^{\mathrm{i}\mathrm{n}\mathrm{t}}$ for magnetic materials) and clarify the nature of the depolarization factor, , which depends on the degree l—however, not on the order m of the mode $(l,m)$ of the applied . Our universal approach can be useful to understand the physics and to facilitate applications of such spherical structures. Full article

In this article, we investigate Ricci solitons occurring on spacelike hypersurfaces of Einstein Lorentzian manifolds. We give the necessary and sufficient conditions for a spacelike hypersurface of a Lorentzian manifold, equipped with a closed conformal timelike vector field $\overline{\xi }$, to be a gradient Ricci soliton having its potential function as the inner product of $\overline{\xi }$ and the timelike unit normal vector field to the hypersurface. Moreover, when the ambient manifold is Einstein and the hypersurface is compact, we establish that, under certain straightforward conditions, the hypersurface is an extrinsic sphere, that is, a totally umbilical hypersurface with a non-zero constant mean curvature. In particular, if the ambient Lorentzian manifold has a constant sectional curvature, we show that the compact spacelike hypersurface is essentially a round sphere. Full article

The aim of this study is to analyze the well-being of young music teachers working in Trentino Music Schools (TMS). Specifically, we assess (i) the extent to which the interaction between teaching and playing affects the well-being of young musicians using a satisfaction measure for their overall professional path as teachers and musicians, and (ii) what extrinsic and intrinsic drivers may guide their involvement in teaching activities in the early stages of their careers. To this end, we analyze original survey data on young musicians teaching in TMS to estimate their relative satisfaction and identify their motivational drivers. Specifically, we estimate from elementary items six constructs concerning material work conditions, immaterial welfare (i.e., the capabilities activated by the schools), and initial monetary and non-monetary motivations to become a music teacher, then we run two ordered logit regressions to test whether a set of variables of interest and the estimated constructs contribute to explaining junior teachers’ satisfaction. Our findings highlight that junior teachers are satisfied if they can preserve the desired proportion of artistic activity and can teach a consistent number of hours so as to leave the desired space and time for making music independently of school activities. They consider teaching to be one of the components of their professional activities and can be expected to try to maintain sufficient space to be able to also develop the independent artistic sphere of their career as musicians. Full article

We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective function by employing Gaussian processes and utilizing the uncertainty in that surrogate by deriving an acquisition function. This acquisition function represents the probability of improvement based on the kernel of the Gaussian process, which guides the search in the optimization process. The critical challenge for designing Bayesian optimization algorithms on manifolds lies in the difficulty of constructing valid covariance kernels for Gaussian processes on general manifolds. Our approach is to employ extrinsic Gaussian processes by first embedding the manifold onto some higher dimensional Euclidean space via equivariant embeddings and then constructing a valid covariance kernel on the image manifold after the embedding. This leads to efficient and scalable algorithms for optimization over complex manifolds. Simulation study and real data analyses are carried out to demonstrate the utilities of our eBO framework by applying the eBO to various optimization problems over manifolds such as the sphere, the Grassmannian, and the manifold of positive definite matrices. Full article

The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some local characterizations of the round spheres and the tori immersed in the 3-dimensional unit sphere, along with the Laplace operator, the spherical Gauss map and the Gauss map associated with the elliptic linear Weingarten metric. Full article

In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold $M^n$ of a complex space form $\tilde{M}\left(4ϵ\right)$ under extrinsic conditions which involve the Laplacian, the squared norm gradient of the warped function, and pointwise slant functions. We show that i-the homology groups of $M^n$ are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold $M^n$, in which $M^n$ is homeomorphic to a sphere ${\mathbb{S}}^n$ if $n\ge 4$ and if $n=3$, then $M^3$ is homotopic to a sphere ${\mathbb{S}}^3$ under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds. Full article

Hirschsprung’s disease (HSCR) is a common developmental anomaly of the gastrointestinal tract in children. The most significant characteristics of aganglionic segments in HSCR are hyperplastic extrinsic nerve fibers and the absence of endogenous ganglion plexus. Double C2 domain alpha (DOC2A) is mainly located in the nucleus and is involved in Ca²⁺-dependent neurotransmitter release. The loss function of DOC2A influences postsynaptic protein synthesis, dendrite morphology, postsynaptic receptor density and synaptic plasticity. It is still unknown why hyperplastic extrinsic nerve fibers grow into aganglionic segments in HSCR. We detected the expression of DOC2A in HSCR aganglionic segment colons and established three DOC2A-knockdown models in the Neuro-2a cell line, neural spheres and zebrafish separately. First, we detected the protein and mRNA expression of DOC2A and found that DOC2A was negatively correlated with AChE⁺ grades. Second, in the Neuro-2a cell lines, we found that the amount of neurite outgrowth and mean area per cell were significantly increased, which suggested that the inhibition of DOC2A promotes nerve fiber formation and the neuron’s polarity. In the neural spheres, we found that the DOC2A knockdown was manifested by a more obvious connection of nerve fibers in neural spheres. Then, we knocked down Doc2a in zebrafish and found that the down-regulation of Doc2a accelerates the formation of hyperplastic nerve fibers in aganglionic segments in zebrafish. Finally, we detected the expression of MUNC13-2 (UNC13B), which was obviously up-regulated in Grade3/4 (lower DOC2A expression) compared with Grade1/2 (higher DOC2A expression) in the circular muscle layer and longitudinal muscle layer. The expression of UNC13B was up-regulated with the knocking down of DOC2A, and there were protein interactions between DOC2A and UNC13B. The down-regulation of DOC2A may be an important factor leading to hyperplastic nerve fibers in aganglionic segments of HSCR. UNC13B seems to be a downstream molecule to DOC2A, which may participate in the spasm of aganglionic segments of HSCR patient colons. Full article

Tumor metastasis is a complex process modulated by both intrinsic and extrinsic factors that ultimately result in poorer patient outcomes, including diminished survival. Pseudogene-derived long non-coding RNAs (lncRNA) play important roles in cancer progression. In the current study, we found that the pseudogene-derived lncRNA LPAL2 is downregulated in hepatocellular carcinoma (HCC) tissues, and further showed that elevated LPAL2 expression is positively correlated with survival outcome. The knockdown of LPAL2 in hepatoma cells induced tumor formation, migration, invasion, sphere formation, and drug resistance. Metalloproteinase 9 (MMP9) was identified as an LPAL2-regulated target gene, consistent with clinical findings that LPAL2 expression is significantly associated with MMP9 expression. Furthermore, patients with a higher expression of LPAL2 and lower expression of MMP9 (LPAL2-high/MMP9-low) had a higher survival rate than those with other combinations. Collectively, our findings establish LPAL2 as a novel tumor suppressor in HCC, and suggest targeting LPAL2 and MMP9 as a therapeutic approach for the treatment of HCC. Full article

The widespread development in wireless technologies and the advancements in multimedia communication have brought about a positive impact on the performance of wireless transceivers. We investigate the performance of our three-stage turbo detected system using state-of-the-art high efficiency video coding (HEVC), also known as the H.265 video standard. The system makes use of sphere packing (SP) modulation with the combinational gain technique of layered steered space-time code (LSSTC). The proposed three-stage system is simulated for the correlated Rayleigh fading channel and the bit-error rate (BER) curve obtained after simulation is free of any floor formation. The system employs low complexity source-bit coding (SBC) for protecting the H.265 coded stream. An intermediate recursive unity-rate code (URC) with an infinite impulse response is employed as an inner precoder. More specifically, the URC assists in the prevention of the BER floor by distributing the information across the decoders. There is an observable gain in the BER and peak signal-to-noise ratio (PSNR) performances with the increasing value of minimum Hamming distance ($d_{H,\min }$) using the three-stage system. Convergence analysis of the proposed system is investigated through an extrinsic information transfer (EXIT) chart. Our proposed system demonstrates better performance of about 22 dB than the benchmarker utilizing LSSTC-SP for iterative source-channel detection, but without exploiting the optimized SBC schemes. Full article

In this paper, we prove that, for compact warped product submanifolds $M^n$ in an Euclidean space ${\mathbb{E}}^{n+k}$, there are no stable p-currents, homology groups are vanishing, and $M^3$ is homotopic to the Euclidean sphere ${\mathbb{S}}^3$ under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds. Full article

The introduction of 5G with excessively high speeds and ever-advancing cellular device capabilities has increased the demand for high data rate wireless multimedia communication. Data compression, transmission robustness and error resilience are introduced to meet the increased demands of high data rates of today. An innovative approach is to come up with a unique setup of source bit codes (SBCs) that ensure the convergence and joint source-channel coding (JSCC) correspondingly results in lower bit error ratio (BER). The soft-bit assisted source and channel codes are optimized jointly for optimum convergence. Source bit codes assisted by iterative detection are used with a rate-1 precoder for performance evaluation of the above mentioned scheme of transmitting sata-partitioned (DP) H.264/AVC frames from source through a narrowband correlated Rayleigh fading channel. A novel approach of using sphere packing (SP) modulation aided differential space time spreading (DSTS) in combination with SBC is designed for the video transmission to cope with channel fading. Furthermore, the effects of SBC with different hamming distances $d_{(H,min)}$ but similar coding rates is explored on objective video quality such as peak signal to noise ratio (PSNR) and also the overall bit error ratio (BER). EXtrinsic Information Transfer Charts (EXIT) are used for analysis of the convergence behavior of SBC and its iterative scheme. Specifically, the experiments exhibit that the proposed scheme of error protection of SBC $d_{(H,min)}$ = 6 outperforms the SBCs having same code rate, but with $d_{(H,min)}$ = 3 by 3 dB with PSNR degradation of 1 dB. Furthermore, simulation results show that a gain of 27 dB $E_b/N_0$ is achieved with SBC having code rate 1/3 compared to the benchmark Rate-1 SBC codes. Full article

This article investigates the performance of various sophisticated channel coding and transmission schemes for achieving reliable transmission of a highly compressed video stream. Novel error protection schemes including Non-Convergent Coding (NCC) scheme, Non-Convergent Coding assisted with Differential Space Time Spreading (DSTS) and Sphere Packing (SP) modulation (NCDSTS-SP) scheme and Convergent Coding assisted with DSTS and SP modulation (CDSTS-SP) are analyzed using Bit Error Ratio (BER) and Peak Signal to Noise Ratio (PSNR) performance metrics. Furthermore, error reduction is achieved using sophisticated transceiver comprising SP modulation technique assisted by Differential Space Time Spreading. The performance of the iterative Soft Bit Source Decoding (SBSD) in combination with channel codes is analyzed using various error protection setups by allocating consistent overall bit-rate budget. Additionally, the iterative behavior of SBSD assisted RSC decoder is analyzed with the aid of Extrinsic Information Transfer (EXIT) Chart in order to analyze the achievable turbo cliff of the iterative decoding process. The subjective and objective video quality performance of the proposed error protection schemes is analyzed while employing H.264 advanced video coding and H.265 high efficient video coding standards, while utilizing diverse video sequences having different resolution, motion and dynamism. It was observed that in the presence of noisy channel the low resolution videos outperforms its high resolution counterparts. Furthermore, it was observed that the performance of video sequence with low motion contents and dynamism outperforms relative to video sequence with high motion contents and dynamism. More specifically, it is observed that while utilizing H.265 video coding standard, the Non-Convergent Coding assisted with DSTS and SP modulation scheme with enhanced transmission mechanism results in $E_b/N_0$ gain of 20 dB with reference to the Non-Convergent Coding and transmission mechanism at the objective PSNR value of 42 dB. It is important to mention that both the schemes have employed identical code rate. Furthermore, the Convergent Coding assisted with DSTS and SP modulation mechanism achieved superior performance with reference to the equivalent rate Non-Convergent Coding assisted with DSTS and SP modulation counterpart mechanism, with a performance gain of 16 dB at the objective PSNR grade of 42 dB. Moreover, it is observed that the maximum achievable PSNR gain through H.265 video coding standard is 45 dB, with a PSNR gain of 3 dB with reference to the identical code rate H.264 coding scheme. Full article

The reliable transmission of multimedia information that is coded through highly compression efficient encoders is a challenging task. This article presents the iterative convergence performance of IrRegular Convolutional Codes (IRCCs) with the aid of the multidimensional Sphere Packing (SP) modulation assisted Differential Space Time Spreading Codes (IRCC-SP-DSTS) scheme for the transmission of H.264/Advanced Video Coding (AVC) compressed video coded stream. In this article, three different regular and irregular error protection schemes are presented. In the presented Regular Error Protection (REP) scheme, all of the partitions of the video sequence are regular error protected with a rate of 3/4 IRCC. In Irregular Error Protection scheme-1 (IREP-1) the H.264/AVC partitions are prioritized as A, B & C, respectively. Whereas, in Irregular Error Protection scheme-2 (IREP-2), the H.264/AVC partitions are prioritized as B, A, and C, respectively. The performance of the iterative paradigm of an inner IRCC and outer Rate-1 Precoder is analyzed by the EXtrinsic Information Transfer (EXIT) Chart and the Quality of Experience (QoE) performance of the proposed mechanism is evaluated using the Bit Error Rate (BER) metric and Peak Signal to Noise Ratio (PSNR)-based objective quality metric. More specifically, it is concluded that the proposed IREP-2 scheme exhibits a gain of 1 dB $E_b/N_0$ with reference to the IREP-1 and $E_b/N_0$ gain of 0.6 dB with reference to the REP scheme over the PSNR degradation of 1 dB. Full article

An incidence and mortality of cancer are rapidly growing worldwide, especially due to heterogeneous character of the disease that is associated with irreversible impairment of cellular homeostasis and function. Targeting apoptosis, one of cancer hallmarks, represents a potent cancer treatment strategy. Carotenoids are phytochemicals represented by carotenes, xanthophylls, and derived compounds such as apocarotenoids that demonstrate a broad spectrum of anti-cancer effects involving pro-apoptotic signaling through extrinsic and intrinsic pathways. As demonstrated in preclinical oncology research, the apoptotic modulation is performed at post-genomic levels. Further, carotenoids demonstrate additive/synergistic action in combination with conventional oncostatic agents. In addition, a sensitization of tumor cells to anti-cancer conventional treatment can be achieved by carotenoids. The disadvantage of anti-cancer application of carotenoids is associated with their low solubility and, therefore, poor bioavailability. However, this deficiency can be improved by using nanotechnological approaches, solid dispersions, microemulsions or biofortification that significantly increase the anti-cancer and pro-apoptotic efficacy of carotenoids. Only limited number of studies dealing with apoptotic potential of carotenoids has been published in clinical sphere. Pro-apoptotic effects of carotenoids should be beneficial for individuals at high risk of cancer development. The article considers the utility of carotenoids in the framework of 3P medicine. Full article