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Physics-informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of partial differential equations (PDEs). We provide upper bounds on the generalization error of PINNs approximating solutions of the forward problem for PDEs. An abstract formalism is introduced and stability properties of the underlying PDE are leveraged to derive an estimate for the generalization error in terms of the training error and number of training samples. This abstract framework is illustrated with several examples of nonlinear PDEs. Numerical experiments, validating the proposed theory, are also presented. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by PINNs in approximating the solutions of a large class of linear parabolic PDEs, namely Kolmogorov equations that include the heat equation and Black-Scholes equation of option pricing, as examples. We construct neural networks, whose PINN residual (generalization error) can be made as small as desired. We also prove that the total L2-error can be bounded by the generalization error, which in turn is bounded in terms of the training error, provided that a sufficient number of randomly chosen training (collocation) points is used. Moreover, we prove that the size of the PINNs and the number of training samples only grow polynomially with the underlying dimension, enabling PINNs to overcome the curse of dimensionality in this context. These results enable us to provide a comprehensive error analysis for PINNs in approximating Kolmogorov PDEs. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for partial differential equations (PDEs). We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation problems, and prove rigorous estimates on the generalization error of PINNs approximating them. An abstract framework is presented and conditional stability estimates for the underlying inverse problem are employed to derive the estimate on the PINN generalization error, providing rigorous justification for the use of PINNs in this context. The abstract framework is illustrated with examples of four prototypical linear PDEs. Numerical experiments, validating the proposed theory, are also presented. [ABSTRACT FROM AUTHOR]

Introduction: Microvasculopathy is characterized by progressive structural and functional damage to the microvessels and plays a key role in the pathogenesis of various connective tissue diseases (CTD). Nailfold videocapillaroscopy is an optimal and validated method for analysis of microvascular abnormalities and is able to differentiate secondary Raynaud's phenomenon (RP) of CTD from primary RP and healthy subjects. Aim: To assess and analyze nailfold capillaroscopic findings in Indian subjects with secondary Raynaud and to compare with findings in healthy subjects. Methods: A total of 62 study participants including cases and controls underwent nailfold videocapillaroscopy. Capillary loop length, capillary width, capillary density, presence/absence of tortuosity, giant loops, neoangiogenesis, microhemorrhages, and avascular areas were the parameters studied. Results: All the quantitative and qualitative parameters studied were significantly associated with secondary RP. Mean loop length in cases of connective tissue diseases was significantly less than in the controls (225.74 μm versus 282.97 μm) (P=0.002). Capillary density was also reduced significantly in the cases as compared to the controls (4.6 versus 7.39/mm) (P<0.01), whereas it was markedly decreased in systemic sclerosis (SSc) and mixed connective tissue diseases (MCTD), and near normal in systemic lupus erythematosus (SLE). Tortuosity was the most frequent (77.4%) qualitative parameter. Scleroderma pattern was found in 62.5% of patients with SSc and in 60% with MCTD. Non-specific pattern was found in 80% of SLE cases and 50% of dermatomyositis cases. Conclusion: Both quantitative and qualitative capillaroscopic changes are significantly associated with secondary RP. Scleroderma pattern was predominant in SSc and MCTD, whereas non-specific pattern was predominantly found in SLE and dermatomyositis. [ABSTRACT FROM AUTHOR]

DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite-dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In particular, we extend the universal approximation property of DeepONets to include measurable mappings in non-compact spaces. By a decomposition of the error into encoding, approximation and reconstruction errors, we prove both lower and upper bounds on the total error, relating it to the spectral decay properties of the covariance operators, associated with the underlying measures. We derive almost optimal error bounds with very general affine reconstructors and with random sensor locations as well as bounds on the generalization error, using covering number arguments. We illustrate our general framework with four prototypical examples of nonlinear operators, namely those arising in a nonlinear forced ordinary differential equation, an elliptic partial differential equation (PDE) with variable coefficients and nonlinear parabolic and hyperbolic PDEs. While the approximation of arbitrary Lipschitz operators by DeepONets to accuracy |$\epsilon $| is argued to suffer from a 'curse of dimensionality' (requiring a neural networks of exponential size in |$1/\epsilon $|⁠), in contrast, for all the above concrete examples of interest, we rigorously prove that DeepONets can break this curse of dimensionality (achieving accuracy |$\epsilon $| with neural networks of size that can grow algebraically in |$1/\epsilon $|⁠).Thus, we demonstrate the efficient approximation of a potentially large class of operators with this machine learning framework. [ABSTRACT FROM AUTHOR]

We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo (QMC) points for training deep neural network (DNN) surrogates of holomorphic Data-to-Observable (DtO) maps in engineering design. Our analysis reveals higher-order consistent, deterministic choices of training points in the input parameter space for both deep and shallow neural networks with holomorphic activation functions such as tanh. We prove that higher-order QMC training points facilitate higher-order decay (in terms of the number of training samples) of the underlying generalization error, with consistency error bounds that are free from the curse of dimensionality in terms of the number of input parameters, provided that DNN weights in hidden layers satisfy certain summability conditions. We present numerical experiments for DtO maps from elliptic and parabolic PDEs with uncertain inputs that confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modelled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalisation error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speedup over competing algorithms. [ABSTRACT FROM AUTHOR]

We propose a supervised deep learning algorithm based on low-discrepancy sequences as the training set. By a combination of theoretical arguments and extensive numerical experiments we demonstrate that the proposed algorithm significantly outperforms standard deep learning algorithms that are based on randomly chosen training data for problems in moderately high dimensions. The proposed algorithm provides an efficient method for building inexpensive surrogates for many underlying maps in the context of scientific computing. [ABSTRACT FROM AUTHOR]

We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity is in the so-called Delort class, i.e., it is a sum of a signed measure and an integrable function. This provides the first convergence proof for a numerical method approximating the Euler equations with such rough initial data and closes the gap between the available existence theory and rigorous convergence results for numerical methods. We also present numerical experiments, including computations of vortex sheets and confined eddies, to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Prolyl‐tRNA synthetase (PRS) is a member of the aminoacyl‐tRNA synthetase family that drives protein translation in cells. The apicomplexan PRSs are validated targets of febrifugine (FF) and its halogenated derivative halofuginone (HF). PRSs are of great interest for drug development against Plasmodium falciparum and Toxoplasma gondii. In this study, structures of apo and FF‐bound T. gondii (TgPRS) are revealed and the dynamic nature of the conformational changes that occur upon FF binding is unraveled. In addition, this study highlights significant conformational plasticity within two different crystal structures of apo PRSs but not within drug‐bound PRSs. The apo PRSs exist in multi‐conformational states and manifest pseudo‐dimeric structures. In contrast, when FF is bound the PRS dimer adopts a highly symmetrical architecture. It is shown that TgPRS does not display extant fold switching, in contrast to P. falciparum PRS, despite having over 65% sequence identity. Finally, structure‐comparison analyses suggest the utility of r.m.s.d. per residue (r.m.s.d./res) as a robust tool to detect structural alterations even when the r.m.s.d. is low. Apo TgPRS reveals FF/HF‐induced rigidity and this work has implications for drug‐design studies that rely on the apo structures of target proteins. [ABSTRACT FROM AUTHOR]

Mitochondria are the powerhouse of cells, which upon dysfunctions may lead to several diseases. Mycotoxins are the toxic secondary metabolites from fungi which are capable of causing diseases and death in humans and animals. They have a versatile mechanism of action in biological systems and can be used as lead compounds to treat some diseases including cancer. The present work encompasses analysis on the effects of mycotoxins on mitochondrial dysfunction. Electronic databases such as PubMed, ScienceDirect, Scopus, Web of Science, and Google Scholar were thoroughly searched for up‐to‐date published information associated with those mycotoxins and their effect on mitochondrial dysfunction. Findings suggest that mycotoxins such as citrinin, aflatoxin, and T‐2 toxin exert multi‐edged sword‐like effects in test systems causing mitochondrial dysfunction. Mycotoxins can induce oxidative stress even at low concentration/dose that may be one of the major causes of mitochondrial dysfunction. On the other hand, activation of apoptotic caspases and other proteins by mycotoxins may lead to apoptotic cell death. Thus, mycotoxins‐mediated mitochondrial dysfunction may be related to several chronic diseases which also makes these mycotoxins considerable as lead compounds for inducing toxic effects in cells. Their cytotoxic effects on cancer cells suggest their possible application as chemotherapeutic tools. © 2018 IUBMB Life, 70(11):1084–1092, 2018 [ABSTRACT FROM AUTHOR]

The difference between observed and modelled precession/nutation reveals unmodelled signals commonly referred to as Celestial Pole Offsets (CPO), denoted by dX and dY. CPO are currently observed only by Very Long Baseline Interferometry (VLBI), but there is nearly 4 weeks of latency by which the data centers provide the most accurate, final CPO series. This latency problem necessitates predicting CPO for high-accuracy, real-time applications that require information regarding Earth rotation, such as spacecraft navigation. Even though the International Earth Rotation and Reference Systems Service (IERS) provides so-called rapid CPO, they are usually less accurate and therefore, may not satisfy the requirements of the mentioned applications. To enhance the quality of CPO predictions, we present a new methodology based on Neural Additive Models (NAMs), a class of interpretable machine learning algorithms. We formulate the problem based on long short-term memory neural networks and derive simple analytical relations for the quantification of prediction uncertainty and feature importance, thereby enhancing the intelligibility of predictions made by machine learning. We then focus on the short-term prediction of CPO with a forecasting horizon of 30 days. We develop an operational framework that consistently provides CPO predictions. Using the CPO series of Jet Propulsion Laboratory as the input to the algorithm, we show that NAMs predictions improve the IERS rapid products on average by 57% for dX and 25% for dY under fully operational conditions. Our predictions are both accurate and overcome the latency issue of final CPO series and thus, can be used in real-time applications. [ABSTRACT FROM AUTHOR]

We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier–Stokes equations with (extended) physics-informed neural networks. We show that the underlying partial differential equation residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

We propose a space–time discontinuous Galerkin (DG) method to approximate multi-dimensional non-conservative hyperbolic systems. The scheme is based on a particular choice of interface fluctuations. The key difference with existing space–time DG methods lies in the fact that our scheme is formulated in entropy variables, allowing us to prove entropy stability for the method. Additional numerical stabilization in the form of streamline diffusion and shock-capturing terms are added. The resulting method is entropy stable, arbitrary high-order accurate, fully discrete, and able to handle complex domain geometries discretized with unstructured grids. We illustrate the method with representative numerical examples. [ABSTRACT FROM AUTHOR]

Environmental aluminum intoxication has shown increasingly alarming negative consequences on reproductive health. This needs mechanistic exploration and preventive management using medicines like herbal supplementation. The ameliorative effects of naringenin (NAR) against AlCl3-induced reproductive toxicity were thus evaluated in this study by assessing testicular dysfunction in albino male mice. A group of mice was treated with AlCl3 (10 mg/kg b.w./day) and then with NAR (10 mg/kg b.w./day) for a total of sixty-two days. Results show that treatment of AlCl3 significantly reduced the body weight and testis weight of mice. AlCl3 caused oxidative damage in mice as evidenced by an increase in the concentration of nitric oxide, advanced oxidation of protein product, protein carbonylation, and lipid peroxidation. Furthermore, diminished activity of antioxidant moieties included superoxide dismutase, catalase, glutathione peroxidase, glutathione reductase, reduced glutathione, and oxidized glutathione. Several histological changes, such as spermatogenic cell degeneration, germinal epithelium detachment, and structural abnormalities in seminiferous tubules, were observed in AlCl3-treated mice. Oral administration of NAR was found to restore body weight and testes weight and ameliorated reproductive dysfunctions. NAR decreased oxidative stress, replenished the antioxidant defense system, and improved histopathological alterations in the AlCl3-treated testes. Therefore, the present study suggests that the supplementation of NAR may be a beneficial strategy to mitigate AlCl3-induced reproductive toxicity and testicular dysfunction. [ABSTRACT FROM AUTHOR]

Stratocumulus clouds are the most common type of boundary layer cloud; their radiative effects strongly modulate climate. Large eddy simulations (LES) of stratocumulus clouds often struggle to maintain fidelity to observations because of the sharp gradients occurring at the entrainment interfacial layer at the cloud top. The challenge posed to LES by stratocumulus clouds is evident in the wide range of solutions found in the LES intercomparison based on the DYCOMS-II field campaign, where simulated liquid water paths for identical initial and boundary conditions varied by a factor of nearly 12. Here we revisit the DYCOMS-II RF01 case and show that the wide range of previous LES results can be realized in a single LES code by varying only the numerical treatment of the equations of motion and the nature of subgrid-scale (SGS) closures. The simulations that maintain the greatest fidelity to DYCOMS-II observations are identified. The results show that using weighted essentially non-oscillatory (WENO) numerics for all resolved advective terms and no explicit SGS closure consistently produces the highest-fidelity simulations. This suggests that the numerical dissipation inherent in WENO schemes functions as a high-quality, implicit SGS closure for this stratocumulus case. Conversely, using oscillatory centered difference numerical schemes for momentum advection, WENO numerics for scalars, and explicitly modeled SGS fluxes consistently produces the lowest-fidelity simulations. We attribute this to the production of anomalously large SGS fluxes near the cloud tops through the interaction of numerical error in the momentum field with the scalar SGS model. [ABSTRACT FROM AUTHOR]

We present a finite difference-(multi-level) Monte Carlo algorithm to efficiently compute statistical solutions of the two-dimensional incompressible Navier-Stokes equations (NSE), with periodic boundary conditions and for arbitrary high Reynolds number. We propose a reformulation of statistical solutions in the sense of Foiaş and Prodi in the vorticity-stream function form. The vorticity-stream function formulation of the NSE in two-space dimensions is discretized with a finite difference scheme. We obtain a convergence rate error estimate for this approximation which is explicit in the viscosity parameter , under realistic assumptions on the solution regularity. We also prove convergence and complexity estimates, for the (multi-level) Monte Carlo finite difference algorithm to compute statistical solutions. Numerical experiments illustrating the validity of our estimates are presented. They show that the multi-level Monte Carlo algorithm can significantly accelerate the computation of statistical solutions in the sense of Foiaş and Prodi, even for very high Reynolds numbers. [ABSTRACT FROM AUTHOR]

We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure-valued solutions of the incompressible Euler equations. The resulting approximate young measures are proved to converge (with increasing numerical resolution) to a measure-valued solution. We present numerical experiments demonstrating the robustness and efficiency of the proposed algorithm, as well as the appropriateness of measure-valued solutions as a solution framework for the Euler equations. Furthermore, we report an extensive computational study of the two-dimensional vortex sheet, which indicates that the computed measure-valued solution is non-atomic and implies possible non-uniqueness of weak solutions constructed by Delort. [ABSTRACT FROM AUTHOR]

Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physical-viscosity solution. Numerical experiments illustrating the robust performance of these schemes are presented. [ABSTRACT FROM AUTHOR]

The prolyl-tRNA synthetase (PRS) is a validated drug target for febrifugine and its synthetic analog halofuginone (HFG) against multiple apicomplexan parasites including Plasmodium falciparum and Toxoplasma gondii. Here, a novel ATP-mimetic centered on 1-(pyridin-4-yl) pyrrolidin-2-one (PPL) scaffold has been validated to bind to Toxoplasma gondii PRS and kill toxoplasma parasites. PPL series exhibited potent inhibition at the cellular (T. gondii parasites) and enzymatic (TgPRS) levels compared to the human counterparts. Cell-based chemical mutagenesis was employed to determine the mechanism of action via a forward genetic screen. Tg-resistant parasites were analyzed with wild-type strain by RNA-seq to identify mutations in the coding sequence conferring drug resistance by computational analysis of variants. DNA sequencing established two mutations, T477A and T592S, proximal to terminals of the PPL scaffold and not directly in the ATP, tRNA, or L-pro sites, as supported by the structural data from high-resolution crystal structures of drug-bound enzyme complexes. These data provide an avenue for structure-based activity enhancement of this chemical series as anti-infectives. Author summary: Nearly one-third of the global population is chronically infected with the apicomplexan parasite Toxoplasma gondii. It does not particularly have any drastic impacts on a healthy individual with a robust immune response. But in immune-compromised patients, the parasite has been found to wreak havoc. The necessity of developing novel antibiotic therapeutics against this ailment is reprised by the limited efficacy of the SP regimen generally prescribed to patients with toxoplasmosis–including suppression of active proliferation–but not the latent stage. This regime has its limitations in the clearance of chronic infection and in the fact that crossing over the blood-brain barrier is troublesome for small molecules, which might not be able to prevent ocular toxoplasmosis in severe cases. Targeting of molecular motors within the protein translation machinery such as prolyl tRNA synthetases with structure-based designed small molecules mimicking the natural substrate, ATP, forms the basis of the work published here as being an avenue for targeting the parasite selectively. [ABSTRACT FROM AUTHOR]

Midazolam is a widely used anesthetic of the benzodiazepine class that has shown cytotoxicity and apoptosisinducing activity in neuronal cells and lymphocytes. This study aims to evaluate the effect of midazolam on growth of K562 human leukemia cells and HT29 colon cancer cells. The in vivo effect of midazolam was investigated in BALB/c-nu mice bearing K562 and HT29 cells human tumor xenografts. The results show that midazolam decreased the viability of K562 and HT29 cells by inducing apoptosis and S phase cell-cycle arrest in a concentration-dependent manner. Midazolam activated caspase-9, capspase-3 and PARP indicating induction of the mitochondrial intrinsic pathway of apoptosis. Midazolam lowered mitochondrial membrane potential and increased apoptotic DNA fragmentation. Midazolam showed reactive oxygen species (ROS) scavenging activity through inhibition of NADPH oxidase 2 (Nox2) enzyme activity in K562 cells. Midazolam caused inhibition of pERK1/2 signaling which led to inhibition of the anti-apoptotic proteins Bcl-X and XIAP and phosphorylation activation of the pro-apoptotic protein Bid. Midazolam inhibited growth of HT29 tumors in xenograft mice. Collectively our results demonstrate that midazolam caused growth inhibition of cancer cells via activation of the mitochondrial intrinsic pathway of apoptosis and inhibited HT29 tumor growth in xenograft mice. The mechanism underlying these effects of midazolam might be suppression of ROS production leading to modulation of apoptosis and growth regulatory proteins. These findings present possible clinical implications of midazolam as an anesthetic to relieve pain during in vivo anticancer drug delivery and to enhance anticancer efficacy through its ROS-scavenging and pro-apoptotic properties. [ABSTRACT FROM AUTHOR]

We prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the underlying cell averages is bounded. Similar sign properties and the boundedness of the jumps hold for the ENO interpolation procedure. These estimates, which are shown to hold for ENO reconstruction and interpolation of arbitrary order of accuracy and on nonuniform meshes, indicate a remarkable rigidity of the piecewise polynomial ENO procedure. [ABSTRACT FROM AUTHOR]

We consider initial-boundary-value problems for systems of conservation laws and design entropy stable finite difference schemes to approximate them. The schemes are shown to be entropy stable for a large class of systems that are equipped with a symmetric splitting, derived from the entropy formulation. Numerical examples for the Euler equations of gas dynamics are presented to illustrate the robust performance of the proposed method. [ABSTRACT FROM AUTHOR]

We consider a sub-model of the Hall-MHD equations: the so-called magnetic induction equations with Hall effect. These equations are non-linear and include third-order spatial and spatio-temporal mixed derivatives. We show that the energy of the solutions is bounded and design finite difference schemes that preserve the energy bounds for the continuous problem. We design both divergence preserving schemes and schemes with bounded divergence. We present a set of numerical experiments that demonstrate the robustness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Abstract: Ethnopharmacological relevance: Chaga mushroom (Inonotus obliquus) has been used in folk medicine to treat several disorders through its various biological functions. I. obliquus is claimed to produce general immune-potentiating and strengthening, antiinflammatory, and antitumor properties, but its effects on intestinal inflammation (ulcerative colitis) are clearly not understood. Aim of the study: To determine the effects and mode of action of an aqueous extract of I. obliquus (IOAE) on experimental colitis in mice induced by dextran sulfate sodium (DSS). Materials and methods: Female 5-week-C57BL/6 mice were randomized into groups differing in treatment conditions (prevention and treatment) and doses of IOAE (50 and 100mg/kg body weight). Mice were exposed to DSS (2%) in their drinking water over 7 day to induce acute intestinal inflammation. In colon tissues, we evaluated histological changes by hematoxylin and eosin staining, levels of iNOS by immuno-histochemical staining, and neutrophil influx by myeloperoxidase assay. mRNA expression of pro-inflammatory mediators TNF-α, IL-1β, IL-6, and IFN-γ was determined by RT-PCR. Results: Histological examinations indicated that IOAE suppressed edema, mucosal damage, and the loss of crypts induced by DSS. IOAE markedly attenuated DSS-induced iNOS levels and myeloperoxidase accumulation in colon tissues, demonstrating its suppressive effect on infiltration of immune cells. In addition, IOAE significantly inhibited mRNA expression of pro-inflammatory cytokines induced by DSS in colon tissues. Conclusion: Our results suggest anti-inflammatory effect of IOAE at colorectal sites due to down-regulation of the expression of inflammatory mediators. Suppression of TNF-α and iNOS together with IL-1β by IOAE denotes that it might be a useful supplement in the setting of inflammatory bowel disease. [Copyright &y& Elsevier]

We introduce a class of numerical schemes that preserve a discrete version of vorticity in conservation laws which involve grad advection. These schemes are based on reformulating finite volume schemes in terms of vertex centered numerical potentials. The resulting potential-based schemes have a genuinely multidimensional structure. A suitable choice of potentials leads to discrete vorticity preserving schemes that are simple to code, computationally inexpensive, and proven to be stable. We extend our discussion to other classes of genuinely multidimensional schemes. Numerical examples for linear grad advection equations, linear and nonlinear wave equation systems, and the Euler equations of gas dynamics are presented. [ABSTRACT FROM AUTHOR]

Abstract: We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we design stable and accurate numerical schemes for conservation laws with stiff source terms. A prime example and the main motivation for our study is the reactive Euler equations of gas dynamics. Furthermore, we consider widely studied scalar model equations. We device one-step IMEX (implicit–explicit) schemes for these equations that treats the convection terms explicitly and the source terms implicitly. For the non-linear scalar equation, we use a novel choice of initial data for the resulting Newton solver and obtain correct propagation speeds, even in the difficult case of rarefaction initial data. For the reactive Euler equations, we choose the numerical diffusion suitably in order to obtain correct wave speeds on under-resolved meshes. We prove that our implicit–explicit scheme converges in the scalar case and present a large number of numerical experiments to validate our scheme in both the scalar case as well as the case of reactive Euler equations. Furthermore, we discuss fundamental differences between the reactive Euler equations and the scalar model equation that must be accounted for when designing a scheme. [ABSTRACT FROM AUTHOR]

We propose a finite volume method for the shallow water equations that accurately approximates the transport of vorticity. The algorithm is based on a predictor-corrector-type projection method. Any consistent finite volume scheme may be used in the prediction step of the algorithm. An elliptic equation is solved and the momentum field is corrected to obtain the correct evolution of vorticity. We describe this projection algorithm for the wave equation and the shallow water equations. The crucial role played by the pseudovorticity transport is highlighted. Numerical experiments demonstrating a considerable gain in computational efficiency with the vorticity projection algorithm are presented. [ABSTRACT FROM AUTHOR]

• Novel machine learning algorithm based on physics informed neural networks (PINNs) for approximating solutions of forward and inverse problems for radiative transfer. • Fast, robust and accurate approach, independent of the equation dimensionality. • Estimates on the generalization error of PINNs for the unsteady and steady forward problem. • Extensive numerical experiments demonstrating the accuracy and efficiency of the proposed algorithm. We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative transfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently. [ABSTRACT FROM AUTHOR]

Abstract: We deal with a Hamilton–Jacobi equation with a Hamiltonian that is discontinuous in the space variable. This is closely related to a conservation law with discontinuous flux. Recently, an entropy framework for single conservation laws with discontinuous flux has been developed which is based on the existence of infinitely many stable semigroups of entropy solutions based on an interface connection. In this paper, we characterize these infinite classes of solutions in terms of explicit Hopf–Lax type formulas which are obtained from the viscosity solutions of the corresponding Hamilton–Jacobi equation with discontinuous Hamiltonian. This also allows us to extend the framework of infinitely many classes of solutions to the Hamilton–Jacobi equation and obtain an alternative representation of the entropy solutions for the conservation law. We have considered the case where both the Hamiltonians are convex (concave). Furthermore, we also deal with the less explored case of sign changing coefficients in which one of the Hamiltonians is convex and the other concave. In fact in convex–concave case we cannot expect always an existence of a solution satisfying Rankine–Hugoniot condition across the interface. Therefore the concept of generalised Rankine–Hugoniot condition is introduced and prove existence and uniqueness. [Copyright &y& Elsevier]

Abstract: We deal with a single conservation law with discontinuous convex–concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine–Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine–Hugoniot condition by a generalized Rankine–Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in . Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. [Copyright &y& Elsevier]

We deal with a single conservation law in one space dimension whose flux function is discontinuous in the space variable and we introduce a proper framework of entropy solutions. We consider a large class of fluxes, namely, fluxes of the convex-convex type and of the concave-convex (mixed) type. The alternative entropy framework that is proposed here is based on a two step approach. In the first step, infinitely many classes of entropy solutions are defined, each associated with an interface connection. We show that each of these class of entropy solutions form a contractive semigroup in L1 and is hence unique. Godunov type schemes based on solutions of the Riemann problem are designed and shown to converge to each class of these entropy solutions. The second step is to choose one of these classes of solutions. This choice depends on the Physics of the problem being considered and we concentrate on the model of two-phase flows in a heterogeneous porous medium. We define an optimization problem on the set of admissible interface connections and show the existence of an unique optimal connection and its corresponding optimal entropy solution. The optimal entropy solution is consistent with the expected solutions for two-phase flows in heterogeneous porous media. [ABSTRACT FROM AUTHOR]

We consider the scalar conservation law with flux function discontinuous in the space variable, i.e., \begin{eqnarray} \label{eq1} u_t+(H(x)f(u)+(1-H(x))g(u))_{x} &=& 0 \quad \mbox{in } \R \times \R_{+}, \nonumber \\ u(0, x) &=& u_{0}(x) \quad \mbox{in } \R, \label{0.1} \end{eqnarray} where $H$ is the Heaviside function and $f$ and $g$ are smooth with the assumptions that either $f$ is convex and $g$ is concave or $f$ is concave and $g$ is convex. The existence of a weak solution of (\ref{eq1}) is proved by showing that upwind finite difference schemes of Godunov and Enquist--Osher type converge to a weak solution. Uniqueness follows from a Kruzkhov-type entropy condition. We also provide explicit solutions to the Riemann problem for (\ref{eq1}). At the level of numerics, we give easy-to-implement numerical schemes of Godunov and Enquist--Osher type. The central feature of this paper is the modification of the singular mapping technique (the main analytical tool for these types of equations) which allows us to show that the numerical schemes converge. Equations of type (\ref{eq1}) with the above hypothesis on the flux may occur when considering the following scalar conservation law with discontinuous flux: \begin{equation} \label{eq2} \begin{array}{r@{\;}l} u_t + (k (x) f (u))_x &= 0, \\ u (0, x) &= u_0 (x), \end{array} \end{equation} with $f$ convex and $k$ of indefinite sign. [ABSTRACT FROM AUTHOR]

We present a novel active learning algorithm, termed as iterative surrogate model optimization (ISMO), for robust and efficient numerical approximation of PDE constrained optimization problems. This algorithm is based on deep neural networks and its key feature is the iterative selection of training data through a feedback loop between deep neural networks and any underlying standard optimization algorithm. Numerical examples for optimal control, parameter identification and shape optimization problems for PDEs are provided to demonstrate that ISMO significantly outperforms a standard deep neural network based surrogate optimization algorithm as well as standard optimization algorithms. [ABSTRACT FROM AUTHOR]

Toxoplasmosis is caused by Toxoplasma gondii and in immunocompromised patients, it may lead to seizures, encephalitis or death. The conserved enzyme prolyl-tRNA synthetase (PRS) is a validated druggable target in Toxoplasma gondii but the traditional 'single target–single drug' approach has its caveats. Here we describe two potent inhibitors namely halofuginone (HFG) and a novel ATP mimetic (L95) that bind to Toxoplasma gondii PRS simultaneously at different neighbouring sites to cover all three of the enzyme substrate subsites. HFG and L95 act as one triple-site inhibitor in tandem and form an unusual ternary complex wherein HFG occupies the 3'-end of tRNA and the L-proline (L-pro) binding sites while L95 occupies the ATP pocket. These inhibitors exhibit nanomolar IC50 and EC50 values independently, and when given together reveal an additive mode of action in parasite inhibition assays. This work validates a novel approach and lays a structural framework for further drug development based on simultaneous targeting of multiple pockets to inhibit druggable proteins. Author summary: Among infectious diseases, parasitic diseases are a major cause of death and morbidity. Toxoplasmosis is caused by an infection of the apicomplexan parasite Toxoplasma gondii. In immunocompromised patients Toxoplasmosis may lead to seizures, encephalitis or death. Novel therapeutics for human parasites are constantly needed. In recent years, the aminoacyl-tRNA synthetase (aaRS) enzyme family has been validated as a drug target for several parasitic infections. The Toxoplasma gondii prolyl-tRNA synthetase inhibitor halofuginone (HFG) has been validated earlier but here we show that an ATP-mimic called L95 is a potent inhibitor and can bind to the target enzyme in the presence of HFG. Thus the two inhibitors described in this study simultaneously occupy all three natural substrate (ATP, L-amino acid and 3'end of tRNA) binding pockets and thereby inhibit the enzyme leading to parasite death. This unprecedented double drugging of a pathogen enzyme may delay resistance mutation generation and this approach opens the path to multi-drugging of validated parasite proteins. [ABSTRACT FROM AUTHOR]

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large number of expensive (forward) numerical solutions of the corresponding PDEs. We propose a machine learning algorithm, based on deep artificial neural networks, that predicts the underlying input parameters to observable map from a few training samples (computed realizations of this map). By a judicious combination of theoretical arguments and empirical observations, we find suitable network architectures and training hyperparameters that result in robust and efficient neural network approximations of the parameters to observable map. Numerical experiments are presented to demonstrate low prediction errors for the trained network networks, even when the network has been trained with a few samples, at a computational cost which is several orders of magnitude lower than the underlying PDE solver. Moreover, we combine the proposed deep learning algorithm with Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods to efficiently compute uncertainty propagation for nonlinear PDEs. Under the assumption that the underlying neural networks generalize well, we prove that the deep learning MC and QMC algorithms are guaranteed to be faster than the baseline (quasi-) Monte Carlo methods. Numerical experiments demonstrating one to two orders of magnitude speed up over baseline QMC and MC algorithms, for the intricate problem of computing probability distributions of the observable, are also presented. • The parameters to observable map in CFD can be efficiently approximated by deep neural networks. • Very low prediction errors with neural networks, trained on a few samples. • Proposed deep learning algorithm for UQ provides speedup over (Quasi)-Monte Carlo. • Training on Sobol points led to greater accuracy than on Random points. [ABSTRACT FROM AUTHOR]

We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic tangent activation function. These bounds provide explicit estimates on the approximation error with respect to the size of the neural networks. We show that tanh neural networks with only two hidden layers suffice to approximate functions at comparable or better rates than much deeper ReLU neural networks. • Explicit bounds for function approximation in Sobolev norms by tanh neural networks. • Tanh networks with 2 hidden layers are at least as expressive as deeper ReLU networks. • Improved convergence rate for neural network approximation of analytic functions. [ABSTRACT FROM AUTHOR]

Celestial Pole Offsets (CPO), denoted by dX and dY, describe the differences in the observed position of the pole in the celestial frame with respect to a certain precession-nutation model. Precession and nutation components are part of the transformation matrix between terrestrial and celestial systems. Therefore, various applications in geodetic science such as high-precision spacecraft navigation require information regrading precession and nutation. For this purpose, CPO can be added to the precession-nutation model to precisely describe the motion of the celestial pole. However, as Very Long Baseline Interferometry (VLBI)—currently the only technique providing CPO—requires long data processing times resulting in several weeks of latency, predictions of CPO become necessary. Here we present a new methodology named Deep Ensemble Geophysics-Informed Neural Networks (DEGINNs) to provide accurate CPO predictions. The methodology has three main elements: (1) deep ensemble learning to provide the prediction uncertainty; (2) broad-band Liouville equation as a geophysical constraint connecting the rotational dynamics of CPO to the atmospheric and oceanic Effective Angular Momentum (EAM) functions and (3) coupled oscillatory recurrent neural networks to model the sequential characteristics of CPO time-series, also capable of handling irregularly sampled time-series. To test the methodology, we use the newest version of the final CPO time-series of International Earth Rotation and Reference Systems Service (IERS), namely IERS 20 C04. We focus on a forecasting horizon of 90 days, the practical forecasting horizon needed in space-geodetic applications. Furthermore, for validation purposes we generate an independent global VLBI solution for CPO since 1984 up to the end of 2022 and analyse the series. We draw the following conclusions. First, the prediction performance of DEGINNs demonstrates up to 25 and 33 percent improvement, respectively, for dX and dY, with respect to the rapid data provided by IERS. Secondly, predictions made with the help of EAM are more accurate compared to those without EAM, thus providing a clue to the role of atmosphere and ocean on the excitation of CPO. Finally, free core nutation period shows temporal variations with a dominant periodicity of around one year, partially excited by EAM. [ABSTRACT FROM AUTHOR]

Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any continuous operator to desired accuracy. Moreover, we suggest a mechanism by which FNOs can approximate operators associated with PDEs efficiently. Explicit error bounds are derived to show that the size of the FNO, approximating operators associated with a Darcy type elliptic PDE and with the incompressible Navier-Stokes equations of fluid dynamics, only increases sub (log)-linearly in terms of the reciprocal of the error. Thus, FNOs are shown to efficiently approximate operators arising in a large class of PDEs. [ABSTRACT FROM AUTHOR]

Rapid provision of Earth orientation parameters (EOPs, here polar motion and dUT1) is indispensable in many geodetic applications and also for spacecraft navigation. There are, however, discrepancies between the rapid EOPs and the final EOPs that have a higher latency but the highest accuracy. To reduce these discrepancies, we focus on a data‐driven approach, present a novel method named ResLearner, and use it in the context of deep ensemble learning. Furthermore, we introduce a geophysically constrained approach for ResLearner. We show that the most important geophysical information to improve the rapid EOPs is the effective angular momentum functions of atmosphere, ocean, land hydrology, and sea level. In addition, semidiurnal, diurnal, and long‐period tides coupled with prograde and retrograde tidal excitations are important features. The influence of some climatic indices on the prediction accuracy of dUT1 is discussed, and El Niño Southern Oscillation is found to be influential. We developed an operational framework, providing the improved EOPs on a daily basis with a prediction window of 63 days to fully cover the latency of final EOPs. We show that under the operational conditions and using the rapid EOPs of the International Earth Rotation and Reference Systems Service (IERS), we achieve improvements as high as 60%, thus significantly reducing the differences between rapid and final EOPs. Furthermore, we discuss how the new final series IERS 20 C04 is preferred over 14 C04. Finally, we compare against EOP hindcast experiments of the European Space Agency, on which ResLearner presents comparable improvements. Plain Language Summary: The International Earth Rotation and Reference Systems Service (IERS) provides rapid Earth orientation parameters (EOPs) using different space‐geodetic techniques to bridge the latency of the final, most accurate EOPs solution. However, these rapid EOPs are not in full agreement with the final EOPs. In order to reduce the differences between the rapid and final EOPs, we focus on the application of machine learning and present a novel method named ResLearner, which is based on geodetic data and geophysical constraints. We present the method in the context of deep ensemble learning, focusing on a prediction window of 63 days. We also attempt to link informative geophysical effects to these discrepancies. We show that they are linked to a mixture of atmospheric, oceanic, hydrological, and sea level effective angular momentum functions, dominance of the Global Navigation Satellite Systems‐derived polar motion, and various short‐ and long‐term tidal excitations. El Niño Southern Oscillation is also relevant for dUT1 prediction. The methodology can provide significant improvements of up to 60% in operational settings with respect to rapid EOPs provided by IERS. Additional validation is done by using the data of Jet Propulsion Laboratory final EOP series and also EOP series provided by the European Space Agency. Key Points: We introduce a novel machine learning algorithm named ResLearner to improve the accuracy of rapid and predicted Earth orientation parameters (EOPs)We also present geophysically constrained ResLearner, using Earth's effective angular momentum functions, tides, and climatic indicesBesides prediction, ResLearner is also able to effectively correct deficits in rapidly processed EOPs with respect to final EOPs [ABSTRACT FROM AUTHOR]

Tunneling delays represent a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here, we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, respectively. Both of these definitions are closely connected to the theory of weak measurement, with Larmor time being the weak measurement value of tunneling time and Bohmian trajectory corresponding to the average particle trajectory, which has been recently reconstructed using weak measurement in a two-slit experiment [S. Kocsis, B. Braverman, S. Ravets, M. J. Stevens, R. P. Mirin, L. K. Shalm, and A. M. Steinberg, Science 332, 1170 (2011)]. We demonstrate a big discrepancy in strong field ionization between the Bohmian and weak measurement values of tunneling time, and we suggest this arises because the tunneling time is calculated for a small probability postselected ensemble of electrons. Our results have important implications for the interpretation of experiments in attosecond science, suggesting that tunneling is unlikely to be an instantaneous process. [ABSTRACT FROM AUTHOR]

Fucosyltransferases are a group of enzymes that catalyse the transfer of l-fucose from a donor substrate to an acceptor molecule. Silybum marianum is also called ‘milk thistle’ due to its characteristic flower shape. It produces two major flavonoids: silymarin and silybin. The plant and its major secondary metabolites are used for treatment/recovery after chronic liver disease, liver rehabilitation after hepatitis and treatment of gallbladder disease. These compounds also act as antioxidants for scavenging free radicals and inhibiting lipid peroxidation. We identified two peptide motifs (YYEAYLSHADEK and TTPDPSCGR designated as motif 1 and motif 2, respectively) of a fucosyltransferase derived from S. marianum that are highly conserved in its counterparts across the plant species and sources. The nature and properties of the motifs are discussed in terms of their putative participation in catalysis and enzyme/active site conformation. [ABSTRACT FROM AUTHOR]

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417-1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate entropy measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to entropy measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an entropy measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed entropy measure-valued solutions. [ABSTRACT FROM AUTHOR]

In the present study, we developed a novel drug-like self-micellizing anticancer lipid (SMAL), and investigated its anticancer activity and effects on cell death pathways in human colorectal cancer (CRC) cell lines. Three self-assembled nanoparticles were prepared, namely, SMAL102 (lauramide derivative), SMAL104 (palmitamide derivative), and SMAL108 (stearamide derivative) by a thin-film hydration technique, and were characterized for physicochemical and biological parameters. SMAL102 were nanosized (160.23 ± 8.11 nm) with uniform spherical shape, while SMAL104 and SMAL108 did not form spherical shape but formed large size nanoparticles and irregular in shape. Importantly, SMAL102 showed a cytotoxic effect towards CRC cell lines (HCT116 and HT-29), and less toxicity to a normal colon fibroblast cell line (CCD-18Co). Conversely, SMAL104 and SMAL108 did not have an anti-proliferative effect on CRC cell lines. SMAL102 nanoparticles were actively taken up by CRC cell lines, localized in the cell membrane, and exhibited remarkable cytotoxicity in a concentration-dependent manner. The normal colon cell line showed significantly less cellular uptake and non-cytotoxicity as compared with the CRC cell lines. SMAL102 nanoparticles induced caspase-3, caspase-9, and PARP cleavage in HT-29 cells, indicating the induction of apoptosis; whereas LC3B was activated in HCT116 cells, indicating autophagy-induced cell death. Collectively, these results demonstrate that SMAL102 induced cell death via activation of apoptosis and autophagy in CRC cell lines. The present study could be a pioneer for further preclinical and clinical development of such compounds. [ABSTRACT FROM AUTHOR]

Aim of the study In this study, we examined the effect of different fractions and components of Chaga mushroom (Inonotus Obliquus) on viability and apoptosis of colon cancer cells. Among them, one component showed the most effective growth inhibition and was identified as ergosterol peroxide by NMR analysis. We investigated the anti-proliferative and apoptosis mechanisms of ergosterol peroxide associated with its anti-cancer activities in human colorectal cancer (CRC) cell lines and tested its anti-tumor effect on colitis-induced CRC developed by Azoxymethane (AOM)/Dextran sulfate sodium (DSS) in a mouse model. Materials and methods We used MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assays, flow cytometry assays, Western blot analysis, colony formation assays, reverse transcription-polymerase chain reaction (RT-PCR), immunohistochemistry (IHC), and AOM/DSS mouse models to study the molecular mechanism of metastatic activities in CRC cells. Results Ergosterol peroxide inhibited cell proliferation and also suppressed clonogenic colony formation in HCT116, HT-29, SW620 and DLD-1 CRC cell lines. The growth inhibition observed in these CRC cell lines was the result of apoptosis, which was confirmed by FACS analysis and Western blotting. Ergosterol peroxide inhibited the nuclear levels of β-catenin, which ultimately resulted in reduced transcription of c-Myc, cyclin D1, and CDK-8. Ergosterol peroxide administration showed a tendency to suppress tumor growth in the colon of AOM/DSS-treated mice, and quantification of the IHC staining showed a dramatic decrease in the Ki67-positive staining and an increase in the TUNEL staining of colonic epithelial cells in AOM/DSS-treated mice by ergosterol peroxide for both prevention and therapy. Conclusion Our data suggest that ergosterol peroxide suppresses the proliferation of CRC cell lines and effectively inhibits colitis-associated colon cancer in AOM/DSS-treated mice. Ergosterol peroxide down-regulated β-catenin signaling, which exerted anti-proliferative and pro-apoptotic activities in CRC cells. These properties of ergosterol peroxide advocate its use as a supplement in colon cancer chemoprevention. [ABSTRACT FROM AUTHOR]

• Cardiac arrhythmias, atrial filtration and ventricular tachycardia, mainly caused by the autonomic nervous system. • Conventional strategies have been overcome using parasympathetic and sympathetic stimulation. • Therapeutic modalities associated with VNS, tragus stimulation, RDN, BAT and CSD may be promising. • Heart rate variability, skin sympathetic nerve activity using microneurography, and alternans are a few autonomic tone evaluation techniques. The pathophysiology of atrial fibrillation and ventricular tachycardia that result in cardiac arrhythmias is related to the sustained complicated mechanisms of the autonomic nervous system. Atrial fibrillation is when the heart beats irregularly, and ventricular arrhythmias are rapid and inconsistent heart rhythms, which involves many factors including the autonomic nervous system. It's a complex topic that requires careful exploration. Cultivation of speculative knowledge on atrial fibrillation; the irregular rhythm of the heart and ventricular arrhythmias; rapid oscillating waves resulting from mistakenly inconsistent P waves, and the inclusion of an autonomic nervous system is an inconceivable approach toward clinical intricacies. Autonomic modulation, therefore, acquires new expansions and conceptions of appealing therapeutic intelligence to prevent cardiac arrhythmia. Notably, autonomic modulation uses the neural tissue's flexibility to cause remodeling and, hence, provide therapeutic effects. In addition, autonomic modulation techniques included stimulation of the vagus nerve and tragus, renal denervation, cardiac sympathetic denervation, and baroreceptor activation treatment. Strong preclinical evidence and early human studies support the annihilation of cardiac arrhythmias by sympathetic and parasympathetic systems to transmigrate the cardiac myocytes and myocardium as efficient determinants at the cellular and physiological levels. However, the goal of this study is to draw attention to these promising early pre-clinical and clinical arrhythmia treatment options that use autonomic modulation as a therapeutic modality to conquer the troublesome process of irregular heart movements. Additionally, we provide a summary of the numerous techniques for measuring autonomic tone such as heart rate oscillations and its association with cutaneous sympathetic nerve activity appear to be substitute indicators and predictors of the outcome of treatment. [ABSTRACT FROM AUTHOR]

We design schemes for the approximation of entropy solutions to nonlinear hyperbolic conservation laws in the regime where small-scale effects drive the dynamics of nonclassical shock waves in these solutions. Typically, the small-scale effects are modeled by adding higher-order dissipation terms taking into account the viscosity, capillarity, the Hall coefficient, etc., of the material under consideration. We analyze a strategy for the design of numerical methods adapted to these problems, referred to as schemes with well-controlled dissipation (WCD). Nonclassical entropy solutions are approximated by (small-scale) consistent and converging schemes with high accuracy--the main challenge being to capture physically relevant shocks. Following earlier works by LeFloch and collaborators, we rely on the equivalent equation, which provides a suitable tool in order to guarantee that small-scale dependent shocks are computed in a consistent and accurate way. WCD schemes are also intended to capture (nonclassical) shocks with arbitrary large strength. Our strategy is exemplified with examples and numerical experiments encompassing the cubic conservation law, the nonlinear elasticity system, and a reduced magnetohydrodynamics model. We compute the kinetic functions associated with the schemes and, as the order of the WCD schemes is increased, we observe convergence toward the exact kinetic function--even for strong shocks. [ABSTRACT FROM AUTHOR]

Morphogen gradients guide the patterning of tissues and organs during the development of multicellular organisms. In many cases, morphogen signaling is also required for tissue growth. The consequences of this interplay between growth and patterning are not well understood. In the Drosophila wing imaginal disc, the morphogen Dpp guides patterning and is also required for tissue growth. In particular, it was recently reported that cell division in the disc correlates with the temporal increase in Dpp signaling. Here we mathematically model morphogen gradient formation in a growing tissue, accounting also for morphogen advection and dilution. Our analysis defines a new scaling mechanism, which we term the morphogen-dependent division rule (MDDR): when cell division depends on the temporal increase in morphogen signaling, the morphogen gradient scales with the growing tissue size, tissue growth becomes spatially uniform and the tissue naturally attains a finite size. This model is consistent with many properties of the wing disc. However, we find that the MDDR is not consistent with the phenotype of scaling-defective mutants, supporting the view that temporal increase in Dpp signaling is not the driver of cell division during late phases of disc development. More generally, our results show that local coupling of cell division with morphogen signaling can lead to gradient scaling and uniform growth even in the absence of global feedbacks. The MDDR scaling mechanism might be particularly beneficial during rapid proliferation, when global feedbacks are hard to implement. [ABSTRACT FROM AUTHOR]

The insulin-like growth factor (IGF) signaling pathway plays an important role in cancer biology. The IGF 1 receptor (IGF1R) overexpression has been associated with a number of hematological neoplasias and solid tumors including breast cancer. However, molecular mechanism involving IGF1R in carcinogenic developments is clearly not known. We investigated the genetic variations across the IGF1R polymorphism and the risk of breast cancer risk in Korean women. A total of 1418 individuals comprising 1026 breast cancer cases and 392 age-matched controls of Korean were included for the analysis. Genomic DNA was extracted from whole blood and single nucleotide polymorphisms (SNPs) were analyzed on the GoldenGate Assay system by Illumina’s Custom Genetic Analysis service. SNPs were selected for linkage disequilibrium (LD) analysis by Haploview. We genotyped total 51 SNPs in the IGF1R gene and examined for association with breast cancer. All the SNPs investigated were in Hardy-Weinberg equilibrium. These SNPs tested were significantly associated with breast cancer risk, after correction for multiple comparisons by adjusting for age at diagnosis, BMI, age at menarche, and age at first parturition. Among 51 IGF1R SNPs, five intron located SNPs (rs8032477, rs7175052, rs12439557, rs11635251 and rs12916884) with homozygous genotype (variant genotype) were associated with decreased risk of breast cancer. Fisher’s combined p-value for the five SNPs was 0.00032. Three intron located SNPs with heterozygous genotypes also had decreased risk of breast cancer. Seven of the 51 IGF1R SNPs were in LD and in one haplotype block, and were likely to be associated with breast cancer risk. Overall, this case-control study demonstrates statistically significant associations between breast cancer risk and polymorphisms in IGF1R gene. [ABSTRACT FROM AUTHOR]