We study a nonlinear parabolic equation with measurable nonlinearity and measure data:  

We obtain an optimal point-wise estimate for the gradient of a solution in terms of a certain Riesz potential of the right-hand measure in a very general setting that the nonlinearity is not only allowed to be measurable in one of spatial variables, but also depends on the variable of the possibly unbounded solution itself.

Gliomas are malignant tumors that are commonly observed in primary brain cancer. Glioma cells migrate through a dense network of normal cells in microenvironment and spread long distances within brain. In this paper we present a two-dimensional multiscale model in which a glioma cell is surrounded by normal cells and its migration is controlled by cell-mechanical components in the microenvironment via the regulation of myosin II in response to chemoattractants. Our simulation results show that the myosin II plays a key role in the deformation of the cell nucleus as the glioma cell passes through the narrow intercellular space smaller than its nuclear diameter. We also demonstrate that the coordination of biochemical and mechanical components within the cell enables a glioma cell to take the mode of amoeboid migration. This study sheds lights on the understanding of glioma infiltration through the narrow intercellular spaces and may provide a potential approach for the development of anti-invasion strategies via the injection of chemoattractants for localization.

Only with 1-D Green function for 1-D elliptic differential operator, we can solve 2-D/3-D general elliptic problems by applying the axial Green function method (AGM). An extension of AGM is proposed to enforce Neumann boundary conditions. This extension is directly available for 2-D problems with straight boundaries parallel to axes on which Neumann boundary conditions are assigned. It is thoroughly attributed to the specific axial Green functions associated with the Neumann conditions. Moreover, since this extended AGM (XAGM) in 1-D satisfies the transmission condition across an interface along which the permittivity is discontinuous, it can be applied to 2-D problems with interfaces parallel to axes without loss of accuracy. Finally, we apply the XAGM in 2-D to 3-D axisymmetric electric potential problems with variable and/or even discontinuous permittivities along interfaces. Owing to the cylindrical coordinate transform, the transformed problem is tractable to solve using this XAGM. Arbitrary distribution of axial lines is available, which must be a marked advantage of XAGM compared to other methods.

The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000)]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.

In this paper, we consider a phase-field model for dendritic growth in a two-dimensional cavity flow and propose a computationally efficient numerical method for solving the model. The crystal is fixed in the space and cannot be convected in most of the previous studies, instead the supercooled melt flows around the crystal, which is hard to be realized in the real world experimental setting. Applying advection to the crystal equation, we have problems such as deformation of crystal shape and ambiguity of the crystal orientation for the anisotropy. To resolve these difficulties, we present a phase-field method by using a moving overset grid for the dendritic growth in a cavity flow. Numerical results show that the proposed method can predict the crystal growth under flow.

Purpose

This study aims to propose a physics­based method of reducing beam­hardening artifacts induced by high­attenuation materials such as metal stents or other metallic implants.

Methods

The proposed approach consists of deriving a sinogram inconsistency formula representing the energy dependence of the attenuation coefficient of high­attenuation materials. This inconsistency formula more accurately represents the inconsistencies of the sinogram than that of a previously reported formula6 (called the MAC­BC method). This is achieved by considering the properties of the high­attenuation materials, which include the materials’ shapes and locations and their effects on the incident X­ray spectrum, including their attenuation coefficients.

Results

Numerical simulation and phantom experiment demonstrate that the modeling error of MAC­BC method are nearly completely red by means of the proposed method.

Conclusion

The proposed method reduces beam­hardening artifacts arising from high­attenuation materials by relaxing the assumptions of the MAC­BC method. In doing so, it outperforms the original MAC­BC method. Further research is required to address other potential sources of metal artifacts, such as photon starvation, scattering, and noise.

Public-Key Cryptography (PKC) based on multivariate quadratic equations is one of the most promising alternatives for classical PKC after the eventual coming of quantum computers. Recently, Shen and Tang proposed a new MQ-signature scheme, RGB, based on three types of variables, Red(r), Green(g) and Blue(b). They claimed that signing for RGB is faster than that of UOV and Rainbow. At ACISP 2016, Tang et al. implemented RGB on S5PV210 and MT6582 microprocessors at 64, 80, 96, 118 and 128-bit security levels for practical use. Their results are much more efficient than other MQ-signature schemes, so RGB is very appealing for resource-limited devices. We show that RGB with their suggested parameters at 64, 80, 96, 118 and 128 security levels are entirely broken by key recovery attacks using good keys. From a practical point of view, we are able to break their parameters at 64, 80, 96, 118 and 128 security levels in less than 0.48 seconds, 1.7 seconds, 90.68 seconds, 11 minutes and 6.82 hours, respectively. Consequently, we show that signing and the key sizes for RGB with secure parameter sets are much slower and larger than those of UOV and Rainbow.

In this article we first introduce some results about the binomial, trinomial, and quadrinomial convolution sums of certain divisor functions and then we provide an identity for the multinomial convolution sums of the divisor function

Multi-user broadcast authentication is an important security service in wireless sensor networks (WSNs), as it allows a large number of mobile users of the WSNs to join in and broadcast messages to WSNs dynamically and authentically. To reduce communication cost due to the transmission of public-key certificates, broadcast authentication schemes based on identity (ID)-based cryptography have been proposed, but the schemes suffer from expensive pairing computations. In this paper, to minimize computation and communication costs, we propose a new provably secure pairing-free ID-based signature schemes with message recovery, MR-IBS, and PMR-IBS. We then construct an ID-based multi-user broadcast authentication scheme, BASIS, based on MR-IBS and PMR-IBS for broadcast authentication between users and a sink. We evaluate the practical feasibility of BASIS on WSN hardware platforms, MICAz and Tmote Sky are used in real-life deployments in terms of computation/communication cost and energy consumption. Consequently, BASIS reduces the total energy consumption on Tmote Sky by up to 72% and 17% compared with Bloom filter-based authentication scheme based on a variant of ECDSA with message recovery and IMBAS based on a ID-based signature scheme with message appendix, respectively.

A WAVE-based cross-layer anonymous authentication scheme based on a variant of ECDSA (Biswas and Misic “A Cross-layer approach to privacy-preserving authentication in WAVE-enabled VANETs,” IEEE Trans. Veh. Technol., vol. 62, no. 5, pp. 2182-2192, Jun. 2013.) was published for authenticity of vehicular safety application messages. Our result shows that, contrary to what is claimed, the scheme is entirely broken due to the insecurity of their underlying signature scheme: Their modification of ECDSA is insecure against secret key recovery attacks where anyone can recover OBUs' or mobile nodes' private keys from transmitted signed messages just eavesping.