An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Relative abundance of full-length and truncated FOXP1 isoforms is associated with differential NFκB activity in Follicular Lymphoma

FOXP1 is a transcriptional repressor that has been proposed to repress the expression of some NFκB-responsive genes. Furthermore, truncated forms of FOXP1 have been associated with a subtype of Diffuse Large B-cell Lymphoma characterised by constitutive NFκB activity, indicating that they may inhibit this repression. We have shown that FL tumors have increased relative abundance of truncated FOXP1 isoforms and this is associated with increased expression of NFκB-associated genes. Our results provide strong evidence that relative FOXP1 isoform abundance is associated with NFκB activity in FL, and could potentially be used as a marker for this gene signature.

Mandatory Reporting Laws and Identification of Child Abuse and Neglect: Consideration of Differential Maltreatment Types, and a Cross-Jurisdictional Analysis of Child Sexual Abuse Reports

Mandatory reporting laws have been created in many jurisdictions as a way of identifying cases of severe child maltreatment on the basis that cases will otherwise remain hidden. These laws usually apply to all four maltreatment types. Other jurisdictions have narrower approaches supplemented by differential response systems, and others still have chosen not to enact mandatory reporting laws for any type of maltreatment. In scholarly research and normative debates about mandatory reporting laws and their effects, the four major forms of child maltreatment—physical abuse, sexual abuse, emotional abuse, and neglect—are often grouped together as if they are homogenous in nature, cause, and consequence. Yet, the heterogeneity of maltreatment types, and different reporting practices regarding them, must be acknowledged and explored when considering what legal and policy frameworks are best suited to identify and respond to cases. A related question which is often conjectured upon but seldom empirically explored, is whether reporting laws make a difference in case identification. This article first considers different types of child abuse and neglect, before exploring the nature and operation of mandatory reporting laws in different contexts. It then posits a differentiation thesis, arguing that different patterns of reporting between both reporter groups and maltreatment types must be acknowledged and analysed, and should inform discussions and assessments of optimal approaches in law, policy and practice. Finally, to contribute to the evidence base required to inform discussion, this article conducts an empirical cross-jurisdictional comparison of the reporting and identification of child sexual abuse in jurisdictions with and withoutmandatory reporting, and concludes that mandatory reporting laws appear to be associated with better case identification.

Optimal HMM filtering and decision feedback equalisation for differential encoded transmission systems

In this paper conditional hidden Markov model (HMM) filters and conditional Kalman filters (KF) are coupled together to improve demodulation of differential encoded signals in noisy fading channels. We present an indicator matrix representation for differential encoded signals and the optimal HMM filter for demodulation. The filter requires O(N3) calculations per time iteration, where N is the number of message symbols. Decision feedback equalisation is investigated via coupling the optimal HMM filter for estimating the message, conditioned on estimates of the channel parameters, and a KF for estimating the channel states, conditioned on soft information message estimates. The particular differential encoding scheme examined in this paper is differential phase shift keying. However, the techniques developed can be extended to other forms of differential modulation. The channel model we use allows for multiplicative channel distortions and additive white Gaussian noise. Simulation studies are also presented.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.