Total Edge Irregularity Strength for Graphs

An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge $e$, denoted by $wt(e)$, is defined as the sum of the label of $e$ and the labels of two vertices which incident with $e$, i.e. if $e=vw$, then $wt(e)=f(e)+f(v)+f(w)$. The minimum $k$ for which $G$ has an edge irregular total $k$-labelling is called the total edge irregularity strength of $G.$ In this paper, we determine total edge irregularity of connected and disconnected graphs

Epidemiology and outcomes of pediatric autosomal recessive polycystic kidney disease in the Middle East and North Africa

The incidence of rare diseases is expected to be comparatively higher in the Middle East and North Africa (MENA) region than in other parts of the world, attributed to the high prevalence of consanguinity. Most MENA countries share social and economic statuses, cultural relativism, religious beliefs, and healthcare policies. Polycystic kidney diseases (PKDs) are the most common genetic causes of kidney failure, accounting for nearly 8.0% of dialysis cases. The development of PKDs is linked to variants in several genes, including PKD1, PKD2, PKHD1, DZIP1L, and CYS1. Autosomal recessive PKD (ARPKD) is the less common yet aggressive form of PKD. ARPKD has an estimated incidence between 1:10,000 and 1:40,000. Most patients with ARPKD require kidney replacement therapy earlier than patients with autosomal dominant polycystic kidney disease (ADPKD), often in their early years of life. This review gathered data from published research studies and reviews of ARPKD, highlighting the epidemiology, phenotypic presentation, investigations, genetic analysis, outcomes, and management. Although limited data are available, the published literature suggests that the incidence of ARPKD may be higher in the MENA region due to consanguineous marriages. Patients with ARPKD from the MENA region usually present at a later disease stage and have a relatively short time to progress to kidney failure. Limited data are available regarding the management practice in the region, which warrants further investigations

Gerakan Salafiyah: Islam, Politik dan Rigiditas Interpretasi Hukum Islam

Salafiyah lately has become the scourge of modern states because the banality of their interpretation of Islamic law is considered rigid and not in line with the global world that is increasingly plural. This article attempts to discuss the various variants of salafism and the purpose behind its militant movement. The fundamental question in this article is about the purpose behind a non-compromising understanding of other understandings that are different from the Salafiyah. This article first describes some variant of Salafism, namely: al-Salafiyah al-Tārīkhiyah, al-Salafiyah al-Wahābiyah, al-Salafiyah al-Ishlāhiyah, al-Salafiyah al-Ta'sīliyah dan al-Salafiyah al-Jihādīyah al-Takfīriyah, and then analyze what the similarity of theological traits of these variant. This study confirms that Salafism is a doctrinal social movement that has political efforts to establish Islam by rejecting the differences that exist. The results of this study indicate that the Salafi initially is group that calls on Muslims to return to the original sources of the Qur'an and the Hadith leads to the resurrection of a new Islamic civilization against the Western world power hegemony (especially the United States), it becomes a group which is face to face with the Muslims themselves. In addition, a rigid interpretation of Islamic law has meaning to build political strength to slowly unify differences that do not correspond with the values of salafiyah

Weighted ℓ_1 minimization for sparse recovery with prior information

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a weighted ℓ_1 minimization recovery algorithm and analyze its performance using a Grassman angle approach. We compute explicitly the relationship between the system parameters (the weights, the number of measurements, the size of the two sets, the probabilities of being non-zero) so that an iid random Gaussian measurement matrix along with weighted ℓ_1 minimization recovers almost all such sparse signals with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We also provide simulations to demonstrate the advantages of the method over conventional ℓ_1 optimization