In this paper, we put forward an information theoretic definition of the redundancy that is observed across the sound inventories of the world’s languages. Through rigorous statistical analysis, we find that this redundancy is an invariant property of the consonant inventories. The statistical analysis further unfolds that the vowel inventories do not exhibit any such property, which in turn po...

It is important that privacy methodology be supported by rigorous theory. The purpose of this paper is to introduce researchers in privacy to some statistical theory that is relevant for privacy. The emphasis is on the role of statistical minimax theory and differential privacy. I will discuss some differences between how statisticians think about these issues versus how computer scientists thi...

gully erosion is one of the most severe types of water erosion that inclusive and global model to represent its development under different environmental circumstances is difficult. moreover, having knowledge about history behaviors of a gully and its advancement requires direct annual monitoring that is not possible in iran conditions because of cost and time. gis and remote sensing with provi...

Depression is a devastating illness. It is the leading cause of disability worldwide, and it afflicts 6.7% of Americans every year ((World Health Organization [WHO], 2012; National Institutes of Mental Health [NIMH], 2014). Worse, there is considerable evidence that traditional therapy—particularly drug therapy—is not particularly effective (Whitaker, 2010; Krystal, Sanacora, & Duman, 2013). Th...

Major depressive disorder (MDD) is a severe and chronic condition affecting 350 million subjects worldwide with 1 million subjects committing suicide every year (World Health Organization 2008). MDD is prevailing in wealthy countries including Italy, where lifetime prevalence was estimated at 9.9% (Bromet et al. 2011). Diagnosis is defined by fulfilling at least five of the nine criteria descri...

The Rigorous Coupled-Wave Analysis (RCWA) is a method to compute diffraction of a field by a given grating structure. Within various applications such as metrology, it is important to know how the field reacts to small perturbations in the grating. This behaviour can be expressed by the field derivatives with respect to a certain parameter. Approximations of these derivatives can be found by us...