In our dissertation we derive the Central Limit Theorems (CLTs) with the remainder terms for the renewal and cumulative processes. A renewal process based on the sequence of random variables {X n } is defined in one of the following ways: 1) 2) N 2 (t) = number of n such that Sn $ t, 3) N 3 (t) = Sup{n: Sn $ t}, where Sn = Xl + ... + X n. If X n > 0 then all three definitions are identical. In ...

In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the pr...

In recent work Cheon, Han, Lee, Ryu, and Stehlé presented an attack on the multilinear map of Coron, Lepoint, and Tibouchi (CLT). They show that given many low-level encodings of zero, the CLT multilinear map can be completely broken, recovering the secret factorization of the CLT modulus. The attack is a generalization of the “zeroizing” attack of Garg, Gentry, and Halevi. We first strengthen ...

Cross-limb transfer (CLT) describes the observation of bilateral performance gains due to unilateral motor practice. Previous research has suggested that CLT may be reduced, or absent, in older adults, possibly due to age-related structural and functional brain changes. Based on research showing increases in CLT due to the provision of mirror visual feedback (MVF) during task execution in young...

For Young systems, i. e. for hyperbolic systems without/with singularities satisfying Young’s axioms [You 98] (which imply exponential decay of correlation and the CLT) a local CLT is proven. In fact, a unified version of the local CLT is found, covering among others the absolutely contionuous and the arithmetic cases. For the planar Lorentz process with a finite horizon this result implies a.)...

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can ...

Abstract We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL), which complements the sample-path and stationary versions of the PLL which we recently established in order to explain the remarkable accuracy in comparisons of data-generated model simulations to direct estimates from the data for the aggregate occupancy level in a hospital emergency department. Our...

For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NS...

In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the pr...

Cognitive Load Theory (CLT) has started to find more applications in medical education research. Unfortunately, misconceptions such as lower cognitive load always being beneficial to learning and the continued use of dated concepts and methods can result in improper applications of CLT principles in medical education design and research. This review outlines how CLT has evolved and presents a s...