In this paper, we prove arithmetic properties modulo 5 and 7 satisfied by the function pod(n) which denotes the number of partitions of n wherein odd parts must be distinct (and even parts are unrestricted). In particular, we prove the following: For all n ≥ 0, pod(135n + 8) ≡ 0 (mod 5), pod(135n + 107) ≡ 0 (mod 5), pod(135n + 116) ≡ 0 (mod 5), pod(675n + 647) ≡ 0 (mod 25), pod(3375n + 1997) ≡ ...

By the early 1990s, scientists knew that programmed cell death, or apoptosis, was important for tissue development and homeostasis as well as for cancer progression. Because apoptotic cells activate nucleases to cleave their chromatin, cell death could be followed in vitro by extracting DNA from a population of tissue culture cells and running it out on an agarose gel to look for a characterist...

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an on-line complexity of O(k), where k is the dimension of POD basis, and therefore is...

A least squares regression interval mapping model was derived to detect quantitative trait loci (QTL) with a unique mode of genomic imprinting, polar overdominance (POD), under a breed cross design model in outbred mammals. Tests to differentiate POD QTL from Mendelian, paternal or maternal expression QTL were also developed. To evaluate the power of the POD models and to determine the ability ...

Nanostructured lipid carriers (NLC) exhibit high skin targeting efficiency and good safety. They are promising vehicles for topical drug delivery. This study aims to increase the skin distribution of podophyllotoxin (POD) by incorporating it into NLCs. Two kinds of POD-loaded NLCs (POD-NLCs)-POD-NLCformulation 1 and POD-NLCformulation 2-were prepared and characterized. Their skin targeting effi...

The derivations of existing error bounds for reduced order models of time varying partial differential equations (PDEs) constructed using proper orthogonal decomposition (POD) have relied on bounding the error between the POD data and various POD projections of that data. Furthermore, the asymptotic behavior of the model reduction error bounds depends on the asymptotic behavior of the POD data ...

In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD b...

Background Hyperbilirubinemia is a common postoperative complication. Elevated direct bilirubin (D-Bil) and indirect bilirubin (I-Bil) levels are related to different pathophysiologies; therefore, their associations with outcomes also differ. However, there have been few comparative studies of such associations in postoperative patients. Methods This retrospective study compared the associati...

Introduction: Risk assessment for post-operative delirium (POD) is poorly developed. Improved metrics could greatly facilitate peri-operative care as costs associated with POD are staggering. In this preliminary study, we develop a novel stress-diathesis model based on comprehensive pre-operative psychiatric and neuropsychological testing, a blood oxygenation level-dependent (BOLD) magnetic res...

BACKGROUND Postoperative delirium (POD) is a common complication in the elderly. This retrospective study investigated the effect of intraoperative hemodynamics on the incidence of POD in elderly patients after major surgery to explore ways to reduce the incidence of POD. MATERIAL/METHODS Based on the incidence of POD, elderly patients (81±6 y) were assigned to a POD (n=137) or non-POD group ...