Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

Development of siRNA-probes for studying intracellular trafficking of siRNA nanoparticles

One important barrier facing the delivery of short interfering RNAs (siRNAs) via synthetic nanoparticles is the rate of nanoparticle disassembly. However, our ability to optimize the release kinetics of siRNAs from nanoparticles for maximum efficacy is limited by the lack of methods to track their intracellular disassembly. Towards this end, we describe the design of two different siRNA-based fluorescent probes whose fluorescence emission changes in response to the assembly state of the nanoparticle. The first probe design involves a redox-sensitive fluorescence-quenched probe that fluoresces only when the nanoparticle is disassembled in a reductive environment. The second probe design is based on a FRET-labeled siRNA pair that fluoresces due to the proximity of the siRNA pair when the nanoparticle is intact. In both approaches, the delivery vehicle need not be labeled. The utility of these probes was investigated with a lipidoid nanoparticle (LNP) as proof-of-concept in both extracellular and intracellular environments. Fluorescence kinetic data from both probes were fit to a two-phase release and decay curve and subsequently quantified to give intracellular disassembly rate constants. Quantitative analysis revealed that the rate constant of siRNA release measured via the fluorescence-quenched probe was almost identical to the rate constant for nanoparticle disassembly measured via the FRET-labeled probes. Furthermore, these probes were utilized to determine subcellular localization of LNPs with the use of automated high-resolution microscopy as they undergo dissociation. Interestingly, this work shows that large amounts of siRNA remain inside vesicular compartments. Altogether, we have developed new siRNA probes that can be utilized with multiple nanocarriers for quantitative and qualitative analysis of nanoparticle dissociation that may serve as a design tool for future delivery systems.National Institutes of Health (U.S.) (Grant R37-EB000244)National Institutes of Health (U.S.) (Grant R01-CA132091)National Institutes of Health (U.S.) (Grant R01-CA132091)National Institutes of Health (U.S.) (Postdoctoral Fellowship

Application performance of elements in a floating–gate FPAA

Field–programmable analog arrays (FPAAs) provide a method for rapidly prototyping analog systems. Currently available commercial and academic FPAAs are typically based on operational amplifiers (or other similar analog primitives) with only a few computational elements per chip. While their specific architectures vary, their small sizes and often restrictive interconnect designs leave current FPAAs limited in functionality, flexibility, and usefulness. In this paper, we explore the use of floating–gate devices as the core programmable element in a signal processing FPAA. A generic FPAA architecture is presented that offers increased functionality and flexibility in realizing analog systems. In addition, the computational analog elements are shown to be widely and accurately programmable while remaining small in area. 1. LOW–POWER SIGNAL PROCESSING The future of FPAAs lie in their ability to speed the implementatio

Post-prandial changes in salivary glucocorticoids: Effects of dietary cholesterol and associations with bile acid excretion

Mechanisms to explain post-prandial increases in circulating glucocorticoids are not well understood and may involve increased adrenal secretion and/or altered steroid metabolism. We have compared salivary levels of cortisol and cortisone levels in healthy male and female volunteers fed either a low or cholesterol-rich midday meal. Urinary levels of steroids, bile acids and markers of lipid peroxidation were also measured. Males and females showed expected circadian changes in salivary steroids and postprandial peaks within 1h of feeding. After a high-cholesterol meal, postprandial cortisol increases were higher in males whereas post-prandial cortisone levels were higher in females. Urinary cortisol but not cortisone levels were higher on the day when males and females ate a high-cholesterol meal. Urinary bile acid excretion and anti-oxidant markers of lipid peroxidation, thiobarbituric acid reactive substances (TBARS), and total phenol content were not affected by dietary cholesterol but tended to be higher in males. Cross-tabulation of correlation coefficients indicated positive associations between urinary markers of peroxidation, bile acids, and cortisol:cortisone ratios. We conclude that dietary cholesterol (a substrate for steroidogenesis) does not have an acute effect on adrenal glucocorticoid synthesis and that gender but not a high-cholesterol meal may influence the interconversion of cortisol and cortisone. Longer term studies of the effects of dietary cholesterol are needed to analyze the associations between bile acids, steroid metabolism, and secretion and lipid peroxidation.11pubpub

Developing large-scale field-programmable analog arrays for rapid prototyping

Field-programmable analog arrays (FPAAs) provide a method for rapidly prototyping analog systems. While currently available FPAAs vary in architecture and interconnect design, they are often limited in size and flexibility. For FPAAs to be as useful and marketable as modern digital reconfigurable devices, new technologies must be explored to provide area efficient, accurately programmable analog circuitry that can be easily integrated into a larger digital/mixed signal system. By leveraging recent advances in floating gate transistors, a new generation of FPAAs are achievable that will dramatically advance the current state of the art in terms of size, functionality, and flexibility

Oxidative phosphorylation and lacunar stroke: Genome-wide enrichment analysis of common variants.

OBJECTIVE: We investigated whether oxidative phosphorylation (OXPHOS) abnormalities were associated with lacunar stroke, hypothesizing that these would be more strongly associated in patients with multiple lacunar infarcts and leukoaraiosis (LA). METHODS: In 1,012 MRI-confirmed lacunar stroke cases and 964 age-matched controls recruited from general practice surgeries, we investigated associations between common genetic variants within the OXPHOS pathway and lacunar stroke using a permutation-based enrichment approach. Cases were phenotyped using MRI into those with multiple infarcts or LA (MLI/LA) and those with isolated lacunar infarcts (ILI) based on the number of subcortical infarcts and degree of LA, using the Fazekas grading. Using gene-level association statistics, we tested for enrichment of genes in the OXPHOS pathway with all lacunar stroke and the 2 subtypes. RESULTS: There was a specific association with strong evidence of enrichment in the top 1% of genes in the MLI/LA (subtype p = 0.0017) but not in the ILI subtype (p = 1). Genes in the top percentile for the all lacunar stroke analysis were not significantly enriched (p = 0.07). CONCLUSIONS: Our results implicate the OXPHOS pathway in the pathogenesis of lacunar stroke, and show the association is specific to patients with the MLI/LA subtype. They show that MRI-based subtyping of lacunar stroke can provide insights into disease pathophysiology, and imply that different radiologic subtypes of lacunar stroke subtypes have distinct underlying pathophysiologic processes.Hugh Markus is supported by an NIHR Senior Investigator award. Hugh Markus and Steve Bevan are supported by the NIHR Cambridge University Hospitals Comprehensive Biomedical Research Centre. Collection of the UK Young Lacunar Stroke Resource was primarily supported by a Functional Genomics grant from the Wellcome Trust with additional support from the Stroke Association. Genotyping and MT were supported by a project grant from the Stroke Association (TSA 2013/01). Dr. Anderson is supported by NIH-NINDS K23 NS086873 and a Fellowship in Therapeutic Investigation sponsored by the Massachusetts General Hospital Department of Neurology and Biogen Idec, Inc.This is the final version of the article. It first appeared from Wolters Kluwer via http://dx.doi.org/10.1212/WNL.000000000000226

Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix

In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that the many-particle eigenvalues and eigenstates of the many-body density matrix $\rho_B$ of a block of $B$ sites cut out from an infinite chain of noninteracting spinless fermions can all be constructed out of the one-particle eigenvalues and one-particle eigenstates respectively. In this paper we developed a statistical-mechanical analogy between the density matrix eigenstates and the many-body states of a system of noninteracting fermions. Each density matrix eigenstate corresponds to a particular set of occupation of single-particle pseudo-energy levels, and the density matrix eigenstate with the largest weight, having the structure of a Fermi sea ground state, unambiguously defines a pseudo-Fermi level. We then outlined the main ideas behind an operator-based truncation of the density matrix eigenstates, where single-particle pseudo-energy levels far away from the pseudo-Fermi level are removed as degrees of freedom. We report numerical evidence for scaling behaviours in the single-particle pseudo-energy spectrum for different block sizes $B$ and different filling fractions \nbar. With the aid of these scaling relations, which tells us that the block size $B$ plays the role of an inverse temperature in the statistical-mechanical description of the density matrix eigenstates and eigenvalues, we looked into the performance of our operator-based truncation scheme in minimizing the discarded density matrix weight and the error in calculating the dispersion relation for elementary excitations. This performance was compared against that of the traditional density matrix-based truncation scheme, as well as against a operator-based plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb, graphicx and mathrsfs package

Degradable Terpolymers with Alkyl Side Chains Demonstrate Enhanced Gene Delivery Potency and Nanoparticle Stability

Degradable, cationic poly(β-amino ester)s (PBAEs) with alkyl side chains are developed for non-viral gene delivery. Nanoparticles formed from these PBAE terpolymers exhibit significantly enhanced DNA transfection potency and resistance to aggregation. These hydrophobic PBAE terpolymers, but not PBAEs lacking alkyl side chains, support interaction with PEG-lipid conjugates, facilitating their functionalization with shielding and targeting moieties and accelerating the in vivo translation of these materials.National Heart, Lung, and Blood InstituteNational Institutes of Health (U.S.) (Program of Excellence in Nanotechnology (PEN) Award, Contract #HHSN268201000045C)National Institutes of Health (U.S.) (NIH Grant R01-EB000244-27)National Institutes of Health (U.S.) (NIH Grant 5-R01-CA132091-04)National Institutes of Health (U.S.) (NIH Grant R01-DE016516-03)National Science Foundation (U.S.) (Graduate Research Fellowship)Juvenile Diabetes Research Foundation International (Grant 17–2007-1063