Sequences in overpartitions.

This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.

Non-Destructive Impedance Monitoring of Bacterial Metabolic Activity towards Continuous Lead Biorecovery.

The adverse health effects of the presence of lead in wastewater streams are well documented, with conventional methods of lead recovery and removal suffering from disadvantages such as high energy costs, the production of toxic sludge, and low lead selectivity. Klebsiella pneumoniae and Paraclostridium bifermentans have been identified as potential lead-precipitating species for use in a lead recovery bioreactor. Electrical impedance spectroscopy (EIS) on a low-cost device is used to determine the potential for the probe-free and label-free monitoring of cell growth in a bioreactor containing these bacteria. A complex polynomial is fit for several reactive equivalent circuit components. A direct correlation is found between the extracted supercapacitance and the plated colony-forming unit count during the exponential growth phase, and a qualitative correlation is found between all elements of the measured reactance outside the exponential growth phase. Strong evidence is found that Pb(II) ions act as an anaerobic respiration co-substrate for both cells observed, with changes in plated count qualitatively mirrored in the Pb(II) concentration. Guidance is given on the implementation of EIS devices for continuous impedance monitoring.

How Ramanujan may have discovered the mock theta functions.

Mock theta functions appeared out of the blue in Ramanujan's last letter to Hardy. What would lead Ramanujan to consider the possibility of such functions in the first place? This paper seeks to provide a plausible answer to this question. This article is part of a discussion meeting issue 'Srinivasa Ramanujan: in celebration of the centenary of his election as FRS'.

The Actuation Mechanism of 3D Printed Flexure-Based Robotic Microtweezers.

We report on the design and the modeling of a three-dimensional (3D) printed flexure-based actuation mechanism for robotic microtweezers, the main body of which is a single piece of nylon. Our design aims to fill a void in sample manipulation between two classes of widely used instruments: nano-scale and macro-scale robotic manipulators. The key component is a uniquely designed cam flexure system, which linearly translates the bending of a piezoelectric bimorph actuator into angular displacement. The 3D printing made it possible to realize the fabrication of the cam with a specifically calculated curve, which would otherwise be costly using conventional milling techniques. We first characterized 3D printed nylon by studying sets of simple cantilevers, which provided fundamental characteristics that could be used for further designs. The finite element method analysis based on the obtained material data matched well with the experimental data. The tweezers showed angular displacement from 0° to 10° linearly to the deflection of the piezo actuator (0-1.74 mm) with the linearity error of 0.1°. Resonant frequency of the system with/without working tweezer tips was discovered as 101 Hz and 127 Hz, respectively. Our design provides simple and low-cost construction of a versatile manipulator system for samples in the micro/meso-scale (0.1-1 mm).

Almost partition identities.

An almost partition identity is an identity for partition numbers that is true asymptotically [Formula: see text] of the time and fails infinitely often. We prove a kind of almost partition identity, namely that the number of parts in all self-conjugate partitions of n is almost always equal to the number of partitions of n in which no odd part is repeated and there is exactly one even part (possibly repeated). Not only does the identity fail infinitely often, but also, the error grows without bound. In addition, we prove several identities involving the number of parts in restricted partitions. We show that the difference in the number of parts in all self-conjugate partitions of n and the number of parts in all partitions of n into distinct odd parts equals the number of partitions of n in which no odd part is repeated, the smallest part is odd, and there is exactly one even part (possibly repeated). We provide both analytic and combinatorial proofs of this identity.

Comparison of real-world outcomes in patients with nonvalvular atrial fibrillation treated with direct oral anticoagulant agents or warfarin.

PURPOSE: To compare patients with atrial fibrillation (AF) initiating direct oral anticoagulants (DOACs) versus warfarin on clinical outcomes including stroke, systemic embolism (SE), bleeding events, and cost of care. METHODS: This retrospective observational study used Medicare Advantage Prescription Drug and fully insured commercial claims from the Humana Research Database. Patients with AF who initiated a DOAC or warfarin from January 1, 2012, through September 30, 2015, were included. Date of the first prescription of DOAC or warfarin was the index date. Patients in the DOAC and warfarin groups were matched on propensity scores. Patients were censored at end of enrollment or study period, discontinuation, or switch of index medication. Clinical outcomes were compared in the matched groups using Cox proportional hazards models. Annualized costs and costs adjusted for censoring using Lin's interval method were also compared between the two cohorts. RESULTS: Patients on DOACs had a significantly lower risk of ischemic stroke (hazard ratio [HR], 0.88; 95% confidence interval [CI], 0.79-0.98), hemorrhagic stroke (HR, 0.65; CI, 0.46-0.92), SE (HR, 0.53; 95% CI, 0.43-0.65), and composite outcome of stroke or SE (HR, 0.78; 95% CI, 0.71-0.86) compared with patients on warfarin. Bleeding risk was not statistically significant (HR, 0.85; 95% CI, 0.71-1.01). While annualized pharmacy costs were higher, annualized medical and total costs were lower in the DOAC group compared with the warfarin group. CONCLUSION: The results of the study indicated that patients on DOACs had lower rates of ischemic stroke, hemorrhagic stroke, SE, and composite outcome of stroke or SE compared with patients on warfarin. No significant differences in bleeding rates between the DOAC and warfarin groups were observed, while total cost of care was lower in the DOAC group.

Factors influencing dabigatran or warfarin medication persistence in patients with nonvalvular atrial fibrillation.

Factors influencing differences in persistence between dabigatran and warfarin in patients with nonvalvular atrial fibrillation (NVAF) remain unclear. AIM: Compare differences in persistence between new dabigatran and warfarin users in patients newly diagnosed with NVAF, adjusting for sociodemographics, clinical characteristics, patient out-of-pocket cost and other covariates. METHODS: A retrospective matched-cohort study was conducted using a US claims database of Medicare and commercially insured patients with NVAF aged≥ 18 years. Persistence and monthly out-of-pocket costs for dabigatran or warfarin were calculated and adjusted for covariates using Cox proportional hazard models. RESULTS & CONCLUSION: Unadjusted persistence was significantly lower among dabigatran users (n = 1025) compared with matched warfarin users (38 vs 46%). Adjusting for covariates rendered this difference insignificant (hazard ratio = 0.930).

Healthcare utilization and costs for patients initiating Dabigatran or Warfarin.

BACKGROUND: Novel oral anticoagulants (NOAC) such as dabigatran, when compared to warfarin, have been shown to potentially reduce the risk of stroke in patients with non-valvular atrial fibrillation (NVAF) together with lower healthcare resource utilization (HCRU) and similar total costs. This study expands on previous work by comparing HCRU and costs for patients newly diagnosed with NVAF and newly initiated on dabigatran or warfarin, and is the first study specifically in a Medicare population. METHODS: A retrospective matched-cohort study was conducted using data from administrative health care claims during the study period 01/01/2010-12/31/2012. Cox regression analyses were used to compare all-cause risk of first hospitalizations and emergency room (ER) visits. Medical, pharmacy, and total costs per-patient-per-month (PPPM) were compared between dabigatran and warfarin users. RESULTS: A total of 1110 patients initiated on dabigatran were propensity score-matched with corresponding patients initiated on warfarin. The mean number of hospitalizations (0.92 vs. 1.13, P = 0.012), ER visits (1.32 vs. 1.56, P < 0.01), office visits (21.43 vs. 29.41; P < 0.01), and outpatient visits (10.86 vs. 22.02; P < 0.01) were lower among dabigatran compared to warfarin users. Patients initiated on dabigatran had significantly lower risk of first all-cause ER visits [hazard ratio (HR): 0.84, 95% confidence interval (CI): 0.73-0.98] compared to those initiated on warfarin. Adjusted mean pharmacy costs PPPM were significantly greater for dabigatran users ($510 vs. $250, P < 0.001); however, mean medical costs PPPM ($1912 vs. $1956, P = 0.55) and mean total costs PPPM ($2381 vs. $2183, P = 0.10) were not significantly different compared to warfarin users. CONCLUSIONS: Dabigatran users had significantly lower HCRU compared to warfarin users. In addition, dabigatran users had lower risk of all-cause ER visits. Despite higher pharmacy costs, the two cohorts did not differ significantly in medical or total all-cause costs.

Cost drivers of prescription opioid abuse in commercial and Medicare populations.

OBJECTIVE: Growth in the number of patients with pain conditions, and the subsequent rise in prescription opioid use for treatment, has been accompanied by an increase in diagnosed opioid abuse. Understanding what drives the incremental healthcare costs of members diagnosed with prescription opioid abuse may assist in developing better screening techniques for abuse. DESIGN: This retrospective analysis examined costs, resource use, and comorbidities 365 days pre- and postdiagnosis in prescription opioid users diagnosed with abuse (cases) vs. their matched nondiagnosed controls. Inclusion criteria for cases were diagnosis of opioid abuse (ICD-9-CM: 304.0x, 304.7x, 305.5x, 965.0x). Multivariate analysis used generalized linear modeling with log-transformed cost as dependent variable, controlling for comorbidities. RESULTS: Final sample sizes were 8,390 cases and 16,780 matched controls. Postindex abuse-related costs were $2,099 for commercial members, $539 for Medicare members aged < 65, and $170 for Medicare members aged ≥ 65. A higher percentage of cases had pain conditions (82.0% vs. 57.4% commercial, 95.9% vs. 87.5% Medicare members aged < 65, 92.9% vs. 82.4% Medicare members aged ≥ 65, P < 0.0001), and a higher numbers of cases had multiple opioid prescribers (3.7 vs. 1.4 commercial, 3.3 vs. 2.2 Medicare < 65, 2.2 vs. 1.6 Medicare ≥ 65, P < 0.0001) than controls preindex. Cases had higher rates of substance abuse and psychiatric diagnoses pre- and postindex (P < 0.0001, all comparisons). Adjusted costs were 28% higher for cases than for controls (P < 0.0001). CONCLUSION: Costs of members diagnosed with prescription opioid abuse are driven by higher pain and psychiatric comorbidities relative to nonabuse controls.

The prevalence of diagnosed opioid abuse in commercial and Medicare managed care populations.

PURPOSE: To measure the prevalence of diagnosed opioid abuse and prescription opioid use in a multistate managed care organization. METHODS: This retrospective claims data analysis reviewed the prevalence of diagnosed opioid abuse and the parallel prevalence of prescription opioid use in half-year intervals for commercial and Medicare members enrolled with Humana Inc., from January 1, 2008 to June 30, 2010. Diagnosis of opioid abuse was defined by ≥ 1 medical claim with any of the following ICD-9-CM codes: 304.0 ×, 304.7 ×, 305.5 ×, 965.0 ×, excluding 965.01, and opioid use was defined by ≥ 1 filled prescription for an opioid. The prevalence of opioid abuse was defined by the number of members with an opioid abuse diagnosis, divided by the number of members enrolled in each 6-month interval. RESULTS: The 6-month prevalence of diagnosed opioid abuse increased from 0.84 to 1.15 among commercial and from 3.17 to 6.35 among Medicare members, per 1,000. In contrast, there was no marked increase in prescription opioid use during the same time period (118.0 to 114.8 for commercial members, 240.6 to 256.9 for Medicare members, per 1,000). The prevalence of diagnosed opioid abuse was highest among members younger than 65 years for both genders in commercial (18- to 34-year-olds) and Medicare (35- to 54-year-olds) populations. CONCLUSIONS: Despite a stable rate of prescription opioid use among the observed population, the prevalence of diagnosed opioid abuse is increasing, particularly in the Medicare population.

Inefficiencies in osteoarthritis and chronic low back pain management.

OBJECTIVE: To identify inefficiencies in drug and medical service utilization related to pain management in patients with osteoarthritis and chronic low back pain. STUDY DESIGN: This retrospective cohort study applied revised measures of pain management inefficiencies to Humana Medicare members with osteoarthritis and/or chronic low back pain. METHODS: Subjects had either 2 or more claims for osteoarthritis on different days or 2 or more claims for low back pain 90 or more days apart, from January 1, 2008, to June 30, 2010, with the first occurrence assigned the index date. Inefficiencies were identified for 365 days postindex.Pain-related healthcare costs postindex were compared between members with and without inefficiencies. A generalized linear model calculated adjusted costs per member controlling for age, sex, and comorbidities. RESULTS: Most members diagnosed with osteoarthritis, chronic low back pain, or both (N = 68,453) had at least 1 inefficiency measure (n = 37,863) during the postindex period. High per member costs were for repeated surgical procedures ($26,451) and inpatient admissions ($19,372) compared with members without inefficiencies ($781; P < .0001). High total costs (prevalence times per member cost) were for repeated diagnostic testing and excessive office visits. Members with an inefficiency had adjusted pain-related costs 5.42 times higher than those of members without an inefficiency (P <.0001). CONCLUSIONS: Pain management inefficiencies are common and costly among Humana Medicare members with osteoarthritis and/or chronic low back pain. Further work by providers and payers is needed to determine benefits of member identification and early intervention for these inefficiencies.

Modeling low-dose mortality and disease incubation period of inhalational anthrax in the rabbit.

There is a need to advance our ability to conduct credible human risk assessments for inhalational anthrax associated with exposure to a low number of bacteria. Combining animal data with computational models of disease will be central in the low-dose and cross-species extrapolations required in achieving this goal. The objective of the current work was to apply and advance the competing risks (CR) computational model of inhalational anthrax where data was collected from NZW rabbits exposed to aerosols of Ames strain Bacillus anthracis. An initial aim was to parameterize the CR model using high-dose rabbit data and then conduct a low-dose extrapolation. The CR low-dose attack rate was then compared against known low-dose rabbit data as well as the low-dose curve obtained when the entire rabbit dose-response data set was fitted to an exponential dose-response (EDR) model. The CR model predictions demonstrated excellent agreement with actual low-dose rabbit data. We next used a modified CR model (MCR) to examine disease incubation period (the time to reach a fever >40 °C). The MCR model predicted a germination period of 14.5h following exposure to a low spore dose, which was confirmed by monitoring spore germination in the rabbit lung using PCR, and predicted a low-dose disease incubation period in the rabbit between 14.7 and 16.8 days. Overall, the CR and MCR model appeared to describe rabbit inhalational anthrax well. These results are discussed in the context of conducting laboratory studies in other relevant animal models, combining the CR/MCR model with other computation models of inhalational anthrax, and using the resulting information towards extrapolating a low-dose response prediction for man.

Inhalational anthrax (Ames aerosol) in naïve and vaccinated New Zealand rabbits: characterizing the spread of bacteria from lung deposition to bacteremia.

There is a need to better understand inhalational anthrax in relevant animal models. This understanding could aid risk assessment, help define therapeutic windows, and provide a better understanding of disease. The aim here was to characterize and quantify bacterial deposition and dissemination in rabbits following exposure to single high aerosol dose (> 100 LD(50)) of Bacillus anthracis (Ames) spores immediately following exposure through 36 h. The primary goal of collecting the data was to support investigators in developing computational models of inhalational anthrax disease. Rabbits were vaccinated prior to exposure with the human vaccine (Anthrax Vaccine Adsorbed, AVA) or were sham-vaccinated, and were then exposed in pairs (one sham and one AVA) so disease kinetics could be characterized in equally-dosed hosts where one group is fully protected and is able to clear the infection (AVA-vaccinated), while the other is susceptible to disease, in which case the bacteria are able to escape containment and replicate uncontrolled (sham-vaccinated rabbits). Between 4-5% of the presented aerosol dose was retained in the lung of sham- and AVA-vaccinated rabbits as measured by dilution plate analysis of homogenized lung tissue or bronchoalveolar lavage (BAL) fluid. After 6 and 36 h, >80% and >96%, respectively, of the deposited spores were no longer detected in BAL, with no detectable difference between sham- or AVA-vaccinated rabbits. Thereafter, differences between the two groups became noticeable. In sham-vaccinated rabbits the bacteria were detected in the tracheobronchial lymph nodes (TBLN) 12 h post-exposure and in the circulation at 24 h, a time point which was also associated with dramatic increases in vegetative CFU in the lung tissue of some animals. In all sham-vaccinated rabbits, bacteria increased in both TBLN and blood through 36 h at which point in time some rabbits succumbed to disease. In contrast, AVA-vaccinated rabbits showed small numbers of CFU in TBLN between 24 and 36 h post-exposure with small numbers of bacteria in the circulation only at 24 h post-exposure. These results characterize and quantify disease progression in naïve rabbits following aerosol administration of Ames spores which may be useful in a number of different research applications, including developing quantitative models of infection for use in human inhalational anthrax risk assessment.

Partitions with short sequences and mock theta functions.

P. A. MacMahon was the first to examine integer partitions in which consecutive integers were not allowed as parts. Such partitions may be described as having sequences of length 1. Recently it was shown that partitions containing no sequences of consecutive integers of length k are of interest in seemingly unrelated problems concerning threshold growth models. The object now is to develop the subject intrinsically to both provide deeper understanding of the theory and application of partitions and reveal the surprising role of Ramanujan's mock theta functions.

Lipid Metabolism and Cardiovascular Morbidity and Mortality in Hemodialysis Patients: Role of Factors Modulating Cytosolic Calcium.

Animal studies indicate that insulin resistance and glucose intolerance leading to dyslipidemia in uremic rats are associated with increased cytosolic calcium ([Ca++ i]). The resistance and intolerance are reversed with verapamil, but recur after its discontinuation. This finding suggests that hyperparathyroid-induced [Ca ++ i] increase is responsible for the metabolic derangement. We retrospectively examined, over a 12-year period, the effects of factors that lower [Ca ++ i] on total serum cholesterol and triglycerides in 332 hemodialysis (HD) patients. Because the study was retrospective, detailed lipid profiles were not available. We therefore relied on morbidity and mortality outcomes related to atherosclerotic vascular disease. Patients with diabetes mellitus were excluded, because their dyslipidemia and vascular disease are mediated via a different mechanism. Four groups emerged: group I [high parathormone (PTH) in the absence of calcium channel blockers (CCBs), n = 107], representing the highest [Ca++ i]; group II (high PTH in the presence of CCBs, n = 76) and group III (lower PTH in the absence of CCBs, n = 66), representing intermediate [Ca ++ i]; and group IV (lower PTH in the presence of CCBs, n = 83) representing the lowest [Ca ++ i]. The theoretically lower [Ca ++ i] was achieved via CCB therapy or lower PTH, or both. The mean serum cholesterol in group I was 322 ± 24 mg/dL and the level of triglycerides was 398 ± 34 mg/dL. Group II had mean serum cholesterol of 196 ± 16 mg/dL and triglycerides of 157 ± 17 mg/dL. Group III had a mean serum cholesterol of 202 ± 19 mg/dL and triglycerides of 160 ± 15 mg/dL. Group IV had a mean serum cholesterol of 183 ± 9 mg/dL and triglycerides of 94 ± 6 mg/dL. The differences in cholesterol and triglyceride levels among four groups were significant (p < 0.001) by one-way analysis of variance (ANOVA). The incidence of cardiovascular morbidity and mortality events was 61% in group I, 24% in group II, 28% in group III, and 18% in group IV (χ 2 = 47.7, p < 0.001). We conclude that, in non diabetic HD patients, hyperparathyroidism, especially in the absence of CCBs, is associated with severe dyslipidemia and increased risk of cardiovascular morbidity and mortality. Dyslipidemia may be related to a hyperparathyroid-induced increase in cytosolic calcium [Ca++ i]. Lowering [Ca++ i] by decreasing PTH or by blocking calcium entry into cells (via CCBs), or both, is associated with less dyslipidemia and improved long-term cardiovascular morbidity and mortality. Prospective randomized studies, with actual measurement of [Ca ++ i], are needed to verify the results of this study.