Locating Complex Roots of Quintic Polynomials

Since there are no general solutions to polynomials of degree higher than four, high school and college students only infrequently investigate quintic polynomials. Additionally, although students commonly investigate real roots of polynomials, only infrequently are complex roots – and, more particularly, the location of complex roots – investigated. This paper considers features of graphs of quintic polynomials and uses analytic constructions to locate the functions’ complex roots. Throughout, hyperlinked dynamic applets are provided for the student reader to experientially participate in the paper. This paper is an extension to other investigations regarding locating complex roots (Bauldry, Bossé, & Otey, 2017)

Visualizing Complex Roots

Avoiding complex geometric and analytic constructions, this paper considers techniques for visualizing the location of complex roots of quadratic, cubic, and quartic real polynomial functions. This provides teachers and students of mathematics with a better understanding of the nature of these functions and their respective real and complex roots

Satellite observed water quality changes in the Laurentian Great Lakes due to invasive species, anthropogenic forcing, and climate change

Long time series of ocean and land color satellite data can be used to measure Laurentian Great Lakes water quality parameters including chlorophyll, suspended minerals, harmful algal blooms (HABs), photic zone and primary productivity on weekly, monthly and annual observational intervals. The observed changes in these water quality parameters over time are a direct result of the introduction of invasive species such as the Dreissena mussels as well as anthropogenic forcing and climate change. Time series of the above mentioned water quality parameters have been generated based on a range of satellite sensors, starting with Landsat in the 1970s and continuing to the present with MODIS and VIIRS. These time series have documented the effect the mussels have had on increased water clarity by decreasing the chlorophyll concentrations. Primary productivity has declined in the lakes due to the decrease in algae. The increased water clarity due to the mussels has also led to an increase in submerged aquatic vegetation. Comparing water quality metrics in Lake Superior to the lower lakes is insightful because Lake Superior is the largest and most northern of the five Great Lakes and to date has not been affected by the invasive mussels and can thus be considered a control. In contrast, Lake Erie, the most southern and shallow of the Laurentian Great Lakes, is heavily influenced by agricultural practices (i.e., nutrient runoff) and climate change, which directly influence the annual extent of HABs in the Western Basin of that lake

Single-Prolonged Stress Impairs Prefrontal Cortex Control of Amygdala and Striatum in Rats

Medial prefrontal cortex (mPFC), amygdala, and striatum neurocircuitry has been shown to play an important role in post-traumatic stress disorder (PTSD) pathology in humans. Clinical studies show hypoactivity in the mPFC and hyperactivity in the amygdala and striatum of PTSD patients, which has been associated with decreased mPFC glutamate levels. The ability to refine neurobiological characteristics of PTSD in an animal model is critical in furthering our mechanistic understanding of the disease. To this end, we exposed male rats to single-prolonged stress (SPS), a validated model of PTSD, and hypothesized that traumatic stress would differentially activate mPFC subregions [prelimbic (PL) and infralimbic (IL) cortices] and increase striatal and amygdalar activity, which would be associated with decreased mPFC glutamate levels. in vivo, neural activity in the subregions of the mPFC, amygdala, and striatum was measured using manganese-enhanced magnetic resonance imaging (MEMRI), and glutamate and N-acetylaspartate (NAA) levels in the mPFC and the dorsal striatum (dSTR) were measured using proton magnetic resonance spectroscopy (1H-MRS) longitudinally, in rats exposed to SPS or control conditions. As hypothesized, SPS decreased MEMRI-based neural activity in the IL, but not PL, cortex concomitantly increasing activity within the basolateral amygdala (BLA) and dorsomedial striatum (dmSTR). 1H-MRS studies in a separate cohort revealed SPS decreased glutamate levels in the mPFC and increased NAA levels in the dSTR. These results confirm previous findings that suggest SPS causes mPFC hypoactivation as well as identifies concurrent hyperactivation in dmSTR and BLA, effects which parallel the clinical neuropathology of PTSD

Designing with and for people with dementia: developing a mindful interdisciplinary co-design methodology

This paper reports on the development of a mindful interdisciplinary design methodology in the context of the MinD project research into designing for and with people with dementia, which takes the particular focus on supporting the subjective well-being and self-empowerment of people with early to mid stage dementia in social context. Existing research is for the most part focussed on functional support and safe-keeping from the perspective of the carer. References to decision-making and empowerment are predominantly related to action planning for dementia care or advance care planning. References to care and social interaction show that caregivers tend to take a deficit-oriented perspective, and occupation of people with dementia is often associated with doing 'something' with little focus on the meaningfulness of the activity. Furthermore, caregivers and people with dementia tend to differ in their perspectives, e.g. on assistive devices, which might offer support. The MinD project, has therefore developed an interdisciplinary co-design methodology in which the voices to people with dementia contribute to better understanding and developing mindful design solutions that support people with dementia with regard to their the subjective well-being and self-empowerment a well as meaningful and equitable social engagement. This paper discussed the design methodological framework and methods developed for the data collection and design development phases of the project, and their rationale. It thus makes a contribution to interdisciplinary methodologies in the area of design for health

Multiplexed imaging of human tuberculosis granulomas uncovers immunoregulatory features conserved across tissue and blood

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis that is distinctly characterized by granuloma formation within infected tissues. Granulomas are dynamic and organized immune cell aggregates that limit dissemination, but can also hinder bacterial clearance. Consequently, outcome in TB is influenced by how granuloma structure and composition shift the balance between these two functions. To date, our understanding of what factors drive granuloma function in humans is limited. With this in mind, we used Multiplexed Ion Beam Imaging by Time-of-Flight (MIBI-TOF) to profile 37 proteins in tissues from thirteen patients with active TB disease from the U.S. and South Africa. With this dataset, we constructed a comprehensive tissue atlas where the lineage, functional state, and spatial distribution of 19 unique cell subsets were mapped onto eight phenotypically-distinct granuloma microenvironments. This work revealed an immunosuppressed microenvironment specific to TB granulomas with spatially coordinated co-expression of IDO1 and PD-L1 by myeloid cells and proliferating regulatory T cells. Interestingly, this microenvironment lacked markers consistent with T-cell activation, supporting a myeloid-mediated mechanism of immune suppression. We observed similar trends in gene expression of immunoregulatory proteins in a confirmatory transcriptomic analysis of peripheral blood collected from over 1500 individuals with latent or active TB infection and healthy controls across 29 cohorts spanning 14 countries. Notably, PD-L1 gene expression was found to correlate with TB progression and treatment response, supporting its potential use as a blood-based biomarker. Taken together, this study serves as a framework for leveraging independent cohorts and complementary methodologies to understand how local and systemic immune responses are linked in human health and disease

Multiplexed imaging of human tuberculosis granulomas uncovers immunoregulatory features conserved across tissue and blood

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis that is distinctly characterized by granuloma formation within infected tissues. Granulomas are dynamic and organized immune cell aggregates that limit dissemination, but can also hinder bacterial clearance. Consequently, outcome in TB is influenced by how granuloma structure and composition shift the balance between these two functions. To date, our understanding of what factors drive granuloma function in humans is limited. With this in mind, we used Multiplexed Ion Beam Imaging by Time-of-Flight (MIBI-TOF) to profile 37 proteins in tissues from thirteen patients with active TB disease from the U.S. and South Africa. With this dataset, we constructed a comprehensive tissue atlas where the lineage, functional state, and spatial distribution of 19 unique cell subsets were mapped onto eight phenotypically-distinct granuloma microenvironments. This work revealed an immunosuppressed microenvironment specific to TB granulomas with spatially coordinated co-expression of IDO1 and PD-L1 by myeloid cells and proliferating regulatory T cells. Interestingly, this microenvironment lacked markers consistent with T-cell activation, supporting a myeloid-mediated mechanism of immune suppression. We observed similar trends in gene expression of immunoregulatory proteins in a confirmatory transcriptomic analysis of peripheral blood collected from over 1500 individuals with latent or active TB infection and healthy controls across 29 cohorts spanning 14 countries. Notably, PD-L1 gene expression was found to correlate with TB progression and treatment response, supporting its potential use as a blood-based biomarker. Taken together, this study serves as a framework for leveraging independent cohorts and complementary methodologies to understand how local and systemic immune responses are linked in human health and disease

Racial and socioeconomic disparities in hip fracture care

BACKGROUND: Despite declines in both the incidence of and mortality following hip fracture, there are racial and socioeconomic disparities in treatment access and outcomes. We evaluated the presence and implications of disparities in delivery of care, hypothesizing that race and community socioeconomic characteristics would influence quality of care for patients with a hip fracture. METHODS: We collected data from the New York State Department of Health Statewide Planning and Research Cooperative System (SPARCS), which prospectively captures information on all discharges from nonfederal acute-care hospitals in New York State. Records for 197,290 New York State residents who underwent surgery for a hip fracture between 1998 and 2010 in New York State were identified from SPARCS using International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) codes. Multivariable regression models were used to evaluate the association of patient characteristics, social deprivation, and hospital/surgeon volume with time from admission to surgery, in-hospital complications, readmission, and 1-year mortality. RESULTS: After adjusting for patient and surgery characteristics, hospital/surgeon volume, social deprivation, and other variables, black patients were at greater risk for delayed surgery (odds ratio [OR] = 1.49; 95% confidence interval [CI] = 1.42, 1.57), a reoperation (hazard ratio [HR] = 1.21; CI = 1.11, 1.32), readmission (OR = 1.17; CI = 1.11, 1.22), and 1-year mortality (HR = 1.13; CI = 1.07, 1.21) than white patients. Subgroup analyses showed a greater risk for delayed surgery for black and Asian patients compared with white patients, regardless of social deprivation. Additionally, there was a greater risk for readmission for black patients compared with white patients, regardless of social deprivation. Compared with Medicare patients, Medicaid patients were at increased risk for delayed surgery (OR = 1.17; CI = 1.10, 1.24) whereas privately insured patients were at decreased risk for delayed surgery (OR = 0.77; CI = 0.74, 0.81), readmission (OR = 0.77; CI = 0.74, 0.81), complications (OR = 0.80; CI = 0.77, 0.84), and 1-year mortality (HR = 0.80; CI = 0.75, 0.85). CONCLUSIONS: There are race and insurance-based disparities in delivery of care for patients with hip fracture, some of which persist after adjusting for social deprivation. In addition to investigation into reasons contributing to disparities, targeted interventions should be developed to mitigate effects of disparities on patients at greatest risk. LEVEL OF EVIDENCE: Prognostic Level III. See Instructions for Authors for a complete description of levels of evidence

Bolaamphiphile Analogues of 12-bis-THA Cl2 Are Potent Antimicrobial Therapeutics with Distinct Mechanisms of Action against Bacterial, Mycobacterial, and Fungal Pathogens

12-Bis-THA Cl2 [12,12'-(dodecane-1,12-diyl)-bis-(9-amino-1,2,3,4-tetrahydroacridinium) chloride] is a cationic bolalipid adapted from dequalinium chloride (DQC), a bactericidal anti-infective indicated for bacterial vaginosis (BV). Here, we used a structure-activity-relationship study to show that the factors that determine effective killing of bacterial, fungal, and mycobacterial pathogens differ, to generate new analogues with a broader spectrum of activity, and to identify synergistic relationships, most notably with aminoglycosides against Acinetobacter baumannii and Pseudomonas aeruginosa, where the bactericidal killing rate was substantially increased. Like DQC, 12-bis-THA Cl2 and its analogues accumulate within bacteria and fungi. More hydrophobic analogues with larger headgroups show reduced potential for DNA binding but increased and broader spectrum antibacterial activity. In contrast, analogues with less bulky headgroups and stronger DNA binding affinity were more active against Candida spp. Shortening the interconnecting chain, from the most lipophilic twelve-carbon chain to six, improved the selectivity index against Mycobacterium tuberculosis in vitro, but only the longer chain analogue was therapeutic in a Galleria mellonella infection model, with the shorter chain analogue exacerbating the infection. In vivo therapy of Escherichia coli ATCC 25922 and epidemic methicillin-resistant Staphylococcus aureus 15 (EMRSA-15) infections in Galleria mellonella was also achieved with longer-chain analogues, as was therapy for an A. baumannii 17978 burn wound infection with a synergistic combination of bolaamphiphile and gentamicin. The present study shows how this class of bolalipids may be adapted further to enable a wider range of potential applications. IMPORTANCE While we face an acute threat from antibiotic resistant bacteria and a lack of new classes of antibiotic, there are many effective antimicrobials which have limited application due to concerns regarding their toxicity and which could be more useful if such risks are reduced or eliminated. We modified a bolalipid antiseptic used in throat lozenges to see if it could be made more effective against some of the highest-priority bacteria and less toxic. We found that structural modifications that rendered the lipid more toxic against human cells made it less toxic in infection models and we could effectively treat caterpillars infected with either Mycobacterium tuberculosis, methicillin resistant Staphylococcus aureus, or Acinetobacter baumannii. The study provides a rationale for further adaptation toward diversifying the range of indications in which this class of antimicrobial may be used

Risk Factors Associated With Infection in Open Fractures of the Upper and Lower Extremities

Introduction: Open fractures are associated with a high risk of infection. The prevention of infection is the single most important goal, influencing perioperative care of patients with open fractures. Using data from 2,500 participants with open fracture wounds enrolled in the Fluid Lavage of Open Wounds trial, we conducted a multivariable analysis to determine the factors that are associated with infections 12 months postfracture. Methods: Eighteen predictor variables were identified for infection a priori from baseline data, fracture characteristics, and surgical data from the Fluid Lavage of Open Wounds trial. Twelve predictor variables were identified for deep infection, which included both surgically and nonoperatively managed infections.We used multivariable Cox proportional hazards regression analyses to identify the factors associated with infection. Irrigation solution and pressure were included as variables in the analysis. The results were reported as adjusted hazard ratios (HRs), 95% confidence intervals (CIs), and associated P values. All tests were two tailed with alpha = 0.05. Results: Factors associated with any infection were fracture location (tibia: HR 5.13 versus upper extremity, 95% CI 3.28 to 8.02; other lower extremity: HR 3.63 versus upper extremity, 95% CI 2.38 to 5.55; overall P\u3c 0.001), low energy injury (HR 1.64, 95% CI 1.08 to 2.46; P = 0.019), degree of wound contamination (severe: HR 2.12 versus mild, 95% CI 1.35 to 3.32; moderate: HR 1.08 versus mild, 95% CI 0.78 to 1.49; overall P = 0.004), and need for flap coverage (HR 1.82, 95% CI 1.11 to 2.99; P = 0.017). Discussion: The results of this study provide a better understanding of which factors are associated with a greater risk of infection in open fractures. In addition, it can allow for surgeons to better counsel patients regarding prognosis, helping patients to understand their individual risk of infection