Mountain Passes and Saddle Points

Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well known, but those for mountain passes or saddle points are less well known. We give an accessible treatment of some criteria for the existence of such points (including the mountain pass lemma), as well as describe a method that could be used to find such points

On Mountain Pass Type Algorithms

We consider constructive proofs of the mountain pass lemma, the saddle point theorem and a linking type theorem. In each, an initial “path” is deformed by pushing it downhill using a (pseudo) gradient flow, and, at each step, a high point on the deformed path is selected. Using these high points, a Palais–Smale sequence is constructed, and the classical minimax theorems are recovered. Because the sequence of high points is more accessible from a numerical point of view, we investigate the behavior of this sequence in the final two sections. We show that if the functional satisfies the Palais–Smale condition and has isolated critical points, then the high points form a Palais–Smale sequence, and—passing to a subsequence—the high points will in fact converge to a critical point

Farm to Forest - The Andrews Community Forest

This thesis project looks at the development of the Andrews Community Forest in Richmond, Vermont. Through a written narrative composed from interviews of main stakeholders in the process of establishing the Andrews Community Forest this thesis seeks to explore the history of the institution of community and town forests in Vermont, as well as their significance to local and state conservation efforts. Additionally, the project also includes a photo narrative section that attempts to capture the cultural history of the Andrews Community Forest by displaying through photos and story vignettes what life was like on the the Andrews Farm, which is now the Andrews Community Forest

Haemophilus influenzae invasive disease in the United States, 1994-1995: near disappearance of a vaccine-preventable childhood disease.

We analyzed national Haemophilus influenzae (Hi) surveillance data from 1994 and 1995 to describe the epidemiology of Hi invasive disease among persons of all ages. Serotype data were available for 376 (56%) of 669 reported Hi cases among children aged 4 years or younger; 184 (49%) were H. influenzae type b (Hib). Among children aged 4 or younger, incidence (per 100,000) of all Hi invasive disease was 1.8 in 1994 and 1.6 (p < 0.05) in 1995. Children aged 5 months or younger had the highest average annual incidence rate of Hib invasive disease (2.2 per 100,000); children aged 6 to 11 months had the next highest rate (1.2 per 100,000)(p < 0.05). Of 181 children with Hib invasive disease whose age in months was known, 85 (47%) were too young (aged 5 months or younger) to have completed a primary series with an Hib-containing vaccine. Of the 83 children with known vaccination status who were eligible to receive a primary series (aged 6 months or older), 52 (63%) were undervaccinated, and the remaining 31 (37%) had completed a primary series in which vaccine failed. Among persons aged 5 years or older with Hi invasive disease, the lowest average annual incidence was among those 20 to 39 years of age (0.15 per 100,000), and the highest was among those aged 80 years or older (2.26 per 100,000). Among persons aged 5 years or older, serotype data were available for 1,372 (71%) of the 1,940 Hi invasive disease cases; 159 (28%) of the 568 Hi cases with known serotype were due to Hib

Children with pertussis inform the investigation of other pertussis cases among contacts

BACKGROUND: The number of reported pertussis has increased in the last two decades. However, many cases of pertussis may be underreported or not diagnosed. The World Health Organization estimates that pertussis causes 200,000-400,000 deaths each year, most deaths are in infants and in developing countries. Infants with pertussis can indicate an undetected source cases in the community. METHODS: At a University Hospital in Brazil individuals that had frequent contacts with a child with confirmed pertussis (the index case) and had recent history of cough were enrolled into the study. Nasopharyngeal swabs were collected from every contact that had cough within the last 21 days. Cases confirmation followed the guidelines of the Center for Disease Control and Prevention-Atlanta, USA. RESULTS: Pertussis diagnosis was confirmed in 51 children, (considered the index cases). Among the index cases, 72.5% (37/51) were under 6 months of age; culture for Bordetella pertussis was positive in 78.4% (40/51). Pertussis was confirmed in 39% (107/276) of the contacts of 51 index cases. Among these contacts identified as a pertussis case, 40.2% (43/107) were between 6 months and 111/2 years of age and 59.8% (64/107) were older than 111/2 years of age. Pertussis was confirmed by culture in 11.2% (12/107) of them and by epidemiologic linkage in 88.8% (95/107). Each index case allowed identifying two new cases of pertussis. CONCLUSION: Public health authorities should consider implementing early recognition of pertussis index cases and searching for pertussis cases among the contacts. Treatment of the cases and prophylaxis of the contacts is fundamental to control outbreaks in the community

Persistence of Diphtheria, Hyderabad, India, 2003–2006

During 2003–2006, diphtheria rates in Hyderabad, India, were higher among persons 5–19 years of age, women, and Muslims than among other groups. Vaccine was efficacious among those who received >4 doses. The proportion of the population receiving boosters was low, especially among Muslims. We recommend increasing booster dose coverage

Procalcitonin as a Marker of Serious Bacterial Infections in Febrile Children Younger Than 3 Years Old

Objectives There is no perfectly sensitive or specific test for identifying young, febrile infants and children with occult serious bacterial infections ( SBI s). Studies of procalcitonin ( PCT ), a 116‐amino‐acid precursor of the hormone calcitonin, have demonstrated its potential as an acute‐phase biomarker for SBI . The objective of this study was to compare performance of serum PCT with traditional screening tests for detecting SBI s in young febrile infants and children. Methods This was a prospective, multicenter study on a convenience sample from May 2004 to December 2005. The study was conducted in four emergency departments ( ED s): one pediatric ED and three ED s with pediatric units, all with academic faculty on staff. A total of 226 febrile children 36 months old or younger who presented to the four participating ED s and were evaluated for SBI by blood, urine, and/or cerebral spinal fluid ( CSF ) cultures were included. Results The test characteristics (with 95% confidence intervals [CIs]) of the white blood cell (WBC) counts including neutrophil and band counts were compared with PCT for identifying SBI. Thirty children had SBIs (13.3%, 95% CI = 8.85 to 17.70). Four (13.3%) had bacteremia (including one with meningitis), 18 (60.0%) had urinary tract infections (UTIs), and eight (26.6%) had pneumonia. Children with SBIs had higher WBC counts (18.6 × 10 9  ± 8.6 × 10 9 cells/L vs. 11.5 × 10 9  ± 5.3 × 10 9 cells/L, p < 0.001), higher absolute neutrophil counts (ANCs; 10.6 × 10 9  ± 6.7 × 10 9 cells/L vs. 5.6 × 10 9  ± 3.8 × 10 9 cells/L, p = 0.009), higher absolute band counts (0.90 × 10 9  ± 1.1 × 10 9 cells/L vs. 0.35 × 10 9  ± 0.6 × 10 9 cells/L, p = 0.009), and higher PCT levels (2.9 ± 5.6 ng/ mL vs. 0.4 ± 0.8 ng/ mL , p = 0.021) than those without SBIs. In a multivariable logistic regression analysis, the absolute band count and PCT were the two screening tests independently associated with SBI, although the area under the receiver operating characteristic (ROC) curve for PCT was the largest (0.80, 95% CI = 0.71 to 0.89). Conclusions Procalcitonin is a more accurate biomarker than traditional screening tests for identifying young febrile infants and children with serious SBI s. Further study on a larger cohort of young febrile children is required to definitively determine the benefit of PCT over traditional laboratory screening tests for SBI s. Resumen Objetivos No existe un test con la sensibilidad o especificidad ideal es para identificar las infecciones bacterianas graves ( IBG ) ocultas en los niños durante su primera infancia con fiebre. Los estudios de procalcitonina ( PCT ), un precursor de 116‐aminoácidos de la hormona calcitonina, han demostrado su potencial como biomarcador de fase aguda para las IBG . El objetivo de este estudio es comparar el rendimiento de la PCT en plasma con las pruebas de despistaje tradicionales para la detección de IBG en los niños durante la primera infancia con fiebre. Metodología Estudio prospectivo multicéntrico en una muestra de conveniencia realizado de mayo de 2004 a diciembre realizado de 2005. Este estudio se llevó a cabo en cuatro servicios de urgencias ( SU ): un SU pediátrico y tres SU con unidades pediátricas, todos ellos con docentes universitarios en la plantilla. Se incluyeron 226 niños de 0 a 36 meses de edad con fiebre que acudieron a los cuatro SU participantes y se les evaluó para IBG mediante cultivos de sangre, orina y/o líquido cefalorraquídeo. Resultados Los resultados (con los intervalos de confianza [IC] al 95%) del número de leucocitos, incluyendo número neutrófilos y blastos, y de la PCT se compararon para identificar las IBG. Treinta niños tuvieron IBG (13,3%, IC 95% = 8,85 a 17,70). Cuatro (13,3%) tuvieron bacteremia (incluyendo uno con meningitis), 18 (60,0%) infección del tracto urinario y 8 (26,6%) neumonía. Los niños con IBG tuvieron mayor número de leucocitos (18.600 ± 8.600 cel/mm 3 vs. 11.500 ± 5.300 cel/mm 3 , p< 0,001), número absoluto de neutrófilos (NAN) (10.600 ± 6.700 cel/mm 3 vs. 5.600 ± 3.800 cel/mm 3 , p = 0,009), número absoluto de blastos (900 ± 1.100 cel/mm 3 vs. 350 ± 600 cel/mm 3 , p = 0,009) y valores de PCT (2,9 ng/ mL  ± 5,6 ng/ mL vs. 0,4 ng/ mL  ± 0,8 ng/ mL , p = 0,021), que aquéllos sin IBG. En un análisis multivariable de regresión logística, el número absoluto de blastos y la PCT fueron los dos test de despistaje que se asociaron de forma independiente con IBG, aunque el área bajo la curva de rendimiento diagnóstico para la PCT fue la mayor de los test de despistaje (0,80, IC 95% = 0,71 a 0,89). Conclusiones La PCT es un biomarcador más preciso que las pruebas de despistaje tradicionales para identificar a los niños durante la primera infancia con IBG . Se requieren futuros estudios en una mayor cohorte de niños durante la primera infancia con fiebre para determinar de forma definitiva el beneficio de la PCT sobre las pruebas de despistaje de laboratorio tradicionales para identificar las IBG .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106122/1/acem12316.pd

Adjusting a cancer mortality-prediction model for disease status-related eligibility criteria

<p>Abstract</p> <p>Background</p> <p>Volunteering participants in disease studies tend to be healthier than the general population partially due to specific enrollment criteria. Using modeling to accurately predict outcomes of cohort studies enrolling volunteers requires adjusting for the bias introduced in this way. Here we propose a new method to account for the effect of a specific form of healthy volunteer bias resulting from imposing disease status-related eligibility criteria, on disease-specific mortality, by explicitly modeling the length of the time interval between the moment when the subject becomes ineligible for the study, and the outcome.</p> <p>Methods</p> <p>Using survival time data from 1190 newly diagnosed lung cancer patients at MD Anderson Cancer Center, we model the time from clinical lung cancer diagnosis to death using an exponential distribution to approximate the length of this interval for a study where lung cancer death serves as the outcome. Incorporating this interval into our previously developed lung cancer risk model, we adjust for the effect of disease status-related eligibility criteria in predicting the number of lung cancer deaths in the control arm of CARET. The effect of the adjustment using the MD Anderson-derived approximation is compared to that based on SEER data.</p> <p>Results</p> <p>Using the adjustment developed in conjunction with our existing lung cancer model, we are able to accurately predict the number of lung cancer deaths observed in the control arm of CARET.</p> <p>Conclusions</p> <p>The resulting adjustment was accurate in predicting the lower rates of disease observed in the early years while still maintaining reasonable prediction ability in the later years of the trial. This method could be used to adjust for, or predict the duration and relative effect of any possible biases related to disease-specific eligibility criteria in modeling studies of volunteer-based cohorts.</p

Clinical Definitions of Pertussis: Summary of a Global Pertussis Initiative Roundtable Meeting, February 2011

Existing clinical case definitions of pertussis are decades old and based largely on clinical presentation in infants and children, yet an increasing burden is borne by adolescents and adults who may manifest distinct signs/symptoms. Therefore, a “one-size-fits-all” clinical case definition is no longer appropriate. Seeking to improve pertussis diagnosis, the Global Pertussis Initiative (GPI) developed an algorithm that delineates the signs/symptoms of pertussis most common to 3 age groups: 0–3 months, 4 months to 9 years, and ≥10 years. These case definitions are based on clinical presentation alone, but do include recommendations on laboratory diagnostics. Until pertussis can be accurately diagnosed, its burden will remain underestimated, making the introduction of epidemiologically appropriate preventive strategies difficult. The proposed definitions are intended to be widely applicable and to encourage the expanded use of laboratory diagnostics. Determination of their utility and their sensitivity and/or specificity versus existing case definitions is required

Tetrodotoxin as a Tool to Elucidate Sensory Transduction Mechanisms: The Case for the Arterial Chemoreceptors of the Carotid Body

Carotid bodies (CBs) are secondary sensory receptors in which the sensing elements, chemoreceptor cells, are activated by decreases in arterial PO2 (hypoxic hypoxia). Upon activation, chemoreceptor cells (also known as Type I and glomus cells) increase their rate of release of neurotransmitters that drive the sensory activity in the carotid sinus nerve (CSN) which ends in the brain stem where reflex responses are coordinated. When challenged with hypoxic hypoxia, the physiopathologically most relevant stimulus to the CBs, they are activated and initiate ventilatory and cardiocirculatory reflexes. Reflex increase in minute volume ventilation promotes CO2 removal from alveoli and a decrease in alveolar PCO2 ensues. Reduced alveolar PCO2 makes possible alveolar and arterial PO2 to increase minimizing the intensity of hypoxia. The ventilatory effect, in conjunction the cardiocirculatory components of the CB chemoreflex, tend to maintain an adequate supply of oxygen to the tissues. The CB has been the focus of attention since the discovery of its nature as a sensory organ by de Castro (1928) and the discovery of its function as the origin of ventilatory reflexes by Heymans group (1930). A great deal of effort has been focused on the study of the mechanisms involved in O2 detection. This review is devoted to this topic, mechanisms of oxygen sensing. Starting from a summary of the main theories evolving through the years, we will emphasize the nature and significance of the findings obtained with veratridine and tetrodotoxin (TTX) in the genesis of current models of O2-sensing