Ehrenfest's Theorem

A one dimensional presentation of Ehrenfest's theorem is presented.

Response to chemotherapy, recurrence and survival in advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish BRCA mutations, compared to those without

Objectives. Previous studies have shown a survival advantage in ovarian cancer patients with Ashkenazi-Jewish (AJ) BRCA founder mutations, compared to sporadic ovarian cancer patients. The purpose of this study was to determine if this association exists in ovarian cancer patients with non-Ashkenazi Jewish BRCA mutations. In addition, we sought to account for possible "survival bias" by minimizing any lead time that may exist between diagnosis and genetic testing. ^ Methods. Patients with stage III/IV ovarian, fallopian tube, or primary peritoneal cancer and a non-Ashkenazi Jewish BRCA1 or 2 mutation, seen for genetic testing January 1996-July 2007, were identified from genetics and institutional databases. Medical records were reviewed for clinical factors, including response to initial chemotherapy. Patients with sporadic (non-hereditary) ovarian, fallopian tube, or primary peritoneal cancer, without family history of breast or ovarian cancer, were compared to similar cases, matched by age, stage, year of diagnosis, and vital status at time interval to BRCA testing. When possible, 2 sporadic patients were matched to each BRCA patient. An additional group of unmatched, sporadic ovarian, fallopian tube and primary peritoneal cancer patients was included for a separate analysis. Progression-free (PFS) & overall survival (OS) were calculated by the Kaplan-Meier method. Multivariate Cox proportional hazards models were calculated for variables of interest. Matched pairs were treated as clusters. Stratified log rank test was used to calculate survival data for matched pairs using paired event times. Fisher's exact test, chi-square, and univariate logistic regression were also used for analysis. ^ Results. Forty five advanced-stage ovarian, fallopian tube and primary peritoneal cancer patients with non-Ashkenazi Jewish (non-AJ) BRCA mutations, 86 sporadic-matched and 414 sporadic-unmatched patients were analyzed. Compared to the sporadic-matched and sporadic-unmatched ovarian cancer patients, non-AJ BRCA mutation carriers had longer PFS (17.9 & 13.8 mos. vs. 32.0 mos., HR 1.76 [95% CI 1.13–2.75] & 2.61 [95% CI 1.70–4.00]). In relation to the sporadic- unmatched patients, non-AJ BRCA patients had greater odds of complete response to initial chemotherapy (OR 2.25 [95% CI 1.17–5.41]) and improved OS (37.6 mos. vs. 101.4 mos., HR 2.64 [95% CI 1.49–4.67]). ^ Conclusions. This study demonstrates a significant survival advantage in advanced-stage ovarian cancer patients with non-AJ BRCA mutations, confirming the previous studies in the Jewish population. Our efforts to account for "survival bias," by matching, will continue with collaborative studies. ^

Improving the health and well-being of women at risk for neural tube defect recurrence

There is growing interest in providing women with internatal care, a package of healthcare and ancillary services that can improve their health during the period after the termination of one pregnancy but before the conception of the next pregnancy. Women who have had a pregnancy affected by a neural tube defect can especially benefit from internatal care because they are at increased risk for recurrence and improvements to their health during the inter-pregnancy period can prevent future negative birth outcomes. The dissertation provides three papers that inform the content of internatal care for women at risk for recurrence by examining descriptive epidemiology to develop an accurate risk profile of the population, assessing whether women at risk for recurrence would benefit from a psychosocial intervention, and determining how to improve health promotion efforts targeting folic acid use.^ Paper one identifies information relevant for developing risk profiles and conducting risk assessments. A number of investigations have found that the risk for neural tube defects differs between non-Hispanic Whites and Hispanics. To understand the risk difference, the descriptive epidemiology of spina bifida and anencephaly was examined for Hispanics and non-Hispanic Whites based on data from the Texas Birth Defects Registry for the years 1999 through 2004. Crude and adjusted birth prevalence ratios and corresponding 95% confidence intervals were calculated between descriptive epidemiologic characteristics and anencephaly and spina bifida for non-Hispanic Whites and for Hispanics. In both race/ethnic groups, anencephaly expressed an inverse relationship with maternal age and a positive linear relationship with parity. Both relationships were stronger in non-Hispanic Whites. Female infants had a higher risk for anencephaly in non-Hispanic Whites. Lower maternal education was associated with increased risk for spina bifida in Hispanics.^ Paper two assesses the need for a psychosocial intervention. For mothers who have children with spina bifida, the transition to motherhood can be stressful. This qualitative study explored the process of becoming a mother to a child with spina bifida focusing particularly on stress and coping in the immediate postnatal environment. Semi-structured interviews were conducted with six mothers who have children with spina bifida. Mothers were asked about their initial emotional and problem-based coping efforts, the quality and kind of support provided by health providers, and the characteristics of their meaning-based coping efforts; questions matched Transactional Model of Stress and Coping (TMSC) constructs. Analysis of the responses revealed a number of modifiable stress and coping transactions, the most salient being: health providers are in a position to address beliefs about self-causality and prevent mothers from experiencing the repercussions that stem from maintaining these beliefs. ^ Paper three identifies considerations when creating health promotion materials targeting folic acid use. A brochure was designed using concepts from the Precaution Adoption Process Model (PAPM). Three focus groups comprising 26 mothers of children with spina bifida evaluated the brochure. One focus group was conducted in Spanish-only, the other two focus groups were conducted in English and Spanish combined. Qualitative analysis of coded transcripts revealed that a brochure is a helpful adjunct. Questions about folic acid support the inclusion of an insert with basic information. There may be a need to develop different educational material for Hispanics so the importance of folic acid is provided in a situational context. Some participants blamed themselves for their pregnancy outcome which may affect their receptivity to messages in the brochure. The women's desire for photographs that affect their perception of threat and their identification with the second role model indicate they belong to PAPM Stage 2 and 3. Participants preferred colorful envelopes, high quality paper, intimidating photographs, simple words, conversational style sentences, and positive messages.^ These papers develop the content of risk assessment, psychosocial intervention, and health promotion components of internatal care as they apply to women at risk for recurrence. The findings provided evidence for considering parity and maternal age when assessing nutritional risk. The two dissimilarities between the two race/ethnic groups, infant sex and maternal education lent support to creating separate risk profiles. Interviews with mothers of children with spina bifida revealed the existence of unmet needs-suggesting that a psychosocial intervention provided as part of internatal care can strengthen and support women's well-being. Segmenting the audience according to race/ethnicity and PAPM stage can improve the relevance of print materials promoting folic acid use.^

Factors governing late-recurrence of disease in a cohort of early-stage breast cancer survivors

Purpose. To determine the risk of late breast cancer recurrence (5 years after treatment) in a population of women diagnosed with early-stage breast cancer at The University of Texas M.D. Anderson Cancer Center (MDACC) between 1985-2000 and to examine the effect of this population’s BMI, smoking history, reproductive history, hormone use, and alcohol intake at the time of diagnosis on risk of late recurrence.^ Methods. Patients included 1,913 members of the Early Stage Breast Cancer Repository recruited at MDACC who had survived without a recurrence for at least five years after their initial diagnosis of early stage breast cancer. Clinical and epidemiological information was ascertained twice on participants during the study—first by medical record abstraction then by patient interview at least five years after receipt of adjuvant treatment. A total of 223 late breast cancer recurrences were captured, with an average follow-up of 10.6 years. Cox proportional hazards models were used to calculate hazard ratios (HR) and 95% confidence intervals (CI). ^

Anesthetic choices and breast cancer recurrence: A retrospective cohort study of risk factors

Background: The impact of anesthetic techniques for breast cancer surgery traditionally has been centered on the incidence of acute pain syndromes and complications immediately after surgery. Evaluating anesthesia management beyond short-term effects is an emerging science. Several animal studies have concluded that regional anesthesia independently reduces cancer recurrence and metastasis. A small number of retrospective clinical studies indicate that reductions in cancer recurrence are attributable to anesthesia technique; however, individual risk factors need to be taken into consideration. ^ Purpose: The aims were to: 1) investigate differences in patient, disease and treatment factors between women who received surgical treatment for breast cancer with paravertebral regional and general anesthesia compared to women who received general anesthesia alone; 2) explore patient, disease and treatment factors associated with recurrence of breast cancer; and 3) test the association between type of anesthesia and breast cancer recurrence and survival over 22–46 months following surgery. ^ Methods: This retrospective cohort study included 358 patients with stage 0-III disease who received a partial or total mastectomy without axillary node dissection between October 2006 and October 2008 at a large academic cancer center. Follow-up ended in August 2010 with a median follow-up time of 28.8 months. ^ Results: The patient demographics were equally represented across anesthesia groups. Mean BMI (kg/m2) was greater for the patients who received general anesthesia (GA) alone (29±6.8) compared to those that received paravertebral regional block (PVB) with GA (28±5.1), p=0.001. The PVB with GA group had more advanced stages of disease (p=0.01) and longer surgeries (p=0.01) than the GA only group. Breast cancer recurrence was detected in only 1.7% of the study population. The mean age was 51±18 in those who had a recurrence compared to 58±11 in the non-recurrent group (p=0.06). Overall, no association between anesthesia type and recurrence was found (p=0.53), with an unadjusted estimated hazard ratio of 1.84 (95% CI 0.34–10.08). ^ Conclusions: In contrast to previous retrospective studies in cancer patients receiving surgical and anesthesia treatment, this study was unable to detect a difference in relating type of anesthesia with decreased breast cancer recurrence. Nonetheless, a significant association between BMI and type of anesthesia was observed and should be taken into account in future studies. Because the overall rate of recurrence was very small in this population, a larger study would be needed to detect any differences in rates of recurrence attributable to type of anesthesia. ^

Venous thromboembolism in patients with acute leukemia: Prevalence, incidence, recurrence of thrombosis, risk factors, and impact on survival

Venous thromboembolism (VTE), including deep vein thrombosis (DVT) and pulmonary embolism (PE), is the third most preventable cardiovascular disease and a growing public health problem in the United States. The incidence of VTE remains high with an annual estimate of more than 600,000 symptomatic events. DVT affects an estimated 2 million American each year with a death toll of 300,000 persons per year from DVT-related PE. Leukemia patients are at high risk for both hemorrhage and thrombosis; however, little is known about thrombosis among acute leukemia patients. The ultimate goal of this dissertation was to obtain deep understanding of thrombotic issue among acute leukemia patients. The dissertation was presented in a format of three papers. First paper mainly looked at distribution and risk factors associated with development of VTE among patients with acute leukemia prior to leukemia treatment. Second paper looked at incidence, risk factors, and impact of VTE on survival of patients with acute lymphoblastic leukemia during treatment. Third paper looked at recurrence and risk factors for VTE recurrence among acute leukemia patients with an initial episode of VTE. Descriptive statistics, Chi-squared or Fisher's exact test, median test, Mann-Whitney test, logistic regression analysis, Nonparametric Estimation Kaplan-Meier with a log-rank test or Cox model were used when appropriate. Results from analyses indicated that acute leukemia patients had a high prevalence, incidence, and recurrent rate of VTE. Prior history of VTE, obesity, older age, low platelet account, presence of Philadelphia positive ALL, use of oral contraceptives or hormone replacement therapy, presence of malignancies, and co-morbidities may place leukemia patients at an increased risk for VTE development or recurrence. Interestingly, development of VTE was not associated with a higher risk of death among hospitalized acute leukemia patients.^

Merging person-specific bio-markers for predicting oral cancer recurrence through an ontology

One of the major problems related to cancer treatment is its recurrence. Without knowing in advance how likely the cancer will relapse, clinical practice usually recommends adjuvant treatments that have strong side effects. A way to optimize treatments is to predict the recurrence probability by analyzing a set of bio-markers. The NeoMark European project has identified a set of preliminary bio-markers for the case of oral cancer by collecting a large series of data from genomic, imaging, and clinical evidence. This heterogeneous set of data needs a proper representation in order to be stored, computed, and communicated efficiently. Ontologies are often considered the proper mean to integrate biomedical data, for their high level of formality and for the need of interoperable, universally accepted models. This paper presents the NeoMark system and how an ontology has been designed to integrate all its heterogeneous data. The system has been validated in a pilot in which data will populate the ontology and will be made public for further research.

The Kramer sampling theorem revisited

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space H through an H -valued kernel K defined on an appropriate domain.

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

7 pages, 4 figures Acknowledgement We are grateful to M. Riedl and G. Ansmann for fruitful discussions and critical comments on earlier versions of the manuscript. This work was supported by the Volkswagen Foundation (Grant Nos. 88461, 88462, 88463, 85390, 85391 and 85392).

From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.

Blood markers and recurrence of stroke in patients with transient ischemic attack

Trabalho Final do Curso de Mestrado Integrado em Medicina, Faculdade de Medicina, Universidade de Lisboa, 2014

A four moments theorem for Gamma limits on a Poisson chaos

This paper deals with sequences of random variables belonging to a fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.