A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

ANTIGEN RECOGNITION AND THE IMMUNE RESPONSE : STRUCTURAL REQUIREMENTS IN THE SIDE CHAIN OF TYROSINE FOR IMMUNOGENICITY OF L-TYROSINE-AZOBENZENEARSONATE

The low molecular weight compound L-tyrosine-azobenzenearsonate (RAT) induces a cellular immune response in guinea pigs. The contribution of the side chain of tyrosine to the immunogenicity of RAT and the structural requirements at that position for immunogenicity were assessed by synthesizing a series of analogs of RAT containing modifications in the side chain of tyrosine and employing them as immunogens. Removal of either the carboxyl or amino group did not markedly affect immunogenicity, measured by the induction of delayed cutaneous sensitivity, whereas deletion of both completely abolished it. However, a charged group was not required since side chains containing a polar hydroxyl group could substitute for chains bearing an amino or carboxyl group. The size of the side chain exerted a pronounced influence; the charged or polar substituent had to be extended from the phenolic ring by at least two carbon atoms in order to confer immunogenicity

Vascular endothelial growth factor (VEGF) fails to improve blood flow and to promote collateralization in a diabetic mouse ischemic hindlimb model

BACKGROUND: Angiogenic therapy with vascular endothelial growth factor (VEGF) has been proposed as a treatment paradigm for patients suffering from an insufficiency of collateral vessels. Diabetes is associated with increase in the production of VEGF and therefore additional VEGF may not be beneficial. Accordingly, we sought to determine the efficacy of VEGF therapy to augment collateral formation and tissue perfusion in a diabetic mouse ischemic hindlimb model. METHODS: Diabetic and non-diabetic mice were studied in parallel for the efficacy of VEGF administration. Diabetes was induced with streptozotocin. Hindlimb ischemia was produced by severing the left iliac artery. An outlet tube from an osmotic infusion pump with placebo/ 500 micrograms of plasmid-DNA encoding VEGF was fenestrated and tunneled into the left quadriceps muscle. RESULTS: VEGF induced more rapid and complete restoration of blood flow in normal mice. However, in the setting of diabetes there was no difference between VEGF Vs. placebo in the rate or adequacy of flow restoration. There was a significant increase in smooth muscle actin and Factor-VIII antigen densities in diabetic animals and in animals which received VEGF. CONCLUSIONS: Angiogenic therapy with VEGF in the setting of diabetes does not appear to have the beneficial effects seen in the absence of diabetes

The Stratified Structure of Spaces of Smooth Orbifold Mappings

We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifold. The remaining two notions carry a stratified structure: The C^r orbifold maps between O and P is locally a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps between O and P locally has the structure of a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds. Furthermore, we give the explicit relationship between these notions of orbifold map. Applying our results to the special case of orbifold diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande

Obstetric and Neonatal Outcomes 1 or More Years After a Diagnosis of Breast Cancer

OBJECTIVE:To evaluate obstetric and neonatal outcomes of the first live birth conceived 1 or more years after breast cancer diagnosis.METHODS:We performed a population-based study to compare live births between women with a history of breast cancer (case group) and matched women with no cancer history (control group). Individuals in the case and control groups were identified using linked data from the California Cancer Registry and California Office of Statewide Health Planning and Development data sets. Individuals in the case group were diagnosed with stage I-III breast cancer at age 18-45 years between January 1, 2000, and December 31, 2012, and conceived 12 or more months after breast cancer diagnosis. Individuals in the control group were covariate-matched women without a history of breast cancer who delivered during 2000-2012. The primary outcome was preterm birth at less than 37 weeks of gestation. Secondary outcomes were preterm birth at less than 32 weeks of gestation, small for gestational age (SGA), cesarean delivery, severe maternal morbidity, and neonatal morbidity. Subgroup analyses were used to assess the effect of time from initial treatment to fertilization and receipt of additional adjuvant therapy before pregnancy on outcomes of interest.RESULTS:Of 30,021 women aged 18-45 years diagnosed with stage I-III breast cancer during 2000-2012, 553 met the study inclusion criteria. Those with a history of breast cancer and matched women in the control group had similar odds of preterm birth at less than 37 weeks of gestation (odds ratio [OR], 1.29; 95% CI 0.95-1.74), preterm birth at less than 32 weeks of gestation (OR 0.77; 95% CI 0.34-1.79), delivering an SGA neonate (less than the 5th percentile: OR 0.60; 95% CI 0.35-1.03; less than the 10th percentile: OR 0.94; 95% CI 0.68-1.30), and experiencing severe maternal morbidity (OR 1.61; 95% CI 0.74-3.50). Patients with a history of breast cancer had higher odds of undergoing cesarean delivery (OR 1.25; 95% CI 1.03-1.53); however, their offspring did not have increased odds of neonatal morbidity compared with women in the control group (OR 1.15; 95% CI 0.81-1.62).CONCLUSION:Breast cancer 1 or more years before fertilization was not strongly associated with obstetric and neonatal complications

Incidence of synchronous appendiceal neoplasm in patients with colorectal cancer and its clinical significance

<p>Abstract</p> <p>Background</p> <p>The aims of this study were to evaluate the incidence of synchronous appendiceal neoplasm in patients with colorectal cancer, and to determine its clinical significance.</p> <p>Methods</p> <p>Pathological reports and medical records were reviewed of patients with colorectal adenocarcinoma who underwent oncological resection of the tumor together with appendectomy at the Faculty of Medicine Siriraj Hospital, Mahidol University, Thailand between September 2000 and April 2008.</p> <p>Results</p> <p>This study included 293 patients with an average age of 62 years (range 19–95) and 51 percent were male. Of the patients studied, 228 (78 percent) had right hemicolectomy, whereas the others (22 percent) had surgery for left-sided colon cancer or rectal cancer. One patient (0.3 percent) had epithelial appendiceal neoplasm (mucinous cystadenoma) and 3 patients (1.0 percent) had metastatic colorectal cancer in the mesoappendix. However, the presence of synchronous appendiceal tumors and/or metastasis did not alter postoperative management, as these patients had received adjuvant therapy and were scheduled for surveillance program because of nodal involvement.</p> <p>Conclusion</p> <p>The incidence of synchronous primary appendiceal neoplasm and secondary (metastatic) appendiceal neoplasm in colorectal cancer patients was 0.3 and 1.0 percent, respectively. However, these findings did not change the postoperative clinical management.</p