Mathematical Support to Braneworld Theory

The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for case of semi-Riemannian manifolds. This theorem consist an essential mathematical support for this new theory. We find the integrability conditions for the existence of space-time submanifolds in a pseudo-Euclidean space. Keywords: Submanifolds, Braneworld, Pseudo-Riemannian geometryComment: 10 page

Introduction to a Biological Systems Science

Biological systems analysis and biodynamic modelling of physiological and biological interrelationships in human body and mammal

Early carotid endarterectomy in symptomatic patients is associated with poorer perioperative outcomes

ObjectiveThe optimal timing of carotid endarterectomy (CEA) after ipsilateral hemispheric stroke is controversial. Although early studies suggested that an interval of about 6 weeks after a completed stroke was preferred, more recent data have suggested that delaying CEA for this period of time is not necessary. With these issues in mind, we reviewed our experience to examine perioperative outcome with respect to the timing of CEA in previously symptomatic patients.MethodsA retrospective review of a prospectively maintained database of all CEAs performed at our institution from 1992 to 2003 showed that 2537 CEA were performed, of which 1158 (45.6%) were in symptomatic patients. Patients who were operated on emergently ≤48 hours of symptoms for crescendo transient ischemic attacks (TIAs) or stroke-in-evolution were excluded from analysis (n = 25). CEA was considered “early” if performed ≤4 weeks of symptoms, and “delayed” if performed after a minimum of a 4-week interval following the most recent symptom.ResultsOf nonurgent CEAs in symptomatic patients, in 87 instances the exact time interval from symptoms to surgery could not be precisely determined secondary to the remoteness of the symptoms (>18 months), and these were excluded from further analysis. Of the remaining 1046 cases, 62.7% had TIAs and 37.3% had completed strokes as their indication for surgery. Among the entire cohort, patients who underwent early CEA were significantly more likely to experience a perioperative stroke than patients who underwent delayed CEA (5.1% vs 1.6%, P = .002). Patients with TIAs alone were more likely to be operated on early rather than in a delayed fashion (64.3% vs 46.7%, P < .0001), likely reflecting institutional bias in selecting delayed CEA for stroke patients. However, even when examined as two separate groups, both TIA patients (n = 656) and CVA patients (n = 390) were significantly more likely to experience a perioperative stroke when operated upon early rather than in a delayed fashion (TIA patients, 3.3% vs 0.9%, P = .05; CVA patients, 9.4% vs 2.4%, P = .003). There were no significant differences in demographics or other meaningful variables between patients who underwent early CEA and those who underwent delayed CEA.ConclusionsIn a large institutional experience, patients who underwent CEA ≤4 weeks of ipsilateral TIA or stroke experienced a significantly increased rate of perioperative stroke compared with patients who underwent CEA in a more delayed fashion. This was true for both TIA and stroke patients, although the results were more impressive among stroke patients. On the basis of these results, we continue to recommend that waiting period of 4 weeks be considered in stroke patients who are candidates for CEA

Carotid endarterectomy in female patients: Are the concerns of the Asymptomatic Carotid Atherosclerosis Study valid?

AbstractObjectives: Although the results of the Asymptomatic Carotid Atherosclerosis Study clearly demonstrated the benefit of surgical over medical management of severe carotid artery stenosis, the results for women in particular were less certain. This was to some extent because of the higher perioperative complication rate observed in the 281 women (3.6% vs 1.7% in men). The objective of this study was to review a large experience with carotid endarterectomy in female patients and to determine whether the perioperative results differed from those of male patients. Methods: A review was conducted of a prospectively compiled database on all carotid endarterectomies performed between 1982 and 1997. Operations performed in 991 female patients were compared with those performed in 1485 male patients. Results: Female patients had a significantly lower incidence of diabetes, coronary artery disease, and contralateral carotid artery occlusion than did male patients. Female patients had a significantly higher incidence of hypertension. There were no significant differences in the age, smoking history, anesthetic route, shunt use, or clamp tolerance between the two groups. Of 991 female patients, 659 (66.5%) had preoperative symptoms, whereas 332 (33.5%) cases were performed for asymptomatic stenosis. Among 1485 male patients, 1041 (70.1%) had symptoms, and 444 (29.9%) were symptom free before surgery. There were no significant differences noted in the perioperative stroke rates between men and women overall (2.3% vs 2.4%, P =.92), or when divided into symptomatic (2.5% vs 3.0%, P =.52) and asymptomatic (2.0% vs 1.2%, P =.55) cases. Conclusions: Carotid endarterectomy can be performed with equally low perioperative stroke rates in men and women in both symptomatic and asymptomatic cases. In this series, symptom-free female patients had the lowest overall stroke rate. The concerns of the Asymptomatic Carotid Atherosclerosis Study regarding the benefit of carotid endarterectomy in female patients should therefore not prevent clinicians from recommending and performing carotid endarterectomy in appropriately selected symptom-free female patients. (J Vasc Surg 2001;33:236-41.

Immediate reexploration for the perioperative neurologic event after carotid endarterectomy: Is it worthwhile?

AbstractPurpose: When managing a new neurologic deficit after carotid endarterectomy (CEA), the surgeon is often preoccupied with determining the cause of the problem, requesting diagnostics tests, and deciding whether the patient should be surgically reexplored. The goal of this study was to analyze a series of perioperative neurologic events and to determine if careful analysis of their timing and mechanisms can predict which cases are likely to improve with reoperation. Methods: A review of 2024 CEAs performed from 1985 to 1997 revealed 38 patients who manifested a neurologic deficit in the perioperative period (1.9%). These cases form the focus of this analysis. Results: The causes of the events included intraoperative clamping ischemia in 5 patients (13.2%); thromboembolic events in 24 (63.2%); intracerebral hemorrhage in 5 (13.2%); and deficits unrelated to the operated artery in 4 (10.5%). Neurologic events manifesting in the first 24 hours after surgery were significantly more likely to be caused by thromboembolic events than by other causes of stroke (88.0% vs 12.0%, P <.002); deficits manifesting after the first 24 hours were significantly more likely to be related to other causes. Of 25 deficits manifesting in the first 24 hours after surgery, 18 underwent immediate surgical reexploration. Intraluminal thrombus was noted in 15 of the 18 reexplorations (83.3%); any technical defects were corrected. After the 18 reexplorations, in 12 cases there was either complete resolution of or significant improvement in the neurologic deficit that had been present (66.7%). Conclusions: Careful analysis of the timing and presentation of perioperative neurologic events after CEA can predict which cases are likely to improve with reoperation. Neurologic deficits that present during the first 24 hours after CEA are likely to be related to intraluminal thrombus formation and embolization. Unless another etiology for stroke has clearly been established, we think immediate reexploration of the artery without other confirmatory tests is mandatory to remove the embolic source and correct any technical problems. This will likely improve the neurologic outcome in these patients, because an uncorrected situation would lead to continued embolization and compromise. (J Vasc Surg 2000;32:1062-70.

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry

In the search for vacuum solutions, with or without a cosmological constant, of the Einstein field equations of Petrov type N with twisting principal null directions, the CR structures to describe the parameter space for a congruence of such null vectors provide a very useful tool. A work of Hill, Lewandowski and Nurowski has given a good foundation for this, reducing the field equations to a set of differential equations for two functions, one real, one complex, of three variables. Under the assumption of the existence of one Killing vector, the (infinite-dimensional) classical symmetries of those equations are determined and group-invariant solutions are considered. This results in a single ODE of the third order which may easily be reduced to one of the second order. A one-parameter class of power series solutions, g(w), of this second-order equation is realized, holomorphic in a neighborhood of the origin and behaving asymptotically as a simple quadratic function plus lower-order terms for large values of w, which constitutes new solutions of the twisting type N problem. The solution found by Leroy, and also by Nurowski, is shown to be a special case in this class. Cartan's method for determining equivalence of CR manifolds is used to show that this class is indeed much more general. In addition, for a special choice of a parameter, this ODE may be integrated once, to provide a first-order Abel equation. It can also determine new solutions to the field equations although no general solution has yet been found for it.Comment: 28 page

Non-Raft AC2 Defines a cAMP Signaling Compartment That Selectively Regulates IL-6 Expression in Airway Smooth Muscle Cells

Adenylyl cyclase (AC) isoforms differ in their tissue distribution, cellular localization, regulation, and protein interactions. Most cell types express multiple AC isoforms. We hypothesized that cAMP produced by different AC isoforms regulates unique cellular responses in human bronchial smooth muscle cells (BSMC). Overexpression of AC2, AC3, or AC6 had distinct effects on forskolin (Fsk)-induced expression of a number of known cAMP-responsive genes. These data show that different AC isoforms can differentially regulate gene expression. Most notable, overexpression and activation of AC2 enhanced interleukin 6 (IL-6) expression, but overexpression of AC3 or AC6 had no effect. IL-6 production by BSMC was induced by Fsk and select G protein-coupled receptor (GPCR) agonists, though IL-6 levels did not directly correlate with global cAMP levels. Treatment with PKA selective 6-Bnz-cAMP or Epac selective 8-CPT-2Me-cAMP cAMP analogs revealed a predominant role for PKA in cAMP-mediated induction of IL-6. IL-6 promoter mutations demonstrated that AP-1 and CRE transcription sites were required for Fsk to stimulate IL-6 expression. Our present study defines an AC2 cAMP signaling compartment that specifically regulates IL-6 expression in BSMC via Epac and PKA and demonstrates that other AC isoforms are excluded from this pool

Molecular Mechanism of the Constitutive Activation of the L250Q Human Melanocortin-4 Receptor Polymorphism †

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65471/1/j.1747-0285.2006.00362.x.pd

PKA and Epac cooperate to augment bradykinin-induced interleukin-8 release from human airway smooth muscle cells

Background: Airway smooth muscle contributes to the pathogenesis of pulmonary diseases by secreting inflammatory mediators such as interleukin-8 (IL-8). IL-8 production is in part regulated via activation of G(q)-and G(s)-coupled receptors. Here we study the role of the cyclic AMP (cAMP) effectors protein kinase A (PKA) and exchange proteins directly activated by cAMP (Epac1 and Epac2) in the bradykinin-induced IL-8 release from a human airway smooth muscle cell line and the underlying molecular mechanisms of this response.Methods: IL-8 release was assessed via ELISA under basal condition and after stimulation with bradykinin alone or in combination with fenoterol, the Epac activators 8-pCPT-2'-O-Me-cAMP and Sp-8-pCPT-2'-O-Me-cAMPS, the PKA activator 6-Bnz-cAMP and the cGMP analog 8-pCPT-2'-O-Me-cGMP. Where indicated, cells were pre-incubated with the pharmacological inhibitors Clostridium difficile toxin B-1470 (GTPases), U0126 (extracellular signal-regulated kinases ERK1/2) and Rp-8-CPT-cAMPS (PKA). The specificity of the cyclic nucleotide analogs was confirmed by measuring phosphorylation of the PKA substrate vasodilator-stimulated phosphoprotein. GTP-loading of Rap1 and Rap2 was evaluated via pull-down technique. Expression of Rap1, Rap2, Epac1 and Epac2 was assessed via western blot. Downregulation of Epac protein expression was achieved by siRNA. Unpaired or paired two-tailed Student's t test was used.Results: The beta(2)-agonist fenoterol augmented release of IL-8 by bradykinin. The PKA activator 6-Bnz-cAMP and the Epac activator 8-pCPT-2'-O-Me-cAMP significantly increased bradykinin-induced IL-8 release. The hydrolysis-resistant Epac activator Sp-8-pCPT-2'-O-Me-cAMPS mimicked the effects of 8-pCPT-2'-O-Me-cAMP, whereas the negative control 8-pCPT-2'-O-Me-cGMP did not. Fenoterol, forskolin and 6-Bnz-cAMP induced VASP phosphorylation, which was diminished by the PKA inhibitor Rp-8-CPT-cAMPS. 6-Bnz-cAMP and 8-pCPT-2'-O-Me-cAMP induced GTP-loading of Rap1, but not of Rap2. Treatment of the cells with toxin B-1470 and U0126 significantly reduced bradykinin-induced IL-8 release alone or in combination with the activators of PKA and Epac. Interestingly, inhibition of PKA by Rp-8-CPT-cAMPS and silencing of Epac1 and Epac2 expression by specific siRNAs largely decreased activation of Rap1 and the augmentation of bradykinin-induced IL-8 release by both PKA and Epac.Conclusion: Collectively, our data suggest that PKA, Epac1 and Epac2 act in concert to modulate inflammatory properties of airway smooth muscle via signaling to the Ras-like GTPase Rap1 and to ERK1/2.</p