Nontrivial classes in H∗(Imb(S1,Rn))H^*(Imb(S^1,\R^n)) from nontrivalent graph cocycles

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.Comment: 10 pages, 11 figures. V2: minor changes, typos correcte

A blast of mistakes: undiagnosed cervical ppondylolisthesis following a bomb explosion

Background: A case of spinal trauma had an unusual clinical course due to medical mistakes, from which we can learn some important lessons. Case Report: We report a case of spondylolisthesis following a bomb explosion, which went undiagnosed for a long time because of a series of mistakes that are highlighted in this article. What makes this case unique is that the spondylolisthesis developed during hospital stay, but the patient had no loss of mobility, strength, or sensitivity. Conclusions: This case shows that establishing the conditions of an organ or a body part upon admission to hospital may not be enough when a patient has suffered extensive and serious trauma, and that it is necessary to carry out more checkups over time, especially if there are new clues and symptoms

The Italian primary school-size distribution and the city-size: a complex nexus

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.Comment: 16 pages, 10 figure

Algebraic structures on graph cohomology

We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even and greater than 3. Finally, we give a new interpretation of the anomaly term for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear in J. Knot Theory Ramification

(Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects

Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by gravity, and any conceivable physical system (other than the vacuum) is bound to break at least some of them. Motivated by this observation, we study how to couple gravity with the Goldstone fields that non-linearly realize spontaneously broken space-time symmetries. This can be done in complete generality by weakly gauging the Poincare symmetry group in the context of the coset construction. To illustrate the power of this method, we consider three kinds of physical systems coupled to gravity: superfluids, relativistic membranes embedded in a higher dimensional space, and rotating point-like objects. This last system is of particular importance as it can be used to model spinning astrophysical objects like neutron stars and black holes. Our approach provides a systematic and unambiguous parametrization of the degrees of freedom of these systems.Comment: 30 page

The galileon as a local modification of gravity

In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]Comment: 35 pages; minor modifications, a typo corrected in eq. (114

Basic fibroblast growth factor mediates carotid plaque instability through metalloproteinase-2 and –9 expression

OBJECTIVE(S): We hypothesized that basic fibroblast growth factor (bFGF) may exert a role in carotid plaque instability by regulating the expression of matrix metalloproteinases (MMP). METHODS: Plaques obtained from 40 consecutive patients undergoing carotid endarterectomy were preoperatively classified as soft or hard. Serum bFGF was pre- and postoperatively measured. The release of MMP-2 and MMP-9 in the blood serum, and the activity, production and expression in the carotid specimens was analyzed. Specific anti-bFGF inhibition tests were performed in vitro on human umbilical artery smooth muscle cells (HUASMC) to evaluate the role of bFGF in the activity, production and expression of MMP-2 and -9. RESULTS: Twenty-one (53%) patients had a soft carotid plaque and 19 (48%) a hard plaque. Preoperative bFGF serum levels were higher in patients with soft plaques [soft=34 (28-39) pg/mL and hard=20 (17-22) pg/mL-p<0.001] and postoperatively returned to normal values (when compared to 10 healthy volunteers). The serum levels of MMP-2 in patients' with soft plaques were higher than those in patients' with hard plaques [soft=1222 (1190-1252) ng/mL and hard=748 (656-793)ng/mL-p<0.0001]. MMP-9 serum values were 26 (22-29) ng/mL for soft plaques and 18 (15-21) ng/mL for hard plaques (p<0.0001). We found increased activity, production and expression of MMP-2 and -9 in soft plaques compared to hard plaques (p<0.001). In vitro inhibition tests on HUASMC showed the direct influence of bFGF on the activity, production and expression of MMP-2 and -9 (p<0.001). CONCLUSIONS: bFGF seems to exert a key role in carotid plaque instability regulating the activity, production and expression of MMP thus altering the physiologic homeostasis of the carotid plaque