Conus medullaris termination in adult females

Objective: The primary objective of this study was to determine the termination level of the spinal cord in a sample population of adult female cadavers. Introduction: The conus medullaris represents the tapered, distal-most end of the spinal cord. It tends to be found somewhere between the L1-L2 lumbar vertebrae and can sometimes be higher or lower. Studies report the conus medullaris can be found anywhere from the lower third of T11 to the upper third of L3 with the average termination point around the lower third of L1. We aim to describe the level of conus medullaris termination in a sample of female cadavers. Methods: Twenty-four female cadavers were dissected as part of the Doctor of Osteopathic Medicine curriculum at the Philadelphia College of Osteopathic Medicine. The end of the conus medullaris was defined as the point where tapering ends distal to the last branches of the posterior nerve rootlets. Using the articulation of the 12th rib as a landmark the termination of the conus medullaris was noted to be either at the level of an intervertebral disc or vertebral body. In the latter cases the vertebral body was divided into upper, middle, and lower thirds. Results: Conus Medullaris termination ranged from the T12-L1 intervertebral disc to the L2-L3 intervertebral disc. The L1-L2 intervertebral disc was the most common termination point with 42% of cadavers demonstrating spinal cord termination at this level. Conclusions: These results demonstrate that there is variation of spinal cord termination, which can play a role in lumbar punctures, spinal anesthesia, and obstetric anesthesia. Due to the risk of cord damage it is imperative to perform any sort of anesthetic procedure fully below the level of L3 in the L3-L4 space or L4-L5 space. An epidural injection above the level of L3 may cause severe spinal cord damage if there is dural puncture and an anatomical variant in which the conus medullaris extends to the L3 level

Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles

Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales.Comment: 13 pages, 11 figure

Deciphering Network Community Structure by Surprise

The analysis of complex networks permeates all sciences, from biology to sociology. A fundamental, unsolved problem is how to characterize the community structure of a network. Here, using both standard and novel benchmarks, we show that maximization of a simple global parameter, which we call Surprise (S), leads to a very efficient characterization of the community structure of complex synthetic networks. Particularly, S qualitatively outperforms the most commonly used criterion to define communities, Newman and Girvan's modularity (Q). Applying S maximization to real networks often provides natural, well-supported partitions, but also sometimes counterintuitive solutions that expose the limitations of our previous knowledge. These results indicate that it is possible to define an effective global criterion for community structure and open new routes for the understanding of complex networks.Comment: 7 pages, 5 figure

Statistically validated networks in bipartite complex systems

Many complex systems present an intrinsic bipartite nature and are often described and modeled in terms of networks [1-5]. Examples include movies and actors [1, 2, 4], authors and scientific papers [6-9], email accounts and emails [10], plants and animals that pollinate them [11, 12]. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set. When one constructs a projected network with nodes from only one set, the system heterogeneity makes it very difficult to identify preferential links between the elements. Here we introduce an unsupervised method to statistically validate each link of the projected network against a null hypothesis taking into account the heterogeneity of the system. We apply our method to three different systems, namely the set of clusters of orthologous genes (COG) in completely sequenced genomes [13, 14], a set of daily returns of 500 US financial stocks, and the set of world movies of the IMDb database [15]. In all these systems, both different in size and level of heterogeneity, we find that our method is able to detect network structures which are informative about the system and are not simply expression of its heterogeneity. Specifically, our method (i) identifies the preferential relationships between the elements, (ii) naturally highlights the clustered structure of investigated systems, and (iii) allows to classify links according to the type of statistically validated relationships between the connected nodes.Comment: Main text: 13 pages, 3 figures, and 1 Table. Supplementary information: 15 pages, 3 figures, and 2 Table

3-Acetyl­benzoic acid

In the crystal structure of the title compound, C9H8O3, essentially planar mol­ecules [the carboxyl group makes a dihedral angle of 4.53 (7)° with the plane of the ring, while the acid group forms a dihedral angle of 3.45 (8)° to the ring] aggregate by centrosymmetric hydrogen-bond pairing of ordered carboxyl groups. This yields dimers which have two orientations in a unit cell, creating a herringbone pattern. In addition, two close C—H⋯O inter­molecular contacts exist: one is between a methyl H atom and the ketone of a symmetry-related mol­ecule and the other involves a benzene H atom and the carboxyl group O atom of another mol­ecule. The crystal studied was a non-merohedral twin with twin law [100, 00, 0] and a domain ratio of 0.8104(14): 0.1896(14)

Early stages of ramified growth in quasi-two-dimensional electrochemical deposition

I have measured the early stages of the growth of branched metal aggregates formed by electrochemical deposition in very thin layers. The growth rate of spatial Fourier modes is described qualitatively by the results of a linear stability analysis [D.P. Barkey, R.H. Muller, and C.W. Tobias, J. Electrochem. Soc. {\bf 136}, 2207 (1989)]. The maximum growth rate is proportional to $(I/c)^\delta$ where $I$ is the current through the electrochemical cell, $c$ the electrolyte concentration, and $\delta = 1.37 \pm 0.08$. Differences between my results and the theoretical predictions suggest that electroconvection in the electrolyte has a large influence on the instability leading to ramified growth.Comment: REVTeX, four ps figure

Dynamics on expanding spaces: modeling the emergence of novelties

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review.Comment: 25 pages, 10 figure

Complete analysis of the B-cell response to a protein antigen, from in vivo germinal centre formation to 3-D modelling of affinity maturation

Somatic hypermutation of immunoglobulin variable region genes occurs within germinal centres (GCs) and is the process responsible for affinity maturation of antibodies during an immune response. Previous studies have focused almost exclusively on the immune response to haptens, which may be unrepresentative of epitopes on protein antigens. In this study, we have exploited a model system that uses transgenic B and CD4<sup>+</sup> T cells specific for hen egg lysozyme (HEL) and a chicken ovalbumin peptide, respectively, to investigate a tightly synchronized immune response to protein antigens of widely differing affinities, thus allowing us to track many facets of the development of an antibody response at the antigen-specific B cell level in an integrated system <i>in</i> <i>vivo</i>. Somatic hypermutation of immunoglobulin variable genes was analysed in clones of transgenic B cells proliferating in individual GCs in response to HEL or the cross-reactive low-affinity antigen, duck egg lysozyme (DEL). Molecular modelling of the antibody–antigen interface demonstrates that recurring mutations in the antigen-binding site, selected in GCs, enhance interactions of the antibody with DEL. The effects of these mutations on affinity maturation are demonstrated by a shift of transgenic serum antibodies towards higher affinity for DEL in DEL-cOVA immunized mice. The results show that B cells with high affinity antigen receptors can revise their specificity by somatic hypermutation and antigen selection in response to a low-affinity, cross-reactive antigen. These observations shed further light on the nature of the immune response to pathogens and autoimmunity and demonstrate the utility of this novel model for studies of the mechanisms of somatic hypermutation