Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Tensor LRR and sparse coding-based subspace clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data, and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of-the-art methods.

Correlation between vertical misfits and stresses transmitted to implants from metal frameworks

An inappropriate prosthetic fit could cause stress over the interface implant/bone. The objective of this study was to compare stresses transmitted to implants from frameworks cast using different materials and to investigate a possible correlation between vertical misfits and these stresses. Fifteen one-piece cast frameworks simulating bars for fixed prosthesis in a model with five implants were fabricated and arranged into three different groups according to the material used for casting: CP Ti (commercially pure titanium), Co-Cr (cobalt-chromium) or Ni-Cr-Ti (nickel-chromium-titanium) alloys. Each framework was installed over the metal model with all screws tightened to a 10 N cm torque and then, vertical misfits were measured using an optical microscope. The stresses transmitted to implants were measured using quantitative photoelastic analysis in values of maximum shear stress (T), when each framework was tightened to the photoelastic model to a 10 N cm standardized torque. Stress data were statistically analyzed using one-way ANOVA and Tukey`s test and correlation tests were performed using Pearson`s rank correlation (alpha = 0.05). Mean and standard deviation values of vertical misfit are presented for CP Ti (22.40 +/- 9.05 mu m), Co-Cr (66.41 +/- 35.47 mu m) and Ni-Cr-Ti (32.20 +/- 24.47 mu m). Stresses generated by Co-Cr alloy (tau = 7.70 +/- 2.16 kPa) were significantly higher than those generated by CP Ti (tau = 5.86 +/- 1.55 kPa, p = 0.018) and Ni-Cr-Ti alloy (tau =5.74 +/- 3.05 kPa, p = 0.011), which were similar (p = 0.982). Correlations between vertical misfits and stresses around the implants were not significant as for any evaluated materials. (C) 2011 Elsevier Ltd. All rights reserved.

Comparison of biological behavior between early-stage adenocarcinoma and squamous cell carcinoma of the uterine cervix

Objectives: (1) To compare the anatomopathological variables and recurrence rates in patients with early-stage adenocarcinoma (AC) and squamous cell carcinoma (SCC) of the uterine cervix; (2) to identify the independent risk factors for recurrence. Study design: This historical cohort study assessed 238 patients with carcinoma of the uterine cervix (113 and IIA), who underwent radical hysterectomy with pelvic lymph node dissection between 1980 and 1999. Comparison of category variables between the two histological types was carried out using the Pearson`s X-2 test or Fisher exact test. Disease-free survival rates for AC and SCC were calculated using the Kaplan-Meier method and the curves were compared using the log-rank test. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Results: There were 35 cases of AC (14.7%) and 203 of SCC (85.3%). AC presented lower histological grade than did SCC (grade 1: 68.6% versus 9.4%; p < 0.001), lower rate of lymphovascular space involvement (25.7% versus 53.7%; p = 0.002), lower rate of invasion into the middle or deep thirds of the uterine cervix (40.0% versus 80.8%; p < 0.001) and lower rate of lymph node metastasis (2.9% versus 16.3%; p = 0.036). Although the recurrence rate was lower for AC than for SCC (11.4% versus 15.8%), this difference was not statistically significant (p = 0.509). Multivariate analysis identified three independent risk factors for recurrence: presence of metastases in the pelvic lymph nodes, invasion of the deep third of the uterine cervix and absence of or slight inflammatory reaction in the cervix. When these variables were adjusted for the histological type and radiotherapy status, they remained in the model as independent risk factors. Conclusion: The AC group showed less aggressive histological behavior than did the SCC group, but no difference in the disease-free survival rates was noted. (C) 2006 Elsevier Ireland Ltd. All rights reserved.

Experience With Lacosamide in a Series of Children With Drug-Resistant Focal Epilepsy

We report our pediatric experience with lacosarnide, a new antiepileptic drug, approved by the US Food and Drug Administration as adjunctive therapy in focal epilepsy in patients more than 17 years old. We retrospectively reviewed charts for lacosamide use and seizure frequency outcome in patients with focal epilepsy (Wilcoxon signed rank test). Sixteen patients (7 boys) were identified (median dose 275 mg daily, 4.7 mg/kg daily; mean age 14.9 years, range 8-21 years). Patients were receiving a median of 2 antiepileptic drugs (interquartile range [IQR] 1.7-3) in addition to having undergone previous epilepsy surgery (n = 3), vagus nerve stimulation (n = 9), and ketogenic diet (n = 3). Causes included structural (encephalomalacia and diffuse encephalitis, 1 each; stroke in 2) and genetic abnormalities (Aarskog and Rett syndromes, 1 each) or cause not known (n = 10). Median seizure frequency at baseline was 57 per month (IQR 7-75), and after a median follow-up of 4 months (range 1-13 months) of receiving lacosamide, it was 12.5 per month (IQR 3-75), (P < 0.01). Six patients (37.5%; 3 seizure free) were classified as having disease that responded to therapy (>= 50% reduction seizure frequency) and 10 as having disease that did not respond to therapy (<50% in 3; increase in 1; unchanged in 6). Adverse events (tics, behavioral disturbance, seizure worsening, and depression with suicidal ideation in 1 patient each) prompted lacosamide discontinuation in 4/16 (25%). This retrospective study of 16 children with drug-resistant focal epilepsy demonstrated good response to adjunctive lacosamide therapy (median seizure reduction of 39.6%; 37.5% with >= 50% seizure reduction) without severe adverse events. (C) 2011 Elsevier Inc. All rights reserved.

The nested assembly of individual-resource networks

P>1. Much of the current understanding of ecological systems is based on theory that does not explicitly take into account individual variation within natural populations. However, individuals may show substantial variation in resource use. This variation in turn may be translated into topological properties of networks that depict interactions among individuals and the food resources they consume (individual-resource networks). 2. Different models derived from optimal diet theory (ODT) predict highly distinct patterns of trophic interactions at the individual level that should translate into distinct network topologies. As a consequence, individual-resource networks can be useful tools in revealing the incidence of different patterns of resource use by individuals and suggesting their mechanistic basis. 3. In the present study, using data from several dietary studies, we assembled individual-resource networks of 10 vertebrate species, previously reported to show interindividual diet variation, and used a network-based approach to investigate their structure. 4. We found significant nestedness, but no modularity, in all empirical networks, indicating that (i) these populations are composed of both opportunistic and selective individuals and (ii) the diets of the latter are ordered as predictable subsets of the diets of the more opportunistic individuals. 5. Nested patterns are a common feature of species networks, and our results extend its generality to trophic interactions at the individual level. This pattern is consistent with a recently proposed ODT model, in which individuals show similar rank preferences but differ in their acceptance rate for alternative resources. Our findings therefore suggest a common mechanism underlying interindividual variation in resource use in disparate taxa.

6-Sulfatoxymelatonin as a predictor of clinical outcome in depressive patients

Objectives This study established the value of the 6-sulfatoxymelatonin (aMT6s) urine concentration as a predictor of the therapeutic response to noradrenaline reuptake inhibitors in depressive patients. Methods Twenty-two women aged 18-60 years were selected. Depressive symptoms were assessed by using the Hamilton Depression Scale. Urine samples were collected at 0600-1200 h, 1200-1800 h, 1800-2400 h, and 2400-0600 h intervals, 1 day before and 1 day after starting on the nortriptyline treatment. Urine aMT6s concentration was analyzed by a one-way analysis of variance/Bonferroni test. Spearman`s rank correlation coefficient was used to analyze the correlation between depressive symptoms after 2 weeks of antidepressant treatment and the increase in aMT6s urine concentration. Results Higher and lower size effect groups were compared by independent Student`s t-tests. At baseline, the 2400- to 0600-h interval differed from all other intervals presenting a significantly higher aMT6s urine concentration. A significant difference in aMT6s urine concentrations was found 1 day after treatment in all four intervals. Higher size effect group had lower levels of depressive symptoms 2 weeks after the treatment. A positive correlation between depressive symptoms and the delta of aMT6s in the 2400-0600h interval was observed. Conclusion Our results reinforce the hypothesis that aMT6s excretion is a predictor of clinical outcome in depression, especially in regard to noradrenaline reuptake inhibitors. Copyright (C) 2011 John Wiley & Sons, Ltd.

iNOS-derived Nitric Oxide Modulates Infection-stimulated Bone Loss

Nitric oxide (NO) derived from inducible nitric oxide synthase (iNOS) plays an important role in host defense, as well as in inflammation-induced tissue lesions. Here we evaluated the role of NO in bone loss in bacterial infection-induced apical periodontitis by using iNOS-deficient mice (iNOS(-/-)). The iNOS(-/-) mice developed greater inflammatory cell recruitment and osteolytic lesions than WT mice. Moreover, tartrate-resistant acid-phosphatase-positive (TRAP(+)) osteoclasts were significantly more numerous in iNOS-/- mice. Furthermore, the increased bone resorption in iNOS(-/-) mice also correlated with the increased expression of receptor activator NF-kappaB (RANK), stromal-cell-derived factor-1 alpha (SDF-1 alpha/CXCL12), and reduced expression of osteoprotegerin (OPG). These results show that NO deficiency was associated with an imbalance of bone-resorption-modulating factors, leading to severe infection-stimulated bone loss.

Corneal graft survival after therapeutic keratoplasty for Acanthamoeba keratitis

Purpose: To describe corneal graft survival and visual outcome after therapeutic penetrating keratoplasty in patients with Acanthamoeba keratitis (AK) that is unresponsive to clinical treatment. Methods: Retrospective study. Thirty-two patients with AK who underwent therapeutic penetrating keratoplasty (tPK) from August 1996 to August 2005 were included. Data relating to clinical features, visual acuity, surgical technique, graft survival and complications were collected. Graft survival was evaluated by the Kaplan-Meier method and comparisons were performed using the Log-rank test. Results: Most patients (62.5%) were female. Mean age [+/- standard deviation (SD)] was 35 (+/- 13) years (range 15-68 years). All patients were contact lens wearers. Eighteen patients (56%) presented paralytic mydriasis and glaucoma during the treatment. Thirteen patients (40%) developed glaucoma after surgery; eight of them (61%) required a second PK because of graft failure. Of the 32 keratoplasty eyes, 56.2% presented graft failure at any follow-up point. Forty-five per cent of graft failures occurred before the 12 month follow-up, so 55% remained clear in the first year after surgery. Twelve patients underwent a second PK; seven of them failed and 45% were clear at 1 year. Two patients presented graft recurrence of amoebic infection. There was no significant difference in graft survival when eyes with or without mydriasis were compared (P = 0.40). Eyes with glaucoma presented a significantly shorter graft survival (P = 0.01). Conclusion: Penetrating keratoplasty is a treatment option for eyes that are unresponsive to clinical treatment infections. However, graft survival is poor; postoperative glaucoma is frequent and is associated with shorter graft survival.

UNIVERSAL COVERING OF DRIFTLESS CONTROL SYSTEMS

Let M be a finite-dimensional manifold and Sigma be a driftless control system on M of full rank. We prove that for a given initial state x epsilon M, the covering space Gamma(Sigma, x) for a monotonic homotopy of trajectories of Sigma which is recently constructed in [1] coincides with the simply connected universal covering manifold of M and that the terminal projection epsilon(x) : Gamma(Sigma, x) -> M given by epsilon(x) ([alpha]) = alpha(1) is a covering mapping.

Realistic calculations of carbon-based disordered systems

Carbon nanotubes rank amongst potential candidates for a new family of nanoscopic devices, in particular for sensing applications. At the same time that defects in carbon nanotubes act as binding sites for foreign species, our current level of control over the fabrication process does not allow one to specifically choose where these binding sites will actually be positioned. In this work we present a theoretical framework for accurately calculating the electronic and transport properties of long disordered carbon nanotubes containing a large number of binding sites randomly distributed along a sample. This method combines the accuracy and functionality of ab initio density functional theory to determine the electronic structure with a recursive Green`s functions method. We apply this methodology on the problem of nitrogen-rich carbon nanotubes, first considering different types of defects and then demonstrating how our simulations can help in the field of sensor design by allowing one to compute the transport properties of realistic nanotube devices containing a large number of randomly distributed binding sites.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

On automorphisms of finite abelian p-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A(p). For a finite abelian p-group A of type (k(1),..., k(n)), simple necessary and sufficient conditions for an n x n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k(1), k(2)) is analyzed. (C) 2008 Mathematical Institute Slovak Academy of Sciences.