Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: 1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case; 2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.Comment: 29 pages, 9 Figures, 6 Tables (39 figure files in total

Smith-Waterman peak alignment for comprehensive two-dimensional gas chromatography-mass spectrometry

<p>Abstract</p> <p>Background</p> <p>Comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC × GC-MS) is a powerful technique which has gained increasing attention over the last two decades. The GC × GC-MS provides much increased separation capacity, chemical selectivity and sensitivity for complex sample analysis and brings more accurate information about compound retention times and mass spectra. Despite these advantages, the retention times of the resolved peaks on the two-dimensional gas chromatographic columns are always shifted due to experimental variations, introducing difficulty in the data processing for metabolomics analysis. Therefore, the retention time variation must be adjusted in order to compare multiple metabolic profiles obtained from different conditions.</p> <p>Results</p> <p>We developed novel peak alignment algorithms for both homogeneous (acquired under the identical experimental conditions) and heterogeneous (acquired under the different experimental conditions) GC × GC-MS data using modified Smith-Waterman local alignment algorithms along with mass spectral similarity. Compared with literature reported algorithms, the proposed algorithms eliminated the detection of landmark peaks and the usage of retention time transformation. Furthermore, an automated peak alignment software package was established by implementing a likelihood function for optimal peak alignment.</p> <p>Conclusions</p> <p>The proposed Smith-Waterman local alignment-based algorithms are capable of aligning both the homogeneous and heterogeneous data of multiple GC × GC-MS experiments without the transformation of retention times and the selection of landmark peaks. An optimal version of the SW-based algorithms was also established based on the associated likelihood function for the automatic peak alignment. The proposed alignment algorithms outperform the literature reported alignment method by analyzing the experiment data of a mixture of compound standards and a metabolite extract of mouse plasma with spiked-in compound standards.</p

Prostate Cancer Postoperative Nomogram Scores and Obesity

Nomograms are tools used in clinical practice to predict cancer outcomes and to help make decisions regarding management of disease. Since its conception, utility of the prostate cancer nomogram has more than tripled. Limited information is available on the relation between the nomograms' predicted probabilities and obesity. The purpose of this study was to examine whether the predictions from a validated postoperative prostate cancer nomogram were associated with obesity.We carried out a cross-sectional analysis of 1220 patients who underwent radical prostatectomy (RP) in southern California from 2000 to 2008. Progression-free probabilities (PFPs) were ascertained from the 10-year Kattan postoperative nomogram. Multivariable logistic regression models estimated odds ratios (ORs) and 95% confidence intervals (CIs).In the present study, aggressive prostate cancer (Gleason ≥7), but not advanced stage, was associated with obesity (p = 0.01). After adjusting for age, black race, family history of prostate cancer and current smoking, an inverse association was observed for 10-year progression-free predictions (OR = 0.50; 95% CI = 0.28–0.90) and positive associations were observed for preoperative PSA levels (OR = 1.23; 95% CI = 1.01–1.50) and Gleason >7 (OR = 1.45; 95% CI = 1.11–1.90).Obese RP patients were more likely to have lower PFP values than non-obese patients, suggesting a higher risk of experiencing prostate cancer progression. Identifying men with potentially higher risks due to obesity may improve disease prognosis and treatment decision-making

Phase 1 Study of a Combination AMA1 Blood Stage Malaria Vaccine in Malian Children

Apical Membrane Antigen-1 (AMA1) is one of the leading blood stage malaria vaccine candidates. AMA1-C1/Alhydrogel consists of an equal mixture of recombinant AMA1 from FVO and 3D7 clones of P. falciparum, adsorbed onto Alhydrogel. A Phase 1 study in semi-immune adults in Mali showed that the vaccine was safe and immunogenic, with higher antibody responses in those who received the 80 microg dose. The aim of this study was to assess the safety and immunogenicity of this vaccine in young children in a malaria endemic area.This was a Phase 1 dose escalating study in 36 healthy children aged 2-3 years started in March 2006 in Donéguébougou, Mali. Eighteen children in the first cohort were randomized 2 ratio 1 to receive either 20 microg AMA1-C1/Alhydrogel or Haemophilus influenzae type b Hiberix vaccine. Two weeks later 18 children in the second cohort were randomized 2 ratio 1 to receive either 80 microg AMA1-C1/Alhydrogel or Haemophilus influenzae type b Hiberix vaccine. Vaccinations were administered on Days 0 and 28 and participants were examined on Days 1, 2, 3, 7, and 14 after vaccination and then about every two months. Results to Day 154 are reported in this manuscript.Of 36 volunteers enrolled, 33 received both vaccinations. There were 9 adverse events related to the vaccination in subjects who received AMA1-C1 vaccine and 7 in those who received Hiberix. All were mild to moderate. No vaccine-related serious or grade 3 adverse events were observed. There was no increase in adverse events with increasing dose of vaccine or number of immunizations. In subjects who received the test vaccine, antibodies to AMA1 increased on Day 14 and peaked at Day 42, with changes from baseline significantly different from subjects who received control vaccine.AMA-C1 vaccine is well tolerated and immunogenic in children in this endemic area although the antibody response was short lived.Clinicaltrials.gov NCT00341250

Ethical Considerations in Crowdfunding

publishedVersio

Radiation-induced cancer after radiotherapy for non-Hodgkin's lymphoma of the head and neck: a retrospective study

<p>Abstract</p> <p>Background</p> <p>survivors of non-Hodgkin's lymphoma (NHL) are well known to be at an increased risk of second malignancies. In this study, we evaluated the incidence and clinical features of head and neck cancer (HNC) occurring after radiotherapy (RT) for NHL.</p> <p>Materials and methods</p> <p>We investigated the clinical records of 322 patients who had received RT for early-stage NHL of the head and neck at our institute between 1952 and 2000.</p> <p>Results</p> <p>There were 4 patients with a second HNC developing in the irradiated field, consisting of 2 patients with gum cancer, 1 case with tongue cancer and 1 case with maxillary sinus cancer. The pathological diagnosis in all the 4 patients was squamous cell carcinoma (SCC). Two of the patients (one with gum cancer and one with maxillary sinus cancer) died of the second HNC, while the remaining 2 patients are still living at the time of writing after therapy for the second HNC, with neither recurrence of the second tumor nor relapse of the primary tumor. The ratio of the observed to the expected number (O/E ratio) of a second HNC was calculated to be 12.7 (95%CI, 4.07–35.0), and the absolute excess risk (AER) per 10,000 person-years was 13.3. The median interval between the RT and the diagnosis of the second HNC was 17.0 years (range, 8.7 to 22.7 years).</p> <p>Conlusion</p> <p>The risk of HNC significantly increased after RT for early-stage NHL. These results suggest that second HNC can be regarded as one of the late complications of RT for NHL of the head and neck.</p

A Fiber-Optic Fluorescence Microscope Using a Consumer-Grade Digital Camera for In Vivo Cellular Imaging

BACKGROUND: Early detection is an essential component of cancer management. Unfortunately, visual examination can often be unreliable, and many settings lack the financial capital and infrastructure to operate PET, CT, and MRI systems. Moreover, the infrastructure and expense associated with surgical biopsy and microscopy are a challenge to establishing cancer screening/early detection programs in low-resource settings. Improvements in performance and declining costs have led to the availability of optoelectronic components, which can be used to develop low-cost diagnostic imaging devices for use at the point-of-care. Here, we demonstrate a fiber-optic fluorescence microscope using a consumer-grade camera for in vivo cellular imaging. METHODS: The fiber-optic fluorescence microscope includes an LED light, an objective lens, a fiber-optic bundle, and a consumer-grade digital camera. The system was used to image an oral cancer cell line labeled with 0.01% proflavine. A human tissue specimen was imaged following surgical resection, enabling dysplastic and cancerous regions to be evaluated. The oral mucosa of a healthy human subject was imaged in vivo, following topical application of 0.01% proflavine. FINDINGS: The fiber-optic microscope resolved individual nuclei in all specimens and tissues imaged. This capability allowed qualitative and quantitative differences between normal and precancerous or cancerous tissues to be identified. The optical efficiency of the system permitted imaging of the human oral mucosa in real time. CONCLUSION: Our results indicate this device as a useful tool to assist in the identification of early neoplastic changes in epithelial tissues. This portable, inexpensive unit may be particularly appropriate for use at the point-of-care in low-resource settings

TRY plant trait database - enhanced coverage and open access

Plant traits-the morphological, anatomical, physiological, biochemical and phenological characteristics of plants-determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait-based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits-almost complete coverage for 'plant growth form'. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait-environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Testing in Mice the Hypothesis That Melanin Is Protective in Malaria Infections

Malaria has had the largest impact of any infectious disease on shaping the human genome, exerting enormous selective pressure on genes that improve survival in severe malaria infections. Modern humans originated in Africa and lost skin melanization as they migrated to temperate regions of the globe. Although it is well documented that loss of melanization improved cutaneous Vitamin D synthesis, melanin plays an evolutionary ancient role in insect immunity to malaria and in some instances melanin has been implicated to play an immunoregulatory role in vertebrates. Thus, we tested the hypothesis that melanization may be protective in malaria infections using mouse models. Congenic C57BL/6 mice that differed only in the gene encoding tyrosinase, a key enzyme in the synthesis of melanin, showed no difference in the clinical course of infection by Plasmodium yoelii 17XL, that causes severe anemia, Plasmodium berghei ANKA, that causes severe cerebral malaria or Plasmodium chabaudi AS that causes uncomplicated chronic disease. Moreover, neither genetic deficiencies in vitamin D synthesis nor vitamin D supplementation had an effect on survival in cerebral malaria. Taken together, these results indicate that neither melanin nor vitamin D production improve survival in severe malaria