NLS ground states on metric trees: existence results and open questions

We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the Pólya–Szegő inequality for radial rearrangements. A key role is played by a new Poincaré inequality with remainder

Uniqueness and non–uniqueness of prescribed mass NLS ground states on metric graphs

We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS equation is constant on the set of ground states of mass μ, up to an at most countable set of masses. Then we apply this result to obtain uniqueness of ground states on two specific noncompact graphs. Finally we construct a graph that admits at least two ground states with the same mass having different Lagrange multipliers. Our proofs are based on careful variational arguments and rearrangement techniques, and hold both for the subcritical range p∈(2,6) and in the critical case p=6

Rainfall interpolation analysis on river Kaduna catchment for climate change assessment

The Inverse Distance Weighing (IDW) technique for rainfall interpolation considered by researchers as a suitable method for predicting missing rainfall records was used to estimate missing rainfall records in River Kaduna Catchment area from 1979-1990. Distances among respective rainfall stations were used to calculate the weighing factor for stations with missing records and radius of influence of 22.5-201km. The Root Mean Square Error (RMSE) was used to test the accuracy of the assessment and the results were validated using correlation coefficient. From the results of the analysis through optimization of steps of α values and radius of influence, the smaller the optimum parameter value the better the prediction and in most cases the accuracy increases at short optimum search radii, also small amount and long duration rainfall values enhances the prediction potential of the IDW.Keywords: Rainfall data, Inverse Distance Weighing, Interpolation, Optimum parameter

No confirmed cases of Taenia solium taeniasis in a group of recently arrived Sub-Saharan migrants to Italy

One-hundred and sixty-four migrants from Sub-Saharan Africa to Italy were screened with the Taenia solium specific enzyme-linked immunosorbent assay coproantigen (ELISA CoAg) and four (2.4%) were recorded as positive, but with optical density values near to the cut-off. No ELISA CoAg positive samples were confirmed by parasitological methods. Low positivity could be attributed to false positive result or cross-reaction with other Taenia species. Further studies are needed to assess the role of migration on sporadic autochthonous transmission of T. solium taeniasis/cysticercosis in Europe

Complementarity of ultrasound and fluorescence imaging in an orthotopic mouse model of pancreatic cancer

<p>Abstract</p> <p>Background</p> <p>Pancreatic cancer is a devastating disease characterized by dismal 5-year survival rates and limited treatment options. In an effort to provide useful models for preclinical evaluation of new experimental therapeutics, we and others have developed orthotopic mouse models of pancreatic cancer. The utility of these models for pre-clinical testing is dependent upon quantitative, noninvasive methods for monitoring <it>in vivo </it>tumor progression in real time. Toward this goal, we performed whole-body fluorescence imaging and ultrasound imaging to evaluate and to compare these noninvasive imaging modalities for assessing tumor burden and tumor progression in an orthotopic mouse model of pancreatic cancer.</p> <p>Methods</p> <p>The human pancreatic cancer cell line XPA-1, engineered for stable, high-level expression of red fluorescent protein (RFP), was implanted into the pancreas of nude mice using orthotopic implantation. The tumors were allowed to grow over a period of one to several weeks during which time the mice were imaged using both fluorescence imaging and ultrasound imaging to measure tumor burden and to monitor tumor growth.</p> <p>Results</p> <p>Whole-body fluorescence imaging and ultrasound imaging both allowed for the visualization and measurement of orthotopic pancreatic tumor implants <it>in vivo</it>. The imaging sessions were well-tolerated by the mice and yielded data which correlated well in the quantitative assessment of tumor burden. Whole-body fluorescence and two-dimensional ultrasound imaging showed a strong correlation for measurement of tumor size over a range of tumor sizes (R²= 0.6627, P = 0.003 for an exposure time of 67 msec and R²= 0.6553, P = 0.003 for an exposure time of 120 msec).</p> <p>Conclusion</p> <p>Our findings suggest a complementary role for fluorescence imaging and ultrasound imaging in assessing tumor burden and tumor progression in orthotopic mouse models of human cancer.</p

Exploring possible selves in a first-year physics foundation class: Engaging students by establishing relevance

Students often complain that they cannot see the relevance of what they are being taught in foundation physics classes. While revising and adjusting the curriculum and teaching are important, this study suggests it might also be useful to help students view their learning in relation to their future career aspirations. This paper reports on a study conducted with first-year students enrolled in a compulsory foundation physics unit with a history of low pass rates.Working within a “possible selves” framework, activities were designed to help students position their learning in relation to possible future lives and careers. Two cohorts of students (N ¼ 93) engaged in an intensive workshop comprising multiple activities relating to self and career. Self-reflection worksheets were analyzed using content analysis. The results indicate that students experience immediate benefits from these activities through self-reflection on the current self, future possible professional selves, and the role of current studies in narrowing the gap between the two

Conditional mouse models demonstrate oncogene-dependent differences in tumor maintenance and recurrence

Diversity in the pathophysiology of breast cancer frustrates therapeutic progress. We need to understand how mechanisms activated by specific combinations of oncogenes, tumor suppressors, and hormonal signaling pathways govern response to therapy and prognosis. A recent series of investigations conducted by Chodosh and colleagues offers new insights into the similarities and differences between specific oncogenic pathways. Expression of three oncogenes relevant to pathways activated in human breast cancers (c-myc, activated neu and Wnt1) were targeted to murine mammary epithelial cells using the same transgenic tetracycline-responsive conditional gene expression system. While the individual transgenic lines demonstrate similarly high rates of tumor penetrance, rates of oncogene-independent tumor maintenance and recurrence following initial regression are significantly different, and are modifiable by mutations in specific cooperating oncogenes or loss of tumor suppressor gene expression. The experiments make three notable contributions. First, they illustrate that rates of tumor regression and recurrence following initial regression are dependent upon the pathways activated by the initiating oncogene. The experiments also demonstrate that altered expression or mutation of specific cooperating oncogenes or tumor suppressor genes results in different rates of tumor regression and recurrence. Finally, they exemplify the power of conditional mouse models for elucidating how specific molecular mechanisms give rise to the complexity of human cancer

A mouse model for Luminal epithelial like ER positive subtype of human breast cancer

<p>Abstract</p> <p>Background</p> <p>Generation of novel spontaneous ER positive mammary tumor animal model from heterozygous NIH nude mice.</p> <p>Methods</p> <p>Using brother-sister mating with pedigree expansion system, we derived a colony of heterozygous breeding females showing ER-Positive tumors around the age of 6 months. Complete blood picture, differential leukocyte count, and serum levels of Estrogen, Alanine amino transferase (SGPT), Aspartate amino transferase (SGOT), total protein and albumin were estimated. Aspiration biopsies and microbiology were carried out. Gross pathology of the tumors and their metastatic potential were assessed. The tumors were excised and further characterized using histopathology, cytology, electron microscopy (EM), molecular markers and Mouse mammary Tumor Virus – Long Terminal Repeats (MMTV LTR) specific RT-PCR.</p> <p>Results</p> <p>The tumors originated from 2^ndor 5^thor both the mammary glands and were multi-nodulated with variable central necrosis accompanied with an accumulation of inflammatory exudate. Significant increases in estrogen, SGPT, SGOT and neutrophils levels were noticed. Histopathologically, invasive nodular masses of pleomorphic tubular neoplastic epithelial cells invaded fibro-vascular stroma, adjacent dermis and subcutaneous tissue. Metastatic spread through hematogenous and regional lymph nodes, into liver, lungs, spleen, heart and dermal lymphatics was observed. EM picture revealed no viral particles and MMTV-negativity was confirmed through MMTV LTR-specific RT-PCR. High expression of ER α, moderate to high expression of proliferating cell nuclear antigen (PCNA), moderate expression of vimentin and Cytokeratin 19 (K19) and low expression of p53 were observed in tumor sections, when compared with that of the normal mammary gland.</p> <p>Conclusion</p> <p>Since 75% of human breast cancer were classified ER-positive and as our model mimics (in most of the characteristics, such as histopathology, metastasis, high estrogen levels) the ER-positive luminal epithelial-like human breast cancer, this model will be an attractive tool to understand the biology of estrogen-dependant breast cancer in women. To our knowledge, this is the first report of a spontaneous mammary model displaying regional lymph node involvement with both hematogenous and lymphatic spread to liver, lung, heart, spleen and lymph nodes.</p

Comparison of mouse mammary gland imaging techniques and applications: Reflectance confocal microscopy, GFP Imaging, and ultrasound

<p>Abstract</p> <p>Background</p> <p>Genetically engineered mouse models of mammary gland cancer enable the <it>in vivo </it>study of molecular mechanisms and signaling during development and cancer pathophysiology. However, traditional whole mount and histological imaging modalities are only applicable to non-viable tissue.</p> <p>Methods</p> <p>We evaluated three techniques that can be quickly applied to living tissue for imaging normal and cancerous mammary gland: reflectance confocal microscopy, green fluorescent protein imaging, and ultrasound imaging.</p> <p>Results</p> <p>In the current study, reflectance confocal imaging offered the highest resolution and was used to optically section mammary ductal structures in the whole mammary gland. Glands remained viable in mammary gland whole organ culture when 1% acetic acid was used as a contrast agent. Our application of using green fluorescent protein expressing transgenic mice in our study allowed for whole mammary gland ductal structures imaging and enabled straightforward serial imaging of mammary gland ducts in whole organ culture to visualize the growth and differentiation process. Ultrasound imaging showed the lowest resolution. However, ultrasound was able to detect mammary preneoplastic lesions 0.2 mm in size and was used to follow cancer growth with serial imaging in living mice.</p> <p>Conclusion</p> <p>In conclusion, each technique enabled serial imaging of living mammary tissue and visualization of growth and development, quickly and with minimal tissue preparation. The use of the higher resolution reflectance confocal and green fluorescent protein imaging techniques and lower resolution ultrasound were complementary.</p