58 research outputs found
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
No full textThis work deals with free transport equations with partly di¤use sto-chastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in L 1 spaces: We prove convergence to equilibrium at the rate O t k 2(k+1)+1 (t ! +1) for L 1 initial data g in a suitable subspace of the domain of the generator T where k 2 N depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quanti…ed version of Ingham's tauberian theorem by showing that Fg(s) := lim"!0 + (is + " T) 1 g exists as a C k function on Rn f0g such that d j ds j Fg(s) C jsj 2(j+1) near s = 0 and bounded as jsj ! 1 (0 j k) : Various preliminary results of independent interest are given and some related open problems are pointed out
CDK4/6 Inhibitors: Promising Opportunities beyond Breast Cancer.
No full textPatnaik and colleagues report on the safety, pharmacokinetics, pharmacodynamics, and preliminary efficacy of abemaciclib for the treatment of advanced solid cancers, demonstrating antitumor activity in advanced breast cancers as well as glioblastoma, melanoma, non-small cell lung cancer, colorectal cancer, and ovarian cancer. The development of abemaciclib and other CDK4/6 inhibitors should now be fully optimized through the use of novel predictive biomarkers of response and rational combinations. Cancer Discov; 6(7); 697-9. ©2016 AACRSee related article by Patnaik et al., p. 740
Lower Order Perturbations of Critical Growth Nonlinearities in Semilinear Elliptic Equations
No full textThe solvability of semilinear elliptic equations with nonlinearities in the critical growth range depends on the terms with lower order growth. We generalize some known results to a wide class of lower order terms and prove a multiplicity result in the left neighborhood of every eigenvalue of \Gamma\Delta when the subcritical term is linear. The proofs are based on variational methods; to assure that the considered minimax levels lie in a suitable range, special classes of approximating functions having disjoint support with the Sobolev "concentrating" functions are constructed. 1 Introduction In this paper we consider the semilinear problem 8 ? ? ! ? ? : \Gamma\Deltau = g(x; u) + juj 2 \Gamma2 u in\Omega u = 0 on @\Omega (1) where \Omega ae IR n (n 3) is an open bounded domain with smooth boundary @ 2 = 2n n\Gamma2 is the critical Sobolev exponent, and g(\Delta; s) has subcritical growth at infinity (i.e. lim jsj!1 g(\Delta;s) jsj 2 \Gamma1 = 0). Consider the..
Applications of nonstandard analysis in additive number theory
No full textThis paper reports recent progress in applying nonstandard analysis to additive number theory, especially to problems involving upper Banach density. 1 Prologue In this paper we use N for the set of all natural numbers. For any two integers a and b, [a; b] denotes the interval of all integers x between a and b (a 6 x 6 b). If S is an internal set, jSj denotes the internal cardinality ofS. The letters A; B; C will be used for sets of natural numbers and the letters i; h; k; m; n will be used for natural numbers. For a set A of natural numbers, the Shnirel'man density (A), the lower density d(A), the upper density d(A) and the Banach density BD(A) ofA are de ned as follows. (A) =inf n>1 jA \ [1;n]j n jA \ [1;n]j d(A) = lim inf n!
Medidas biométricas envolvendo a porção terminal do ducto torácico no nível cervical IV à esquerda: um estudo anatômico
No full textBACKGROUND: During a neck dissection involving the left IV level, the final segment of the thoracic duct (TD) may be injured, significantly increasing postoperative morbi-mortality. The best treatment is its prevention. However, there is a lack of helpful biometric measurements focusing on the TD termination in the literature. MATERIALS AND METHODS: The TD termination was identified and some helpful biometric measurements were obtained on 25 non-preserved cadavers. Statistical analysis was performed to analyze correlations. RESULTS: TD termination was found on the jugulo-subclavian junction (JSJ - 60%), on the left internal jugular vein (LIJV - 36%), and on the left brachiocephalic vein in 4%. A statistically significant association was found between TD termination on the JSJ and the distance between LIJV and omohyoid muscle (Measurement #1). Individuals with TD termination on the JSJ had median Measurement #1 of 34.5±12.0mm, compared with median Measurement #1 of 22.3±8.7mm among individuals with TD termination on LIJV (p=0.015 – Student´s t-test). The logistic regression showed for every 10mm increment of Measurement #1 there was 1.12x chance to find the TD termination on the JSJ (OR=1.12; CI95%:1,01-1,25; p=0.032). A 19mm cut-off was established for this distance as a diagnostic test to predict the TD termination on the JSJ, with sensitivity of 86.7% (CI95%:59.5-98.3%), specificity of 55.6% (CI95%:21.2-86.3%), PPV of 76.5% (CI95%:50.1-93.2%), NPV of 71.4% (CI95%:25.8-97.2%) and ROC AUC of 79.3% (CI95%: 58.0-92.9%). CONCLUSION: This anatomic study demonstrated the most frequent TD termination was on JSJ and Measurement #1 is able to predict the localization of TD termination.INTRODUÇÃO: No esvaziamento cervical do nível IV à esquerda, a porção final do ducto torácico (DT) pode ser lesada, aumentando significativamente a morbimortalidade pós-operatória. O melhor tratamento é a prevenção. Contudo, não há disponível na literatura medidas biométricas que auxiliem a identificação da desembocadura do DT. MATERIAIS E MÉTODOS: a desembocadura do DT foi identificada e distâncias úteis foram medidas em 25 cadáveres não-formolizados. Análise estatística foi realizada para verificar associações. RESULTADOS: a desembocadura do DT ocorreu na confluência jugulo-subclávia (CJS – 60%), na veia jugular interna esquerda (VJIE – 36%) e na veia braquiocefálica esquerda (4%). Uma associação estatisticamente significante foi encontrada entre a desembocadura na confluência jugulo-subclávia e a distância entre a VJIE e o músculo omo-hioide (Medida #1). Indivíduos cujo DT desemboca na CJS apresentaram a Medida #1 com mediana de 34.5±12.0mm, já os com desembocadura na VJIE apresentaram mediana de 22.3±8.7mm (p=0.015 – Student´s t-test). A regressão logística demonstrou que para cada aumento de 10mm na Medida #1 há uma chance de 1.12x de encontrar a desembocadura do DT na CJS (OR=1.12; CI95%:1,01-1,25; p=0.032). Para essa Medida #1 estabeleceu-se um cut-off de 19mm como teste diagnóstico para prever a desembocadura do DT na CJS, com sensibilidade de 86.7% (CI95%:59.5-98.3%), especificidade de 55.6% (CI95%:21.2-86.3%), PPV de 76.5% (CI95%:50.1-93.2%), NPV de 71.4% (CI95%:25.8-97.2%) e ROC AUC de 79.3% (CI95%: 58.0-92.9%). CONCLUSÃO: este estudo anatômico demonstrou que o local de desembocadura do DT mais frequente é a CJS e que a Medida #1 é capaz de prever o local de desembocadura do DT
Topics in Dehn surgery
No full textPh.D.Two Dehn surgeries on a knot are called purely cosmetic if the resulting manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in S3 do not admit purely cosmetic surgeries. In this thesis, we confirm this conjecture for cable knots and composite knots. The proof is based on an explicit analysis of the JSJ-structures of the Dehn surgered manifolds.一个扭结的两个Dehn手术被称为与"purely cosmetic" ，如果这两个Dehn手术产生的可定向流形是同胚的。Gordon猜想到，三维球面中的非平凡扭结都不存 在"purely cosmetic"的Dehn手术。在这篇论文中，我们对cable 扭结和复杂扭结证明这个猜想。这个证明基于对Dehn手术产生的流形的JSJ结构进行具体的分析。Tao, Ran.Thesis Ph.D. Chinese University of Hong Kong 2018.Includes bibliographical references (leaves 52-55).Abstracts also in Chinese.Title from PDF title page (viewed on …)
Towards Precision Medicine in the Clinic: From Biomarker Discovery to Novel Therapeutics.
No full textPrecision medicine continues to be the benchmark to which we strive in cancer research. Seeking out actionable aberrations that can be selectively targeted by drug compounds promises to optimize treatment efficacy and minimize toxicity. Utilizing these different targeted agents in combination or in sequence may further delay resistance to treatments and prolong antitumor responses. Remarkable progress in the field of immunotherapy adds another layer of complexity to the management of cancer patients. Corresponding advances in companion biomarker development, novel methods of serial tumor assessments, and innovative trial designs act synergistically to further precision medicine. Ongoing hurdles such as clonal evolution, intra- and intertumor heterogeneity, and varied mechanisms of drug resistance continue to be challenges to overcome. Large-scale data-sharing and collaborative networks using next-generation sequencing (NGS) platforms promise to take us further into the cancer 'ome' than ever before, with the goal of achieving successful precision medicine
Maintaining breast cancer care in the face of COVID-19
No full text10.1002/bjs.11835British Journal of Surgery107101245-124
Finiteness of 3-manifolds associated with non-zero degree mappings
No full text34 pages, 5 figuresInternational audienceWe prove a finiteness result for the -patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and -irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a given compact 3-manifold belong, up to homeomorphism, to a finite collection of compact 3-manifolds. We show also that any closed orientable 3-manifold dominates only finitely many integral homology spheres and any compact 3-manifolds orientable 3-manifold dominates only finitely many exterior of knots in
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