A field-theoretic approach to the Wiener Sausage

The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome.Comment: 45 pages, 3 Figures, Springer styl

A framework for ETH-Tight algorithms and lower bounds in geometric intersection graphs

We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to a wide range of geometric intersection graphs (intersections of similarly sized fat objects), yielding algorithms with running time 2O(n1−1/d) for any fixed dimension d ≥ 2 for many well known graph problems, including Independent Set, r-Dominating Set for constant r, and Steiner Tree. For most problems, we get improved running times compared to prior work; in some cases, we give the first known subexponential algorithm in geometric intersection graphs. Additionally, most of the obtained algorithms work on the graph itself, i.e., do not require any geometric information. Our algorithmic framework is based on a weighted separator theorem and various treewidth techniques. The lower bound framework is based on a constructive embedding of graphs into d-dimensional grids, and it allows us to derive matching 2Ω(n1−1/d) lower bounds under the Exponential Time Hypothesis even in the much more restricted class of d-dimensional induced grid graphs

Does shear wave ultrasound independently predict axillary lymph node metastasis in women with invasive breast cancer?

Shear wave elastography (SWE) shows promise as an adjunct to greyscale ultrasound examination in assessing breast masses. In breast cancer, higher lesion stiffness on SWE has been shown to be associated with features of poor prognosis. The purpose of this study was to assess whether lesion stiffness at SWE is an independent predictor of lymph node involvement. Patients with invasive breast cancer treated by primary surgery, who had undergone SWE examination were eligible. Data were retrospectively analysed from 396 consecutive patients. The mean stiffness values were obtained using the Aixplorer(®) ultrasound machine from SuperSonic Imagine Ltd. Measurements were taken from a region of interest positioned over the stiffest part of the abnormality. The average of the mean stiffness value obtained from each of two orthogonal image planes was used for analysis. Associations between lymph node involvement and mean lesion stiffness, invasive cancer size, histologic grade, tumour type, ER expression, HER-2 status and vascular invasion were assessed using univariate and multivariate logistic regression. At univariate analysis, invasive size, histologic grade, HER-2 status, vascular invasion, tumour type and mean stiffness were significantly associated with nodal involvement. Nodal involvement rates ranged from 7 % for tumours with mean stiffness <50 kPa to 41 % for tumours with a mean stiffness of >150 kPa. At multivariate analysis, invasive size, tumour type, vascular invasion, and mean stiffness maintained independent significance. Mean stiffness at SWE is an independent predictor of lymph node metastasis and thus can confer prognostic information additional to that provided by conventional preoperative tumour assessment and staging

Lactate Regulates Metabolic and Proinflammatory Circuits in Control of T Cell Migration and Effector Functions

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Transplanckian axions !?

We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: Single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range. A similar result holds for multi-axion models with lattice alignment (like the Kim-Nilles-Peloso model). Finally, theories with $N$ axions can still achieve a moderately superplanckian periodicity (by a $\sqrt{N}$ factor) with no higher harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in this case due to the absence of some instantons, which are forbidden by a discrete $\mathbf{Z}_N$ gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications.Comment: 46 pages, 6 figures. Added references, clarifications, and missing factor of 1/2 to instanton action. Conclusions unchange

D-brane potentials in the warped resolved conifold and natural inflation

In this paper we obtain a model of Natural Inflation from string theory with a Planckian decay constant. We investigate D-brane dynamics in the background of the warped resolved conifold (WRC) throat approximation of Type IIB string compactifications on Calabi-Yau manifolds. When we glue the throat to a compact bulk Calabi-Yau, we generate a D-brane potential which is a solution to the Laplace equation on the resolved conifold. We can exactly solve this equation, including dependence on the angular coordinates. The solutions are valid down to the tip of the resolved conifold, which is not the case for the more commonly used deformed conifold. This allows us to exploit the effect of the warping, which is strongest at the tip. We inflate near the tip using an angular coordinate of a D5-brane in the WRC which has a discrete shift symmetry, and feels a cosine potential, giving us a model of Natural Inflation, from which it is possible to get a Planckian decay constant whilst maintaining control over the backreaction. This is because the decay constant for a wrapped brane contains powers of the warp factor, and so can be made large, while the wrapping parameter can be kept small enough so that backreaction is under control.Comment: 41 pages, 3 appendices, 1 figure, PDFLaTex; various clarifications added along with a new appendix on b-axions and wrapped D5 branes;version matches the one published in JHE

MDM2 antagonist Nutlin-3a potentiates antitumour activity of cytotoxic drugs in sarcoma cell lines

<p>Abstract</p> <p>Background</p> <p>Frequent failure and severe side effects of current sarcoma therapy warrants new therapeutic approaches. The small-molecule MDM2 antagonist Nutlin-3a activates the p53 pathway and efficiently induces apoptosis in tumours with amplified <it>MDM2 </it>gene and overexpression of MDM2 protein. However, the majority of human sarcomas have normal level of MDM2 and the therapeutic potential of MDM2 antagonists in this group is still unclear. We have investigated if Nutlin-3a could be employed to augment the response to traditional therapy and/or reduce the genotoxic burden of chemotherapy.</p> <p>Methods</p> <p>A panel of sarcoma cell lines with different <it>TP53 </it>and <it>MDM2 </it>status were treated with Nutlin-3a combined with Doxorubicin, Methotrexate or Cisplatin, and their combination index determined.</p> <p>Results</p> <p>Clear synergism was observed when Doxorubicin and Nutlin-3a were combined in cell lines with wild-type <it>TP53 </it>and amplified <it>MDM2</it>, or with Methotrexate in both <it>MDM2 </it>normal and amplified sarcoma cell lines, allowing for up to tenfold reduction of cytotoxic drug dose. Interestingly, Nutlin-3a seemed to potentiate the effect of classical drugs as Doxorubicin and Cisplatin in cell lines with mutated <it>TP53</it>, but inhibited the effect of Methotrexate.</p> <p>Conclusion</p> <p>The use of Nutlin in combination with classical sarcoma chemotherapy shows promising preclinical potential, but since clear biomarkers are still lacking, clinical trials should be followed up with detailed tumour profiling.</p

Histopathological evaluation of thrombus in patients presenting with stent thrombosis. A multicenter European study: a report of the prevention of late stent thrombosis by an interdisciplinary global European effort consortium

Background Stent thrombosis (ST) is a rare but serious complication following percutaneous coronary intervention. Analysis of thrombus composition from patients undergoing catheter thrombectomy may provide important insights into the pathological processes leading to thrombus formation. We performed a large-scale multicentre study to evaluate thrombus specimens in patients with ST across Europe. Methods Patients presenting with ST and undergoing thrombus aspiration were eligible for inclusion. Thrombus collection was performed according to a standardized protocol and specimens were analysed histologically at a core laboratory. Serial tissue cross sections were stained with haematoxylin–eosin (H&E), Carstairs and Luna. Immunohistochemistry was performed to identify leukocyte subsets, prothrombotic neutrophil extracellular traps (NETs), erythrocytes, platelets, and fibrinogen. Results Overall 253 thrombus specimens were analysed; 79 (31.2%) from patients presenting with early ST, 174 (68.8%) from late ST; 79 (31.2%) were from bare metal stents, 166 (65.6%) from drug-eluting stents, 8 (3.2%) were from stents of unknown type. Thrombus specimens displayed heterogeneous morphology with platelet-rich thrombus and fibrin/fibrinogen fragments most abundant; mean platelet coverage was 57% of thrombus area. Leukocyte infiltrations were hallmarks of both early and late ST (early: 2260 ± 1550 per mm2 vs. late: 2485 ± 1778 per mm2; P = 0.44); neutrophils represented the most prominent subset (early: 1364 ± 923 per mm2 vs. late: 1428 ± 1023 per mm2; P = 0.81). Leukocyte counts were significantly higher compared with a control group of patients with thrombus aspiration in spontaneous myocardial infarction. Neutrophil extracellular traps were observed in 23% of samples. Eosinophils were present in all stent types, with higher numbers in patients with late ST in sirolimus-and everolimus-eluting stents. Conclusion In a large-scale study of histological thrombus analysis from patients presenting with ST, thrombus specimens displayed heterogeneous morphology. Recruitment of leukocytes, particularly neutrophils, appears to be a hallmark of ST. The presence of NETs supports their pathophysiological relevance. Eosinophil recruitment suggests an allergic component to the process of ST