A Centre-Stable Manifold for the Focussing Cubic NLS in R1+3R^{1+3}

Consider the focussing cubic nonlinear Schr\"odinger equation in $R^3$: $$i\psi_t+\Delta\psi = -|\psi|^2 \psi.$$ It admits special solutions of the form $e^{it\alpha}\phi$, where $\phi$ is a Schwartz function and a positive ($\phi>0$) solution of $$-\Delta \phi + \alpha\phi = \phi^3.$$ The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form $e^{i(v \cdot + \Gamma)} \phi(\cdot - y, \alpha)$. We prove that any solution starting sufficiently close to a standing wave in the $\Sigma = W^{1, 2}(R^3) \cap |x|^{-1}L^2(R^3)$ norm and situated on a certain codimension-one local Lipschitz manifold exists globally in time and converges to a point on the manifold of standing waves. Furthermore, we show that \mc N is invariant under the Hamiltonian flow, locally in time, and is a centre-stable manifold in the sense of Bates, Jones. The proof is based on the modulation method introduced by Soffer and Weinstein for the $L^2$-subcritical case and adapted by Schlag to the $L^2$-supercritical case. An important part of the proof is the Keel-Tao endpoint Strichartz estimate in $R^3$ for the nonselfadjoint Schr\"odinger operator obtained by linearizing around a standing wave solution.Comment: 56 page

Examining the effect of Libet clock stimulus parameters on temporal binding

Temporal binding refers to the subjective temporal compression between actions and their outcomes. It is widely used as an implicit measure of sense of agency, that is, the experience of controlling our actions and their consequences. One of the most common measures of temporal binding is the paradigm developed by Haggard, Clark and Kalogeras (2002) based on the Libet clock stimulus. Although widely used, it is not clear how sensitive the temporal binding effect is to the parameters of the clock stimulus. Here, we present five experiments examining the effects of clock speed, number of clock markings and length of the clock hand on binding. Our results show that the magnitude of temporal binding increases with faster clock speeds, whereas clock markings and clock hand length do not significantly influence temporal binding. We discuss the implications of these results

Archaeoseismology: Methodological issues and procedure

Archaeoseismic research contributes important data on past earthquakes. A limitation of the usefulness of archaeoseismology is due to the lack of continuous discussion about the methodology. The methodological issues are particularly important because archaeoseismological investigations of past earthquakes make use of a large variety of methods. Typical in situ investigations include: (1) reconstruction of the local archaeological stratigraphy aimed at defining the correct position and chronology of a destruction layer, presumably related to an earthquake; (2) analysis of the deformations potentially due to seismic shaking or secondary earthquake effects, detectable on walls; (3) analysis of the depositional characteristics of the collapsed material; (4) investigations of the local geology and geomorphology to define possible natural cause(s) of the destruction; (5) investigations of the local factors affecting the ground motion amplifications; and (6) estimation of the dynamic excitation, which affected the site under investigation. Subsequently, a 'territorial' approach testing evidence of synchronous destruction in a certain region may delineate the extent of the area struck by the earthquake. The most reliable results of an archaeoseismological investigation are obtained by application of modern geoarchaeological practice (archaeological stratigraphy plus geological–geomorphological data), with the addition of a geophysical-engineering quantitative approach and (if available) historical information. This gives a basic dataset necessary to perform quantitative analyses which, in turn, corroborate the archaeoseismic hypothesis. Since archaeoseismological investigations can reveal the possible natural causes of destruction at a site, they contribute to the wider field of environmental archaeology, that seeks to define the history of the relationship between humans and the environment. Finally, through the improvement of the knowledge on the past seismicity, these studies can contribute to the regional estimation of seismic hazard

High-resolution analysis of HLA class I alterations in colorectal cancer

BACKGROUND: Previous studies indicate that alterations in Human Leukocyte Antigen (HLA) class I expression are frequent in colorectal tumors. This would suggest serious limitations for immunotherapy-based strategies involving T-cell recognition. Distinct patterns of HLA surface expression might conceal different immune escape mechanisms employed by the tumors and are worth further study. METHOD: We applied four-color multiparameter flow cytometry (FCM), using a large panel of alloantigen-specific anti-HLA-A and -B monoclonal antibodies, to study membranous expression of individual HLA alleles in freshly isolated colorectal cancer cell suspensions from 21 patients. RESULTS: Alterations in HLA class I phenotype were observed in 8 (38%) of the 21 tumors and comprised loss of a single A or B alleles in 4 cases, and loss of all four A and B alleles in the other 4 cases. Seven of these 8 tumors were located on the right side of the colon, and those showing loss of both HLA-A and -B membranous expression were all of the MSI-H phenotype. CONCLUSION: FCM allows the discrimination of complex phenotypes related to the expression of HLA class I. The different patterns of HLA class I expression might underlie different tumor behavior and influence the success rate of immunotherapy