Traveling dark-bright solitons in a reduced spin-orbit coupled system: application to Bose-Einstein condensates

In the present work, we explore the potential of spin-orbit (SO) coupled Bose-Einstein condensates to support multi-component solitonic states in the form of dark-bright (DB) solitons. In the case where Raman linear coupling between components is absent, we use a multiscale expansion method to reduce the model to the integrable Mel'nikov system. The soliton solutions of the latter allow us to reconstruct approximate traveling DB solitons for the reduced SO coupled system. For small values of the formal perturbation parameter, the resulting waveforms propagate undistorted, while for large values thereof, they shed some dispersive radiation, and subsequently distill into a robust propagating structure. After quantifying the relevant radiation effect, we also study the dynamics of DB solitons in a parabolic trap, exploring how their oscillation frequency varies as a function of the bright component mass and the Raman laser wavenumber

Molecular classification of breast cancer tumors according to histological grade (H1, H2, and H3) by tumor tissue protein expression profiling, using recombinant scFv antibody microarrays.

<p>Unfiltered data was used in all analysis. A) A ROC curve and AUC value obtained for H1 vs. H3, using a LOOC SVM (left panel). A PCA plot for H1 vs. H3 (right panel). B) A ROC curve and AUC value obtained for H1 vs. H2, using a LOOC SVM (left panel). A PCA plot for H1 vs. H2 (right panel). C) A ROC curve and AUC value obtained for H1 vs. H3, using a LOOC SVM (left panel). A PCA plot for H2 vs. H3 (right panel).</p

Validation of antibody microarray data using an orthogonal method (ELISA).

<p>A) Histological grade 1 vs. 2 based on ELISA data (left panel) and antibody microarray data (right panel). B) Histological grade 2 vs. 3, based on ELISA data (left panel) and antibody microarray data (right panel). C) Histological grade 1 vs. 3, based on ELISA data (left panel) and antibody microarray data (right panel). In all comparisons, a Welsh t-test was used to evaluate the level of significance.</p

Patient demographics and clinical parameters.

<p>Patient demographics and clinical parameters.</p

Significant analytes from SVM leave one out cross validation on unfiltered data for H2 vs. H3.

<p>Significant analytes from SVM leave one out cross validation on unfiltered data for H2 vs. H3.</p

First model for refined molecular grading of breast cancer.

<p>A) Backward elimination analysis of the data set (grade 1 and grade 3 tumors), resulting in a condensed signature of 20 antibodies (indicated by an arrow). The panel of antibodies (specificities) are shown (in order of last removed antibody). B) A frozen SVM classification model was generated using the 20-plex antibody panel in A, based on all grade 1 and 3 tumors. The grade 2 tumors were then applied as test set. The resulting classification decision values are shown, where tumors with values ≥ 0.5 are defined as being more similar grade 1 tumors, 0.5 to -0.5 is defined as a grey zone (i.e. grade 2 tumors), and ≤ -0.5 are defined as being more similar to grade 3 tumors. C) The decision values for the grade 1 and grade 3 tumors used to build the SVM model are plotted. The same arbitrary cut-off as in B) is indicated (dashed line).</p