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

Western blot of primary breast cancer-associated fibroblasts (CAFs).

<p>CAFs are derived from patients with ERα-positive breast cancer and have been cultured in serumfree media to allow detection of basal ERK phosphorylation levels (lower band: ERK2 42kDa, upper band: ERK1 44kDa).</p

Kaplan-Meier plots.

<p>Recurrence-free survival according to CAF-pERK level (A-C) and CAF-SMAα expression (D-F) of patients in cohort I (ERα-positive patients). Plots represent prognostic (A, D) or tamoxifen treatment-predictive information (B, C and E, F) (<i>P</i>-value: Univariate Cox regression, HR: Hazard Ratio, CI: Confidence Interval, RFS: Recurrence-Free Survival).</p

Prognostic and molecular parameters.

1<p>Mann-Whitney <i>U</i>,</p>2<p>Pearson’s chi-square,</p>3<p>Spearman.</p><p>Distribution of CAF-pERK staining categorization according to clinico-pathological and molecular characteristics. (CAF: Cancer-associated fibroblasts, percentages in parenthesis).</p

Patient and tumor characteristics in relation to AIB1.

<p>Patient and tumor characteristics in relation to AIB1.</p

Prognosis after CBC in relation to AIB1-status of BC2.

<p>Prognosis after CBC in relation to AIB1-status of BC2.</p

Flow-chart of inclusion <i>vs</i>. exclusion in the study cohort.

<p>In analysis 36 patients with a local/regional recurrence of BC1 before diagnosis of BC2 were excluded in order not to confuse the results by eventual treatment given for the recurrence. We also excluded 3 patients with ambiguous distant metastasis-status and 1 patient with BC2 diagnosed at autopsy. Abbreviations: AIB1 <i>Amplified in breast cancer 1</i>, BC1 f<i>irst breast cancer</i>, BC2 <i>second breast cancer</i>, TMA <i>tissue microarray</i></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

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