Dynamic changes during the treatment of pancreatic cancer

This manuscript follows a single patient with pancreatic adenocarcinoma for a five year period, detailing the clinical record, pathology, the dynamic evolution of molecular and cellular alterations as well as the responses to treatments with chemotherapies, targeted therapies and immunotherapies. DNA and RNA samples from biopsies and blood identified a dynamic set of changes in allelic imbalances and copy number variations in response to therapies. Organoid cultures established from biopsies over time were employed for extensive drug testing to determine if this approach was feasible for treatments. When an unusual drug response was detected, an extensive RNA sequencing analysis was employed to establish novel mechanisms of action of this drug. Organoid cell cultures were employed to identify possible antigens associated with the tumor and the patient\u27s T-cells were expanded against one of these antigens. Similar and identical T-cell receptor sequences were observed in the initial biopsy and the expanded T-cell population. Immunotherapy treatment failed to shrink the tumor, which had undergone an epithelial to mesenchymal transition prior to therapy. A warm autopsy of the metastatic lung tumor permitted an extensive analysis of tumor heterogeneity over five years of treatment and surgery. This detailed analysis of the clinical descriptions, imaging, pathology, molecular and cellular evolution of the tumors, treatments, and responses to chemotherapy, targeted therapies, and immunotherapies, as well as attempts at the development of personalized medical treatments for a single patient should provide a valuable guide to future directions in cancer treatment

S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Transverse Spin Structure of the Nucleon through Target Single Spin Asymmetry in Semi-Inclusive Deep-Inelastic (e,e′π±)(e,e^\prime \pi^\pm) Reaction at Jefferson Lab

Jefferson Lab (JLab) 12 GeV energy upgrade provides a golden opportunity to perform precision studies of the transverse spin and transverse-momentum-dependent structure in the valence quark region for both the proton and the neutron. In this paper, we focus our discussion on a recently approved experiment on the neutron as an example of the precision studies planned at JLab. The new experiment will perform precision measurements of target Single Spin Asymmetries (SSA) from semi-inclusive electro-production of charged pions from a 40-cm long transversely polarized $^3$He target in Deep-Inelastic-Scattering kinematics using 11 and 8.8 GeV electron beams. This new coincidence experiment in Hall A will employ a newly proposed solenoid spectrometer (SoLID). The large acceptance spectrometer and the high polarized luminosity will provide precise 4-D ($x$, $z$, $P_T$ and $Q^2$) data on the Collins, Sivers, and pretzelocity asymmetries for the neutron through the azimuthal angular dependence. The full 2$\pi$ azimuthal angular coverage in the lab is essential in controlling the systematic uncertainties. The results from this experiment, when combined with the proton Collins asymmetry measurement and the Collins fragmentation function determined from the e$^+$e$^-$ collision data, will allow for a quark flavor separation in order to achieve a determination of the tensor charge of the d quark to a 10% accuracy. The extracted Sivers and pretzelocity asymmetries will provide important information to understand the correlations between the quark orbital angular momentum and the nucleon spin and between the quark spin and nucleon spin.Comment: 23 pages, 13 figures, minor corrections, matches published versio