arXiv subjects
Publications and source records attributed to Adam Coffman.
For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.
Personalized neoantigen vaccines represent a promising immunotherapy approach that harnesses tumor-specific antigens to stimulate anti-tumor immune responses. However, the design of these vaccines requires sophisticated computational workflows to predict and prioritize neoantigen candidates from patient sequencing data, coupled with rigorous review to ensure candidate quality. While numerous computational tools exist for neoantigen prediction, to our knowledge, there are no established protocols detailing the complete process from raw sequencing data through systematic candidate selection. Here, we present ImmunoNX (Immunogenomics Neoantigen eXplorer), an end-to-end protocol for neoantigen prediction and vaccine design that has supported over 185 patients across 11 clinical trials. The workflow integrates tumor DNA/RNA and matched normal DNA sequencing data through a computational pipeline built with Workflow Definition Language (WDL) and executed via Cromwell on Google Cloud Platform. ImmunoNX employs consensus-based variant calling, in-silico HLA typing, and pVACtools for neoantigen prediction. Additionally, we describe a two-stage immunogenomics review process with prioritization of neoantigen candidates, enabled by pVACview, followed by manual assessment of variants using the Integrative Genomics Viewer (IGV). This workflow enables vaccine design in under three months. We demonstrate the protocol using the HCC1395 breast cancer cell line dataset, identifying 78 high-confidence neoantigen candidates from 322 initial predictions. Although demonstrated here for vaccine development, this workflow can be adapted for diverse neoantigen therapies and experiments. Therefore, this protocol provides the research community with a reproducible, version-controlled framework for designing personalized neoantigen vaccines, supported by detailed documentation, example datasets, and open-source code.
We establish a unique continuation property for solutions of the differential inequality $|\nabla u|\leq V|u|$, where $V$ is locally $L^n$ integrable on a domain in $\mathbb R^n$. A stronger uniqueness result is obtained if in addition the solutions are locally Lipschitz. One application is a finite order vanishing property in the $L^2$ sense for the exponential of $W^{1,n}$ functions. We further discuss related results for the Cauchy-Riemann operator $\bar\partial$ and characterize the vanishing order for smooth extension of holomorphic functions across the boundary.
Suppose that the inverse image of the zero vector by a continuous map $f:{\mathbb R}^n\to{\mathbb R}^q$ has an isolated point $P$. There is a local obstruction to removing this isolated zero by a small perturbation, generalizing the notion of index for vector fields, the $q=n$ case. The existence of a continuous map $g$ which approximates $f$ but is nonvanishing near $P$ is equivalent to a topological property we call "locally inessential," and for dimensions $n$, $q$ where $\pi_{n-1}(S^{q-1})$ is trivial, every isolated zero is locally inessential. We consider the problem of constructing such an approximation $g$, and show that there exists a continuous homotopy from $f$ to $g$ through locally nonvanishing maps. If $f$ is a semialgebraic map, then there exists such a homotopy which is also semialgebraic. For $q=2$ and $f$ real analytic with a locally inessential isolated zero, there exists a H\"older continuous homotopy $F(x,t)$ which, for $(x,t)\ne(P,0)$, is real analytic and nonvanishing. The existence of a smooth homotopy, given a smooth map $f$, is stated as an open question.
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the solution set can be explicitly calculated. The methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures.
For a certain class of configurations of points in space, Eves' Theorem gives a ratio of products of distances that is invariant under projective transformations, generalizing the cross-ratio for four points on a line. We give a generalization of Eves' theorem, which applies to a larger class of configurations and gives an invariant with values in a weighted projective space. We also show how the complex version of the invariant can be determined from classically known ratios of products of determinants, while the real version of the invariant can distinguish between configurations that the classical invariants cannot.
We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which vanishes to infinite order at the origin, and such that the ratio of the norm of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to infinite order. This gives a counterexample to strong unique continuation for a vector valued analogue of the Beltrami equation.
We consider some second order quasilinear partial differential inequalities for real valued functions on the unit ball and find conditions under which there is a lower bound for the supremum of nonnegative solutions that do not vanish at the origin. As a consequence, for complex valued functions $f(z)$ satisfying $\partial f/\partial\bar z=|f|^α$, $0<α<1$, and $f(0)\ne0$, there is also a lower bound for $\sup|f|$ on the unit disk. For each $α$, we construct a manifold with an $α$-Hölder continuous almost complex structure where the Kobayashi-Royden pseudonorm is not upper semicontinuous.
CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic coefficients determine an intersection index, which appears in global enumerative formulas for CR singularities of compact submanifolds.