A 2-chain can interlock with a k-chain

One of the open problems posed in [3] is: what is the minimal number k such that an open, flexible k-chain can interlock with a flexible 2-chain? In this paper, we establish the assumption behind this problem, that there is indeed some k that achieves interlocking. We prove that a flexible 2-chain can interlock with a flexible, open 16-chain.Comment: 10 pages, 6 figure

The parameterized complexity of some geometric problems in unbounded dimension

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in \Rd, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in \Rd, decide whether they can be separated by two hyperplanes. iii) Given a system of $n$ linear inequalities with $d$ variables, find a maximum-size feasible subsystem. We show that (the decision versions of) all these problems are W[1]-hard when parameterized by the dimension $d$. %and hence not solvable in ${O}(f(d)n^c)$ time, for any computable function $f$ and constant $c$ %(unless FPT=W[1]). Our reductions also give a $n^{\Omega(d)}$-time lower bound (under the Exponential Time Hypothesis)

A polynomial bound for untangling geometric planar graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput. Geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed. We answer this question in the affirmative with \epsilon=1/4. The previous best known bound was \Omega((\log n / \log\log n)^{1/2}). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was O(n\log n)^{2/3}. We answer a question of Spillner and Wolff [arXiv:0709.0170 2007] by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than 3(n^{1/2}-1) vertices fixed. Moreover, we improve the lower bound to (n/2)^{1/2}.Comment: 14 pages, 7 figure

Identification and single-cell functional characterization of an endodermally biased pluripotent substate in human embryonic stem cells

Human embryonic stem cells (hESCs) display substantial heterogeneity in gene expression, implying the existence of discrete substates within the stem cell compartment. To determine whether these substates impact fate decisions of hESCs we used a GFP reporter line to investigate the properties of fractions of putative undifferentiated cells defined by their differential expression of the endoderm transcription factor, GATA6, together with the hESC surface marker, SSEA3. By single-cell cloning, we confirmed that substates characterized by expression of GATA6 and SSEA3 include pluripotent stem cells capable of long-term self-renewal. When clonal stem cell colonies were formed from GATA6-positive and GATA6-negative cells, more of those derived from GATA6-positive cells contained spontaneously differentiated endoderm cells than similar colonies derived from the GATA6-negative cells. We characterized these discrete cellular states using single-cell transcriptomic analysis, identifying a potential role for SOX17 in the establishment of the endoderm-biased stem cell state

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Feasibility of Tomotherapy-Based Image-Guided Radiotherapy to Reduce Aspiration Risk in Patients with Non-Laryngeal and Non-Pharyngeal Head and Neck Cancer

PURPOSE: The study aims to assess the feasibility of Tomotherapy-based image-guided radiotherapy (IGRT) to reduce the aspiration risk in patients with non-laryngeal and non-hypopharyngeal cancer. A retrospective review of 48 patients undergoing radiation for non-laryngeal and non-hypopharyngeal head and neck cancers was conducted. All patients had a modified barium swallow (MBS) prior to treatment, which was repeated one month following radiotherapy. Mean middle and inferior pharyngeal dose was recorded and correlated with the MBS results to determine aspiration risk. RESULTS: Mean pharyngeal dose was 23.2 Gy for the whole group. Two patients (4.2%) developed trace aspiration following radiotherapy which resolved with swallowing therapy. At a median follow-up of 19 months (1-48 months), all patients were able to resume normal oral feeding without aspiration. CONCLUSION AND CLINICAL RELEVANCE: IGRT may reduce the aspiration risk by decreasing the mean pharyngeal dose in the presence of large cervical lymph nodes. Further prospective studies with IGRT should be performed in patients with non-laryngeal and non-hypopharyngeal head and neck cancers to verify this hypothesis

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005]

Transduction of Human T Cells with a Novel T-Cell Receptor Confers Anti-HCV Reactivity

Hepatitis C Virus (HCV) is a major public health concern, with no effective vaccines currently available and 3% of the world's population being infected. Despite the existence of both B- and T-cell immunity in HCV-infected patients, chronic viral infection and HCV-related malignancies progress. Here we report the identification of a novel HCV TCR from an HLA-A2-restricted, HCV NS3:1073–1081-reactive CTL clone isolated from a patient with chronic HCV infection. We characterized this HCV TCR by expressing it in human T cells and analyzed the function of the resulting HCV TCR-transduced cells. Our results indicate that both the HCV TCR-transduced CD4+ and CD8+ T cells recognized the HCV NS3:1073–1081 peptide-loaded targets and HCV+ hepatocellular carcinoma cells (HCC) in a polyfunctional manner with cytokine (IFN-γ, IL-2, and TNF-α) production as well as cytotoxicity. Tumor cell recognition by HCV TCR transduced CD8− Jurkat cells and CD4+ PBL-derived T cells indicated this TCR was CD8-independent, a property consistent with other high affinity TCRs. HCV TCR-transduced T cells may be promising for the treatment of patients with chronic HCV infections

Contemporary management of primary parapharyngeal space tumors

The parapharyngeal space is a complex anatomical area. Primary parapharyngeal tumors are rare tumors and 80% of them are benign. A variety of tumor types can develop in this location; most common are salivary gland neoplasm and neurogenic tumors. The management of these tumors has improved greatly owing to the developments in imaging techniques, surgery, and radiotherapy. Most tumors can be removed with a low rate of complications and recurrence. The transcervical approach is the most frequently used. In some cases, minimally invasive approaches may be used alone or in combination with a limited transcervical route, allowing large tumors to be removed by reducing morbidity of expanded approaches. An adequate knowledge of the anatomy and a careful surgical plan is essential to tailor management according to the patient and the tumor. The purpose of the present review was to update current aspects of knowledge related to this more challenging area of tumor occurrence.Peer reviewe