On the Chromatic Thresholds of Hypergraphs

Let F be a family of r-uniform hypergraphs. The chromatic threshold of F is the infimum of all non-negative reals c such that the subfamily of F comprising hypergraphs H with minimum degree at least $c \binom{|V(H)|}{r-1}$ has bounded chromatic number. This parameter has a long history for graphs (r=2), and in this paper we begin its systematic study for hypergraphs. {\L}uczak and Thomass\'e recently proved that the chromatic threshold of the so-called near bipartite graphs is zero, and our main contribution is to generalize this result to r-uniform hypergraphs. For this class of hypergraphs, we also show that the exact Tur\'an number is achieved uniquely by the complete (r+1)-partite hypergraph with nearly equal part sizes. This is one of very few infinite families of nondegenerate hypergraphs whose Tur\'an number is determined exactly. In an attempt to generalize Thomassen's result that the chromatic threshold of triangle-free graphs is 1/3, we prove bounds for the chromatic threshold of the family of 3-uniform hypergraphs not containing {abc, abd, cde}, the so-called generalized triangle. In order to prove upper bounds we introduce the concept of fiber bundles, which can be thought of as a hypergraph analogue of directed graphs. This leads to the notion of fiber bundle dimension, a structural property of fiber bundles that is based on the idea of Vapnik-Chervonenkis dimension in hypergraphs. Our lower bounds follow from explicit constructions, many of which use a hypergraph analogue of the Kneser graph. Using methods from extremal set theory, we prove that these Kneser hypergraphs have unbounded chromatic number. This generalizes a result of Szemer\'edi for graphs and might be of independent interest. Many open problems remain.Comment: 37 pages, 4 figure

Revolutionaries and spies: Spy-good and spy-bad graphs

We study a game on a graph $G$ played by $r$ {\it revolutionaries} and $s$ {\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever. Let $\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume |V(G)|\ge r-m+1\ge\floor{r/m}\ge 1. The easy bounds are then \floor{r/m}\le \sigma(G,m,r)\le r-m+1. We prove that the lower bound is sharp when $G$ has a rooted spanning tree $T$ such that every edge of $G$ not in $T$ joins two vertices having the same parent in $T$. As a consequence, \sigma(G,m,r)\le\gamma(G)\floor{r/m}, where $\gamma(G)$ is the domination number; this bound is nearly sharp when $\gamma(G)\le m$. For the random graph with constant edge-probability $p$, we obtain constants $c$ and $c'$ (depending on $m$ and $p$) such that $\sigma(G,m,r)$ is near the trivial upper bound when $r<c\ln n$ and at most $c'$ times the trivial lower bound when $r>c'\ln n$. For the hypercube $Q_d$ with $d\ge r$, we have $\sigma(G,m,r)=r-m+1$ when $m=2$, and for $m\ge 3$ at least $r-39m$ spies are needed. For complete $k$-partite graphs with partite sets of size at least $2r$, the leading term in $\sigma(G,m,r)$ is approximately $\frac{k}{k-1}\frac{r}{m}$ when $k\ge m$. For $k=2$, we have \sigma(G,2,r)=\bigl\lceil{\frac{\floor{7r/2}-3}5}\bigr\rceil and \sigma(G,3,r)=\floor{r/2}, and in general $\frac{3r}{2m}-3\le \sigma(G,m,r)\le\frac{(1+1/\sqrt3)r}{m}$.Comment: 34 pages, 2 figures. The most important changes in this revision are improvements of the results on hypercubes and random graphs. The proof of the previous hypercube result has been deleted, but the statement remains because it is stronger for m<52. In the random graph section we added a spy-strategy resul

The effect of processing load on loss of information from short-term memory.

We report an experiment in which we varied the nature of the articulatory suppression task being performed during a filled retention interval in serial recall. During the retention interval participants performed one of three computer-paced colour naming tasks designed to prevent subvocal rehearsal: A Stroop color-interference task with items presented at a rate of one every 750 ms, and two color-consistent control tasks at a rate of either 750 ms or 500 ms per item. Memory performance over a 12 s interval declined much more dramatically with the Stroop task and the 500 ms control task than with the 750 ms control. There was no difference between the Stroop condition and the 500 ms control. These results pose problems for models that assume that loss of information from memory is determined entirely by interference, as there are more interfering events in the control 500 ms condition than the 750 ms Stroop. They also pose problems for models relying solely on time-based decay and articulatory rehearsal because all three conditions should block rehearsal and produce equivalent performance. The results illustrate that articulatory suppression tasks are not all equivalent, and suggest that the rate of decay from short-term memory is strongly influenced by the resource demands of concurrent processing

A Model and Test of Individual and Organization Factors Influencing Individual Adaptation to Change

This study analyzed the antecedents and outcomes of individual adaptation to a changing work environment. We developed and tested a model of both individual factors and organizational factors affecting individual responses to change. We hypothesized that individuals reporting higher levels of the antecedent variables would also report higher levels of adaptability. We also hypothesized better adaptors would perceive better work outcomes. The model was tested in a field study of 169 participants across four different organizations experiencing varying changes. Results indicated participation, role clarity, and optimism were positively related to adaptability. Further, we found that better adaptors were more satisfied with their jobs, were less likely to quit the organization, and perceived higher performance after the change. Change managers can take heart in that most of the variables associated with successful adaptation are under the organization’s influence, so facilitating change is not an impossible task

The Optical Green Valley Versus Mid-infrared Canyon in Compact Groups

Compact groups of galaxies provide conditions similar to those experienced by galaxies in the earlier universe. Recent work on compact groups has led to the discovery of a dearth of mid-infrared transition galaxies (MIRTGs) in Infrared Array Camera (3.6-8.0 micrometers) color space as well as at intermediate specific star formation rates. However, we find that in compact groups these MIRTGs have already transitioned to the optical ([gr]) red sequence. We investigate the optical color-magnitude diagram (CMD) of 99 compact groups containing 348 galaxies and compare the optical CMD with mid-infrared (mid-IR) color space for compact group galaxies. Utilizing redshifts available from Sloan Digital Sky Survey, we identified new galaxy members for four groups. By combining optical and mid-IR data, we obtain information on both the dust and the stellar populations in compact group galaxies. We also compare with more isolated galaxies and galaxies in the Coma Cluster, which reveals that, similar to clusters, compact groups are dominated by optically red galaxies. While we find that compact group transition galaxies lie on the optical red sequence, LVL (Local Volume Legacy) + (plus) SINGS (Spitzer Infrared Nearby Galaxies Survey) mid-IR (infrared) transition galaxies span the range of optical colors. The dearth of mid-IR transition galaxies in compact groups may be due to a lack of moderately star-forming low mass galaxies; the relative lack of these galaxies could be due to their relatively small gravitational potential wells. This makes them more susceptible to this dynamic environment, thus causing them to more easily lose gas or be accreted by larger members

Pilot trial of a type I - polarized autologous dendritic cell vaccine incorporating tumor blood vessel antigen-derived peptides in patients with metastatic breast cancer

Cancer vaccines based on tumor-associated antigens are rarely curative in advanced cancer. This limitation relates to the heterogeneity of cancer due to defects in antigen presentation and altered immunophenotypes. Therefore, another method to promote anti-tumor immunity is to prime T cells against tumor-associated stromal cells. We have reported [1] that IL-12 gene therapy of established HLA-A2neg B16 melanomas in HLA-A2+ transgenic mice resulted in CD8+ T cell-mediated immunity against the host HLA-A2+ stromal cells within the tumor microenvironment (TME). We have also shown [2] that vaccines based on a subset of tumor blood vessel antigen (TBVA)-derived peptides (DLK1, EphA2, HBB, NRP1, PDGFRβ, RGS5 or TEM1) prevented HLA-A2neg MC38 tumor establishment and promoted the regression of tumors in HLA-A2+ mice by CD8+ T cell targeting of HLA-A2+ pericytes and vascular endothelial cells in the TME. Based on this pre-clinical data, we propose to undertake a Susan G. Komen -funded (IIR13261822) clinical trial of chemo-immunotherapy using the immunomodulatory drug gemcitabine with a dendritic cell vaccine pulsed with six HLA-A2-presented TBVA-derived peptides (DLK1310-318, EphA2883-891, HBB31-39, NRP1433-441, RGS55-13 and TEM1691-700) in 30 HLA-A2+ patients with metastatic breast cancer. The specific aims of this study are to determine vaccine-induced generation of TBVA-Tc1 immunity and clinical response

Efficiency and safety of varying the frequency of whole blood donation (INTERVAL): a randomised trial of 45 000 donors

Background: Limits on the frequency of whole blood donation exist primarily to safeguard donor health. However, there is substantial variation across blood services in the maximum frequency of donations allowed. We compared standard practice in the UK with shorter inter-donation intervals used in other countries. Methods: In this parallel group, pragmatic, randomised trial, we recruited whole blood donors aged 18 years or older from 25 centres across England, UK. By use of a computer-based algorithm, men were randomly assigned (1:1:1) to 12-week (standard) versus 10-week versus 8-week inter-donation intervals, and women were randomly assigned (1:1:1) to 16-week (standard) versus 14-week versus 12-week intervals. Participants were not masked to their allocated intervention group. The primary outcome was the number of donations over 2 years. Secondary outcomes related to safety were quality of life, symptoms potentially related to donation, physical activity, cognitive function, haemoglobin and ferritin concentrations, and deferrals because of low haemoglobin. This trial is registered with ISRCTN, number ISRCTN24760606, and is ongoing but no longer recruiting participants. Findings: 45 263 whole blood donors (22 466 men, 22 797 women) were recruited between June 11, 2012, and June 15, 2014. Data were analysed for 45 042 (99·5%) participants. Men were randomly assigned to the 12-week (n=7452) versus 10-week (n=7449) versus 8-week (n=7456) groups; and women to the 16-week (n=7550) versus 14-week (n=7567) versus 12-week (n=7568) groups. In men, compared with the 12-week group, the mean amount of blood collected per donor over 2 years increased by 1·69 units (95% CI 1·59–1·80; approximately 795 mL) in the 8-week group and by 0·79 units (0·69–0·88; approximately 370 mL) in the 10-week group (p&lt;0·0001 for both). In women, compared with the 16-week group, it increased by 0·84 units (95% CI 0·76–0·91; approximately 395 mL) in the 12-week group and by 0·46 units (0·39–0·53; approximately 215 mL) in the 14-week group (p&lt;0·0001 for both). No significant differences were observed in quality of life, physical activity, or cognitive function across randomised groups. However, more frequent donation resulted in more donation-related symptoms (eg, tiredness, breathlessness, feeling faint, dizziness, and restless legs, especially among men [for all listed symptoms]), lower mean haemoglobin and ferritin concentrations, and more deferrals for low haemoglobin (p&lt;0·0001 for each) than those observed in the standard frequency groups. Interpretation: Over 2 years, more frequent donation than is standard practice in the UK collected substantially more blood without having a major effect on donors' quality of life, physical activity, or cognitive function, but resulted in more donation-related symptoms, deferrals, and iron deficiency. Funding: NHS Blood and Transplant, National Institute for Health Research, UK Medical Research Council, and British Heart Foundation