(n,m)-fold covers of spheres

A well-known consequence of the Borsuk-Ulam theorem is that if the d-dimensional sphere Sd is covered with less than d + 2 open sets, then there is a set containing a pair of antipodal points. In this paper we provide lower and upper bounds on the minimum number of open sets, not containing a pair of antipodal points, needed to cover the d-dimensional sphere n times, with the additional property that the northern hemisphere is covered m > n times. We prove that if the open northern hemisphere is to be covered m times, then at least ⌈(d − 1)/2⌉ + n + m and at most d + n + m sets are needed. For the case of n = 1 and d ≥ 2, this number is equal to d + 2 if m ≤ ⌊d/2⌋ + 1 and equal to ⌊(d − 1)/2⌋ + 2 + m if m > ⌊d/2⌋ + 1. If the closed northern hemisphere is to be covered m times, then d + 2m − 1 sets are needed; this number is also sufficient. We also present results on a related problem of independent interest. We prove that if Sd is covered n times with open sets not containing a pair of antipodal points, then there exists a point that is covered at least ⌈d/2⌉ + n times. Furthermore, we show that there are covers in which no point is covered more than n + d times. © 2015, Pleiades Publishing, Ltd

Rainbow polygons for colored point sets in the plane

Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let rb-index(S) denote the smallest size of a perfect rainbow polygon for a colored point set S, and let rb-index(k) be the maximum of rb-index(S) over all k-colored point sets in general position; that is, every k-colored point set S has a perfect rainbow polygon with at most rb-index(k) vertices. In this paper, we determine the values of rb-index(k) up to k=7, which is the first case where rb-index(k)¿k, and we prove that for k=5, [Formula presented] Furthermore, for a k-colored set of n points in the plane in general position, a perfect rainbow polygon with at most [Formula presented] vertices can be computed in O(nlogn) time. © 2021 Elsevier B.V

Atomistic Simulations of Nanotube Fracture

The fracture of carbon nanotubes is studied by atomistic simulations. The fracture behavior is found to be almost independent of the separation energy and to depend primarily on the inflection point in the interatomic potential. The rangle of fracture strians compares well with experimental results, but predicted range of fracture stresses is marketly higher than observed. Various plausible small-scale defects do not suffice to bring the failure stresses into agreement with available experimental results. As in the experiments, the fracture of carbon nanotubes is predicted to be brittle. The results show moderate dependence of fracture strength on chirality.Comment: 12 pages, PDF, submitted to Phy. Rev.

Ex vivo Inhibition of NF-κB Signaling in Alloreactive T-cells Prevents Graft-Versus-Host Disease

The ex vivo induction of alloantigen-specific hyporesponsiveness by costimulatory pathway blockade or exposure to immunoregulatory cytokines has been shown to inhibit proliferation, IL-2 production, and the GVHD capacity of adoptively transferred T-cells. We hypothesized that inhibition of the intracellular NF-κB pathway in alloreactive T-cells, which is critical for T cell activation events including IL-2 transcription, could lead to alloantigen hyporesponsiveness and loss of GVHD capacity. We demonstrate that treatment of mixed lymphocyte reaction (MLR) cultures with PS1145, a potent inhibitor of NF-κB activation, can induce T cell hyporesponsiveness to alloantigen in primary and secondary responses while preserving in vitro responses to potent mitogenic stimulation. GVHD lethality in recipients of ex vivo PS1145-treated cells was profoundly inhibited. Parking of control- or PS1145- treated MLR cells in syngeneic Rag−/− recipients resulted in intact contact hypersensitivity responses. However, GVHD lethality capacity also was restored, suggesting that lymphopenic expansion uncoupled alloantigen hyporesponsiveness. These results indicate that the NF-κB pathway is a critical regulator of alloresponses and provide a novel small molecule inhibitor based approach that is effective in preventing early post-transplant GVHD lethality but that also permits donor T cell responses to recover after a period of lymphopenic expansion

FOXP3 Expression Is Upregulated in CD4+T Cells in Progressive HIV-1 Infection and Is a Marker of Disease Severity

Understanding the role of different classes of T cells during HIV infection is critical to determining which responses correlate with protective immunity. To date, it is unclear whether alterations in regulatory T cell (Treg) function are contributory to progression of HIV infection.FOXP3 expression was measured by both qRT-PCR and by flow cytometry in HIV-infected individuals and uninfected controls together with expression of CD25, GITR and CTLA-4. Cultured peripheral blood mononuclear cells were stimulated with anti-CD3 and cell proliferation was assessed by CFSE dilution.HIV infected individuals had significantly higher frequencies of CD4(+)FOXP3(+) T cells (median of 8.11%; range 1.33%-26.27%) than healthy controls (median 3.72%; range 1.3-7.5%; P = 0.002), despite having lower absolute counts of CD4(+)FOXP3(+) T cells. There was a significant positive correlation between the frequency of CD4(+)FOXP3(+) T cells and viral load (rho = 0.593 P = 0.003) and a significant negative correlation with CD4 count (rho = -0.423 P = 0.044). 48% of our patients had CD4 counts below 200 cells/microl and these patients showed a marked elevation of FOXP3 percentage (median 10% range 4.07%-26.27%). Assessing the mechanism of increased FOXP3 frequency, we found that the high FOXP3 levels noted in HIV infected individuals dropped rapidly in unstimulated culture conditions but could be restimulated by T cell receptor stimulation. This suggests that the high FOXP3 expression in HIV infected patients is likely due to FOXP3 upregulation by individual CD4(+) T cells following antigenic or other stimulation.FOXP3 expression in the CD4(+) T cell population is a marker of severity of HIV infection and a potential prognostic marker of disease progression

Observing many researchers using the same data and hypothesis reveals a hidden universe of uncertainty

This study explores how researchers’ analytical choices affect the reliability of scientific findings. Most discussions of reliability problems in science focus on systematic biases. We broaden the lens to emphasize the idiosyncrasy of conscious and unconscious decisions that researchers make during data analysis. We coordinated 161 researchers in 73 research teams and observed their research decisions as they used the same data to independently test the same prominent social science hypothesis: that greater immigration reduces support for social policies among the public. In this typical case of social science research, research teams reported both widely diverging numerical findings and substantive conclusions despite identical start conditions. Researchers’ expertise, prior beliefs, and expectations barely predict the wide variation in research outcomes. More than 95% of the total variance in numerical results remains unexplained even after qualitative coding of all identifiable decisions in each team’s workflow. This reveals a universe of uncertainty that remains hidden when considering a single study in isolation. The idiosyncratic nature of how researchers’ results and conclusions varied is a previously underappreciated explanation for why many scientific hypotheses remain contested. These results call for greater epistemic humility and clarity in reporting scientific findings

The Crowdsourced Replication Initiative: Investigating Immigration and Social Policy Preferences. Executive Report.

In an era of mass migration, social scientists, populist parties and social movements raise concerns over the future of immigration-destination societies. What impacts does this have on policy and social solidarity? Comparative cross-national research, relying mostly on secondary data, has findings in different directions. There is a threat of selective model reporting and lack of replicability. The heterogeneity of countries obscures attempts to clearly define data-generating models. P-hacking and HARKing lurk among standard research practices in this area.This project employs crowdsourcing to address these issues. It draws on replication, deliberation, meta-analysis and harnessing the power of many minds at once. The Crowdsourced Replication Initiative carries two main goals, (a) to better investigate the linkage between immigration and social policy preferences across countries, and (b) to develop crowdsourcing as a social science method. The Executive Report provides short reviews of the area of social policy preferences and immigration, and the methods and impetus behind crowdsourcing plus a description of the entire project. Three main areas of findings will appear in three papers, that are registered as PAPs or in process

Gray Code Enumeration of Plane Straight-Line Graphs

We develop Gray code enumeration schemes for geometric graphs in the plane. The considered graph classes include plane straight-line graphs, plane spanning trees, and connected plane straight-line graphs. Previous results were restricted to the case where the underlying vertex set is in convex position

On the number of plane graphs

We investigate the number of plane geometric, i.e., straight-line, graphs, a set S of n points in the plane admits. We show that the number of plane graphs is minimized when S is in convex position, and that the same result holds for several relevant subfamilies. In addition we construct a new extremal configuration, the so-called double zig-zag chain. Most noteworthy this example bears Θ ∗ ( √ 72 n) = Θ ∗ (8.4853 n) triangulations and Θ ∗ (41.1889 n) plane graphs (omitting polynomial factors in both cases), improving the previously known best maximizing examples