LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Rips Complexes of Planar Point Sets

Fix a finite set of points in Euclidean $n$-space \euc^n, thought of as a point-cloud sampling of a certain domain D\subset\euc^n. The Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-computed but high-dimensional approximation to the homotopy type of $D$. There is a natural ``shadow'' projection map from the Rips complex to \euc^n that has as its image a more accurate $n$-dimensional approximation to the homotopy type of $D$. We demonstrate that this projection map is 1-connected for the planar case $n=2$. That is, for planar domains, the Rips complex accurately captures connectivity and fundamental group data. This implies that the fundamental group of a Rips complex for a planar point set is a free group. We show that, in contrast, introducing even a small amount of uncertainty in proximity detection leads to `quasi'-Rips complexes with nearly arbitrary fundamental groups. This topological noise can be mitigated by examining a pair of quasi-Rips complexes and using ideas from persistent topology. Finally, we show that the projection map does not preserve higher-order topological data for planar sets, nor does it preserve fundamental group data for point sets in dimension larger than three.Comment: 16 pages, 8 figure

β\beta-Stars or On Extending a Drawing of a Connected Subgraph

We consider the problem of extending the drawing of a subgraph of a given plane graph to a drawing of the entire graph using straight-line and polyline edges. We define the notion of star complexity of a polygon and show that a drawing $\Gamma_H$ of an induced connected subgraph $H$ can be extended with at most $\min\{ h/2, \beta + \log_2(h) + 1\}$ bends per edge, where $\beta$ is the largest star complexity of a face of $\Gamma_H$ and $h$ is the size of the largest face of $H$. This result significantly improves the previously known upper bound of $72|V(H)|$ [5] for the case where $H$ is connected. We also show that our bound is worst case optimal up to a small additive constant. Additionally, we provide an indication of complexity of the problem of testing whether a star-shaped inner face can be extended to a straight-line drawing of the graph; this is in contrast to the fact that the same problem is solvable in linear time for the case of star-shaped outer face [9] and convex inner face [13].Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Geometric Embeddability of Complexes Is ∃R-Complete

We show that the decision problem of determining whether a given (abstract simplicial) k-complex has a geometric embedding in Rd is complete for the Existential Theory of the Reals for all d ≥ 3 and k ∈ {d− 1, d}. Consequently, the problem is polynomial time equivalent to determining whether a polynomial equation system has a real solution and other important problems from various fields related to packing, Nash equilibria, minimum convex covers, the Art Gallery Problem, continuous constraint satisfaction problems, and training neural networks. Moreover, this implies NP-hardness and constitutes the first hardness result for the algorithmic problem of geometric embedding (abstract simplicial) complexes. This complements recent breakthroughs for the computational complexity of piece-wise linear embeddability

The Complexity of Geodesic Spanners

A geometric t-spanner for a set S of n point sites is an edge-weighted graph for which the (weighted) distance between any two sites p, q ∈ S is at most t times the original distance between p and q. We study geometric t-spanners for point sets in a constrained two-dimensional environment P. In such cases, the edges of the spanner may have non-constant complexity. Hence, we introduce a novel spanner property: the spanner complexity, that is, the total complexity of all edges in the spanner. Let S be a set of n point sites in a simple polygon P with m vertices. We present an algorithm to construct, for any constant ε > 0 and fixed integer k ≥ 1, a (2k + ε)-spanner with complexity O(mn1/k + n log2 n) in O(n log2 n + m log n + K) time, where K denotes the output complexity. When we consider sites in a polygonal domain P with holes, we can construct such a (2k + ε)-spanner of similar complexity in O(n2 log m + nm log m + K) time. Additionally, for any constant ε ∈ (0, 1) and integer constant t ≥ 2, we show a lower bound for the complexity of any (t − ε)-spanner of (Equation presented)

Impact of Immunization Technology and Assay Application on Antibody Performance – A Systematic Comparative Evaluation

Antibodies are quintessential affinity reagents for the investigation and determination of a protein's expression patterns, localization, quantitation, modifications, purification, and functional understanding. Antibodies are typically used in techniques such as Western blot, immunohistochemistry (IHC), and enzyme-linked immunosorbent assays (ELISA), among others. The methods employed to generate antibodies can have a profound impact on their success in any of these applications. We raised antibodies against 10 serum proteins using 3 immunization methods: peptide antigens (3 per protein), DNA prime/protein fragment-boost (“DNA immunization”; 3 per protein), and full length protein. Antibodies thus generated were systematically evaluated using several different assay technologies (ELISA, IHC, and Western blot). Antibodies raised against peptides worked predominantly in applications where the target protein was denatured (57% success in Western blot, 66% success in immunohistochemistry), although 37% of the antibodies thus generated did not work in any of these applications. In contrast, antibodies produced by DNA immunization performed well against both denatured and native targets with a high level of success: 93% success in Western blots, 100% success in immunohistochemistry, and 79% success in ELISA. Importantly, success in one assay method was not predictive of success in another. Immunization with full length protein consistently yielded the best results; however, this method is not typically available for new targets, due to the difficulty of generating full length protein. We conclude that DNA immunization strategies which are not encumbered by the limitations of efficacy (peptides) or requirements for full length proteins can be quite successful, particularly when multiple constructs for each protein are used

Risks of mining to salmonid-bearing watersheds

Mining provides resources for people but can pose risks to ecosystems that support cultural keystone species. Our synthesis reviews relevant aspects of mining operations, describes the ecology of salmonid-bearing watersheds in northwestern North America, and compiles the impacts of metal and coal extraction on salmonids and their habitat. We conservatively estimate that this region encompasses nearly 4000 past producing mines, with present-day operations ranging from small placer sites to massive open-pit projects that annually mine more than 118 million metric tons of earth. Despite impact assessments that are intended to evaluate risk and inform mitigation, mines continue to harm salmonid-bearing watersheds via pathways such as toxic contaminants, stream channel burial, and flow regime alteration. To better maintain watershed processes that benefit salmonids, we highlight key windows during the mining governance life cycle for science to guide policy by more accurately accounting for stressor complexity, cumulative effects, and future environmental change.This review is based on an October 2019 workshop held at the University of Montana Flathead Lake Biological Station (more information at https://flbs.umt.edu/ newflbs/research/working-groups/mining-and-watersheds/). We thank E. O’Neill and other participants for valuable contributions. A. Beaudreau, M. LaCroix, P. McGrath, K. Schofield, and L. Brown provided helpful reviews of earlier drafts. Three anonymous reviewers provided thoughtful critiques that greatly improved the manuscript. The views expressed in this article are those of the authors and do not necessarily represent the views or policies of the U.S. Environmental Protection Agency. Our analysis comes from a western science perspective and hence does not incorporate Indigenous knowledge systems. We acknowledge this gap and highlight that the lands and waters we explore in this review have been stewarded by Indigenous Peoples for millennia and continue to be so. Funding: The workshop was cooperatively funded by the Wilburforce Foundation and The Salmon Science Network funded by the Gordon and Betty Moore Foundation. Author contributions: C.J.S. led the review process, writing, and editing. C.J.S. and E.K.S. co-organized the workshop. E.K.S. and J.W.M. extensively contributed to all aspects of the review conceptualization, writing, and editing. A.R.W., S.A.N., J.L.E., D.M.C., S.L.O., R.L.M., F.R.H., D.C.W., and J.W. significantly contributed to portions of the review conceptualization, writing, and editing. J.C., M.Ca., M.Co., C.A.F., G.K., E.D.L., R.M., V.M., J.K.M., M.V.M., and N.S. provided writing and editing and are listed alphabetically. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.Ye

Staphylococcus aureus α-Hemolysin Activates the NLRP3-Inflammasome in Human and Mouse Monocytic Cells

Community Acquired Methicillin Resistant Staphylococcus aureus (CA-MRSA) causes severe necrotizing infections of the skin, soft tissues, and lungs. Staphylococcal α-hemolysin is an essential virulence factor in mouse models of CA-MRSA necrotizing pneumonia. S. aureus α-hemolysin has long been known to induce inflammatory signaling and cell death in host organisms, however the mechanism underlying these signaling events were not well understood. Using highly purified recombinant α-hemolysin, we now demonstrate that α-hemolysin activates the Nucleotide-binding domain and leucine-rich repeat containing gene family, pyrin domain containing 3 protein (NLRP3)-inflammasome, a host inflammatory signaling complex involved in responses to pathogens and endogenous danger signals. Non-cytolytic mutant α-hemolysin molecules fail to elicit NLRP3-inflammasome signaling, demonstrating that the responses are not due to non-specific activation of this innate immune signaling system by bacterially derived proteins. In monocyte-derived cells from humans and mice, inflammasome assembly in response to α-hemolysin results in activation of the cysteine proteinase, caspase-1. We also show that inflammasome activation by α-hemolysin works in conjunction with signaling by other CA-MRSA-derived Pathogen Associated Molecular Patterns (PAMPs) to induce secretion of pro-inflammatory cytokines IL-1β and IL-18. Additionally, α-hemolysin induces cell death in these cells through an NLRP3-dependent program of cellular necrosis, resulting in the release of endogenous pro-inflammatory molecules, like the chromatin-associated protein, High-mobility group box 1 (HMGB1). These studies link the activity of a major S. aureus virulence factor to a specific host signaling pathway. The cellular events linked to inflammasome activity have clear relevance to the disease processes associated with CA-MRSA including tissue necrosis and inflammation

Формирование эмоциональной культуры как компонента инновационной культуры студентов

Homozygosity has long been associated with rare, often devastating, Mendelian disorders1 and Darwin was one of the first to recognise that inbreeding reduces evolutionary fitness2. However, the effect of the more distant parental relatedness common in modern human populations is less well understood. Genomic data now allow us to investigate the effects of homozygosity on traits of public health importance by observing contiguous homozygous segments (runs of homozygosity, ROH), which are inferred to be homozygous along their complete length. Given the low levels of genome-wide homozygosity prevalent in most human populations, information is required on very large numbers of people to provide sufficient power3,4. Here we use ROH to study 16 health-related quantitative traits in 354,224 individuals from 102 cohorts and find statistically significant associations between summed runs of homozygosity (SROH) and four complex traits: height, forced expiratory lung volume in 1 second (FEV1), general cognitive ability (g) and educational attainment (nominal p<1 × 10−300, 2.1 × 10−6, 2.5 × 10−10, 1.8 × 10−10). In each case increased homozygosity was associated with decreased trait value, equivalent to the offspring of first cousins being 1.2 cm shorter and having 10 months less education. Similar effect sizes were found across four continental groups and populations with different degrees of genome-wide homozygosity, providing convincing evidence for the first time that homozygosity, rather than confounding, directly contributes to phenotypic variance. Contrary to earlier reports in substantially smaller samples5,6, no evidence was seen of an influence of genome-wide homozygosity on blood pressure and low density lipoprotein (LDL) cholesterol, or ten other cardio-metabolic traits. Since directional dominance is predicted for traits under directional evolutionary selection7, this study provides evidence that increased stature and cognitive function have been positively selected in human evolution, whereas many important risk factors for late-onset complex diseases may not have been