IA Scholar Query: On the Strong Chromatic Index of Sparse Graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 03 Oct 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings
https://scholar.archive.org/work/6lsggig7dffmtmv5hpi7g3mgvm
In 1973, Erdős conjectured the existence of high girth (n,3,2)-Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Just this year, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture. As for Steiner systems with more general parameters, Glock, Kühn, Lo, and Osthus conjectured the existence of high girth (n,q,r)-Steiner systems. We prove the approximate version of their conjecture. This result follows from our general main results which concern finding perfect or almost perfect matchings in a hypergraph G avoiding a given set of submatchings (which we view as a hypergraph H where V(H)=E(G)). Our first main result is a common generalization of the classical theorems of Pippenger (for finding an almost perfect matching) and Ajtai, Komlós, Pintz, Spencer, and Szemerédi (for finding an independent set in girth five hypergraphs). More generally, we prove this for coloring and even list coloring, and also generalize this further to when H is a hypergraph with small codegrees (for which high girth designs is a specific instance). Indeed, the coloring version of our result even yields an almost partition of K_n^r into approximate high girth (n,q,r)-Steiner systems. Our main results also imply the existence of a perfect matching in a bipartite hypergraph where the parts have slightly unbalanced degrees. This has a number of applications; for example, it proves the existence of Δ pairwise disjoint list colorings in the setting of Kahn's theorem; it also proves asymptotic versions of various rainbow matching results in the sparse setting (where the number of times a color appears could be much smaller than the number of colors) and even the existence of many pairwise disjoint rainbow matchings in such circumstances.Michelle Delcourt, Luke Postlework_6lsggig7dffmtmv5hpi7g3mgvmMon, 03 Oct 2022 00:00:00 GMTOn endomorphism universality of sparse graph classes
https://scholar.archive.org/work/c2eeh4wlvrehha6q66gpv5warm
Solving a problem of Babai and Pultr from 1980 we show that every commutative idempotent monoid (a.k.a lattice) is the endomorphism monoid of a graph of bounded degree. Indeed we show that maximum degree 3 suffices, which is best-possible. On the way we generalize a classic result of Frucht by showing that every group is the endomorphism monoid of a graph of maximum degree 3 and we answer a question of Nešetřil and Ossona de Mendez from 2012, presenting a class of bounded expansion such that every monoid is the endomorphism monoid of one of its members. On the other hand we strengthen a result of Babai and Pultr and show that no class excluding a topological minor can have all completely regular monoids among its endomorphism monoids. Moreover, we show that no class excluding a minor can have all commutative idempotent monoids among its endomorphism monoids.Kolja Knauer, Gil Puig i Surrocawork_c2eeh4wlvrehha6q66gpv5warmFri, 30 Sep 2022 00:00:00 GMTMatter-antimatter asymmetry restrains the dimensionality of neural representations: quantum decryption of large-scale neural coding
https://scholar.archive.org/work/owy6xa2v3bcx3muopa5kiug5hm
Projections from the study of the human universe onto the study of the self-organizing brain are herein leveraged to address certain concerns raised in latest neuroscience research, namely (i) the extent to which neural codes are multidimensional; (ii) the functional role of neural dark matter; (iii) the challenge to traditional model frameworks posed by the needs for accurate interpretation of large-scale neural recordings linking brain and behavior. On the grounds of (hyper-)self-duality under (hyper-)mirror supersymmetry, inter-relativistic principles are introduced, whose consolidation, as spin-geometrical pillars of a network- and game-theoretical construction, is conducive to (i) the high-precision reproduction of core experimental observations on neural coding in the self-organizing brain, whereby the instantaneous geometric dimensionality of neural representations of a spontaneous behavioral state is proven to be at most 16, unidirectionally; (ii) spinor (co-)representations, as the latent building blocks of self-organizing cortical circuits subserving (co-)behavioral states; (iii) an early crystallization of pertinent multidimensional synaptic (co-)architectures, whereby Lorentz (co-)partitions are in principle verifiable; and, ultimately, (iv) potentially inverse insights into matter-antimatter asymmetry. New avenues for the decryption of large-scale neural coding in health and disease are being discussed.Sofia Karamintziouwork_owy6xa2v3bcx3muopa5kiug5hmThu, 29 Sep 2022 00:00:00 GMTThe Spectroscopic Data Processing Pipeline for the Dark Energy Spectroscopic Instrument
https://scholar.archive.org/work/5tsesdige5h2rpwftsyeyoo64e
We describe the spectroscopic data processing pipeline of the Dark Energy Spectroscopic Instrument (DESI), which is conducting a redshift survey of about 40 million galaxies and quasars using a purpose-built instrument on the 4-m Mayall Telescope at Kitt Peak National Observatory. The main goal of DESI is to measure with unprecedented precision the expansion history of the Universe with the Baryon Acoustic Oscillation technique and the growth rate of structure with Redshift Space Distortions. Ten spectrographs with three cameras each disperse the light from 5000 fibers onto 30 CCDs, covering the near UV to near infrared (3600 to 9800 Angstrom) with a spectral resolution ranging from 2000 to 5000. The DESI data pipeline generates wavelength- and flux-calibrated spectra of all the targets, along with spectroscopic classifications and redshift measurements. Fully processed data from each night are typically available to the DESI collaboration the following morning. We give details about the pipeline's algorithms, and provide performance results on the stability of the optics, the quality of the sky background subtraction, and the precision and accuracy of the instrumental calibration. This pipeline has been used to process the DESI Survey Validation data set, and has exceeded the project's requirements for redshift performance, with high efficiency and a purity greater than 99 percent for all target classes.J. Guy, S. Bailey, A. Kremin, Shadab Alam, C. Allende Prieto, S. BenZvi, A. S. Bolton, D. Brooks, E. Chaussidon, A. P. Cooper, K. Dawson, A. de la Macorra, A. Dey, Biprateep Dey, G. Dhungana, D. J. Eisenstein, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, D. Green, K. Honscheid, M. Ishak, R. Kehoe, D. Kirkby, T. Kisner, Sergey E. Koposov, Ting-Wen Lan, M. Landriau, L. Le Guillou, Michael E. Levi, C. Magneville, Christopher J. Manser, P. Martini, Aaron M. Meisner, R. Miquel, J. Moustakas, Adam D. Myers, Jeffrey A. Newman, Jundan Nie, N. Palanque-Delabrouille, W. J. Percival, C. Poppett, F. Prada, A. Raichoor, C. Ravoux, A. J. Ross, E. F. Schlafly, D. Schlegel, M. Schubnell, Ray M. Sharples, Gregory Tarlé, B. A. Weaver, Christophe Yèche, Rongpu Zhou, Zhimin Zhou, H. Zouwork_5tsesdige5h2rpwftsyeyoo64eThu, 29 Sep 2022 00:00:00 GMTObstructions to faster diameter computation: Asteroidal sets
https://scholar.archive.org/work/t7krlf4h5fahlgfhe5ygabpy44
An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let Ext_α be the class of all connected graphs whose quotient graph obtained from modular decomposition contains no more than α pairwise nonadjacent extremities. Our main contributions are as follows. First, we prove that the diameter of every m-edge graph in Ext_α can be computed in deterministic O(α^3 m^3/2) time. We then improve the runtime to linear for all graphs with bounded clique-number. Furthermore, we can compute an additive +1-approximation of all vertex eccentricities in deterministic O(α^2 m) time. This is in sharp contrast with general m-edge graphs for which, under the Strong Exponential Time Hypothesis (SETH), one cannot compute the diameter in O(m^2-ϵ) time for any ϵ > 0. As important special cases of our main result, we derive an O(m^3/2)-time algorithm for exact diameter computation within dominating pair graphs of diameter at least six, and an O(k^3m^3/2)-time algorithm for this problem on graphs of asteroidal number at most k. We end up presenting an improved algorithm for chordal graphs of bounded asteroidal number, and a partial extension of our results to the larger class of all graphs with a dominating target of bounded cardinality. Our time upper bounds in the paper are shown to be essentially optimal under plausible complexity assumptions.Guillaume Ducoffework_t7krlf4h5fahlgfhe5ygabpy44Mon, 26 Sep 2022 00:00:00 GMTOn the first-order transduction quasiorder of hereditary classes of graphs
https://scholar.archive.org/work/byjb4zuornhvjhr6c7alk5v3aq
Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures, and several important class properties can be defined in terms of transductions. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs. Surprisingly, this quasiorder is very complex, though shaped by the locality properties of first-order logic. This contrasts with the conjectured simplicity of the monadic second order (MSO) transduction quasiorder. We first establish a local normal form for FO transductions, which is of independent interest. This normal form allows to prove, among other results, that the local variants of (monadic) stability and (monadic) dependence are equivalent to their non-local versions. Then we prove that the quotient partial order is a bounded distributive join-semilattice, and that the subposet of additive classes is also a bounded distributive join-semilattice. We characterize transductions of paths, cubic graphs, and cubic trees in terms of bandwidth, bounded degree, and treewidth. We establish that the classes of all graphs with pathwidth at most k, for k≥ 1 form a strict hierarchy in the FO transduction quasiorder and leave open whether the same holds for the classes of all graphs with treewidth at most k. We identify the obstructions for a class to be a transduction of a class with bounded degree, leading to an interesting transduction duality formulation. Eventually, we discuss a notion of dense analogs of sparse transduction-preserved class properties, and propose several related conjectures.Samuel Braunfeld, Jaroslav Nešetřil, Patrice Ossona de Mendez, Sebastian Siebertzwork_byjb4zuornhvjhr6c7alk5v3aqThu, 22 Sep 2022 00:00:00 GMTStable graphs of bounded twin-width
https://scholar.archive.org/work/x4tn3q3n3feslmazqo6jbmaam4
We prove that every class of graphs 𝒞 that is monadically stable and has bounded twin-width can be transduced from some class with bounded sparse twin-width. This generalizes analogous results for classes of bounded linear cliquewidth and of bounded cliquewidth. It also implies that monadically stable classes of bounded twin-widthare linearly χ-bounded.Jakub Gajarský, Michał Pilipczuk, Szymon Toruńczykwork_x4tn3q3n3feslmazqo6jbmaam4Sat, 17 Sep 2022 00:00:00 GMTProving a directed analogue of the Gyárfás-Sumner conjecture for orientations of P_4
https://scholar.archive.org/work/c364c4f7gfgzteavs2ud67zl6u
An oriented graph is a digraph that does not contain a directed cycle of length two. An (oriented) graph D is H-free if D does not contain H as an induced sub(di)graph. The Gyárfás-Sumner conjecture is a widely-open conjecture on simple graphs, which states that for any forest F, there is some function f such that every F-free graph G with clique number ω(G) has chromatic number at most f(ω(G)). Aboulker, Charbit, and Naserasr [Extension of Gyárfás-Sumner Conjecture to Digraphs; E-JC 2021] proposed an analogue of this conjecture to the dichromatic number of oriented graphs. The dichromatic number of a digraph D is the minimum number of colors required to color the vertex set of D so that no directed cycle in D is monochromatic. Aboulker, Charbit, and Naserasr's χ-boundedness conjecture states that for every oriented forest F, there is some function f such that every F-free oriented graph D has dichromatic number at most f(ω(D)), where ω(D) is the size of a maximum clique in the graph underlying D. In this paper, we perform the first step towards proving Aboulker, Charbit, and Naserasr's χ-boundedness conjecture by showing that it holds when F is any orientation of a path on four vertices.Linda Cook, Tomáš Masařík, Marcin Pilipczuk, Amadeus Reinald, Uéverton S. Souzawork_c364c4f7gfgzteavs2ud67zl6uTue, 13 Sep 2022 00:00:00 GMTVisual perception in far peripheral visual space and its artistic representations
https://scholar.archive.org/work/e76nngaj4bhahmvwwxbjybbr74
Far peripheral visual field occupies the vast majority of human visual field. With some recent exceptions (Freeman & Simoncelli, 2011; Strasburger, H., Rentschler, I., & Jüttner, M., 2011; Fortenbaugh, Sanghvi, Silver & Robertson, 2012; Vishwanath et al., 2005) research on visual perception has traditionally focused on central vision, with the far peripheral visual field and the entirety of visual space still remaining fields open to investigation. The present research integrated artistic and scientific knowledgetocontributeto our understanding of the relationship between those two disciplines and to investigate that complex phenomenon that goes under the name of visual experience.Linear perspective is a simple and effective way to depict the physical world on a flat surface. Nowadays the vast majority of cameras and digital media rely on the principles of linear perspective, making it the most used method in western society to visually depict a scene. Starting from the common ground that linear perspective shares with light –which travels in straight lines—, many scientists have claimed that it is the optimal way to represent our visual experience (Gombrich, 1960; Pirenne, 1970; Gibson, 1971; Ward, 1976; Rehkämper, 2003). However, human perception does not simply record the geometrical projection of light paths hitting our retina, but it is a complex and active process which interprets sensory inputs and reconstructs a useful representation of the surrounding environment, enabling us to navigate in the space. Although scientists generally agree that visual perception does not correspond faithfully to the geometry of physical space (Ogle, 1964; Koenderink, Van Doorn, & Lappin, 2000; Hatfield, 2003; Foley et al. 2004; Wagner, 2006; Koenderink & van Doorn, 2008) the nature of this relationship is far from being fully understood. This research is part of the bigger interdisciplinary project, Fovography, undertaken with Prof. Robert Pepperell and Alistair Burleigh, that combines art, psycholo [...]Nicole Rutawork_e76nngaj4bhahmvwwxbjybbr74Fri, 09 Sep 2022 00:00:00 GMTValuative invariants for large classes of matroids
https://scholar.archive.org/work/qyjbv2bl3rfn5ojlu3ogww2irm
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a "stressed subset". This framework provides a new combinatorial characterization of the class of elementary split matroids, which is expected to be asymptotically predominant. Moreover, it permits to describe an explicit matroid subdivision of a hypersimplex, which in turn can be used to write down concrete formulas for the evaluations of any valuative invariant on these matroids. This shows that evaluations depend solely on the behavior of the invariant on a well-behaved small subclass of Schubert matroids that we call "cuspidal matroids". Along the way, we make an extensive summary of the tools and methods one might use to prove that an invariant is valuative, and we use them to provide new proofs of the valuativeness of several invariants. We address systematically the consequences of our approach for a comprehensive list of invariants. They include the volume and Ehrhart polynomial of base polytopes, the Tutte polynomial, Kazhdan-Lusztig polynomials, the Whitney numbers of the first and second kind, spectrum polynomials and a generalization of these by Denham, chain polynomials and Speyer's g-polynomials, as well as Chow rings of matroids and their Hilbert-Poincaré series. The flexibility of this setting allows us to give a unified explanation for several recent results regarding the listed invariants; furthermore, we emphasize it as a powerful computational tool to produce explicit data and concrete examples.Luis Ferroni, Benjamin Schröterwork_qyjbv2bl3rfn5ojlu3ogww2irmThu, 08 Sep 2022 00:00:00 GMTImages Enhancement of Ancient Mural Painting of Bey's Palace Constantine, Algeria and Lacuna Extraction Using Mahalanobis Distance Classification Approach
https://scholar.archive.org/work/3h7jxl34qrfwbi73rya4a5qxni
As a result of human activity and environmental changes, several types of damages may occur to ancient mural paintings; indeed, lacunae, which refer to the area of paint layer loss, are the most prevalent kind. The presence of lacuna is an essential sign of the progress of mural painting deterioration. Most studies have focused on detecting and removing cracks from old paintings. However, lacuna extraction has not received the necessary consideration and is not well-explored. Furthermore, most recent studies have focused on using deep learning for mural protection and restoration, but deep learning requires a large amount of data and computational resources which is not always available in heritage institutions. In this paper, we present an efficient method to automatically extract lacunae and map deterioration from RGB images of ancient mural paintings of Bey's Palace in Algeria. Firstly, a preprocessing was applied using Dark Channel Prior (DCP) to enhance the quality and improve visibility of the murals. Secondly, a determination of the training sample and pixel's grouping was assigned to their closest sample based on Mahalanobis Distance (MD) by calculating both the mean and variance of the classes in three bands (R, G, and B), in addition to the covariance matrix of all the classes to achieve lacuna extraction of the murals. Finally, the accuracy of extraction was calculated. The experimental results showed that the proposed method can achieve a conspicuously high accuracy of 94.33% in extracting lacunae from ancient mural paintings, thus supporting the work of a specialist in heritage institutions in terms of the time- and cost-consuming documentation process.Adel Nasri, Xianfeng Huangwork_3h7jxl34qrfwbi73rya4a5qxniFri, 02 Sep 2022 00:00:00 GMTRandom Geometric Graph: Some recent developments and perspectives
https://scholar.archive.org/work/5q2xyt5gpbaadiuhtnqrduv7fy
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such as the small-world phenomenon and clustering. Originally introduced to model wireless communication networks, RGGs are now very popular with applications ranging from network user profiling to protein-protein interactions in biology. RGGs are also of purely theoretical interest since the underlying geometry gives rise to challenging mathematical questions. Their resolutions involve results from probability, statistics, combinatorics or information theory, placing RGGs at the intersection of a large span of research communities. This paper surveys the recent developments in RGGs from the lens of high dimensional settings and non-parametric inference. We also explain how this model differs from classical community based random graph models and we review recent works that try to take the best of both worlds. As a by-product, we expose the scope of the mathematical tools used in the proofs.Quentin Ducheminwork_5q2xyt5gpbaadiuhtnqrduv7fyWed, 24 Aug 2022 00:00:00 GMTDagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issue
https://scholar.archive.org/work/scntyrlsivecdcac4psbic4qzy
Dagstuhl Reports, Volume 12, Issue 2, February 2022, Complete Issuework_scntyrlsivecdcac4psbic4qzyTue, 23 Aug 2022 00:00:00 GMTSelf-Supervised Pretraining of Graph Neural Network for the Retrieval of Related Mathematical Expressions in Scientific Articles
https://scholar.archive.org/work/pc2c4jmqabeadkukbl64fgwocy
Given the increase of publications, search for relevant papers becomes tedious. In particular, search across disciplines or schools of thinking is not supported. This is mainly due to the retrieval with keyword queries: technical terms differ in different sciences or at different times. Relevant articles might better be identified by their mathematical problem descriptions. Just looking at the equations in a paper already gives a hint to whether the paper is relevant. Hence, we propose a new approach for retrieval of mathematical expressions based on machine learning. We design an unsupervised representation learning task that combines embedding learning with self-supervised learning. Using graph convolutional neural networks we embed mathematical expression into low-dimensional vector spaces that allow efficient nearest neighbor queries. To train our models, we collect a huge dataset with over 29 million mathematical expressions from over 900,000 publications published on arXiv.org. The math is converted into an XML format, which we view as graph data. Our empirical evaluations involving a new dataset of manually annotated search queries show the benefits of using embedding models for mathematical retrieval. This work was originally published at KDD 2020.Lukas Pfahler, Katharina Morikwork_pc2c4jmqabeadkukbl64fgwocyMon, 22 Aug 2022 00:00:00 GMTSandwiching random regular graphs between binomial random graphs
https://scholar.archive.org/work/lotkjrf6cfhjzbcjhfxmhrmcuy
Kim and Vu made the following conjecture (Advances in Mathematics, 2004): if d≫log n, then the random d-regular graph 𝒢(n,d) can asymptotically almost surely be "sandwiched" between 𝒢(n,p_1) and 𝒢(n,p_2) where p_1 and p_2 are both (1+o(1))d/n. They proved this conjecture for log n≪ d≤ n^1/3-o(1), with a defect in the sandwiching: 𝒢(n,d) contains 𝒢(n,p_1) perfectly, but is not completely contained in 𝒢(n,p_2). Recently, the embedding 𝒢(n,p_1) ⊆𝒢(n,d) was improved by Dudek, Frieze, Ruciński and Šileikis to d=o(n). In this paper, we prove Kim–Vu's sandwich conjecture, with perfect containment on both sides, for all d≫ n/√(log n). For d=O(n/√(log n)), we prove a weaker version of the sandwich conjecture with p_2 approximately equal to (d/n)log n, without any defect. In addition to sandwiching regular graphs, our results cover graphs whose degrees are asymptotically equal. The proofs rely on estimates for the probability that a random factor of a pseudorandom graph contains a given edge, which is of independent interest. As applications, we obtain new results on the properties of random graphs with given near-regular degree sequences, including Hamiltonicity and universality in subgraph containment. We also determine several graph parameters in these random graphs, such as the chromatic number, small subgraph counts, the diameter, and the independence number. We are also able to characterise many phase transitions in edge percolation on these random graphs, such as the threshold for the appearance of a giant component.Pu Gao, Mikhail Isaev, Brendan McKaywork_lotkjrf6cfhjzbcjhfxmhrmcuyMon, 22 Aug 2022 00:00:00 GMTIdentifying Gravitational Wave Counterparts with Near-infrared Image Subtraction: Automating the Detection of GW Counterparts for VISTA
https://scholar.archive.org/work/m6b7otqucvgkzj7jy733ne2q2m
The field of gravitational wave observational astronomy has only just begun, with the first binary black hole merger detected in 2015 and the first electromagnetic counterpart associated to a GW event being found in 2017. With the recent introduction of new entries into the detector network (e.g. Virgo, KAGRA), the planned expansion of the network (e.g. LISA) and with frequent improvements being made to existing detectors, the number of GW detections is set to increase in the coming years. This will encourage additional electromagnetic follow-up, particularly in the infra-red in the search for kilonovae. This thesis is framed around the primary motivation for this work – to automate the process of investigating near-infrared follow up images obtained from the VISTA telescope. This involves both the identification of potential transient objects which might be associated with an event, and the photometric analysis of known kilonova detections. To demonstrate the effectiveness of this work, the automated pipeline is tested against data obtained within the localisation regions of GW170814, GW190814 and GW200114. A revised estimate is also produced for GW170817 photometry which is in accordance with previous studies. Overall, the IGNIS (Identifying Gravitational wave counterparts with near Infrared Image Subtraction) pipeline is proven to be almost as effective as manually searching for transient objects to depths of mAB = 20.5 - 22, with automated detection improved on longer exposures (240s+). This work estimates VISTA-associated false positive rates at 0.048-0.06 objects per tile (one object found per 16.7-20.8 deg2).Skye Sonja Rosettiwork_m6b7otqucvgkzj7jy733ne2q2mMon, 15 Aug 2022 00:00:00 GMTDeformation Monitoring of Tailings Reservoir Based on Polarimetric Time Series InSAR: Example of Kafang Tailings Reservoir, China
https://scholar.archive.org/work/fac5gfj4vnchlc72buiareyeym
Safe operation of tailings reservoirs is essential to protect downstream life and property, but current monitoring methods are inadequate in scale and refinement, and most reservoirs are built in low coherence areas far from cities. Use of polarization data to monitor deformation may improve area coherence and thus point selection density. With the example of the Kafang tailings reservoir and dual-polarization Sentinel-1 data from 9 August 2020 to 24 May 2021, homogeneous points of different polarization channels were identified with the hypothesis test of the confidence interval method. Results were fused, and BEST, sub-optimum scattering mechanism (SOM), and equal scattering mechanism (ESM) methods were used to optimize phase quality of persistent scatterer (PS) and distributed scatterer (DS) pixels and obtain more detailed deformation information on the area with time series processing. The fusion of homogeneous point sets obtained from different polarization intensity data increased the number of homogeneous points, which was 3.86% and 8.45% higher than that of VH and VV polarization images, respectively. The three polarization optimization methods improved point selection density. Compared with the VV polarization image, the high coherence point density increased by 1.83 (BEST), 3.66 (SOM), and 5.76 (ESM) times, whereas it increased by 1.17 (BEST), 1.84 (SOM), and 2.04 (ESM) times in the tailings reservoir. The consistency and reliability of different methods were good. By comparing the monitoring results of the three methods using polarization data, the hypothesis test of the confidence interval (HTCI) algorithm, and the polarization optimization method will effectively increase the point selection number of the study area, and the ESM method can show the deformation of tailings area more comprehensively. Monitoring indicated deformation of the tailings reservoir tended to diffuse outward from the area with the largest deformation and was relatively stable.Hao Wu, Xiangyuan Zheng, Hongdong Fan, Zeming Tianwork_fac5gfj4vnchlc72buiareyeymFri, 29 Jul 2022 00:00:00 GMTCommon graphs with arbitrary chromatic number
https://scholar.archive.org/work/34q5rwajmrh4lkxsnnhuntgcqe
Ramsey's Theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdos conjectured that the random 2-edge-coloring minimizes the number of monochromatic copies of K_k, and the conjecture was extended by Burr and Rosta to all graphs. In the late 1980s, the conjectures were disproved by Thomason and Sidorenko, respectively. A classification of graphs whose number of monochromatic copies is minimized by the random 2-edge-coloring, which are referred to as common graphs, remains a challenging open problem. If Sidorenko's Conjecture, one of the most significant open problems in extremal graph theory, is true, then every 2-chromatic graph is common, and in fact, no 2-chromatic common graph unsettled for Sidorenko's Conjecture is known. While examples of 3-chromatic common graphs were known for a long time, the existence of a 4-chromatic common graph was open until 2012, and no common graph with a larger chromatic number is known. We construct connected k-chromatic common graphs for every k. This answers a question posed by Hatami, Hladky, Kral, Norine and Razborov [Combin. Probab. Comput. 21 (2012), 734-742], and a problem listed by Conlon, Fox and Sudakov [London Math. Soc. Lecture Note Ser. 424 (2015), 49-118, Problem 2.28]. This also answers in a stronger form the question raised by Jagger, Stovicek and Thomason [Combinatorica 16, (1996), 123-131] whether there exists a common graph with chromatic number at least four.Daniel Kral and Jan Volec and Fan Weiwork_34q5rwajmrh4lkxsnnhuntgcqeFri, 22 Jul 2022 00:00:00 GMTRobust Factorizations and Colorings of Tensor Graphs
https://scholar.archive.org/work/qltv2l3x7jbwtovkwe23svnp3a
Since the seminal result of Karger, Motwani, and Sudan, algorithms for approximate 3-coloring have primarily centered around SDP-based rounding. However, it is likely that important combinatorial or algebraic insights are needed in order to break the n^o(1) threshold. One way to develop new understanding in graph coloring is to study special subclasses of graphs. For instance, Blum studied the 3-coloring of random graphs, and Arora and Ge studied the 3-coloring of graphs with low threshold-rank. In this work, we study graphs which arise from a tensor product, which appear to be novel instances of the 3-coloring problem. We consider graphs of the form H = (V,E) with V =V( K_3 × G) and E = E(K_3 × G) ∖ E', where E' ⊆ E(K_3 × G) is any edge set such that no vertex has more than an ϵ fraction of its edges in E'. We show that one can construct H = K_3 ×G with V(H) = V(H) that is close to H. For arbitrary G, H satisfies |E(H) Δ E(H)| ≤ O(ϵ|E(H)|). Additionally when G is a mild expander, we provide a 3-coloring for H in polynomial time. These results partially generalize an exact tensor factorization algorithm of Imrich. On the other hand, without any assumptions on G, we show that it is NP-hard to 3-color H.Joshua Brakensiek, Sami Davieswork_qltv2l3x7jbwtovkwe23svnp3aMon, 18 Jul 2022 00:00:00 GMTTwo technologies for single-molecule proteomics, three technologies for image analysis
https://scholar.archive.org/work/yo6z3ron7vgvdezejpeqpebil4
Proteins are central players in biology. Being able to detect and quantify proteins in various circumstances such as in biochemically fractionated cellular lysates has proven to be highly informative about their characteristics, functions, and relationships with other proteins and cellular components in general. We currently lack high-throughput technologies for quantifying proteins that would resolve complex mixtures at single-molecule resolution across the large dynamic ranges found in cells. Here I present progress towards the two single-molecule proteomics technologies my colleagues and I have been developing: fluorosequencing and reverse translation. We computationally explore the feasibility and informational power of each technique, motivating further work. We demonstrate a working proof-of-concept for fluorosequencing, and significant progress towards a proof-of-concept for reverse translation. In addition to proteomics, I have contributed three computational technologies that can broadly be grouped as image analysis: quantitation of fluorescent nerve agent probes by chromaticity changes; recovery of molecular positions by DNA sequencing of immobilized, barcoded oligonucleotides; and automated, quantitative co-localization of protein puncta in cells.Alexander Alexeyvich Boulgakov, 0000-0002-7446-1120, Austin, The University Of Texas At, Edward M. Marcottework_yo6z3ron7vgvdezejpeqpebil4Fri, 15 Jul 2022 00:00:00 GMT