IA Scholar Query: Symmetries and Ramsey properties of trees.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgFri, 18 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Particle Physics at the European Spallation Source
https://scholar.archive.org/work/s3bnceenszgszp2k24dzwcw37m
Presently under construction in Lund, Sweden, the European Spallation Source (ESS) will be the world's brightest neutron source. As such, it has the potential for a particle physics program with a unique reach and which is complementary to that available at other facilities. This paper describes proposed particle physics activities for the ESS. These encompass the exploitation of both the neutrons and neutrinos produced at the ESS for high precision (sensitivity) measurements (searches).H. Abele, A. Alekou, A. Algora, K. Andersen, S. Baessler, L. Barron-Palos, J. Barrow, E. Baussan, P. Bentley, Z. Berezhiani, Y. Bessler, A. K. Bhattacharyya, A. Bianchi, J. Bijnens, C. Blanco, N. Blaskovic Kraljevic, M. Blennow, K. Bodek, M. Bogomilov, C. Bohm, B. Bolling, E. Bouquerel, G. Brooijmans, L. J. Broussard, O. Buchan, A. Burgman, H. Calen, C. J. Carlile, J. Cederkall, E. Chanel, P. Christiansen, V. Cirigliano, J. I. Collar, M. Collins, C. B. Crawford, E. Cristaldo Morales, P. Cupial, L. D'Alessi, J. I. M. Damian, H. Danared, D. Dancila, J. P. A. M. de Andre, J. P. Delahaye, S. Degenkolb, D. D. Di Julio, M. Dracos, K. Dunne, I. Efthymiopoulos, T. Ekelof, L. Eklund, M. Eshraqi, I. Esteban, G. Fanourakis, A. Farricker, E. Fernandez-Martinez, M. J. Ferreira, M. Fertl, P. Fierlinger, B. Folsom, A. Frank, A. Fratangelo, U. Friman-Gayer, T. Fukuda, H .O .U. Fynbo, A. Garcia Sosa, N. Gazis, B. Galnander, Th. Geralis, M. Ghosh, G. Gokbulut, J .J. Gomez-Cadenas, M. Gonzalez-Alonso, F. Gonzalez, L. Halic, C. Happe, P. Heil, A. Heinz, H. Herde, M. Holl, T. Jenke, M. Jenssen, E. Jericha, H. T. Johansson, R. Johansson, T. Johansson, Y. Kamyshkov, A. Kayis Topaksu, B. Kildetoft, K. Kirch, B. Klicek, E. Klinkby, R. Kolevatov, G. Konrad, M. Koziol, K. Krhac, A. Kupsc, L. Lacny, L. Larizgoitia, C. M. Lewis, M. Lindroos, E. Lychagin, E. Lytken, C. Maiano, P. Marciniewski, G. Markaj, B. Markisch, C. Marrelli, C. Martins, B. Meirose, M. Mezzetto, N. Milas, D. Milstead, F. Monrabal, G. Muhrer, A. Nepomuceno, V. Nesvizhevsky, T. Nilsson, P. Novella, M. Oglakci, T. Ohlsson, M. Olvegard, A. Oskarsson, T. Ota, J. Park, D. Patrzalek, H. Perrey, M. Persoz, G. Petkov, F.M. Piegsa, C. Pistillo, P. Poussot, P. Privitera, B. Rataj, D. Ries, N. Rizzi, S. Rosauro-Alcaraz, D. Rozpedzik, D. Saiang, V. Santoro, U. Schmidt, H. Schober, I. Schulthess, S. Silverstein, A. Simon, H. Sina, J. Snamina, W. M. Snow, T. Soldner, G. Stavropoulos, M. Stipcevic, B. Szybinski, A. Takibayev, Z. Tang, R. Tarkeshian, C. Theroine, J. Thorne, F. Terranova, J. Thomas, T. Tolba, P. Torres-Sanchez, E. Trachanas, R. Tsenov, U. I. Uggerhoj, G. Vankova-Kirilova, N. Vassilopoulos, R. Wagner, X. Wang, E. Wildner, M. Wolke, J. Wurtz, S. C. Yiu, S. G. Yoon, A. R. Young, L. Zanini, J. Zejma, D. Zerzion, O. Zimmer, O. Zormpa, Y. Zouwork_s3bnceenszgszp2k24dzwcw37mFri, 18 Nov 2022 00:00:00 GMTOn the Ramsey number of daisies II
https://scholar.archive.org/work/ujd4onwk6fgwtpwcl2hg53rox4
A (k+r)-uniform hypergraph H on (k+m) vertices is an (r,m,k)-daisy if there exists a partition of the vertices V(H)=K∪ M with |K|=k, |M|=m such that the set of edges of H is all the (k+r)-tuples K∪ P, where P is an r-tuple of M. Complementing results in ["On the Ramsey number of daisies I"], we obtain an (r-2)-iterated exponential lower bound to the Ramsey number of an (r,m,k)-daisy for 2-colors. This matches the order of magnitude of the best lower bounds for the Ramsey number of a complete r-graph.Marcelo Saleswork_ujd4onwk6fgwtpwcl2hg53rox4Fri, 18 Nov 2022 00:00:00 GMTReport of the Frontier For Rare Processes and Precision Measurements
https://scholar.archive.org/work/6lrmujql5zgi5khexexrip5bly
This is the Snowmass 2021 Rare and Precision Frontier Report. The Rare Processes and Precision Measurements Frontier, referred to as the "Rare and Precision Frontier", or RPF, encompasses searches for extremely rare processes or tiny deviations from the Standard Model (SM) that can be studied with intense sources and high-precision detectors. Our community studies have identified several unique research opportunities that may pin down the scales associated with New Physics (NP) interactions and constrain the couplings of possible new degrees of freedom. Searches for rare flavor transition processes and precision measurements are indispensable probes of flavor and fundamental symmetries, and provide insights into physics that manifests itself at higher energy or through weaker interactions than those directly accessible at high-energy colliders.Marina Artuso, Robert H. Bernstein, Alexey A. Petrovwork_6lrmujql5zgi5khexexrip5blyThu, 17 Nov 2022 00:00:00 GMTOn some of Brouwer's axioms
https://scholar.archive.org/work/qbwopabaafhspiarxed5tfvp7y
We discuss the position of intuitionistic mathematics within the field of constructive mathematics. We discuss some principles defended and used by Brouwer but rejected by Bishop, like the Coninuity Principle, the Fan Theorem and the Bar Theorem. We explain some of their consequences in the development of constructive mathematics, like the Borel Hierarchy Theorem and the Intuitionistic Ramsey Theorem. We go into the theory of measure and integration as Bishop followed in this field a path different from Brouwer's.Wim Veldmanwork_qbwopabaafhspiarxed5tfvp7yFri, 11 Nov 2022 00:00:00 GMTOn the Turán number of the hypercube
https://scholar.archive.org/work/kzoplqrl4bck3oikrzrv7f7yme
In 1964, Erdős proposed the problem of estimating the Turán number of the d-dimensional hypercube Q_d. Since Q_d is a bipartite graph with maximum degree d, it follows from results of Füredi and Alon, Krivelevich, Sudakov that ex(n,Q_d)=O_d(n^2-1/d). A recent general result of Sudakov and Tomon implies the slightly stronger bound ex(n,Q_d)=o(n^2-1/d). We obtain the first power-improvement for this old problem by showing that ex(n,Q_d)=O_d(n^2-1/d-1+1/(d-1)2^d-1). This answers a question of Liu. Moreover, our techniques give a power improvement for a larger class of graphs than cubes. We use a similar method to prove that any n-vertex, properly edge-coloured graph without a rainbow cycle has at most O(n(log n)^2) edges, improving the previous best bound of n(log n)^2+o(1) by Tomon. Furthermore, we show that any properly edge-coloured n-vertex graph with ω(nlog n) edges contains a cycle which is almost rainbow: that is, almost all edges in it have a unique colour. This latter result is tight.Oliver Janzer, Benny Sudakovwork_kzoplqrl4bck3oikrzrv7f7ymeFri, 11 Nov 2022 00:00:00 GMTConant-independence and generalized free amalgamation
https://scholar.archive.org/work/7uwgl5p5hvaw7hkqorf5xrefri
We initiate the study of a generalization of Kim-independence, Conant-independence, based on the "strong Kim-dividing" of Kaplan, Ramsey and Shelah. We introduce an axiom on stationary independence relations essentially generalizing the "freedom" axiom in some of the free amalgamation theories of Conant, and show that this axiom provides the correct setting for carrying out arguments of Chernikov, Kaplan and Ramsey on NSOP_1 theories relative to a stationary independence relation. Generalizing Conant's results on free amalgamation to the limits of our knowledge of the NSOP_n hierarchy, we show using methods from Conant as well as our previous work that any theory where the equivalent conditions of this local variant of NSOP_1 holds is either NSOP_1 or SOP_3 and is either simple or TP_2, and observe that these theories give an interesting class of examples of theories where Conant-independence is symmetric, including all of Conant's examples, the small cycle-free random graphs of Shelah and the (finite-language) ω-categorical Hrushovski constructions of Evans and Wong. We then answer a question of Conant, showing that the generic functional structures of Conant and Kruckman are examples of non-modular free amalgamation theories, and show that any free amalgamation theory is NSOP_1 or SOP_3, while an NSOP_1 free amalgamation theory is simple if and only if it is modular. Finally, we show that every theory where Conant-independence is symmetric is NSOP_4. Therefore, symmetry for Conant-independence gives the next known neostability-theoretic dividing line on the NSOP_n hierarchy beyond NSOP_1. We explain the connection to some established open questions.Scott Mutchnikwork_7uwgl5p5hvaw7hkqorf5xrefriWed, 09 Nov 2022 00:00:00 GMTThe Phenomenology of Quadratically Coupled Ultra Light Dark Matter
https://scholar.archive.org/work/shubh6ihvzazhpzhd33jt5umbi
We discuss models of ultralight scalar Dark Matter (DM) with linear and quadratic couplings to the Standard Model (SM). In addition to studying the phenomenology of linear and quadratic interactions separately, we examine their interplay. We review the different experiments that can probe such interactions and present the current and expected future bounds on the parameter space. In particular, we discuss the scalar field solution presented in [A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik and P. Wolf, Phys.Rev.D 98 (2018) 6, 064051], and extend it to theories that capture both the linear and the quadratic couplings of the DM field to the SM. Furthermore, we discuss the theoretical aspects and the corresponding challenges for natural models in which the quadratic interactions are of phenomenological importance.Abhishek Banerjee, Gilad Perez, Marianna Safronova, Inbar Savoray, Aviv Shalitwork_shubh6ihvzazhpzhd33jt5umbiWed, 09 Nov 2022 00:00:00 GMTSome exact values on Ramsey numbers related to fans
https://scholar.archive.org/work/fbm6ect7rrh3rekbjnnvfnfax4
For two given graphs F and H, the Ramsey number R(F,H) is the smallest integer N such that any red-blue edge-coloring of the complete graph K_N contains a red F or a blue H. When F=H, we simply write R_2(H). For an positive integer n, let K_1,n be a star with n+1 vertices, F_n be a fan with 2n+1 vertices consisting of n triangles sharing one common vertex, and nK_3 be a graph with 3n vertices obtained from the disjoint union of n triangles. In 1975, Burr, Erdős and Spencer proved that R_2(nK_3)=5n for n≥2. However, determining the exact value of R_2(F_n) is notoriously difficult. So far, only R_2(F_2)=9 has been proved. Notice that both F_n and nK_3 contain n triangles and |V(F_n)|<|V(nK_3)| for all n≥ 2. Chen, Yu and Zhao (2021) speculated that R_2(F_n)≤ R_2(nK_3)=5n for n sufficiently large. In this paper, we first prove that R(K_1,n,F_n)=3n-ε for n≥1, where ε=0 if n is odd and ε=1 if n is even. Applying the exact values of R(K_1,n,F_n), we will confirm R_2(F_n)≤ 5n for n=3 by showing that R_2(F_3)=14.Qinghong Zhao, Bing Weiwork_fbm6ect7rrh3rekbjnnvfnfax4Mon, 07 Nov 2022 00:00:00 GMTOnline size Ramsey numbers: Odd cycles vs connected graphs
https://scholar.archive.org/work/mhhbzjxs3janjbgjov2ivyzqpu
Given two graph families ℋ_1 and ℋ_2, a size Ramsey game is played on the edge set of K_ℕ. In every round, Builder selects an edge and Painter colours it red or blue. Builder is trying to force Painter to create as soon as possible a red copy of a graph from ℋ_1 or a blue copy of a graph from ℋ_2. The online (size) Ramsey number r̃(ℋ_1,ℋ_2) is the smallest number of rounds in the game provided Builder and Painter play optimally. We prove that if ℋ_1 is the family of all odd cycles and ℋ_2 is the family of all connected graphs on n vertices and m edges, then r̃(ℋ_1,ℋ_2)≥φ n + m-2φ+1, where φ is the golden ratio, and for n≥ 3, m≤ (n-1)^2/4 we have r̃(ℋ_1,ℋ_2)≤ n+2m+O(√(m-n+1)). We also show that r̃(C_3,P_n)≤ 3n-4 for n≥ 3. As a consequence we get 2.6n-3≤r̃(C_3,P_n)≤ 3n-4 for every n≥ 3.Grzegorz Adamski, Małgorzata Bednarska-Bzdęgawork_mhhbzjxs3janjbgjov2ivyzqpuTue, 01 Nov 2022 00:00:00 GMTHadwiger's Conjecture with Certain Forbidden Induced Subgraphs
https://scholar.archive.org/work/62oe7n43jbfcbaykfgfeucwohi
We prove that {K_3, H}-free graphs are not counterexamples to Hadwiger's Conjecture, where H is any one of 33 graphs on seven, eight, or nine vertices, or H=K_8. This improves on past results of Plummer-Stiebitz-Toft, Kriesell, and Bosse. The proofs are mostly computer-assisted.Daniel Carterwork_62oe7n43jbfcbaykfgfeucwohiTue, 01 Nov 2022 00:00:00 GMTLectures on Lagrangian torus fibrations
https://scholar.archive.org/work/bbpdrcfyljb67j2ef3wc62jmzi
This is a book aimed at graduate students and researchers in symplectic geometry, based on a course I taught in 2019. The primary message is that the base of a Lagrangian torus fibration inherits an integral affine structure, which you can use to "read off" a lot of interesting geometry of the total space. Topics covered include: action-angle coordinates, symplectic reduction, toric manifolds, visible and tropical Lagrangians, almost toric systems, Milnor fibres of cyclic quotient singularities, mutation of polygons, non-toric blow-up, an almost toric view on Lisca's classification of fillings of lens spaces, resolutions of cusp singularities, Markov triples and Vianna tori. The book ends with a short list of open problems. Throughout there is an emphasis on examples and there are some exercises with solutions.Jonathan David Evanswork_bbpdrcfyljb67j2ef3wc62jmziFri, 28 Oct 2022 00:00:00 GMTA survey of Bayesian Network structure learning
https://scholar.archive.org/work/gab7csxktfgmfcp4fhpgtz2wnu
Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true in real-world areas where we seek to answer complex questions based on hypothetical evidence to determine actions for intervention. However, determining the graphical structure of a BN remains a major challenge, especially when modelling a problem under causal assumptions. Solutions to this problem include the automated discovery of BN graphs from data, constructing them based on expert knowledge, or a combination of the two. This paper provides a comprehensive review of combinatoric algorithms proposed for learning BN structure from data, describing 74 algorithms including prototypical, well-established and state-of-the-art approaches. The basic approach of each algorithm is described in consistent terms, and the similarities and differences between them highlighted. Methods of evaluating algorithms and their comparative performance are discussed including the consistency of claims made in the literature. Approaches for dealing with data noise in real-world datasets and incorporating expert knowledge into the learning process are also covered.Neville K. Kitson, Anthony C. Constantinou, Zhigao Guo, Yang Liu, Kiattikun Chobthamwork_gab7csxktfgmfcp4fhpgtz2wnuTue, 25 Oct 2022 00:00:00 GMTImpurities in ultracold quantum gases: from polaron formation to mediated interactions
https://scholar.archive.org/work/svwbri7knzgtbfl4cqw2f3wovy
In this thesis, we investigate the properties of Bose polarons in various settings. The overarching theme of this work is that, in contrast to many existing treatments of the Bose polaron, we apply semi-classical methods from first principles. Most of this thesis is based on [JJ1,JJ2,JJ3,JJ4]. Our first result addresses the Bose polaron in one dimension. We develop a primarily analytical treatment of the one-dimensional Bose polaron, which takes the impurity condensate interaction into account already on the mean-field level. Additionally, we show how to include first-order quantum corrections. Our results show excellent agreement with quasi-exact Quantum Monte Carlo simulations. Motivated by the success of using semi-classical methods, we develop a truncated Wigner like approximation to address out of equilibrium settings. Using the Keldysh path integral formalism, we arrive at a set of differential equations with stochastic initial conditions. This enables us to incorporate quantum fluctuations up to first order and study the impurity dynamics and polaron formation after a sudden quench of the impurity-boson interaction. Subsequently, we turn our attention to a three-dimensional system and again rely on semiclassical approximations to study the condensate mediated interaction between two impurities. The two impurities can form a bound state called the bipolaron for sufficiently large mediated interactions. We discuss how standard methods lead to inadequate results and show how these limitations can be remedied by correctly accounting for boson-boson interaction. We calculate the shape of the mediated interaction potential and the ground state of the two impurities, thus characterising the bipolaron formation. Thereafter, we point out the similarities between the semi-classical approximations of the polaron problem considered so far and colloids interacting with a fluctuating field. We develop a general framework that perturbatively treats a broad class of field theories and arrive at an effective action only de [...]Jonas Hugo Jager, Ryan Barnett, Engineering And Physical Sciences Research Councilwork_svwbri7knzgtbfl4cqw2f3wovyMon, 24 Oct 2022 00:00:00 GMTCrowns in Linear $3$-Graphs of Minimum Degree $4$
https://scholar.archive.org/work/o7bou2neengtbpfkedhcmjulbq
A 3-graph is a pair H = (V, E) of sets, where elements of V are called points or vertices and E contains some 3-element subsets of V , called edges. A 3-graph is called linear if any two distinct edges intersect in at most one vertex.There is a recent interest in extremal properties of 3-graphs containing no crown, three pairwise disjoint edges and a fourth edge which intersects all of them. We show that every linear 3-graph with minimum degree 4 contains a crown. This is not true if 4 is replaced by 3.Alvaro Carbonero, Willem Fletcher, Jing Guo, András Gyárfás, Rona Wang, Shiyu Yanwork_o7bou2neengtbpfkedhcmjulbqFri, 21 Oct 2022 00:00:00 GMTKim-forking for hyperimaginaries in NSOP1 theories
https://scholar.archive.org/work/ikflx2qjf5htpp3hkyi72atogm
We adapt the properties of Kim-independence in NSOP1 theories with existence proven in [5],[4] and [2] by Ramsey, Kaplan, Chernikov, Dobrowolski and Kim to hyperimaginaries by adding the assumption of existence for hyperimaginaries. We show that Kim-independence over hyperimaginaries satisfies a version of Kim's lemma, symmetry, the independence theorem, transitivity and witnessing. As applications we adapt Kim's results around colinearity and weak canonical bases from [8] to hyperimaginaries and give some new results about Lascar strong types and Kim-forking using boundedly closed hyperimaginaries.Yvon Bossutwork_ikflx2qjf5htpp3hkyi72atogmFri, 21 Oct 2022 00:00:00 GMTReport of the Topical Group on Physics Beyond the Standard Model at Energy Frontier for Snowmass 2021
https://scholar.archive.org/work/pvmnwp55ojb23ltmretmyhvpli
This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The report includes a general introduction to BSM motivations and the comparative prospects for proposed future experiments for a broad range of potential BSM models and signatures, including compositeness, SUSY, leptoquarks, more general new bosons and fermions, long-lived particles, dark matter, charged-lepton flavor violation, and anomaly detection.Tulika Bose, Antonio Boveia, Caterina Doglioni, Simone Pagan Griso, James Hirschauer, Elliot Lipeles, Zhen Liu, Nausheen R. Shah, Lian-Tao Wang, Kaustubh Agashe, Juliette Alimena, Sebastian Baum, Mohamed Berkat, Kevin Black, Gwen Gardner, Tony Gherghetta, Josh Greaves, Maxx Haehn, Phil C. Harris, Robert Harris, Julie Hogan, Suneth Jayawardana, Abraham Kahn, Jan Kalinowski, Simon Knapen, Ian M. Lewis, Meenakshi Narain, Katherine Pachal, Matthew Reece, Laura Reina, Tania Robens, Alessandro Tricoli, Carlos E.M. Wagner, Riley Xu, Felix Yu, Filip Zarnecki, Amin Aboubrahim, Andreas Albert, Michael Albrow, Wolfgang Altmannshofer, Gerard Andonian, Artur Apresyan, Kétévi Adikle Assamagan, Patrizia Azzi, Howard Baer, Michael J. Baker, Avik Banerjee, Vernon Barger, Brian Batell, Martin Bauer, Hugues Beauchesne, Samuel Bein, Alexander Belyaev, Ankit Beniwal, Mikael Berggren, Prudhvi N. Bhattiprolu, Nikita Blinov, Alain Blondel, Oleg Brandt, Giacomo Cacciapaglia, Rodolfo Capdevilla, Marcela Carena, Cesare Cazzaniga, Francesco Giovanni Celiberto, Cari Cesarotti, Sergei V. Chekanov, Hsin-Chia Cheng, Thomas Y. Chen, Yuze Chen, R. Sekhar Chivukula, Matthew Citron, James Cline, Tim Cohen, Jack H. Collins, Eric Corrigan, Nathaniel Craig, Daniel Craik, Andreas Crivellin, David Curtin, Smita Darmora, Arindam Das, Sridhara Dasu, Annapaola de Cosa, Aldo Deandrea, Antonio Delgado, Zeynep Demiragli, David d'Enterria, Frank F. Deppisch, Radovan Dermisek, Nishita Desai, Abhay Deshpande, Jordy de Vries, Jennet Dickinson, Keith R. Dienes, Karri Folan Di Petrillo, Matthew J. Dolan, Peter Dong, Patrick Draper, Marco Drewes, Etienne Dreyer, Peizhi Du, Florian Eble, Majid Ekhterachian, Motoi Endo, Rouven Essig, Jesse N. Farr, Farida Fassi, Jonathan L. Feng, Gabriele Ferretti, Daniele Filipetto, Thomas Flacke, Karri Folan Di Petrillo, Roberto Franceschini, Diogo Buarque Franzosi, Keisuke Fujii, Benjamin Fuks, Sri Aditya Gadam, Boyu Gao, Aran Garcia-Bellido, Isabel Garcia Garcia, Maria Vittoria Garzelli, Stephen Gedney, Marie-Hélène Genest, Tathagata Ghosh, Mark Golkowski, Giovanni Grilli di Cortona, Emine Gurpinar Guler, Yalcin Guler, C. Guo, Nate Graf, Ulrich Haisch, Jan Hajer, Koichi Hamaguchi, Tao Han, Philip Harris, Sven Heinemeyer, Christopher S. Hill, Joshua Hiltbrand, Tova Ray Holmes, Samuel Homiller, Sungwoo Hong, Walter Hopkins, Shih-Chieh Hsu, Phil Ilten, Wasikul Islam, Sho Iwamoto, Daniel Jeans, Laura Jeanty, Haoyi Jia, Sergo Jindariani, Daniel Johnson, Felix Kahlhoefer, Yonatan Kahn, Paul Karchin, Thomas Katsouleas, Shin-ichi Kawada, Junichiro Kawamura, Chris Kelso, Elham E Khoda, Valery Khoze, Doojin Kim, Teppei Kitahara, Juraj Klaric, Michael Klasen, Kyoungchul Kong, Wojciech Kotlarski, Ashutosh V. Kotwal, Jonathan Kozaczuk, Richard Kriske, Suchita Kulkarni, Jason Kumar, Manuel Kunkel, Greg Landsberg, Kenneth Lane, Clemens Lange, Lawrence Lee, Jiajun Liao, Benjamin Lillard, Lingfeng Li, Shuailong Li, Shu Li, Jenny List, Tong Li, Hongkai Liu, Jia Liu, Jonathan D Long, Enrico Lunghi, Kun-Feng Lyu, Danny Marfatia, Dakotah Martinez, Stephen P. Martin, Navin McGinnis, Karrick McGinty, Krzysztof Mękała, Federico Meloni, Oleksii Mikulenko, Ming Huang, Rashmish K. Mishra, Manimala Mitra, Vasiliki A. Mitsou, Chang-Seong Moon, Alexander Moreno, Takeo Moroi, Gerard Mourou, Malte Mrowietz, Patric Muggli, Jurina Nakajima, Pran Nath, J. Nelson, Matthias Neubert, Laura Nosler, Maria Teresa Núñez Pardo de Vera, Nobuchika Okada, Satomi Okada, Vitalii A. Okorokov, Yasar Onel, Tong Ou, Maksym Ovchynnikov, Rojalin Padhan, Priscilla Pani, Luca Panizzi, Andreas Papaefstathiou, Kevin Pedro, Cristián Peña, Federica Piazza, James Pinfold, Deborah Pinna, Werner Porod, Chris Potter, Markus Tobias Prim, Stefano Profumo, James Proudfoot, Mudit Rai, Filip Rajec, Reese Ramos, Michael J. Ramsey-Musolf, Javier Resta-Lopez, Jürgen Reuter, Andreas Ringwald, Chiara Rizzi, Thomas G. Rizzo, Giancarlo Rossi, Richard Ruiz, L. Rygaard, Aakash A. Sahai, Shadman Salam, Pearl Sandick, Deepak Sathyan, Christiane Scherb, Pedro Schwaller, Leonard Schwarze, Pat Scott, Sezen Sekmen, Dibyashree Sengupta, S. Sen, Anna Sfyrla, Eric Shackelford, T. Sharma, Varun Sharma, Jessie Shelton, William Shepherd, Seodong Shin, Elizabeth H. Simmons, Zoie Sloneker, Carlos Vázquez Sierra, Torbjörn Sjöstrand, Scott Snyder, Huayang Song, Giordon Stark, Patrick Stengel, Joachim Stohr, Daniel Stolarski, Matt Strassler, Nadja Strobbe, Julia Gonski, Rebeca Gonzalez Suarez, Taikan Suehara, Shufang Su, Wei Su, Raza M. Syed, Tim M.P. Tait, Toshiki Tajima, Andy Tang, Xerxes Tata, Teodor Tchalokov, Andrea Thamm, Brooks Thomas, Natalia Toro, Nhan V. Tran, Loan Truong, Yu-Dai Tsai, Eva Tuecke, Nikhilesh Venkatasubramanian, Chris B. Verhaaren, Carl Vuosalo, Xiao-Ping Wang, Xing Wang, Yikun Wang, Zhen Wang, Christian Weber, Glen White, Martin White, Anthony G. Williams, Brady Williams, Mike Williams, Stephane Willocq, Alex Woodcock, Yongcheng Wu, Ke-Pan Xie, Keping Xie, Si Xie, C.-H. Yeh, Ryo Yonamine, David Yu, S.-S. Yu, Mohamed Zaazoua, Aleksander Filip Żarnecki, Kamil Zembaczynski, Danyi Zhang, Jinlong Zhang, Frank Zimmermann, Jose Zuritawork_pvmnwp55ojb23ltmretmyhvpliTue, 18 Oct 2022 00:00:00 GMTMonochromatic spanning trees and matchings in ordered complete graphs
https://scholar.archive.org/work/mdn6ce2dmnhb7gefipbumvgvwi
Two independent edges in ordered graphs can be nested, crossing or separated. These relations define six types of subgraphs, depending on which relations are forbidden. We refine a remark by Erdős and Rado that every 2-coloring of the edges of a complete graph contains a monochromatic spanning tree. We show that forbidding one relation we always have a monochromatic (non-nested, non-crossing, non-separated) spanning tree in a 2-edge-colored ordered complete graph. On the other hand, if two relations are forbidden, then it is possible that we have monochromatic (nested, separated, crossing) subtrees of size only half the number of vertices. The existence of a monochromatic non-nested spanning tree in 2-colorings of ordered complete graphs verifies a more general conjecture for twisted drawings. Our second subject is to refine the Ramsey number of matchings for ordered complete graphs. Cockayne and Lorimer proved that for given positive integers t, n, m=(t-1)(n-1)+2n is the smallest integer with the following property: every t-coloring of the edges of a complete graph Km contains a monochromatic matching with n edges. We conjecture a strengthening: t-colored ordered complete graphs on m vertices contain monochromatic non-nested and also non-separated matchings with n edges. We prove this conjecture for some special cases. (i) Every t-colored ordered complete graph on t+3 vertices contains a monochromatic non-nested matching of size two. (ii) Every 2-colored ordered complete graph on 3n-1 vertices contains a monochromatic non-separated matching of size n. For nested, separated, and crossing matchings the situation is different. The smallest m ensuring a monochromatic matching of size n in every t-coloring is 2(t(n-1))+1) in the first two cases and one less in the third case.János Barát and András Gyárfás and Géza Tóthwork_mdn6ce2dmnhb7gefipbumvgvwiTue, 18 Oct 2022 00:00:00 GMTNotes on CSPs and Polymorphisms
https://scholar.archive.org/work/kouwgol6o5h55lxjkqyjupnv2i
These are notes from a multi-year learning seminar on the algebraic approach to Constraint Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures with few subpowers, the theory of absorbing subalgebras and its applications to studying CSP templates which can be solved by local consistency methods, and the dichotomy theorem for conservative CSP templates. Subsections and appendices cover supplementary material.Zarathustra Bradywork_kouwgol6o5h55lxjkqyjupnv2iThu, 13 Oct 2022 00:00:00 GMTTemporal Locality in Online Algorithms
https://scholar.archive.org/work/7kppqrhi7bbn3g77d76stpmrda
Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they do not necessarily make consistent decisions. In this work we introduce time-local online algorithms. These are online algorithms where the output at a given time only depends on T = O(1) latest inputs. The use of (deterministic) time-local algorithms in a distributed setting automatically leads to globally consistent decisions. Our key observation is that time-local online algorithms (in which the output at a given time only depends on local inputs in the temporal dimension) are closely connected to local distributed graph algorithms (in which the output of a given node only depends on local inputs in the spatial dimension). This makes it possible to interpret prior work on distributed graph algorithms from the perspective of online algorithms. We describe an algorithm synthesis method that one can use to design optimal time-local online algorithms for small values of T. We demonstrate the power of the technique in the context of a variant of the online file migration problem, and show that e.g. for two nodes and unit migration costs there exists a 3-competitive time-local algorithm with horizon T=4, while no deterministic online algorithm (in the classic sense) can do better. We also derive upper and lower bounds for a more general version of the problem; we show that there is a 6-competitive deterministic time-local algorithm and a 2.62-competitive randomized time-local algorithm for any migration cost α≥ 1.Maciej Pacut, Mahmoud Parham, Joel Rybicki, Stefan Schmid, Jukka Suomela, Aleksandr Tereshchenkowork_7kppqrhi7bbn3g77d76stpmrdaThu, 13 Oct 2022 00:00:00 GMTFormalising Szemerédi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions in Isabelle/HOL
https://scholar.archive.org/work/v73cbf2vwnf57b2fgjitrb4lim
We have formalised Szemer\'edi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant Isabelle/HOL. For the latter formalisation, we used the former to first show the Triangle Counting Lemma and the Triangle Removal Lemma: themselves important technical results. Here, in addition to showcasing the main formalised statements and definitions, we focus on sensitive points in the proofs, describing how we overcame the difficulties that we encountered.Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulsonwork_v73cbf2vwnf57b2fgjitrb4limThu, 13 Oct 2022 00:00:00 GMT