65 research outputs found

    How to build a brick

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    A graph is matching covered if it connected, has at least two vertices and each of its edges is contained in a perfect matching. A 3-connected graph G is a brick if, for any two vertices u and v of G, the graph G - {u, v) has a perfect matching. As shown by Lovasz [Matching structure and the matching lattice, J. Combin. Theory Ser. B 43 (1987) 187-222] every matching covered graph G may be decomposed, in an essentially unique manner, into bricks and bipartite graphs known as braces. The number of bricks resulting from this decomposition is denoted by b(G). The object of this paper is to present a recursive procedure for generating bricks. We define four simple operations that can be used to construct new bricks from given bricks. We show that all bricks may be generated from three basic bricks K-4, (C) over bar (6) and the Petersen graph by means of these four operations. In order to establish this, it turns out to be necessary to show that every brick G distinct from the three basic bricks has a thin edge, that is, an edge e such that (i) G - e is a matching covered graph with b(G - e) = 1 and (ii) for each barrier B of G - e, the graph G - e - B has precisely I B I - I isolated vertices, each of which has degree two in G - e. Improving upon a theorem proved in [M.H. de Carvalho, C.L. Lucchesi, U.S.R. Murty, On a conjecture of Lovasz concerning bricks, 1, The characteristic of a matching covered graph, J. Combin. Theory Ser. B 85 (2002) 94-436; M.H. de Carvalho, C.L. Lucchesi, U.S.R. Murty, On a conjecture of Lovasz concerning bricks, 11, Bricks of finite characteristic, J. Combin. Theory Ser. B 85 (2002) 137-180] we show here that every brick different from the three basic bricks has an edge that is thin. A cut of a matching covered graph G is separating if each of the two graphs obtained from G by shrinking the shores of the cut to single vertices is also matching covered. A brick is solid if it does not have any nontrivial separating cuts. Solid bricks have many interesting properties, but the complexity status of deciding whether a given brick is solid is not known. Here, by using our theorem on the existence of thin edges, we show that every simple planar solid brick is an odd wheel. (c) 2006 Elsevier B.V. All rights reserved.30619-202383241

    Ear decompositions of matching covered graphs

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    Ear decompositions of matching covered graphs are important for understanding their structure. By exploiting the properties of the dependence relation introduced by Carvalho and Lucchesi in [2], we are able to provide simple proofs of several well-known theorems concerning ear decompositions. Our method actually provides proofs of generalizations of these theorems. For example, we show that every matching covered graph G different from K-2 and C-2n has at least Delta edge-disjoint removable ears, where Delta is the maximum degree of G. This shows that any matching covered graph G has at least Delta! different ear decompositions, and thus is a generalization of the fundamental theorem of Lovasz and Plummer establishing the existence of ear decompositions. We also show that every brick G different from K-4 and (C) over bar(6) has Delta-2 edges, each of which is a removable edge in G, that is, an edge whose deletion from G results in a matching covered graph. This generalizes a well-known theorem of Lovasz. We also give a simple proof of another theorem due to Lovasz which says that every nonbipartite matching covered graph has a canonical ear decomposition, that is, one in which either the third graph in the sequence is an odd-subdivision of K-4 or the fourth graph in the sequence is an odd-subdivision of (C) over bar(6). Our method in fact shows that every nonbipartite matching covered graph has a canonical ear decomposition which is optimal, that is one which has as few double ears as possible. Most of these results appear in the Ph. D. thesis of the first author [1], written under the supervision of the second author.19215117

    The perfect matching polytope and solid bricks

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    The perfect matching polytope of a graph G is the convex hull of the set of incidence vectors of perfect matchings of G. Edmonds (J. Res. Nat. Bur. Standards Sect. B 69B 1965 125) showed that a vector x in Q(E) belongs to the perfect matching polytope of G if and only if it satisfies the inequalities: (i) x greater than or equal to 0 (non-negativity), (ii) x (partial derivative(v)) = 1, for all v is an element of V (degree constraints) and (iii) x(partial derivative(S)) greater than or equal to 1, for all odd subsets S of V (odd set constraints). In this paper, we characterize graphs whose perfect matching polytopes are determined by non-negativity and the degree constraints. We also present a proof of a recent theorem of Reed and Wakabayashi. (C) 2004 Elsevier Inc. All rights reserved.92231932

    Selected aspects of the university social responsibility (USR) in Poland

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    Motivation: In accordance with the Law on Higher Education, the mission of the Polish education and science system is to provide top quality education and scientific activity, develop civic attitudes, and be involved in social development and creation of an innovation-based economy. The third mission of an academy focusing on social responsibility is to build mutual relations with the community in order to popularise and implement research results. In recent years, university social responsibility (USR) has turned into one of the priorities for Polish academic authorities, although research shows this to be a new matter in this area, which often leads to incorrect classification of activities resulting from regular obedience of the law as activities confirming the social responsibility of the organisation. Aim: The main objective of this article is to identify examples of socially responsible activity assumed by Polish academies and demonstrate the similarities with such activities conducted by other foreign academies. The author also wanted to associate the name of Professor Karol Adamiecki with social responsibility affairs what is usually overlooked in studies on this subject. Results: The conducted analyses confirmed that Polish academies are assuming socially responsible activity voluntarily and not just in order to fulfil the criterion of conformity with the currently effective laws. Furthermore, these results also confirm that — in comparison with academies abroad — the involvement of Polish academies in implementation of the concept of social responsibility is on the right path of development, although not as popularised, which only confirms the genuine and non-marketing approach to the matter of social responsibility

    Author-Kit

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    [SC 2020] output from commands that gather execution environment information. # Environment information of Sunway Taihulight: 1. MPI version cp/usr/swmpp/mpi2/mpiswgcc/bin/mpichversion./ cp /usr/sw-mpp/mpi2/mpiswgcc/bin/mpichversion ./ bsub -I -n 1 -q q_sw_expr ./mpichversion Job has been submitted to queue waiting for dispatch ... dispatching ... MVAPICH2 Version: 2.2a MVAPICH2 Release date: Mon Aug 17 20:00:00 EDT 2015 MVAPICH2 Device: ch3:mrail MVAPICH2 configure: --without-cma --with-rdma=gen2 -prefix=/usr/sw-mpp/mpi2/mpiswgcc --with-pm=no --with-ib-include=/usr/sw-mpp/include --with-ib-libpath=/usr/sw-mpp/lib --enable-threads=single --enable-cxx --enable-f77 --enable-fc --enable-romio --with-ch3-rank-bits=32 --without-mpe --without-hwloc --disable-rdma-cm --disable-mcast --with-atomic-primitives=no --disable-fuse --disable-shared --enable-static --with-cross=crossfile --disable-registration-cache --host=sw --disable-smpcoll MVAPICH2 CC: sw5gcc -mhost -DCONFIG_SWIB -DNDEBUG -DNVALGRIND -O2 MVAPICH2 CXX: sw5g++ -mhost -DNDEBUG -DNVALGRIND -O2 MVAPICH2 F77: sw5gfortran -mhost -L/usr/sw-mpp/lib -O2 MVAPICH2 FC: sw5gfortran -mhost -O2 Job 48191998 has been finished. 2. uname -a bsub -I -n 1 -q q_sw_expr uname -a Job has been submitted to queue waiting for dispatch ... dispatching ... Linux vn000001 3.8.0-sw5 # SMP Wed Apr 25 10:49:45 CST 2018 sw_64 GNU/Linux Job 48192008 has been finished. 3. cpuinfo bsub -I -n 1 -q q_sw_expr lscpu || cat /proc/cpuinfo Job has been submitted to queue waiting for dispatch ... dispatching ... vn000000: exec_task: execvp(/usr/bin/lscpu) failed. errno= 2, reason: No such file or directory [48192041 ## Sun Apr 19 11:28:11 2020] warning: node [0]: user's mpe task: tid= 0, pid= 11761, exit_code= 2 Job 48192041 has been finished. exit_code is 2 bsub -I -n 1 -q q_sw_expr cat /proc/cpuinfo Job has been submitted to queue waiting for dispatch ... dispatching ... cpu : SW_64 cpu model : SW5 cpu variation : 1 cpu revision : 0 cpu serial number : system type : shenwei system variation : 0 system revision : 0 system serial number : cycle frequency [Hz] : 1450000000 timer frequency [Hz] : 0.24 page size [bytes] : 8192 phys. address bits : 44 max. addr. space # : 255 BogoMIPS : 0.81 kernel unaligned acc : 0 (pc=0,va=0) user unaligned acc : 848883545 (pc=4ff041fca8,va=5000281914) platform string : N/A cpus detected : 4 cpus active : 4 cpu active mask : 0000000000001111 cpus core_start : 000000000000000f mem cycle freq : 500 L1 Icache : 64K, 2-way, 64b line L1 Dcache : 64K, 2-way, 64b line L2 cache : n/a L3 cache : n/a Job 48192044 has been finished. 4. meninfo bsub -I -n 1 -q q_sw_expr cat /proc/meminfo Job has been submitted to queue waiting for dispatch ... dispatching ... MemTotal: 2038472 kB MemFree: 372600 kB Buffers: 0 kB Cached: 1371984 kB SwapCached: 0 kB Active: 718224 kB Inactive: 715008 kB Active(anon): 131576 kB Inactive(anon): 8 kB Active(file): 586648 kB Inactive(file): 715000 kB Unevictable: 70912 kB Mlocked: 2904 kB SwapTotal: 0 kB SwapFree: 0 kB Dirty: 0 kB Writeback: 0 kB AnonPages: 132136 kB Mapped: 4224 kB Shmem: 24 kB Slab: 22040 kB SReclaimable: 5144 kB SUnreclaim: 16896 kB KernelStack: 4368 kB PageTables: 328 kB NFS_Unstable: 0 kB Bounce: 0 kB WritebackTmp: 0 kB CommitLimit: 1019232 kB Committed_AS: 200360 kB VmallocTotal: 8388608 kB VmallocUsed: 12208 kB VmallocChunk: 8376400 kB AnonHugePages: 0 kB HugePages_Total: 0 HugePages_Free: 0 HugePages_Rsvd: 0 HugePages_Surp: 0 Hugepagesize: 8192 kB ======================= cg0 ===================== UserPages_Mem_size: 8192 MB UserPages_Conti_Total: 7680 MB UserPages_Conti_Free: 7680 MB UserPages_Conti_Used: 0 MB UserPages_Cross_Size: 0 MB ======================= cg1 ===================== UserPages_Mem_size: 8192 MB UserPages_Conti_Total: 7680 MB UserPages_Conti_Free: 7680 MB UserPages_Conti_Used: 0 MB UserPages_Cross_Size: 0 MB ======================= cg2 ===================== UserPages_Mem_size: 8192 MB UserPages_Conti_Total: 7680 MB UserPages_Conti_Free: 7680 MB UserPages_Conti_Used: 0 MB UserPages_Cross_Size: 0 MB ======================= cg3 ===================== UserPages_Mem_size: 8192 MB UserPages_Conti_Total: 7680 MB UserPages_Conti_Free: 7680 MB UserPages_Conti_Used: 0 MB UserPages_Cross_Size: 0 MB Job 48192086 has been finished. ## Environment information of TianHe 2 we run script provided by Author-Kit on login node of TianHe2 #! /bin/sh # Linux data-gathering commands; adjust as necessary for your platform. # # Be sure to remove any information from the output that would violate # SC's double-blind review policies. env | sed "s/USER/USER/g" set -x lsb_release -a uname -a lscpu || cat /proc/cpuinfo cat /proc/meminfo inxi -F -c0 lsblk -a lsscsi -s module list nvidia-smi (lshw -short -quiet -sanitize || lspci) | cat the output is in file collect_environment-tianhe2-output.txt of current repository

    Bibliometric analysis of scientific production on university social responsibility in Latin America and the Caribbean [version 2; peer review: 2 approved]

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    Objective: To evaluate the scientific production on university social responsibility (USR) from institutions in Latin America and the Caribbean. Methods: A bibliometric analysis was conducted on documents published in indexed journals in the Scopus database from its inception until April 2023. Eligible documents included those on USR describing experiences carried out by universities in Latin America and the Caribbean. The number of articles per author, average authors per article, average citations per article, and the number of documents with one or more author were described. Bibliometric indicators regarding authors per article, co-authors per article, and institutional collaboration were presented. Bibliometric networks were constructed based on bibliographic coupling analysis of documents by countries and term co-occurrence in titles and abstracts. Results: Of a total of 4075 documents retrieved from Scopus, 150 were included. Documents published between 1997 and 2023 were identified, with an average annual growth rate of 2.7%. A total of 439 authors were identified, 18 articles had a single author, and an average of 0.3 articles per author and a co-authorship index of 3.13 were found. The percentage of international collaborations was 30.7%. Brazil had the highest proportion of publications (26.4%), followed by Chile (17%) and Colombia (13.2%). Opción and Revista de Ciencias Sociales were the journals with the highest number of articles published (13 each). In the analysis of term co-occurrence, recent years showed an increase in the use of terms related to e-learning, information and communication technologies, virtual education, COVID-19, sustainable development goals, and URSULA (initiative on USR in institutions in Latin America and the Caribbean). Conclusions: A growth in scientific production on USR in Latin America and the Caribbean was identified. The interest in USR documents in recent years has been focused on COVID-19 and the challenges of virtual education and sustainable development

    Sirian and Iranian feminine figurines in the collections of MAE/USP

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    This article intends to present twelve terracotta figurines preserved in MAE-USR The author gives an up-to-date classification of this material, considering provenience and chronology. The magic functions of these figurines in Ancient Near Eastern Societies are algo considered

    Social responsibility of high education institution in Vietnam

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    Dang, T.T.H. Social Responsibility of Higher Education Institution in Vietnam, Bachelor Thesis. Brno: Mendel University, 2017.This Bachelor Thesis is concern about Social Responsibility in Higher Education Institution (USR). The aim of the Thesis is to give recommendation on the field of Corporate Social Responsibility to a Vietnamese Higher Education Institution with economic focus-Economic Faculty, Thu Dau Mot University (EF-TDMU)by comparison with the Faculty of Businiess and Management, Mendel University (FBE-MENDELU). The recommendation is obtained based on qualitative method, benchmarking and desk research method. The study examines their awareness, knowledge and usage of CSR principles. EF-TDMU appears to practice USR passively and it is significantly surpassed by FBE-MENDELU.As a result, the EF is recommended to include USR in their policies and strategies in the long-term. The author is highly stresses USR pratice not only in higher education, but also from kindergarten to grow and develop a seed of love in kids, love for human beings, nonhuman beings and nature, and a need for expressing love and mindfulness in certain activities

    Zakaria Rhani

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    is a professor of anthropology at Université Mohamed V (Institut Universitaire de la Recherche Scientifique) and Research Associate at Centre Jaques Berque (CNRS USR-3136). He is working on : Political and Religious Process in the Arab world; Sexual Symbolism; Trauma, Memory and History of Political Violence. He is the author of Le pouvoir de guérir. Mythe, mystique et politique au Maroc (2014, Leiden/Boston: Brill). He has also published numerous articles in International Journals (i.e. L’Ho..

    High-Dimensional Graphical Model Search with the gRapHD R Package

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    This paper presents the R package gRapHD for efficient selection of high-dimensional undirected graphical models. The package provides tools for selecting trees, forests, and decomposable models minimizing information criteria such as AIC or BIC, and for displaying the independence graphs of the models. It has also some useful tools for analysing graphical structures. It supports the use of discrete, continuous, or both types of variables.
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