{"results":[{"id":"doaj_10.31743/vp.19258","title":"From the Council of Nicaea to Vatican II: Professing the Faith, the Creeds, and the Church’ s Credibility 31st International Theological Symposium (Split, Chorwacja, 16-17.10.2025)","authors":[{"name":"Marcin Wysocki"}],"abstract":"\nSprawozdanie z międzynarodowej konferencji naukowej From the Council of Nicaea to Vatican II: Professing the Faith, the Creeds, and the Church’ s Credibility, 31st International Theological Symposium, która odbyła się w dniach 16-17.10.2025 na Wydziale Teologicznym Uniwersytetu w Splicie, w Chorwacji.\n","source":"DOAJ","year":2025,"language":"","subjects":["Early Christian literature. Fathers of the Church, etc.","Philosophy of religion. Psychology of religion. Religion in relation to other subjects","Philosophy. Psychology. Religion"],"doi":"10.31743/vp.19258","url":"https://czasopisma.kul.pl/index.php/vp/article/view/19258","is_open_access":true,"published_at":"","score":69},{"id":"arxiv_2509.08198","title":"Computation of Singular Godeaux Surfaces and a New Explicit Fake Quadric (With an Appendix by Christian Gleissner and Noah Ruhland)","authors":[{"name":"Carlos Rito"},{"name":"Christian Gleissner"},{"name":"Noah Ruhland"}],"abstract":"We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obtain explicit examples with many singularities. In particular, we construct a Godeaux surface whose singular locus consists of two $\\mathsf A_1$ and two $\\mathsf A_3$ singularities. We show that this surface admits a $\\mathbb{Z}/2 \\times \\mathbb{Z}/4$ abelian cover which is a smooth minimal surface of general type with invariants $K^2=8$ and $p_g=0$, i.e. a fake quadric. Together with the result in the Appendix, this provides the first explicit construction of a fake quadric that does not arise as a quotient of a product of curves.","source":"arXiv","year":2025,"language":"en","subjects":["math.AG"],"url":"https://arxiv.org/abs/2509.08198","pdf_url":"https://arxiv.org/pdf/2509.08198","is_open_access":true,"published_at":"2025-09-10T00:04:21Z","score":69},{"id":"arxiv_2505.18161","title":"On the orientation of historic Christian churches of Fuerteventura: conciliating tradition, winds and topography","authors":[{"name":"Maria Florencia Muratore"},{"name":"Alejandro Gangui"},{"name":"Maitane Urrutia-Aparicio"},{"name":"Carmelo Cabrera"},{"name":"Juan Antonio Belmonte"}],"abstract":"We present the results of an analysis of the precise spatial orientation of colonial Christian churches located in the Canary Island of Fuerteventura (Spain). Our sample consists of 48 churches, most built during the period between the Castilian conquest led by the Norman Jean de Béthencourt in the 15th century and the end of the 19th century. We examine whether the standard tradition was followed regarding the orientation of the apses of historic churches eastwards. While most of the religious constructions in the sample have their main axes oriented within the solar range, the statistical analysis also reveals the presence of two different groups of churches with different possible interpretations. For the first group, mainly composed of churches located in the central part of the island, an anomalous tendency to orientate them towards a declination of c. -14 degrees is detected. We provide some possible explanations for this, which include the date of a traditional Canarian celebration, an eventual imprint of topography, and the possibility of sunset orientations. Also, this particular value of declination is close to -16.3 degrees, the declination of Sirius during the 17th century. Therefore, we provide ethnographic data that might support an eventually controversial 'bright star' orientation. For the second group, meanwhile, we find a pattern of orientation where the apse of the churches points slightly to the north of due east. We propose this might signal constructions that were oriented to the rising Sun on dates close to Easter, one of the most important festivities of Christianity.","source":"arXiv","year":2025,"language":"en","subjects":["physics.hist-ph","astro-ph.IM","physics.soc-ph"],"doi":"10.1558/jsa.22808","url":"https://arxiv.org/abs/2505.18161","pdf_url":"https://arxiv.org/pdf/2505.18161","is_open_access":true,"published_at":"2025-05-11T15:49:04Z","score":69},{"id":"arxiv_2502.08016","title":"The CEGM NLSM","authors":[{"name":"Nick Early"}],"abstract":"Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes. However, extending this to generalizations of other quantum field theories remains a central challenge. Recently it has been discovered that the nonlinear sigma model (NLSM) emerges after a certain zero-preserving deformation from $\\text{tr}(φ^3)$. In this work, we find a much richer story of zero-preserving deformations in the CEGM context, yielding generalized NLSM amplitudes. We prove an explicit formula for the residual embedding of an $n$-point NLSM amplitude in a mixed $n+2$ point generalized NLSM amplitude, which provides a strong consistency check on our generalization. We show that the dimension of the space of pure kinematic deformations is $\\gcd(k,n)-1$, we introduce a deformation-compatible modification of the Global Schwinger Parameterization, and we include a new proof, using methods from matroidal blade arrangements, of the linear independence for the set of planar kinematic invariants for CEGM amplitudes. Our framework is compatible with string theory through recent generalizations of the Koba-Nielsen string integral to any positive configuration space $X^+(k,n)$, where the usual Koba-Nielsen string integral corresponds to $X(2,n) = \\mathcal{M}_{0,n}$.","source":"arXiv","year":2025,"language":"en","subjects":["hep-th","math.CO"],"url":"https://arxiv.org/abs/2502.08016","pdf_url":"https://arxiv.org/pdf/2502.08016","is_open_access":true,"published_at":"2025-02-11T23:31:39Z","score":69},{"id":"arxiv_2310.12130","title":"Moduli Space Tilings and Lie-Theoretic Color Factors","authors":[{"name":"Nick Early"}],"abstract":"A detailed understanding of the moduli spaces $X(k,n)$ of $n$ points in projective $k-1$ space is essential to the investigation of generalized biadjoint scalar amplitudes, as discovered by Cachazo, Early, Guevara and Mizera (CEGM) in 2019. But in math, conventional wisdom says that it is completely hopeless due to the arbitrarily high complexity of realization spaces of oriented matroids. In this paper, we nonetheless find a path forward.   We present a Lie-theoretic realization of color factors for color-dressed generalized biadjoint scalar amplitudes, formulated in terms of certain tilings of the real moduli space $X(k,n)$ and collections of logarithmic differential forms, resolving an important open question from recent work by Cachazo, Early and Zhang. The main idea is to replace the realization space decomposition of $X(k,n)$ with a large class of overlapping tilings whose topologies are individually relatively simple. So we obtain a collection of color-dressed amplitudes, each of which satisfies $U(1)$ decoupling separately. The essential complexity appears when they are all superposed.","source":"arXiv","year":2023,"language":"en","subjects":["hep-th","math.AG","math.CO"],"url":"https://arxiv.org/abs/2310.12130","pdf_url":"https://arxiv.org/pdf/2310.12130","is_open_access":true,"published_at":"2023-10-18T17:41:02Z","score":67},{"id":"arxiv_2304.07351","title":"Generalized Color Orderings: CEGM Integrands and Decoupling Identities","authors":[{"name":"Freddy Cachazo"},{"name":"Nick Early"},{"name":"Yong Zhang"}],"abstract":"In a recent paper, we defined generalized color orderings (GCO) and Feynman diagrams (GFD) to compute color-dressed generalized biadjoint amplitudes. In this work, we study the Cachazo-Early-Guevara-Mizera (CEGM) representation of generalized partial amplitudes and ``decoupling\" identities. This representation is a generalization of the Cachazo-He-Yuan (CHY) formulation as an integral over the configuration space $X(k,n)$ of $n$ points on $\\mathbb{CP}^{k-1}$ in generic position.   Unlike the $k=2$ case, Parke-Taylor-like integrands are not enough to compute all partial amplitudes for $k\u003e2$. Here we give a set of constraints that integrands associated with GCOs must satisfy and use them to construct all $(3,n\u003c9)$ integrands, all $(3,9)$ integrands up to four undetermined constants, and $95 \\%$ of $(4,8)$ integrands up to 24 undetermined constants.   $k=2$ partial amplitudes are known to satisfy identities. Among them, the so-called $U(1)$ decoupling identities are the simplest ones. These are characterized by a label $i$ and a color ordering in $X(2,|[n]\\setminus \\{i\\}|)$. Here we introduce decoupling identities for $k\u003e2$ determined combinatorially using GCOs. Moreover, we identify the natural analog of $U(1)$ identities as those characterized by a pair of labels $i\\neq j$, and a pair of GCOs, one in $X(k,|[n]\\setminus \\{i\\}|)$ and the other in $X(k-1,|[n]\\setminus \\{j\\}|)$. We call them {\\it double extension} identities.   We also provide explicit connections among different ways of representing GCOs, such as configurations of lines, configurations of points, and reorientation classes of uniform oriented matroids (chirotopes).","source":"arXiv","year":2023,"language":"en","subjects":["hep-th","math.AG","math.CO"],"doi":"10.1016/j.nuclphysb.2024.116552","url":"https://arxiv.org/abs/2304.07351","pdf_url":"https://arxiv.org/pdf/2304.07351","is_open_access":true,"published_at":"2023-04-14T18:57:06Z","score":67},{"id":"arxiv_2204.01743","title":"Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes","authors":[{"name":"Freddy Cachazo"},{"name":"Nick Early"}],"abstract":"In the Grassmannian formulation of the S-matrix for planar $\\mathcal{N}=4$ Super Yang-Mills, $N^{k-2}MHV$ scattering amplitudes for $k$ negative and $n-k$ positive helicity gluons can be expressed, by an application of the global residue theorem, as a signed sum over a collection of $(k-2)(n-k-2)$-dimensional residues. These residues are supported on certain positroid subvarieties of the Grassmannian $G(k,n)$. In this paper, we replace the Grassmannian $G(3,n)$ with its torus quotient, the moduli space of $n$ points in the projective plane in general position, and planar $\\mathcal{N}=4$ SYM with generalized biadjoint scalar amplitudes $m^{(3)}_n$ as introduced by Cachazo-Early-Guevara-Mizera (CEGM). Whereas in the Grassmannian formulation residues of the Parke-Taylor form correspond to individual BCFW, or on-shell diagrams, we show that each such $(n-5)$-dimensional residue of $m^{(3)}_n$ is an entire biadjoint scalar partial amplitude $m^{(2)}_n$, that is a sum over all tree-level Feynman diagrams for a fixed planar order. We propose a generalization which would give rise to identifications of $m^{(2)}_n$ inside $m^{(k)}_n$ for $k\\ge 4$, via $(k-2)(n-k-2)$-dimensional residues. Our proof for $k=3$ uses the CEGM formula for $m^{(3)}_n$; it predicts a new Minkowski sum realization of the associahedron in terms of certain positroid polytopes in the second hypersimplex $Δ_{2,n}$.","source":"arXiv","year":2022,"language":"en","subjects":["hep-th","math.CO"],"url":"https://arxiv.org/abs/2204.01743","pdf_url":"https://arxiv.org/pdf/2204.01743","is_open_access":true,"published_at":"2022-04-04T18:00:01Z","score":66},{"id":"arxiv_2211.16623","title":"Factorization for Generalized Biadjoint Scalar Amplitudes via Matroid Subdivisions","authors":[{"name":"Nick Early"}],"abstract":"We study the problem of factorization for residues of generalized biadjoint scalar scattering amplitudes $m^{(k)}_n$, introduced by Cachazo, Early, Guevara and Mizera (CEGM), involving multi-dimensional residues which factorize generically into $k$-ary products of lower-point generalized biadjoint amplitudes of the same type $m^{(k)}_{n_1}\\cdots m^{(k)}_{n_k}$, where $n_1+\\cdots +n_k = n+k(k-1)$, noting that smaller numbers of factors arise as special cases. Such behavior is governed geometrically by regular matroid subdivisions of hypersimplices and cones in the positive tropical Grassmannian, and combinatorially by collections of compatible decorated ordered set partitions, considered modulo cyclic rotation. We make a proposal for conditions under which this happens and we develop $k=3,4$ in detail. We conclude briefly to propose a novel formula to construct coarsest regular matroid subdivisions of all hypersimplices $Δ_{k,n}$ and rays of the positive tropical Grassmannian, which should be of independent interest.","source":"arXiv","year":2022,"language":"en","subjects":["math.CO","hep-th","math.AG"],"url":"https://arxiv.org/abs/2211.16623","pdf_url":"https://arxiv.org/pdf/2211.16623","is_open_access":true,"published_at":"2022-11-29T23:00:58Z","score":66},{"id":"arxiv_2210.04940","title":"The Galactic Chemical Evolution of phosphorus observed with IGRINS","authors":[{"name":"G. Nandakumar"},{"name":"N. Ryde"},{"name":"M. Montelius"},{"name":"B. Thorsbro"},{"name":"H. Jönsson"},{"name":"G. Mace"},{"name":"Lund Observatory"},{"name":"Department of Astronomy"},{"name":"Theoretical Physics"},{"name":"Lund University"},{"name":"Box 43"},{"name":"SE-221 00 Lund"},{"name":" Sweden"},{"name":"Kapteyn Astronomical Institute"},{"name":"University of Groningen"},{"name":"Landleven 12"},{"name":"NL-9747 AD Groningen"},{"name":"the Netherlands"},{"name":"Department of Astronomy"},{"name":"School of Science"},{"name":"The University of Tokyo"},{"name":"7-3-1 Hongo"},{"name":" Bunkyo-ku"},{"name":"Tokyo 113-0033"},{"name":" Japan"},{"name":"Materials Science"},{"name":"Applied Mathematics"},{"name":"Malmö University"},{"name":"SE-205 06 Malmö"},{"name":" Sweden"},{"name":"Department of Astronomy"},{"name":"McDonald Observatory"},{"name":"The University of Texas"},{"name":" Austin"},{"name":"TX 78712"},{"name":" USA"}],"abstract":"Phosphorus (P) is considered to be one of the key elements for life, making it an important element to look for in the abundance analysis of spectra of stellar systems. Yet, there exists only a handful of spectroscopic studies to estimate the P abundances and investigate its trend across a range of metallicities. We have observed full HK band spectra at a spectral resolving power of R=45,000 with IGRINS instrument. Abundances are determined using SME in combination with 1D MARCS stellar atmosphere models. The investigated sample of stars have reliable stellar parameters estimated using optical FIES spectra (GILD; Jönsson et al. in prep.). In order to determine the P abundances from the 16482.92 Angstrom P line, we take special care of the CO($ν=7-4$) blend. We determine the C, N, O abundances from atomic carbon and a range of non-blended molecular lines (CO, CN, OH) which are aplenty in the H band region of K giant stars, assuring an appropriate modelling of the blending CO($ν=7-4$) line. We present [P/Fe] vs [Fe/H] trend for 38 K giant stars in the metallicity range of -1.2 dex $\u003c$ [Fe/H] $\u003c$ 0.4 dex. We find that our trend matches well with the compiled literature sample of prominently dwarf stars and limited number of giant stars. Our trend is found to be higher by $\\sim$ 0.05 - 0.1 dex compared to the theoretical chemical evolution trend in Cescutti et al. 2012 resulting from core collapse supernova (type II) of massive stars with the P yields from Kobayashi et al. (2006) arbitrarily increased by a factor of 2.75. Thus the enhancement factor might need to be $\\sim$ 0.05 - 0.1 dex higher to match our trend. We also find an empirically determined primary behaviour for phosphorus. Furthermore, the phosphorus abundance is found to be elevated by $\\sim$ 0.6 - 0.9 dex in two metal poor s-enriched stars compared to the theoretical chemical evolution trend.","source":"arXiv","year":2022,"language":"en","subjects":["astro-ph.SR","astro-ph.GA"],"doi":"10.1051/0004-6361/202244724","url":"https://arxiv.org/abs/2210.04940","pdf_url":"https://arxiv.org/pdf/2210.04940","is_open_access":true,"published_at":"2022-10-10T18:16:50Z","score":66},{"id":"doaj_List+gratulacyjny+Podziemnego+Radia++%22Solidarno%C5%9B%C4%87%22","title":"List gratulacyjny Podziemnego Radia  \"Solidarność\"","authors":null,"abstract":"","source":"DOAJ","year":2021,"language":"","subjects":["Early Christian literature. Fathers of the Church, etc.","Philosophy of religion. Psychology of religion. Religion in relation to other subjects","Philosophy. Psychology. Religion"],"url":"https://czasopisma.kul.pl/index.php/vp/article/view/12858","is_open_access":true,"published_at":"","score":65},{"id":"arxiv_2106.13800","title":"Archaeoastronomical study of Christian churches in Fuerteventura","authors":[{"name":"Maria Florencia Muratore"},{"name":"Alejandro Gangui"}],"abstract":"We present an archaeoastronomical study of the orientations of the colonial Christian churches on the island of Fuerteventura, in the Canary Islands, Spain, mostly built from the period of the Norman conquest in the 15th century to the 19th century. Our goal is to analyze the possible astronomical influence on the orientation of these churches. Preliminary results suggest that the vast majority of the island's religious constructions have their axes oriented within the solar range, between the extreme azimuths of the annual movement of the Sun as it crosses the local horizon. This differs from what was found on the islands of Lanzarote and La Gomera (also in the Canaries) previously studied.","source":"arXiv","year":2021,"language":"en","subjects":["physics.hist-ph","astro-ph.IM"],"url":"https://arxiv.org/abs/2106.13800","pdf_url":"https://arxiv.org/pdf/2106.13800","is_open_access":true,"published_at":"2021-06-25T17:56:13Z","score":65},{"id":"arxiv_2112.14191","title":"Smoothly Splitting Amplitudes and Semi-Locality","authors":[{"name":"Freddy Cachazo"},{"name":"Nick Early"},{"name":"Bruno Umbert"}],"abstract":"In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity. This behavior exhibits properties which we call $\\textit{smooth splitting}$ and $\\textit{semi-locality}$. The former means that an amplitude becomes the product of exactly three amputated Berends-Giele currents, while the latter means that any two currents share one external particle. We call these smooth splittings 3-splits. In fact, there are exactly $\\binom{n}{3}-n$ such 3-splits, one for each generic, interior triangle in a polygon; as they cannot be obtained from standard factorization, they are a new phenomenon in Quantum Field Theory. In fact, the resulting splitting is analogous to the one first seen in Cachazo-Early-Guevara-Mizera (CEGM) amplitudes which generalize standard cubic scalar amplitudes from their ${\\rm Tr}\\, G(2,n)$ formulation to ${\\rm Tr}\\, G(k,n)$, where ${\\rm Tr}\\, G(k,n)$ is the tropical Grassmannian. Along the way, we show how smooth splittings naturally lead to the discovery of mixed amplitudes in the NLSM and special Galileon theories and to novel BCFW-like recursion relations for NLSM amplitudes.","source":"arXiv","year":2021,"language":"en","subjects":["hep-th","math.AG","math.CO"],"doi":"10.1007/JHEP08(2022)252","url":"https://arxiv.org/abs/2112.14191","pdf_url":"https://arxiv.org/pdf/2112.14191","is_open_access":true,"published_at":"2021-12-28T15:42:54Z","score":65},{"id":"arxiv_2106.07142","title":"Planarity in Generalized Scattering Amplitudes: PK Polytope, Generalized Root Systems and Worldsheet Associahedra","authors":[{"name":"Nick Early"}],"abstract":"In this paper we study the role of planarity in generalized scattering amplitudes, through several closely interacting structures in combinatorics, algebraic and tropical geometry.   The generalized biadjoint scalar amplitude, introduced recently by Cachazo-Early-Guevara-Mizera (CEGM), is a rational function of homogeneous degree $-(k-1)(n-k-1)$ in $\\binom{n}{k}-n$ independent variables; its poles can be constructed directly from the rays of the positive tropical Grassmannian.   We introduce for each pair of integers $(k,n)$ with $2\\le k\\le n-2$ a system of generalized positive roots which arises as a specialization of the planar basis of kinematic invariants. We prove that the higher root polytope $\\mathcal{R}^{(k)}_{n-k}$ has volume the k-dimensional Catalan number $C^{(k)}_{n-k}$, via a flag unimodular triangulation into simplices, in bijection with noncrossing collections of $k$-element subsets. We also give a bijection between certain positroidal subdivisions, called tripods, of the hypersimplex $Δ_{3,n}$ and noncrossing pairs of 3-element subsets that are not weakly separated.   We show that the facets of the Planar Kinematics (PK) polytope, introduced recently by Cachazo and the author, are exactly the $\\binom{n}{k}-n$ generalized positive roots. We show that the PK specialization of the generalized biadjoint amplitude evaluates to $C^{(k)}_{n-k}$.   Looking forward, we give defining equations and conjecture explicit solutions using $(\\mathbb{CP}^{n-k-1})^{\\times (k-1)}$ via a notion of compatibility degree for noncrossing collections, for a two parameter family of generalized worldsheet associahedra $\\mathcal{W}^+_{k,n}$. These specialize when $k=2$ to a certain dihedrally invariant partial compactification of the configuration space $M_{0,n}$ of $n$ distinct points in $\\mathbb{CP}^{1}$. Many detailed examples are given throughout to motivate future work.","source":"arXiv","year":2021,"language":"en","subjects":["math.CO","hep-th","math.AG"],"url":"https://arxiv.org/abs/2106.07142","pdf_url":"https://arxiv.org/pdf/2106.07142","is_open_access":true,"published_at":"2021-06-14T02:46:04Z","score":65},{"id":"arxiv_2111.08833","title":"Subexponential growth of early Christianity","authors":[{"name":"Jorge C. Lucero"}],"abstract":"This paper presents a simple mathematical model for the growth of the Christian population in the Roman Empire during the first to fourth centuries. The model has a subexponential growth rate of order $e^{o(t)}$, where $o$ denotes the \"little-o\" asymptotic bound, but still superpolynomial, and it fits available Christian population estimates with good accuracy.","source":"arXiv","year":2021,"language":"en","subjects":["physics.soc-ph","q-bio.PE"],"url":"https://arxiv.org/abs/2111.08833","pdf_url":"https://arxiv.org/pdf/2111.08833","is_open_access":true,"published_at":"2021-11-16T23:33:24Z","score":65},{"id":"crossref_10.14232/jp.pgy.2021.1","title":"The “Dialogue” between Calvin and the Church Fathers on the Sacrament of Baptism","authors":[{"name":"György Papp"}],"abstract":"","source":"CrossRef","year":2021,"language":"en","subjects":null,"doi":"10.14232/jp.pgy.2021.1","url":"https://doi.org/10.14232/jp.pgy.2021.1","pdf_url":"http://acta.bibl.u-szeged.hu/72896/1/in_aetatum_confiniis_007-097.pdf","is_open_access":true,"published_at":"","score":65},{"id":"arxiv_2003.07958","title":"Minimal Kinematics: An All $k$ and $n$ Peek into ${\\rm Trop}^+{\\rm G}(k,n)$","authors":[{"name":"Freddy Cachazo"},{"name":"Nick Early"}],"abstract":"In this note we present a formula for the Cachazo-Early-Guevara-Mizera (CEGM) generalized biadjoint amplitudes for all $k$ and $n$ on what we call the minimal kinematics. We prove that on the minimal kinematics, the scattering equations on the configuration space of $n$ points on $\\mathbb{CP}^{k-1}$ has a unique solution, and that this solution is in the image of a Veronese embedding. The minimal kinematics is an all $k$ generalization of the one recently introduced by Early for $k=2$ and uses a choice of cyclic ordering. We conjecture an explicit formula for $m_n^{(k)}(\\mathbb{I},\\mathbb{I})$ which we have checked analytically through $n=10$ for all $k$. The answer is a simple rational function which has only simple poles; the poles have the combinatorial structure of the circulant graph ${\\rm C}_n^{(1,2,\\dots, k-2)}$. Generalized biadjoint amplitudes can also be evaluated using the positive tropical Grassmannian ${\\rm Tr}^+{\\rm G}(k,n)$ in terms of generalized planar Feynman diagrams. We find perfect agreement between both definitions for all cases where the latter is known in the literature. In particular, this gives the first strong consistency check on the $90\\,608$ planar arrays for ${\\rm Tr}^+{\\rm G}(4,8)$ recently computed by Cachazo, Guevara, Umbert and Zhang. We also introduce another class of special kinematics called planar-basis kinematics which generalizes the one introduced by Cachazo, He and Yuan for $k=2$ and uses the planar basis recently introduced by Early for all $k$. Based on numerical computations through $n=8$ for all $k$, we conjecture that on the planar-basis kinematics $m_n^{(k)}(\\mathbb{I},\\mathbb{I})$ evaluates to the multidimensional Catalan numbers, suggesting the possibility of novel combinatorial interpretations. For $k=2$ these are the standard Catalan numbers.","source":"arXiv","year":2020,"language":"en","subjects":["hep-th","math.CO"],"doi":"10.3842/SIGMA.2021.078","url":"https://arxiv.org/abs/2003.07958","pdf_url":"https://arxiv.org/pdf/2003.07958","is_open_access":true,"published_at":"2020-03-17T21:43:46Z","score":64},{"id":"doaj_Si%C5%82y+dobra+i+z%C5%82a+w+pierwszych+wiekach+Ko%C5%9Bcio%C5%82a+%28Tours%2C+Universit%C3%A9+Francois+Rabelais%2C+11-13+IX+2008%29","title":"Siły dobra i zła w pierwszych wiekach Kościoła (Tours, Université Francois Rabelais, 11-13 IX 2008)","authors":[{"name":"Stanisław Longosz"}],"abstract":"\nnie dotyczy\n","source":"DOAJ","year":2018,"language":"","subjects":["Early Christian literature. Fathers of the Church, etc.","Philosophy of religion. Psychology of religion. Religion in relation to other subjects","Philosophy. Psychology. Religion"],"url":"https://czasopisma.kul.pl/index.php/vp/article/view/4452","is_open_access":true,"published_at":"","score":62},{"id":"doaj_Obchody+1600.+rocznicy+%C5%9Bmierci+Jana+Chryzostoma+w+%C5%9Bwiecie+%28Sympozja+chryzostomia%C5%84skie%29","title":"Obchody 1600. rocznicy śmierci Jana Chryzostoma w świecie (Sympozja chryzostomiańskie)","authors":[{"name":"Stanisław Longosz"}],"abstract":"\nnie dotyczy\n","source":"DOAJ","year":2018,"language":"","subjects":["Early Christian literature. Fathers of the Church, etc.","Philosophy of religion. Psychology of religion. Religion in relation to other subjects","Philosophy. Psychology. Religion"],"url":"https://czasopisma.kul.pl/index.php/vp/article/view/4441","is_open_access":true,"published_at":"","score":62},{"id":"arxiv_1810.03246","title":"Honeycomb Tessellations and Graded Permutohedral Blades","authors":[{"name":"Nick Early"}],"abstract":"This paper investigates enumerative aspects of permutohedral blades, which provide a generalization of the notion of the tropical hyperplane arrangement. Blade provide the combinatorial underpinning of generalized biadjoint scalar scattering amplitudes in work of Cachazo, Early, Guevara and Mizera (CEGM). We construct a graded basis for a vector space of indicator functions of blades, with the grading determined by the dimension of the support of the function. We prove a Minkowski sum decomposition law into lines and tripods and we explore connections to the cohomology ring of certain moduli spaces and a non-planar analog of the square move for plabic graphs.   We give a closed formula for the graded dimension of the basis. It is shown in an Appendix by Donghyun Kim that the coefficients appearing in the numerator of the generating function for the graded dimension are symmetric, and that they sum to $\\frac{(2j)!}{j!}$. Unimodality is still open.","source":"arXiv","year":2018,"language":"en","subjects":["math.CO","hep-th","math.RT"],"url":"https://arxiv.org/abs/1810.03246","pdf_url":"https://arxiv.org/pdf/1810.03246","is_open_access":true,"published_at":"2018-10-08T02:00:08Z","score":62},{"id":"arxiv_1710.05833","title":"Multi-messenger Observations of a Binary Neutron Star Merger","authors":[{"name":" LIGO Scientific Collaboration"},{"name":" Virgo Collaboration"},{"name":"Fermi GBM"},{"name":" INTEGRAL"},{"name":"IceCube Collaboration"},{"name":"AstroSat Cadmium Zinc Telluride Imager Team"},{"name":"IPN Collaboration"},{"name":"The Insight-Hxmt Collaboration"},{"name":"ANTARES Collaboration"},{"name":"The Swift Collaboration"},{"name":"AGILE Team"},{"name":"The 1M2H Team"},{"name":"The Dark Energy Camera GW-EM Collaboration"},{"name":"the DES Collaboration"},{"name":"The DLT40 Collaboration"},{"name":" GRAWITA"},{"name":" :"},{"name":"GRAvitational Wave Inaf TeAm"},{"name":"The Fermi Large Area Telescope Collaboration"},{"name":" ATCA"},{"name":" :"},{"name":"Australia Telescope Compact Array"},{"name":" ASKAP"},{"name":" :"},{"name":"Australian SKA Pathfinder"},{"name":"Las Cumbres Observatory Group"},{"name":" OzGrav"},{"name":" DWF"},{"name":" AST3"},{"name":"CAASTRO Collaborations"},{"name":"The VINROUGE Collaboration"},{"name":"MASTER Collaboration"},{"name":" J-GEM"},{"name":" GROWTH"},{"name":" JAGWAR"},{"name":"Caltech- NRAO"},{"name":" TTU-NRAO"},{"name":"NuSTAR Collaborations"},{"name":" Pan-STARRS"},{"name":"The MAXI Team"},{"name":"TZAC Consortium"},{"name":"KU Collaboration"},{"name":"Nordic Optical Telescope"},{"name":" ePESSTO"},{"name":" GROND"},{"name":"Texas Tech University"},{"name":"SALT Group"},{"name":" TOROS"},{"name":" :"},{"name":"Transient Robotic Observatory of the South Collaboration"},{"name":"The BOOTES Collaboration"},{"name":" MWA"},{"name":" :"},{"name":"Murchison Widefield Array"},{"name":"The CALET Collaboration"},{"name":"IKI-GW Follow-up Collaboration"},{"name":"H. E. S. S. Collaboration"},{"name":"LOFAR Collaboration"},{"name":" LWA"},{"name":" :"},{"name":"Long Wavelength Array"},{"name":"HAWC Collaboration"},{"name":"The Pierre Auger Collaboration"},{"name":"ALMA Collaboration"},{"name":"Euro VLBI Team"},{"name":"Pi of the Sky Collaboration"},{"name":"The Chandra Team at McGill University"},{"name":" DFN"},{"name":" :"},{"name":"Desert Fireball Network"},{"name":" ATLAS"},{"name":"High Time Resolution Universe Survey"},{"name":" RIMAS"},{"name":" RATIR"},{"name":"SKA South Africa/MeerKAT"}],"abstract":"On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\\sim$1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg$^2$ at a luminosity distance of $40^{+8}_{-8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Msun. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\\sim$40 Mpc) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over $\\sim$10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position $\\sim$9 and $\\sim$16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. (Abridged)","source":"arXiv","year":2017,"language":"en","subjects":["astro-ph.HE","gr-qc"],"doi":"10.3847/2041-8213/aa91c9","url":"https://arxiv.org/abs/1710.05833","pdf_url":"https://arxiv.org/pdf/1710.05833","is_open_access":true,"published_at":"2017-10-16T16:57:18Z","score":61}],"total":3794720,"page":1,"page_size":20,"sources":["DOAJ","arXiv","CrossRef"],"query":"Early Christian literature. Fathers of the Church, etc."}