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Measuring says that for every sequence ${\left( {{C_\delta }} \right)_{\delta < {\omega _1}}}$ with each ${C_\delta }$ being a closed subset of δ there is a club $C \subseteq {\omega _1}$ such that for every $\delta \in C$ , a tail of $C\mathop \cap \nolimits \delta$ is either contained in or disjoint from ${C_\delta }$ . We answer a question of Justin Moore by building a forcing extension satisfying measuring together with ${2^{{\aleph _0}}} > {\aleph _2}$ . The construction works over any model of ZFC + CH and can be described as a finite support forcing iteration with systems of countable structures as side conditions and with symmetry constraints imposed on its initial segments. One interesting feature of this iteration is that it adds dominating functions $f:{\omega _1} \to {\omega _1}$ mod. countable at each stage.

Status of tau lepton decay Monte Carlo generator TAUOLA, its main applications and recent developments are reviewed. It is underlined, that in recent efforts on development of new hadronic currents, the multi-dimensional nature of distributions of the experimental data must be taken with a great care: lesson from comparison and fits to the BaBar and Belle data is recalled. It was found, that as in the past at a time of comparisons with CLEO and ALEPH data, proper fitting, to as detailed as possible representation of the experimental data, is essential for appropriate developments of models of tau decay dynamic. This multi-dimensional nature of distributions is also important for observables where tau leptons are used to constrain experimental data. In later part of the presentation,use of the TAUOLA program for phenomenology of W,Z,H decays at LHC is addressed, in particular in the context of the Higgs boson parity measurements. Some new results, relevant for QED lepton pair emission are mentioned as well., Comment: Presented on the 14th International Workshop on Tau Lepton Physics, 19-23 September, 2016, IHEP, Beijing, China. arXiv admin note: text overlap with arXiv:1412.2937

I define a homogeneous \(\aleph _2\)–c.c. proper product forcing for adding many clubs of \(\omega _1\) with finite conditions. I use this forcing to build models of \(\mathfrak {b}(\omega _1)=\aleph _2\), together with \(\mathfrak {d}(\omega _1)\) and \(2^{\aleph _0}\) large and with very strong failures of club guessing at \(\omega _1\).

We show that metric abstract elementary classes (mAECs) are, in the sense of [LR] (i.e. arXiv:1404.2528), coherent accessible categories with directed colimits, with concrete $\aleph_1$-directed colimits and concrete monomorphisms. More broadly, we define a notion of $\kappa$-concrete AEC---an AEC-like category in which only the $\kappa$-directed colimits need be concrete---and develop the theory of such categories, beginning with a category-theoretic analogue of Shelah's Presentation Theorem and a proof of the existence of an Ehrenfeucht-Mostowski functor in case the category is large. For mAECs in particular, arguments refining those in [LR] yield a proof that any categorical mAEC is $\mu$-d-stable in many cardinals below the categoricity cardinal., Comment: v2: changed terminology. v3: tightened inequalities. v4: clarifying notes added. v5: referee's comments incorporated, with substantial improvements

It is consistent that P(ω1) is the union of less than \({2^{{\aleph _1}}}\) parts such that if A0,..., An−1, B0,..., Bm−1 are distinct elements of the same part, then |A0 ∩ · · · ∩ An−1 ∩ (ω1 − B0) ∩ · · ·∩ (ω1 − Bm−1)| = N1.

By forcing with $\mathbb{P}_{\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\omega_2$ and $\omega_3$ fail. In particular, we obtain a model of $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 + \lnot\square(\omega_2) + \lnot\square(\omega_3)$., Comment: Revised version, incorporating the referee's suggestions

We show that an arbitrary infinite graph can be compactified by its ${\aleph_0}$-tangles in much the same way as the ends of a locally finite graph compactify it in its Freudenthal compactification. In general, the ends then appear as a subset of its ${\aleph_0}$-tangles. The ${\aleph_0}$-tangles of a graph are shown to form an inverse limit of the ultrafilters on the sets of components obtained by deleting a finite set of vertices. The ${\aleph_0}$-tangles that are ends are precisely the limits of principal ultrafilters. The ${\aleph_0}$-tangles that correspond to a highly connected part, or $\aleph_0$-block, of the graph are shown to be precisely those that are closed in the topological space of its finite-order separations., Comment: References updated, no final

The strong coupling from ALEPH tau decays. We use the publically available non-strange spectral function from ALEPH tau decays to critically analyze the different determinations of αs(mτ2) that can be found in the literature and the numerical impact of their possible weaknesses. We also introduce some novel approaches. We find that perturbative uncertainties dominate. Our results with different approaches are very stable. Our final value is αs(mτ2)=0.328±0.013.

We use basic tools of descriptive set theory to prove that a closed set $\mathcal S$ of marked groups has $2^{\aleph_0}$ quasi-isometry classes provided every non-empty open subset of $\mathcal S$ contains at least two non-quasi-isometric groups. It follows that every perfect set of marked groups having a dense subset of finitely presented groups contains $2^{\aleph_0}$ quasi-isometry classes. These results account for most known constructions of continuous families of non-quasi-isometric finitely generated groups. They can also be used to prove the existence of $2^{\aleph_0}$ quasi-isometry classes of finitely generated groups having interesting algebraic, geometric, or model-theoretic properties., Minor corrections. To appear in the Journal of Topology

Se ofrece un panorama general del uso del sistema aleph en la Biblioteca Conjunta de Ciencias de la Tierra de la Universidad Nacional Autónoma de México, mostrando las diversas aplicaciones en donde se ha implementado, que van desde la generación de catálogos bibliográficos hasta la conformación de bases de datos con imágenes y textos completos de apoyo directo a la investigación.Así mismo, se hace una evaluación de los resultados obtenidos hasta el momento y se presentan los recursos generados con aleph, así como el uso e impacto de las interfaces creadas por la Dirección General de Bibliotecas (dgb-unam) y aplicadas para los diferentes catálogos y bases de datos, señalando los beneficios y problemas a los que nos enfrentamos a lo largo del proyecto.

Diplomsko delo raziskuje tematiko neskončnosti in njeno simboliko pri argentinskem pisatelju Jorgeju Luisu Borgesu. Za analizo uporablja kratke zgodbe Alef (Aleph 1949), Babilonska knjižnica (La biblioteca de Babel 1941) in Vrt razcepljenih stez (El jardín de senderos que se bifurcan 1941). Borges se je s tematiko neskončnosti in večnosti na zanimiv način ukvarjal čez svoj celoten opus do te mere, da so ga poimenovali za »pisatelja neskončnosti«. Najbolj značilni simboli, ki jih lahko povezujemo s konceptom neskončnosti v njegovih delih, so zrcala, sanje, labirinti in knjige. V zgodbi Alef je neskončnost prikazana kot točka, ki vključuje celotno vesolje, vključno s to točko, kar dela njo in vesolje neskončno. V Babilonski knjižnici se srečamo s knjižnico (metafora za svet), ki je neomejena in ciklična, s tem pa neskončna. V Vrtu razcepljenih stez avtor bralcu predstavi časovni labirint, v katerem je čas neskončen, pluralen, zmožen se je deliti in cepiti. Neskončnost avtor uporablja, da bi bralca prepričal, da nič ni realno, da živimo v neskončnem vesolju, ki nima nikakršnega transcendentalnega smisla. V vseh treh delih Borges ustvari literarni (neskončni) labirint, s katerim namiguje na pomembnost literature, ki je v svetu brez smisla sama smisel in v katerem ima pisatelj božjo moč. Undergraduate thesis researches the theme of infinity and her symbols in Argentinian writer Jorge Luis Borges. For analisis uses short stories Aleph (Aleph 1949), The Library of Babel (La biblioteca de Babel 1941), The Garden of Forking Paths (El jardín de senderos que se bifurcan 1941). Borges explored in a very interesting way the themes of infinity and eternity throughout his entire opus so much that he was named »the writer of infinity«. The most typical symbols that we can relate to the concept of infinity in his work are mirrors, dreams, labyrinths and books. In Aleph the infinity is shown as a dot that includes all universe including this particular dot, which makes it and the universe infinite. In The Library of Babel we are met with a library (metaphor for the world) that is unlimited and cyclic and with that infinite. The Garden of Forking Paths is a time labyrinth in which the time is eternal, plural, able to divide and fork. Infinity is used by the author to convince the reader that nothing is real, that we are living in an infinite universe that has no transcendent sense. In all three stories mentioned Borges creates literary (infinite) labyrinth with which he implies on the importance of literature that is, in a world with no sense, the only sense and in which the author has a power of God.

We review how the current precision attained in the extraction of αs(mτ)from hadronic τ decays requires the inclusion of Duality Violations (DVs) in the analysis, even though these decays are largely dominated by perturbation theory. A weighted average using the OPAL and ALEPH experimental data yields αs(mZ) =0.1165±0.0012 andαs(mZ) =0.1185±0.0015 in fixed-order and contour-improved perturbation theory, respectively.

We present nonperturbative fragmentation functions (FFs) for bottom-flavored (B) hadrons both at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order in the ¯¯¯¯¯¯MS factorization scheme with five massless quark flavors. They are determined by fitting all available experimental data of inclusive single B-hadron production in e+e− annihilation, from the ALEPH, DELPHI, and OPAL collaborations at CERN LEP1 and the SLD collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using the Hessian approach. We perform comparisons with available NLO sets of B-hadron FFs. We apply our new FFs to generate theoretical predictions for the energy distribution of B hadrons produced through the decay of unpolarized or polarized top quarks, to be measured at the CERN LHC.

In this paper, we define and study generalizations of expansiveness, namely n- expansiveness, $\aleph_0$-expansiveness, continuum-wise expansive and meagre expansiveness for non-autonomous discrete dynamical systems. We discuss various properties of such non-autonomous systems and give necessary examples. We prove results related to non-existence of $\aleph_0$-expansive and meagre expansive non-autonomous system on certain spaces. We also study relation between $\aleph_0$-expansive and meagre-expansive non-autonomous systems., 17 pages

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on ${\aleph}_{\omega+1}$ which is generated by fewer than ${2}^{{\aleph}_{\omega+1}}$ sets., Comment: 8 pages. Submitted

This chapter is devoted to infinitary combinatorics: Club filter, nonstationary ideal, the pressing down lemma, variants of the Δ-system lemma, and Kueker’s structure theorem for clubs in \([\mathsf {X}]^{\aleph _0}\).

Current research on knowledge graph completion is often concerned with latent approaches that are based on the idea to embed a knowledge graph into a low dimensional vector space. At the same time symbolic approaches have attracted less attention [13]. However, such approaches have a big advantage: they yield an explanation in terms of the rules that trigger a prediction. In this paper we propose a bottom-up technique for efficiently learning logical rules from large knowledge graphs inspired by classic bottom-up rule learning approaches as Golem [8] and Aleph [10]. Our approach is called AnyBURL (Anytime Bottom-Up Rule Learning). We report on experiments where we evaluated AnyBURL on datasets that have been labelled as hard cases for simple (rule-based) approaches. Our approach performs as good as and sometimes better than most models that have been proposed recently. Moreover, the required resources in terms of memory and runtime are significantly smaller compared to latent approaches. This paper is an extended abstract of an IJCAI 2019 paper [6].

We prove in ZFC that an abelian group $C$ is cotorsion if and only if $\operatorname{Ext}(F,C) = 0$ for every $\aleph_k$-free group $F$, and discuss some consequences and related results. This short note includes a condensed overview of the $\bar\lambda$-Black Box for $\aleph_k$-free constructions in ZFC.

A new finite integral involving two general class of polynomials with the Aleph function has been obtained in the present paper. This integral is supposed to be one of the most universal integral evaluated until now and act as a key component from which we can obtain as its different special cases, integrals relating a large number of simpler special functions and polynomials. Some useful unique cases of the main outcome have also been discussed in the paper.

Cilj. U članku je predstavljena radionica Ključni knjižničari za modul katalogizacije koja se održala na Stručnom skupu Knjižnični podaci: interoperabilnost, povezivanje i razmjena 28. i 29. studenog 2017. u Nacionalnoj i sveučilišnoj knjižnici u Zagrebu. Osnovne zadaće ključnih knjižničara jesu: stručna podrška redovnom radu knjižnica u sustavu, testiranje novih funkcionalnosti modula, praćenje i kontrola rada sustava temeljeni na izvještajima o radu, testiranje i analiza rada servisnih izvještaja na razini cijelog sustava, suradnja sa savjetnikom za integrirani knjižnični sustav, redaktorima baza, administratorom sustava, sistemskim i ključnim knjižničarima zaduženim za administrativno upravljanje sustavom te pružanje pomoći i edukacija sudionika u sustavu. Metodologija. Polazeći od osnovnih aspekata uloge i rada ključnih knjižničara u okviru Integriranog knjižničnog sustava Nacionalne i sveučilišne knjižnice u Zagrebu te knjižnica iz sustava znanosti i visokog obrazovanja opisan je svaki aspekt rada u modulu katalogizacije. Rezultati. Integrirani knjižnični sustav temelji se na primjeni zajedničkog programskog sustava Aleph, formata MARC 21, središnje normativne kontrole i nacionalnog predmetnog sustava. Nacionalna i sveučilišna knjižnica u Zagrebu, kao središnja knjižnica u sustavu, osigurava stručnu, tehničku i administrativnu podršku u radu zajedničkog informacijsko-knjižničnog sustava. Ključni knjižničari u modulu katalogizacije održavaju redovite tečajeve Osnove modula Katalogizacija, kao i demonstracijske vježbe. Knjižnice u sustavu zajednički koriste normativnu bazu Nacionalne i sveučilišne knjižnice i predloške za rad, dok se kataložni zapisi preuzimaju prema potrebi iz baza u sustavu ili se izrađuju novi. Putem Sustava za podršku https://iks.nsk.hr/podrska/ šalju se prijavnice u kojima se navode poteškoće s kojima se susreću knjižničari, a rješavaju ih redaktori, ključni i sistemski knjižničari. Praktična primjena. Rezultati ovoga rada mogu pomoći knjižničarima iz knjižnica članica Integriranog sustava u njihovu svakodnevnom radu. Originalnost. Široj se knjižničnoj zajednici nastoji približiti termin ključni knjižničari te njihova uloga u razvoju struke.

We present a fast and scalable algorithm to induce non-monotonic logic programs from statistical learning models. We reduce the problem of search for best clauses to instances of the High-Utility Itemset Mining (HUIM) problem. In the HUIM problem, feature values and their importance are treated as transactions and utilities respectively. We make use of TreeExplainer, a fast and scalable implementation of the Explainable AI tool SHAP, to extract locally important features and their weights from ensemble tree models. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics and running time of the training algorithm compared to ALEPH, a state-of-the-art Inductive Logic Programming (ILP) system., Comment: In Proceedings ICLP 2019, arXiv:1909.07646. arXiv admin note: substantial text overlap with arXiv:1808.00629, arXiv:1905.11226, arXiv:1802.06462, arXiv:1707.02693

Measurements of two-particle angular correlations of charged particles emitted in hadronic $Z$ decays are presented. The archived $e^+e^-$ annihilation data at a center-of-mass energy of 91 GeV were collected with the ALEPH detector at LEP between 1992 and 1995. The correlation functions are measured over a broad range of pseudorapidity and full azimuth as a function of charged particle multiplicity. No significant long-range correlation is observed in either the lab coordinate analysis or the thrust coordinate analysis, where the latter is sensitive to a medium expanding transverse to the color string between the outgoing $q\bar{q}$ pair from $Z$ boson decays. The associated yield distributions in both analyses are in better agreement with the prediction from the PYTHIA v6.1 event generator than from HERWIG v7.1.5. They provide new insights to showering and hadronization modeling. These results serve as an important reference to the observed long-range correlation in proton-proton, proton-nucleus, and nucleus-nucleus collisions., Comment: Replaced with the published version. Added the journal reference and the DOI

The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics.

En el canto XXX del Purgatorio, Dante es nombrado por primera y última vez en la Comedia. Aparece Beatrice y desaparece Virgilio, una procesión visionaria recibe al poeta-peregrino en el Paraíso terrenal. Borges intuye que este encuentro es el centro de la obra, su aleph. Nosotros proponemos un acercamiento a esta escena genial y enigmática desde las profecías visionarias de Joaquín de Fiore e intentamos demostrar, con el maestro argentino, que, en efecto, la visión de Dante de este aleph es la fuente generatriz de toda la obra, entendida como libro infinito. On Canto XXX of Purgatory, Dante is named for the first and last time in his Divine Comedy. Beatrice appears whilst Virgilio disappears, a visionary procession welcomes the poet-pilgrim to Paradise. Borges claims that this meeting is the main part of Dante's work, his aleph. We propose an approach to this magnificent and enigmatic scene including Joaquin de Fiore's prophecies and we try to prove that Dante's vision of this aleph is the generative source of Divine Comedy, understood as an infinite book.

We prove that the Devlin-Shelah weak diamond implies Galvin's property. On the other hand, Galvin's property is consistent with the negation of the weak diamond, and even with Martin's axiom. We show that the proper forcing axiom implies a relative to the negation of Galvin's property for $\aleph_1$.

We remove the assumption of the continuum hypothesis from the Akemann-Doner construction of a non-separable $C^*$-algebra $A$ with only separable commutative $C^*$-subalgebras. We also extend a result of Farah and Wofsey's, constructing $\aleph_1$ commuting projections in the Calkin algebra with no commutative lifting. This removes the assumption of the continuum hypothesis from a version of a result of Anderson. Both results are based on Luzin's almost disjoint family construction.