Books by Joey McCollum
Brepols Library of Christian Sources, 2022
The Acts of John is a second-or third-century work of unknown authorship combining elements of th... more The Acts of John is a second-or third-century work of unknown authorship combining elements of the apocryphal acts and pious romance genres. It was labeled heretical by both Eusebius and Augustine, and condemned at the Second Council of Nicea (787). Scholars debate the influence of Gnosticism and docetism upon the work.
This narrative presents the lifelong ministry of the apostle John preaching and performing miracles in Ephesus, Smyrna, and elsewhere. At different turns in the exciting account, John resurrects the dead, reunites families, heals the sick, confronts pagan opponents, commands bedbugs, and divulges mysteries about his travels with Jesus.
The present edition offers the celebrated Greek text of Junod and Kaestli (Corpus Christianorum, Series Apocryphorum, 1-2, 1983) alongside a new English translation on the facing pages, complete with hundreds of cross-references and other helpful notes for the reader.
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Gorgias Press, 2020
When Beatrix Potter wrote The Tale of Peter Rabbit at the turn of the twentieth century, a Koine ... more When Beatrix Potter wrote The Tale of Peter Rabbit at the turn of the twentieth century, a Koine Greek translation of her work would never have crossed her mind. Almost no one writes anything, especially works of fiction, in the language of the New Testament anymore. Almost no one has for centuries. This is why students of Koine Greek are largely limited in their selection of reading material to the New Testament, Septuagint, and Apostolic Fathers. But wouldn’t it be nice if Greek students could immerse themselves more fully in the language? If students had access to a wide variety of reading materials, ancient and modern, they would have even more opportunities to read and learn how the language works. They might even read for pleasure. Beatrix Potter would surely have supported such an enterprise.
Because of our purpose and intended audience, this translation is written in Koine style and only uses vocabulary found in the Greek New Testament and Septuagint (including the Apocrypha). Because students of biblical Greek typically learn all the words that appear in the New Testament fifty times and more, translational glosses for all words appearing fifty times and fewer are included at the bottom of each page. English equivalents for proper names are only given at their first occurrence in the book. We have also included an English translation of the Greek text in the back of the book.
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Max and Moritz in Biblical Greek , 2019
Max and Moritz in Biblical Greek is a translation of Max and Moritz: A Story of Seven Boyish Pran... more Max and Moritz in Biblical Greek is a translation of Max and Moritz: A Story of Seven Boyish Pranks, written and illustrated by Wilhelm Busch (originally in German). The Greek wording is based on idioms of the Greek NT and Septuagint. The vocabulary is selective and limited by design to better serve the interests of students of biblical Greek. All words appearing fifty times or fewer in the Greek NT have been footnoted and glossed at the bottom of each page. Beginning Greek students typically learn Greek words occurring fifty times or more; thus, after completing two semesters of Greek, a student will be able to read this work without the aid of a lexicon. There is also a new English translation of the Greek text in the back of the book. Each chapter is a "trick" (δόλος), numbered using the standard convention of a Greek letter marked with an overline (e.g., α is 1, β is 2, etc.). Proper names are footnoted only at their first occurrence within each chapter. The text is divided into lengthy portions and, for ease of reference, verse numbers have been added.
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Papers by Joey McCollum
Novum Testamentum, 2024
[This article is freely accessible at https://doi.org/10.1163/15685365-bja10066.] This article co... more [This article is freely accessible at https://doi.org/10.1163/15685365-bja10066.] This article concerns the likelihoods of competing textual reconstructions in the Chester Beatty Papyrus 𝔓⁴⁶ based on the available space in its lacunose lines. To quantify these relative probabilities, the author uses statistical models of line lengths in 𝔓⁴⁶ and a recently described technique for calculating the likelihood of a reconstructed lacunose text. He first demonstrates the power and versatility of this approach with examples in Gal 4:17 and 3:1. He then revisits two more contested textual reconstructions proposed for 𝔓⁴⁶: the absence of τῷ θεῷ in Heb 11:4, suggested by G.D. Kilpatrick in 1941, and the absence of σὺν ἐπισκόποις καὶ διακόνοις in Phil 1:1, suggested by T.C. Skeat in 1995. He shows that Kilpatrick's proposed shorter reading in 𝔓⁴⁶ is six times more likely than the longer reading in Heb 11:4, while the evidence is not decisive between the readings in Phil 1:1.
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Journal for the Study of the New Testament, 2024
[This article is freely accessible at https://doi.org/10.1177/0142064X231226158.] This study revi... more [This article is freely accessible at https://doi.org/10.1177/0142064X231226158.] This study revisits a contested textual variant concerning the presence, placement, and person of an imperative directed at wives in Eph. 5.22. Most previous treatments of this variant have decided the matter (typically in favor of the reading without an imperative) on the basis of manuscript support and transcriptional arguments about how readers and copyists of the text would have changed it, but the intrinsic probabilities of what the author would have written based on his argument and style have generally been neglected. This study fills this gap by assessing the intrinsic probabilities of the variant readings in Eph. 5.22 using discourse and information structure, the pragmatics of the Greek imperative, and stylistic observations in Ephesians. As a result of this analysis, the reading with the highest intrinsic probability is shown to be τοῖς ἰδίοις ἀνδράσιν ὑποτασσέσθωσαν, which bolsters the recent case made by Gurry (2021) for the same reading.
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Digital Scholarship in the Humanities, 2024
[This article is freely accessible at https://doi.org/10.1093/llc/fqad089.] Bayesian phylogenetic... more [This article is freely accessible at https://doi.org/10.1093/llc/fqad089.] Bayesian phylogenetic methods offer various models that would be especially suitable in the reconstruction of textual traditions, but text-critical applications of phylogenetics to date have generally not taken advantage of these features. In this article, we offer a way forward for text-critical phylogenetics. On the side of theory, we highlight multiple Bayesian phylogenetic models and discuss their relevance to textual criticism. More practically, we show how TEI XML collations of textual traditions can be encoded to facilitate robust analyses using these models in BEAST 2, with the teiphy Python package mediating the conversion from TEI XML to BEAST XML. Finally, we give a proof of concept for this approach, showing that the results of BEAST 2 analyses of a sample collation of the Epistle to the Ephesians under different clock models cohere with established findings on the textual tradition of this work.
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Digital Scholarship in the Humanities, 2023
[This article is freely accessible at https://doi.org/10.1093/llc/fqac078.] This article presents... more [This article is freely accessible at https://doi.org/10.1093/llc/fqac078.] This article presents an approach to quantify the likelihood of a given reconstruction of lacunose text in a manuscript using statistics on line lengths (in letters), information about the line-breaking conventions and scribal habits of the scribe who copied the manuscript, and the well-known computational technique of dynamic programming. The approach and its value are illustrated with an application to a textual contest between the readings τὸ μυστήριον τοῦ εὐαγγελίου and τὸ μυστήριον in Ephesians 6:19, where the early papyrus witness P. Chester Beatty II/P. Mich. Inv. 6238 (Gregory-Aland P46) is lacunose. The study shows that under reasonable assumptions, P46 is over fifty times more likely to have read τὸ μυστήριον.
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Journal of Open Source Software, 2022
[This article is freely accessible at https://doi.org/10.21105/joss.04879.] Textual scholars have... more [This article is freely accessible at https://doi.org/10.21105/joss.04879.] Textual scholars have been using phylogenetics to analyze manuscript traditions since the early 1990s (Robinson & O’Hara, 1992). Many standard phylogenetic software packages accept as input the NEXUS file format (Maddison et al., 1997). The teiphy program takes a collation of texts encoded in TEI XML format and can convert it to any of the following formats amenable to phylogenetic analysis: NEXUS (with support for ambiguous states and clock model calibration data blocks for MrBayes or BEAST2), Hennig86, PHYLIP (relaxed for use with RAxML), FASTA (relaxed for use with RAxML), and STEMMA (designed for Stephen C. Carlson’s stemmatic software tailored for textual data). For machine learning-based analyses, teiphy can also convert a TEI XML collation to a collation matrix in NumPy, Pandas DataFrame, CSV, TSV, or Excel format
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IEEE Transactions on Quantum Engineering, 2020
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TC: A Journal of Biblical Textual Criticism, 2021
[This paper and its appendix are freely accessible at http://jbtc.org/v26/index.html.] Bibliothèq... more [This paper and its appendix are freely accessible at http://jbtc.org/v26/index.html.] Bibliothèque nationale de France Suppl. Gr. 79, also known as Gregory-Aland (GA) 274, is a tenth-century minuscule manuscript of the gospels. Perhaps due to the common character of its main text, its only feature that has received any detailed discussion in scholarly literature is the inclusion of the rare intermediate ending of Mark in its margin. What other scholars have missed is that many of the nearly one hundred other notes that also appear in the margin preserve uncommon and early variations on the text. In this study, I attempt to close the information gap by providing the first comprehensive survey of the marginal readings of this manuscript. I first identify readings in the main text of GA 274 that may have been derived from sources other than its presumed Byzantine exemplar. I then examine all of the marginal readings of GA 274, distinguishing between those that represent corrections to common errors, those that are related to lectionary usage, and those that indicate knowledge of textual variants. On the basis of an extensive collation of 140 Greek manuscript witnesses, I evaluate the textual affinity of the readings in the last category and find that these readings agree frequently with the decidedly non-Byzantine manuscripts GA 33 and 1342. A commentary offering details of the collation and justifications for my classifications of the marginal notes is included as an appendix. Questions about the hands responsible for the marginal notes, the critical sigla used in the margin and their functions, and the role of block mixture in the production of the manuscript all receive attention. The results of this examination show that despite this manuscript’s ordinary text, the extraordinary content preserved in its margin commends it for consideration in future text-critical work on the New Testament.
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2021 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN), 2021
In this work, a novel signal detection approach for dense co-channel environments is developed th... more In this work, a novel signal detection approach for dense co-channel environments is developed that leverages the intelligent combination of traditional signal preprocessing and deep radio frequency machine learning. Specifically, a novel multi-antenna preprocessing stage is developed to ease the signal processing burden of the deep learning algorithm. Easing this burden enables deep learning to be focused on specifically solving the sensing problem which helps minimize its footprint, improves its convergence during training, and reduces the required size of training datasets. Performance results of the proposed approach demonstrate that this intelligent combination of traditional and deep learning approaches leads to a detector that minimizes the impact of interference sources and nuisance signals and compensates for challenging propagation environments.
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IEEE Transactions on Quantum Engineering, 2020
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Theoretical Computer Science, 2021
The longest path problem on graphs is an NP-hard optimization problem, and as such, it is not kno... more The longest path problem on graphs is an NP-hard optimization problem, and as such, it is not known to have an efficient classical solution in the general case. This study develops two quadratic unconstrained binary optimization (QUBO) formulations of this well-known problem. The first formulation is based on an approach outlined by (Bauckhage et al., 2018) for the shortest path problem and follows simply from the principle of assigning positions on the path to vertices; using k|V| binary variables, this formulation will find the longest path that visits exactly k of a graph's |V| vertices, if such a path exists. As a point of theoretical interest, we present a second formulation based on degree constraints that is more complicated, but reduces the dependence of the number of variables on k to logarithmic; specifically, it requires |V| + 2|E|log2 k + 3|E| binary variables to encode the longest path problem. We adapt these basic formulations for several variants of the standard longest path problem. Scaling factors for penalty terms and preprocessing time required to construct the Q matrix representing the problem are made explicit in the paper.
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Filología Neotestamentaria, 2020
The variant in Luke 9,35 concerning the description that follows οὗτός ἐστιν ὁ υἱός μου is a quin... more The variant in Luke 9,35 concerning the description that follows οὗτός ἐστιν ὁ υἱός μου is a quintessential example of internal philological considerations opposing the reading found in the majority of manuscripts. The presence of multiple layers of harmonization in this variation unit serves as an instructive example of harmonistic influence among scribes, which in this case was likely polygenetic, occurring multiple times independently.
Sadly, this variant is not covered in the Text und Textwert Luke volume, so its most extensive collation to date is that of the 1984 volume by the International Greek New Testament Project (IGNTP). To improve matters, this study considers over 2500 Greek witnesses at this unit (including lectionaries, corrections, marginal readings, and commentaries) and collates the readings of 2200 Greek witnesses that contain it. Relevant versional and patristic evidence is also discussed.
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IEEE Transactions on Quantum Engineering, 2020
This article addresses the question of implementing a maximum flow algorithm on directed graphs i... more This article addresses the question of implementing a maximum flow algorithm on directed graphs in a formulation suitable for a quantum annealing computer. Three distinct approaches are presented. In all three cases, the flow problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem amenable to quantum annealing. The first implementation augments a graph with integral edge capacities into a multigraph with unit-capacity edges and encodes the fundamental objective and constraints of the maximum flow problem using a number of qubits equal to the total capacity of the graph ∑i ci . The second implementation, which encodes flows through edges using a binary representation, reduces the required number of qubits to O(|E|logCmax) , where |E| and Cmax denote the number of edges and maximum edge capacity of the graph, respectively. The third implementation adapts the dual minimum cut formulation and encodes the problem instance using |V| qubits, where |V| is the number of vertices in the graph. Scaling factors for penalty terms and coupling matrix construction times are made explicit in this article.
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IEEE Transactions on Quantum Engineering, 2020
This article addresses the formulation for implementing a single source, single-destination short... more This article addresses the formulation for implementing a single source, single-destination shortest path algorithm on a quantum annealing computer. Three distinct approaches are presented. In all the three cases, the shortest path problem is formulated as a quadratic unconstrained binary optimization problem amenable to quantum annealing. The first implementation builds on existing quantum annealing solutions to the traveling salesman problem, and requires the anticipated maximum number of vertices on the solution path |P| to be provided as an input. For a graph with |V| vertices, |E| edges, and no self-loops, it encodes the problem instance using |V||P| qubits. The second implementation adapts the linear programming formulation of the shortest path problem, and encodes the problem instance using |E| qubits for directed graphs or 2|E| qubits for undirected graphs. The third implementation, designed exclusively for undirected graphs, encodes the problem in |E|+|V| qubits. Scaling factors for penalty terms, complexity of coupling matrix construction, and numerical estimates of the annealing time required to find the shortest path are made explicit in the article.
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Andrews University Seminary Studies, 2019
[This paper is freely accessible at https://digitalcommons.andrews.edu/auss/vol57/iss1/6/.]
Th... more [This paper is freely accessible at https://digitalcommons.andrews.edu/auss/vol57/iss1/6/.]
The text-critical practice of grouping witnesses into families or texttypes often faces two obstacles: the methodological question of how exactly to isolate the groups, given the chicken-and-egg relationship between “good” group readings and “good” group manuscripts, and contamination in the manuscript tradition. I introduce non-negative matrix factorization (NMF) as a simple, automated, and efficient solution to both problems. Within minutes, NMF can cluster hundreds of manuscripts and readings simultaneously, producing an output that details potential contamination according to an easy-to-interpret mixture model. I apply this method to Wasserman’s extensive collation of the Epistle of Jude, showing that the resulting clusters correspond to human-identified textual families and their characteristic readings correctly divide witnesses into their groups. Due to its demonstrated accuracy, versatility, and speed, NMF could replace prior state-of-the-art classification methods and find fruitful application in a number of text-critical settings.
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New York Journal of Mathematics, 2011
We examine a parametrized family of functions $F_a$, all of
which are continuous and some of whic... more We examine a parametrized family of functions $F_a$, all of
which are continuous and some of which are nowhere or almost nowhere differentiable, we explore the behavior of $F'_a$ and $F''_a$ almost everywhere for different values of $a$, focusing on specific questions regarding $F_a$’s differentiability for certain $a$, and we calculate the Hausdorff dimension of the graphs of all $F_a$.
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Conference Presentations by Joey McCollum
In his introduction to The New Testament in the Original Greek, F. J. A. Hort laid out a taxonomy... more In his introduction to The New Testament in the Original Greek, F. J. A. Hort laid out a taxonomy of evidence for text-critical judgments that is still followed today. In addition to the external evidence pertaining to the textual affinities, dates, and provenances of manuscripts, versions, and patristic quotations, he divided the internal evidence of readings into two categories: intrinsic probabilities, concerning what the author was most likely to have written, and transcriptional probabilities, concerning how emendators were most likely to change this. Hort's description of internal evidence in terms of probabilities, while mostly figurative, turned out to be prophetic: after a century and half of development (largely outside of New Testament textual criticism), cutting-edge genealogical methods work in the realm of probabilities and approach the task of reconstructing a textual history as one of testing different hypotheses in the presence of unknown variables.
In this talk, I show how Bayesian phylogenetics, a technique for inferring family trees in evolutionary biology, aligns nicely with Hort's taxonomy of text-critical evidence and offers a clear separation of concerns between the parts of this taxonomy that rely on human judgments and those that can be automated by the computer. Using worked examples from my dissertation on Ephesians, I demonstrate how assessments of internal evidence can be input into this process. Then, using toy examples from the UBS collation data for different New Testament corpora (Gospels, Praxapostolos, Pauline Epistles, and Revelation), I demonstrate how stemmata relating the external evidence are evaluated and output by this process.
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Annual Meeting of the Society of Biblical Literature, Dec 9, 2020
The open-cbgm library is an open-source software implementation of the Coherence-Based Genealogic... more The open-cbgm library is an open-source software implementation of the Coherence-Based Genealogical Method (CBGM) designed with customizability and performance on large-scale collations in mind. The library is free to use or modify and has been tested on real data from the Editio Critica Maior (ECM) of the New Testament. This presentation first offers a summary treatment of the library's features and optimizations. Special attention is given to the topic of specifying and modifying local stemmata in the input files. Changes made from existing CBGM implementations and their justifications are also discussed. Finally, the usage and speed of the library's modules are demonstrated in a walkthrough of constructing and revising the local stemmata of variants and the global stemma of witnesses for 3 John. In this practical demonstration, the library not only handles the unprecedented task of constructing a complete global stemma for a New Testament book, but does so in a matter of seconds.
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Books by Joey McCollum
This narrative presents the lifelong ministry of the apostle John preaching and performing miracles in Ephesus, Smyrna, and elsewhere. At different turns in the exciting account, John resurrects the dead, reunites families, heals the sick, confronts pagan opponents, commands bedbugs, and divulges mysteries about his travels with Jesus.
The present edition offers the celebrated Greek text of Junod and Kaestli (Corpus Christianorum, Series Apocryphorum, 1-2, 1983) alongside a new English translation on the facing pages, complete with hundreds of cross-references and other helpful notes for the reader.
Because of our purpose and intended audience, this translation is written in Koine style and only uses vocabulary found in the Greek New Testament and Septuagint (including the Apocrypha). Because students of biblical Greek typically learn all the words that appear in the New Testament fifty times and more, translational glosses for all words appearing fifty times and fewer are included at the bottom of each page. English equivalents for proper names are only given at their first occurrence in the book. We have also included an English translation of the Greek text in the back of the book.
Papers by Joey McCollum
Sadly, this variant is not covered in the Text und Textwert Luke volume, so its most extensive collation to date is that of the 1984 volume by the International Greek New Testament Project (IGNTP). To improve matters, this study considers over 2500 Greek witnesses at this unit (including lectionaries, corrections, marginal readings, and commentaries) and collates the readings of 2200 Greek witnesses that contain it. Relevant versional and patristic evidence is also discussed.
The text-critical practice of grouping witnesses into families or texttypes often faces two obstacles: the methodological question of how exactly to isolate the groups, given the chicken-and-egg relationship between “good” group readings and “good” group manuscripts, and contamination in the manuscript tradition. I introduce non-negative matrix factorization (NMF) as a simple, automated, and efficient solution to both problems. Within minutes, NMF can cluster hundreds of manuscripts and readings simultaneously, producing an output that details potential contamination according to an easy-to-interpret mixture model. I apply this method to Wasserman’s extensive collation of the Epistle of Jude, showing that the resulting clusters correspond to human-identified textual families and their characteristic readings correctly divide witnesses into their groups. Due to its demonstrated accuracy, versatility, and speed, NMF could replace prior state-of-the-art classification methods and find fruitful application in a number of text-critical settings.
which are continuous and some of which are nowhere or almost nowhere differentiable, we explore the behavior of $F'_a$ and $F''_a$ almost everywhere for different values of $a$, focusing on specific questions regarding $F_a$’s differentiability for certain $a$, and we calculate the Hausdorff dimension of the graphs of all $F_a$.
Conference Presentations by Joey McCollum
In this talk, I show how Bayesian phylogenetics, a technique for inferring family trees in evolutionary biology, aligns nicely with Hort's taxonomy of text-critical evidence and offers a clear separation of concerns between the parts of this taxonomy that rely on human judgments and those that can be automated by the computer. Using worked examples from my dissertation on Ephesians, I demonstrate how assessments of internal evidence can be input into this process. Then, using toy examples from the UBS collation data for different New Testament corpora (Gospels, Praxapostolos, Pauline Epistles, and Revelation), I demonstrate how stemmata relating the external evidence are evaluated and output by this process.
This narrative presents the lifelong ministry of the apostle John preaching and performing miracles in Ephesus, Smyrna, and elsewhere. At different turns in the exciting account, John resurrects the dead, reunites families, heals the sick, confronts pagan opponents, commands bedbugs, and divulges mysteries about his travels with Jesus.
The present edition offers the celebrated Greek text of Junod and Kaestli (Corpus Christianorum, Series Apocryphorum, 1-2, 1983) alongside a new English translation on the facing pages, complete with hundreds of cross-references and other helpful notes for the reader.
Because of our purpose and intended audience, this translation is written in Koine style and only uses vocabulary found in the Greek New Testament and Septuagint (including the Apocrypha). Because students of biblical Greek typically learn all the words that appear in the New Testament fifty times and more, translational glosses for all words appearing fifty times and fewer are included at the bottom of each page. English equivalents for proper names are only given at their first occurrence in the book. We have also included an English translation of the Greek text in the back of the book.
Sadly, this variant is not covered in the Text und Textwert Luke volume, so its most extensive collation to date is that of the 1984 volume by the International Greek New Testament Project (IGNTP). To improve matters, this study considers over 2500 Greek witnesses at this unit (including lectionaries, corrections, marginal readings, and commentaries) and collates the readings of 2200 Greek witnesses that contain it. Relevant versional and patristic evidence is also discussed.
The text-critical practice of grouping witnesses into families or texttypes often faces two obstacles: the methodological question of how exactly to isolate the groups, given the chicken-and-egg relationship between “good” group readings and “good” group manuscripts, and contamination in the manuscript tradition. I introduce non-negative matrix factorization (NMF) as a simple, automated, and efficient solution to both problems. Within minutes, NMF can cluster hundreds of manuscripts and readings simultaneously, producing an output that details potential contamination according to an easy-to-interpret mixture model. I apply this method to Wasserman’s extensive collation of the Epistle of Jude, showing that the resulting clusters correspond to human-identified textual families and their characteristic readings correctly divide witnesses into their groups. Due to its demonstrated accuracy, versatility, and speed, NMF could replace prior state-of-the-art classification methods and find fruitful application in a number of text-critical settings.
which are continuous and some of which are nowhere or almost nowhere differentiable, we explore the behavior of $F'_a$ and $F''_a$ almost everywhere for different values of $a$, focusing on specific questions regarding $F_a$’s differentiability for certain $a$, and we calculate the Hausdorff dimension of the graphs of all $F_a$.
In this talk, I show how Bayesian phylogenetics, a technique for inferring family trees in evolutionary biology, aligns nicely with Hort's taxonomy of text-critical evidence and offers a clear separation of concerns between the parts of this taxonomy that rely on human judgments and those that can be automated by the computer. Using worked examples from my dissertation on Ephesians, I demonstrate how assessments of internal evidence can be input into this process. Then, using toy examples from the UBS collation data for different New Testament corpora (Gospels, Praxapostolos, Pauline Epistles, and Revelation), I demonstrate how stemmata relating the external evidence are evaluated and output by this process.
In the first talk of this session, Zachary Ardern (postdoctoral fellow, Wellcome Sanger Institute, Cambridge) will introduce the diverse questions considered in evolutionary genetics and the usefulness of a Bayesian approach to inferring phylogenies. Bayesian phylogenetic approaches can consider many hypotheses concerning evolutionary relationships and underlying biological processes and infer their probabilities (with associated uncertainties) in relation to the observed data.
In the second talk, Joey McCollum (PhD candidate, Australian Catholic University) will show how this approach can be fine-tuned for textual criticism. The mechanisms of Bayesian phylogenetics fit naturally into a traditional text-critical model, and familiar judgments of intrinsic and transcriptional factors in variation units can be used to inform the phylogenetic model. The second half of the talk will demonstrate how this process works in practice, using variation units in Ephesians.
Note: Some links to external files will not work from this isolated PDF; they should work in the version of the presentation hosted at https://github.com/jjmccollum/cbgm-csntm-talk.