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Presentation given at the closing event of the ERC-COG fundedproject "Linking Latin"

Resumen Los sistemas flexivos presentan, entre otras características, un grado variable de congruencia, al resultar su configuración interna de la tensión que se produce entre cierta tendencia a la complejidad, asociada a la ausencia de congruencia interna, y a la sistematicidad, entendida en términos de canonicidad. Por otra parte, los usuarios de una lengua, y particularmente los aprendices, tienden a interpretar su sistema flexivo de acuerdo con unas pautas de congruencia que pueden no solo resultar diferentes de las que se consideran propias de dicho sistema, sino incluso tener el efecto de incrementar su complejidad. Intentamos mostrar que una caracterización basada en estas características permite una representación más simple de los paradigmas de los lexemas verbales, al requerir solo aquellas formas que resultan impredecibles (‘formas de referencia’, Stump y Finkel 2013, 2015). Estas últimas entran en dos tipos de relaciones: relaciones de doble implicación o simétricas entre ellas, ligadas a afinidades de carácter procesual, y relaciones de implicación o asimétricas con las formas predecibles, asociadas a afinidades formales. Cotejamos las implicaciones de este tipo de representación con otras basadas exclusivamente en afinidades formales y en unidades subléxicas y resaltamos el interés teórico y pedagógico de generalizaciones basadas en el concepto de ‘forma de referencia’. Abstract Inflectional systems present, among other characteristics, a variable degree of internal congruence, as their internal configuration results from the tension that occurs between a certain tendency to complexity, associated with the absence of internal congruence, and to systematicity, understood in terms of canonicity. On the other hand, users of a language, and particularly learners, tend to interpret its inflectional system according to congruence patterns that may not only be different from those considered proper to that system, but even have the effect of increase its complexity. We show that a characterization based on such features allows a simpler representation of the paradigms of the verbal lexemes, by requiring only those forms that are unpredictable (‘principal parts’, Stump & Finkel 2013, 2015). Such forms fall into two types of relationships: doubly implicational or symmetrical relationships between them, linked to processual affinities, and implicational or asymmetrical relationships with predictable forms, associated with formal affinities. We compare the implications of this type of representation with others based exclusively on formal affinities and sublexical units, and we highlight the theoretical and pedagogical interest of generalizations based on the concept of ‘principal part’.

This paper provides a fully word-based, abstractive analysis of predictability in Latin verb paradigms. After reviewing previous traditional and theoretically grounded accounts of Latin verb inflection, a procedure is outlined where the uncertainty in guessing the content of paradigm cells given knowledge of one or more inflected wordforms is measured by means of the information-theoretic notions of unary and n-ary implicative entropy, respectively, in a quantitative approach that uses the type frequency of alternation patterns between wordforms as an estimate of their probability of application. Entropy computations are performed by using the Qumin toolkit on data taken from the inflected lexicon LatInfLexi. Unary entropy values are used to draw a mapping of the verbal paradigm in zones of full interpredictability, composed of cells that can be inferred from one another with no uncertainty. N-ary entropy values are used to extract categorical and near principal part sets, that allow to fill the rest of the paradigm with little or no uncertainty. Lastly, the issue of the impact of information on the derivational relatedness of lexemes on uncertainty in inflectional predictions is tackled, showing that adding a classification of verbs in derivational families allows for a relevant reduction of entropy, not only for derived verbs, but also for simple ones.

We design an FST-driven computational method to calculate the minimal number of nominal forms—the principal parts—one must know to be able to fully inflect a lexeme in standard Finnish. To do this, we model the nominal inflection pattern as an FST according to the KOTUS inflectional classes. Our results show that knowing five forms always suffices to uniquely determine a nominal’s inflectional class, and to subsequently correctly inflect all the remaining forms. This contrasts with most sources in the literature that tend to assume seven forms are needed.

In this article, we consider a general second-order hyperbolic equation. We first establish a modified Carleman estimate for this equation by adding some functions of adjustment. Then general conditions imposed on the principal parts, mixed with the weight function and the functions of adjustment are derived. Finally, we give the realizations of the weight functions by choosing suitable adjustments such that the above general conditions are satisfied in some specific cases.

The aim of this chapter is to introduce prime ends and the Caratheodory topology of simply connected domains and see how impressions of prime ends are related to unrestricted limits and principal parts of prime ends can be used to understand the non-tangential behavior of univalent functions. Finally, we prove Caratheodory’s extension theorems.

This paper presents the submission by the CU Ling team from the University of Colorado to SIGMORPHON 2020 shared task 0 on morphological inflection. The task is to generate the target inflected word form given a lemma form and a target morphosyntactic description. Our system uses the Transformer architecture. Our overall approach is to treat the morphological inflection task as a paradigm cell filling problem and to design the system to leverage principal parts information for better morphological inflection when the training data is limited. We train one model for each language separately without external data. The overall average performance of our submission ranks the first in both average accuracy and Levenshtein distance from the gold inflection among all submissions including those using external resources.

This paper shows that the theories of fuzzy rough sets, F-transforms and fuzzy automata can be unified in the framework of fuzzy relational structures. Specifically, the key concepts in such theories are represented as lattice-based aggregations in the form of compositions with suitable fuzzy relations. Furthermore, it is shown that the principal parts of morphisms between all considered fuzzy relational structures coincide.

In this paper we solve the multiple interpolation problem in the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic under the condition that interpolation nodes are contained in a finite union of Stolz angles and describe the principal parts of a Laurent series of meromorphic functions with the same restrictions on the Nevanlinna characteristic.

Metric regularity theory lies at the very heart of variational analysis, a relatively new discipline whose appearance was, to a large extent, determined by the needs of modern optimization theory in which such phenomena as nondifferentiability and set-valued mappings naturally appear. The roots of the theory go back to such fundamental results of the classical analysis as the implicit function theorem, Sard theorem and some others. This paper offers a survey of the state of the art of some principal parts of the theory along with a variety of its applications in analysis and optimization.

In the last twenty years a number of papers appeared aiming to construct locally free replacements of the sheaf of principal parts for families of Gorenstein curves. The main goal of this survey is to present to the widest possible audience of mathematical readers a catalogue of such constructions, discussing the related literature and reporting on a few applications to classical problems in Enumerative Algebraic Geometry., Minor revisions, improved exposition

Many of the world’s languages contain an abundance of inflected forms for each lexeme. A critical task in processing such languages is predicting these inflected forms. We develop a novel statistical model for the problem, drawing on graphical modeling techniques and recent advances in deep learning. We derive a Metropolis-Hastings algorithm to jointly decode the model. Our Bayesian network draws inspiration from principal parts morphological analysis. We demonstrate improvements on 5 languages.

The main aim of the actual problem is to obtain Lagrange equations when the chosen parameters do not respect material rigidity, so inducing strains (and Continuum Mechanics). The proposed method consist of two principal parts: first the definition of a family of generalised displacements involving strains and second the elimination of the Cauchy stress tensor in the Virtual Work Principle valuable in Continuum Mechanics. As a final statement the rigidity law is introduced on the parameters to complete the obtained equations. On a friction problem, it is highlighted the necessity to really distinguish between these mathematical compatibility conditions taking account of the nature of the material and other relations expressing some experimental boundary conditions like friction laws.

Although the definition and usage of the term ‘morphome’ differs in the academic literature, the original definition of a morphome by Aronoff (1994) is that it is a function which determines the distribution of form within the inflectional paradigm and beyond. More importantly, however, morphomes suppose the existence of what Aronoff terms ‘a morphomic level’ which embodies an empirical claim about the structure of language: ‘the mapping from morphosyntax to phonological realization is not direct but passes through an intermediate level’ (Aronoff in Morphology by itself, MIT Press, Cambridge, 1994:25). This is a strong claim concerning all types of morphological exponence. In this article, after an analysis of Aronoff’s model of morphology, I draw upon the distinction which Blevins (J. Linguist. 42:531–573, 2006) makes between constructive and abstractive models of morphology. I note that the introduction of a morphomic level merely constitutes an incorporation of a partial paradigmatic dimension into a constructive model of morphology. With reference to a semantically and phonologically unmotivated distribution of allomorphy in Romance I argue that although the introduction of the morphomic level is beneficial, since it can formalise systematic and ‘psychologically real’ homonymies in synchronic grammars in a way which is not merely coincidental, a constructive morphomic theory of morphology does not present significant advantages over abstractive theories as regards the formalisation of the synchronic facts and presents disadvantages as regards the motivation of diachronic tendencies which this particular distribution of allomorphy shows cross-linguistically. I argue that these historical tendencies support a more paradigmatic theory of morphology inherent in abstractive models, which consider the word as the basic unit of analysis and word formation a matter of analogical deduction based on the predictable capacity of stored exemplar paradigms and principal parts.

In this paper, an estimate of the area between the early exercise boundaries is established for the American put option with different local volatility functions through the uniform distance between the volatilities. The constant factor on the right-hand side of the estimate is given in explicit form. The derivation of the estimate is based on the detailed analysis of the related parabolic obstacle problem with different principal parts in the corresponding differential operator.

We obtain asymptotic expansions for densities in the central limit theorem. Explicit expressions for principal parts of the Edgeworth--Cramer expansion are given in terms of Chebyshev--Hermitian moments.

The Natchez dependent verb has four principal parts or root shapes, which encode the number of that verb's subjects and objects. This system of root shapes is created by an abstract system of suffixation, the rules for which are complicated but completely regular. However, the occurrence of these principal parts in natural texts suggests that the semantics of the system are far more complex than previously understood, and that in addition to marking objects as singular and plural, the system also marks objects for dual number.[Keywords: Natchez, dual number, morphology, semantics, verb formation]

The Word and Paradigm approach to morphology associates lexemes with tables of surface forms for different morphosyntactic property sets. Researchers express their realizational theories, which show how to derive these surface forms, using formalisms such as Network Morphology and Paradigm Function Morphology. The tables of surface forms also lend themselves to a study of the implicative theories, which infer the realizations in some cells of the inflectional system from the realizations of other cells. There is an art to building realizational theories. First, the theories should be correct, that is, they should generate the right surface forms. Second, they should be elegant, which is much harder to capture, but includes the desiderata of simplicity and expressiveness. Without software to test a realizational theory, it is easy to sacrifice correctness for elegance. Therefore, software that takes a realizational theory and generates surface forms is an essential part of any theorist’s toolbox. Discovering implicative rules that connect the cells in an inflectional system is often quite difficult. Some rules are immediately apparent, but others can be subtle. Software that automatically analyzes an entire table of surface forms for many lexemes can help automate the discovery process. Researchers can use Web-based computerized tools to test their realizational theories and to discover implicative rules.

International audience; This paper contributes to addressing the Paradigm Cell Filling Problem (PCFP) in inflectional paradigms, as defined by Ackerman et al. (2009). We define a method for extending the use of conditional entropy to address the PCFP to prediction based on multiple paradigm cells. We apply this method to French and European Portugese and show that, on average, knowledge of multiple paradigm cells is dramatically more predictive than knowledge of a single cell. Moreover, this new entropy measure proves useful in studying principal parts systems, which correspond to sets of predictors yielding a null entropy. Using a graded measure allows us to highlight the relevance of non-categorical or “good enough” principal parts systems.

An ℝ-linear conjugation problem modelling the process of power fields forming in a heterogeneous infinite planar structure with an elliptical inclusion is considered. Exact analytical solutions are derived in the class of piece-wise meromorphic functions with their principal parts fixed. Cases with internal singularities and with singularities of the given principal parts at the interface are investigated.

We investigate the Cauchy problem for second-order hyperbolic operators in the framework of the space of C∞ functions. In the case where the coefficients of their principal parts depend only on the time variable and are real analytic, we give a sufficient condition for C∞ well-posedness, which is also a necessary one when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions (e.g., polynomials) of the time variable.

The case-number suffixes of the Western Nilotic language Nuer (Frank 1999) display a remarkable combination of formal simplicity and distributional complexity, which is manifested in: (i) a seemingly erratic form-function mapping that precludes attributing a consistent meaning to the suffixes, and (ii) a wealth of inflection classes only barely differentiated from each other. The suffixes looks as if they were rule-generated, but behave as if they were memorized. I advance a model of inflection combining principal parts, implicational rules, and default inheritance, in which the bulk of the complexity is attributed to the lexical stem, revealing the underlying systematicity behind suffix assignment.

This paper consists of three principal parts. The first part discusses the problem of safety of Slovak level crossings, seen through the statistic data, and explains distinctive features identified on the base of comparison with level crossings operated in other EU countries. The second part deals with knowledge-based approach applied to diagnostics of electronic/computer-based level crossing installations. In the last part the authors present their methodology which has been designed and which is to be applied to the level crossing systems of a particular producer and describe possible architectures of such a system.

We find principal parts of asymptotic mean-square errors of semirecursive nonparametric estimators of functionals of a multidimensional density function under the assumption that observations satisfy a strong mixing condition. Results are illustrated by an example of a nonlinear autoregression process.

Let Γ be an H-group. In 1974 Marvin Knopp conjectured that the Eichler cohomology group, with base space taken to be the set of all functions holomorphic in the upper half-plane, of polynomial growth at the real line (including oo), and with a weight k,multiplier system v linear fractional action of r, is isomorphic to the space of cusp forms on r of weight 2 — κ and multiplier system D, in the range 0 < κ < 2. In this article the authors prove the conjecture by making essential use of Hans Petersson's "principal parts condition" for automorphic forms (1955).

Some three-dimensional variants of Goursat and Darboux problems for higher-order hyperbolic equations with dominating principal part are set and investigated. Conditions to the problems' data which in some cases ensure the well-posedness of the problem in question and in other cases, despite the solvability of the problem, imply the presence of an infinite set of linearly independent solutions of corresponding homogeneous problem, are found. We consider both generalized and classical solutions.

In this paper we consider the regularity of solutions of semilinear differential equations principal parts of which consist of linear polynomial operators constructed from real vector fields. Based on the study of fine properties of the principal linear parts we then obtain the regularity of solutions of the nonlinear equations. Some results obtained in this article are also new in the frame of linear theory.

Like the numbers in a sudoku puzzle, a lexeme’s principal parts provide enough information–but only enough–to deduce all of the remaining forms in its paradigm. Because principal parts are a distillation of the implicative relations that exist among the members of a lexeme’s paradigm, they afford an important (but heretofore neglected) basis for typological classification. We recognize three logically distinct sorts of principal-part systems that might be postulated for a given language: static, adaptive, and dynamic. Focussing for present purposes on dynamic systems, we propose five crosscutting criteria for the typological classification of principal-part systems. These criteria relate to (i) how many principal parts are needed to determine a lexeme’s paradigm; (ii) whether distinct lexemes possess parallel sets of principal parts; (iii) how many principal parts are needed to determine a given word in a lexeme’s paradigm; (iv) what sort of morphological relation exists between a principal part and the forms that it is used to deduce; and (v) whether lexemes’ nonprincipal parts are inferred from their principal parts in the same way from one inflection class to another. Drawing on these criteria, we propose a novel classification of a range of typologically diverse languages.

In this paper, we provide an explicit construction of weight $0$ meromorphic modular forms. Following work of Petersson, we build these via Poincar\'e series. There are two main aspects of our investigation which differ from his approach. Firstly, the naive definition of the Poincar\'e series diverges and one must analytically continue via Hecke's trick. Hecke's trick is further complicated in our situation by the fact that the Fourier expansion does not converge everywhere due to singularities in the upper half-plane so it cannot solely be used to analytically continue the functions. To explain the second difference, we recall that Petersson constructed linear combinations from a family of meromorphic functions which are modular if a certain principal parts condition is satisfied. In contrast to this, we construct linear combinations from a family of non-meromorphic modular forms, known as polar harmonic Maass forms, which are meromorphic whenever the principal parts condition is satisfied.

In the modern Abazin language the names are not сhange by the cases, don’t have the grammatical category of mood, and that’s why the grammatical relations of the subject (and object along with it) and predicate are recorded with assistance of class-personal affixes. The subject, direct and indirect object and their corresponding indicators (subject, direct and indirect objects) coincide (conform) in the person, number and class in the absolute majority of cases. However, there are cases, when such stable, double-sided connection between the basic structure-forming parts of the sentence is violated. The article deals with description of these cases. DOI: 10.5901/mjss.2015.v6n2s4p137

We construct a substitute for principal parts for systems of algebras with a natural local presentation by free modules. The main application of the theory is to families of locally complete inters ...

The differential Hilbert series of a commutative local algebra R/R0 which is essentially of finite type is the generating function of the numerical function which associates with each \( n\in \Bbb N\) the minimal number of generators of the algebra \(P^n_{R/R_0}\) of principal parts of order n, considered as an R-module. It can be expressed as a rational function over the integers. We wish to compute this rational function in terms of other invariants of the local algebra or at least give estimates of it. We obtain formulas which generalize wellknown facts about the minimal number of generators of the module of Kahler differentials.

We formulate conditions for the existence of stationary and bounded solutions of differential inclusions with homogeneous principal parts and establish formulae for the calculation of the index of the zero singular point of a homogeneous multivalued vector field.

A general theory of dynamic similarity, which includes processes with strong disequilibrium and considers the generalized similarity of processes, is discussed. The basic laws of the theory, viz., the measures of action and dynamic correspondence, are formulated. A basic tool for dynamic correspondence, viz., the object-process classifier, is proposed. An initial description of the principal parts of the theory is given. Possible effects and the relations describing them are indicated.

Must we believe in logical necessity? I examine an argument for an affirmative answer given by Ian McFetridge in his posthumously published paper "Logical Necessity: Some Issues", and explain why it fails, as it stands, to establish his conclusion. I contend, however, that McFetridge's argument can be effectively buttressed by drawing upon another argument aimed at establishing that we ought to believe that some propositions are logically necessary, given by Crispin Wright in his paper "Inventing Logical Necessity". My contention is that Wright's argument, whilst it likewise fails, as it stands, to establish the necessity of necessity, establishes enough to close off what appears to me to be the only effective-looking sceptical response to McFetridge's original argument. My paper falls into four principal parts. In the first, I expound McFetridge's argument and draw attention to the possibility of a certain type of sceptical counter to it. In the second, I begin a response to this sceptical move, taking it as far as I can without reliance upon argument of the kind given by Wright. Turning, then, to Wright's argument, I explain to what extent I think it is successful and seek to rebut some objections to the argument which, were they well-taken, would show that the argument cannot enjoy even the partial success I wish to claim for it. Finally, I return to my main theme and try to show, with the assistance of what I take to be solidly established by Wright's argument, that the sceptical response collapses.

A complete description of the principal parts of meromorphic functions of finite order and normal type in their Laurent decomposition near singular points is presented. Bibliography: 6 titles.

This paper reports a detailed evaluation of the effectiveness of a system that has been developed for the identification and retrieval of morphological variants in searches of Latin text databases. A user of the retrieval system enters the principal parts of the search term (two parts for a noun or adjective, three parts for a deponent verb, and four parts for other verbs), this enabling the identification of the type of word that is to be processed and of the rules that are to be followed in determining the morphological variants that should be retrieved. Two different search algorithms are described. The algorithms are applied to the Latin portion of the Hartlib Papers Collection and to a range of classical, vulgar and medieval Latin texts drawn from the Patrologia Latina and from the PHI Disk 5.3 datasets. The effectiveness of these searches demonstrates the effectiveness of our procedures in providing access to the full range of classical and post-classical Latin text databases.