The topic of "negative end" of change is, contrary to the fields of innovation and emergence, largely under-researched. Yet, it has lately started to gain an increasing attention from language scholars worldwide. The main focus of this article is threefold, namely to discuss the i) terminology; ii) concepts and iii) causes associated with the "negative end" of change in grammar. The article starts with an overview of research conducted on the topic. It then moves to situating phenomena referred to as loss, decline or obsolescence among processes of language change, before elaborating on the terminology and concepts behind it. The last part looks at possible causes for constructions to display a (gradual or rapid, but very consistent) decrease in the frequency of use over time, which continues until the construction disappears or there are only residual or fossilised forms left.

The paper is an empirical case study of grammatical obsolescence in progress. The main studied variable is the purpose subordinator in order that, which is shown to be steadily decreasing in the frequency of use starting from the beginning of the twentieth century. This work applies a data-driven approach for the investigation and description of obsolescence, recently developed by the Rudnicka (2019). The methodology combines philological analysis with statistical methods used on data acquired from mega-corpora. Moving from the description of possible symptoms of obsolescence to different causes for it, the paper aims at presenting a comprehensive account of the studied phenomenon. Interestingly, a very significant role in the decline of in order that can be ascribed to the so-called higher-order processes, understood as processes influencing the constructional level from above. Two kinds of higher-order processes are shown to play an important role, namely i) an externally-motivated higher-order process exemplified by the drastic socio-cultural changes of the 19th and 20th centuries; ii) an internally-motivated higher-order processes instantiated by the rise of the to-infinitive (rise of infinite clauses).

Languages can encode temporal subordination lexically, via subordinating conjunctions, and morphologically, by marking the relation on the predicate. Systematic cross-linguistic variation among the former can be studied using well-established token-based typological approaches to token-aligned parallel corpora. Variation among different morphological means is instead much harder to tackle and therefore more poorly understood, despite being predominant in several language groups. This paper explores variation in the expression of generic temporal subordination ('when'-clauses) among the languages of Latin America and the Caribbean, where morphological marking is particularly common. It presents probabilistic semantic maps computed on the basis of the languages of the region, thus avoiding bias towards the many world's languages that exclusively use lexified connectors, incorporating associations between character $n$-grams and English $when$. The approach allows capturing morphological clause-linkage devices in addition to lexified connectors, paving the way for larger-scale, strategy-agnostic analyses of typological variation in temporal subordination.

In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly, we propose a novel approach for the construction of sparsityinducing nonconvex penalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionally, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of negative Kullback-Leiber (KL) distance functions. Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.

The difficulties of automatic extraction of definitions and methods from scientific documents lie in two aspects: (1) the complexity and diversity of natural language texts, which requests an analysis method to support the discovery of pattern; and, (2) a complete definition or method represented by a scientific paper is usually distributed within text, therefore an effective approach should not only extract single sentence definitions and methods but also integrate the sentences to obtain a complete definition or method. This paper proposes an analysis method for discovering patterns of definition and method and uses the method to discover patterns of definition and method. Completeness of the patterns at the semantic level is guaranteed by a complete set of semantic relations that identify definitions and methods respectively. The completeness of the patterns at the syntactic and lexical levels is guaranteed by syntactic and lexical constraints. Experiments on the self-built dataset and two public definition datasets show that the discovered patterns are effective. The patterns can be used to extract definitions and methods from scientific documents and can be tailored or extended to suit other applications.

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail to model uncertainty adequately and may over-smooth inferences. Here we extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours, while retaining a tractable conditional GP structure through an infinite mixture of non-homogeneous GPs representation. The conditional GP structure is obtained by conditioning the observations on a latent transformed input space and the random evolution of the latent transformation is modelled using a L\'{e}vy process which allows Bayesian inference in both the posterior predictive density and the latent transformation function. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits compared to a standard GP.

In this paper we present a sequential hypothesis test for the detection of general jump size distrubution. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the crude oil data set, and the deterministic component is implemented to improve the Barndorff-Nielsen and Shephard model, a commonly used stochastic model for derivative and commodity market analysis.

A commonly used stochastic model for derivative and commodity market analysis is the Barndorff-Nielsen and Shephard (BN-S) model. Though this model is very efficient and analytically tractable, it suffers from the absence of long range dependence and many other issues. For this paper, the analysis is restricted to crude oil price dynamics. A simple way of improving the BN-S model with the implementation of various machine learning algorithms is proposed. This refined BN-S model is more efficient and has fewer parameters than other models which are used in practice as improvements of the BN-S model. The procedure and the model show the application of data science for extracting a "deterministic component" out of processes that are usually considered to be completely stochastic. Empirical applications validate the efficacy of the proposed model for long range dependence.

In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional L\'{e}vy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete compound Poisson subordinators. We exemplify four specific subordinators: Gamma, Poisson, negative binomial and squared Bessel subordinators. The Laplace exponents of the subordinators are Bernstein functions, so they can be used as sparsity-inducing nonconvex penalty functions. We exploit these subordinators in regression problems, yielding a hierarchical model with multiple regularization parameters. We devise ECME (Expectation/Conditional Maximization Either) algorithms to simultaneously estimate regression coefficients and regularization parameters. The empirical evaluation of simulated data shows that our approach is feasible and effective in high-dimensional data analysis.

In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly,we propose a novel approach for the construction of sparsityinducing nonconvexpenalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma and compound Poisson subordinators, respectively. Additionally, we explore the concave conjugate of nonconvex penalties. We find that the LOG and EXP penalties are the concave conjugates of negative Kullback-Leiber (KL) distance functions.Furthermore, the relationship between these two penalties is due to asymmetricity of the KL distance.