Integrative Approach Uncovers New Patterns of Ecomorphological Convergence in Slow Arboreal Xenarthrans

Identifying ecomorphological convergence examples is a central focus in evolutionary biology. In xenarthrans, slow arboreality independently arose at least three times, in the two genera of ‘tree sloths’, Bradypus and Choloepus, and the silky anteater, Cyclopes. This specialized locomotor ecology is expectedly reflected by distinctive morpho-functional convergences. Cyclopes, although sharing several ecological features with ‘tree sloths’, do not fully mirror the latter in their outstandingly similar suspensory slow arboreal locomotion. We hypothesized that the morphology of Cyclopes is closer to ‘tree sloths’ than to anteaters, but yet distinct, entailing that slow arboreal xenarthrans evolved through ‘incomplete’ convergence. In a multivariate trait space, slow arboreal xenarthrans are hence expected to depart from their sister taxa evolving toward the same area, but not showing extensive phenotypical overlap, due to the distinct position of Cyclopes. Conversely, a pattern of ‘complete’ convergence (i.e., widely overlapping morphologies) is hypothesized for ‘tree sloths’. Through phylogenetic comparative methods, we quantified humeral and femoral convergence in slow arboreal xenarthrans, including a sample of extant and extinct non-slow arboreal xenarthrans. Through 3D geometric morphometrics, cross-sectional properties (CSP) and trabecular architecture, we integratively quantified external shape, diaphyseal anatomy and internal epiphyseal structure. Several traits converged in slow arboreal xenarthrans, especially those pertaining to CSP. Phylomorphospaces and quantitative convergence analyses substantiated the expected patterns of ‘incomplete’ and ‘complete’ convergence for slow arboreal xenarthrans and ‘tree sloths’, respectively. This work, highlighting previously unidentified convergence patterns, emphasizes the value of an integrative multi-pronged quantitative approach to cope with complex mechanisms underlying ecomorphological convergence.

An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model *

We consider a wavelet based image reconstruction model with the ℓ p (0 < p < 1) quasi-norm regularization, which is a non-convex and non-Lipschitz minimization problem. For solving this model, Figueiredo et al (2007 IEEE Trans. Image Process. 16 2980–2991) utilized the classical majorization-minimization framework and proposed the so-called Isoft algorithm. This algorithm is computationally efficient, but whether it converges or not has not been concluded yet. In this paper, we propose a new algorithm to accelerate the Isoft algorithm, which is based on Nesterov’s extrapolation technique. Furthermore, a complete convergence analysis for the new algorithm is established. We prove that the whole sequence generated by this algorithm converges to a stationary point of the objective function. This convergence result contains the convergence of Isoft algorithm as a special case. Numerical experiments demonstrate good performance of our new algorithm.

Uniate Sacral Architecture in the Grand Duchy of Lithuania: A Synthesis of Confessional Architecture

Summary The architectural legacy of the Unitarians in the former Grand Duchy of Lithuania has received little attention from researchers to this day. This article presents an architectural synthesis of the Uniate and Order of Basilians that reflected the old succession of Orthodox architectural heritage, but at the same time was increasingly influenced by the architectural traditions formed in Catholic churches. This article presents the tendencies of the development of Uniate architecture, paying attention to the brick and wooden sacral buildings belonging to the Uniate and Order of Basilians in the territory of the Grand Duchy of Lithuania. The early Uniate sacral examples reflected the still striking features of the synthesis, which were particularly marked in the formation of the Greek cross plan and apses in the different axes of the building. All this marked the architectural influences of Ukraine, Moldova and other areas of Central and South-Eastern Europe, which were also clearly visible in Orthodox architecture. Wooden Uniate architecture, as in the case of masonry buildings, had distinctly inherited features of Orthodox architecture, and in the late period, as early as the 18th century, there was a tendency to adopt the principles of Catholic church architecture, which resulted in complete convergence of most Uniate buildings with examples of Catholic church buildings. Vilnius Baroque School, formed in the late Baroque era, formed general tendencies in the construction of Uniate and Catholic sacral buildings, among which the clearer divisions of the larger structural and artistic principles are no longer noticeable in the second half of 18th century. The article also presents the image of baroque St. Nicholas Church, the only Uniate parish church in Vilnius city, which was lost after the reconstruction in the second half of the 19th century.

NEW EXPONENTIAL PROBABILITY INEQUALITY AND COMPLETE CONVERGENCE FOR F-LNQD RANDOM VARIABLES SEQUENCE WITH APPLICATION TO AR(1)MODEL GENERATED BY F-LNQD ERRORS

The exponential probability inequalities have been important tools in probability and statistics. In this paper, we prove a new tail probability inequality for the distri-butions of sums of conditionally linearly negative quadrant dependent (F-LNQD , in short) random variables, and obtain a result dealing with conditionally complete con-vergence of first-order autoregressive processes with identically distributed (F-LNQD) innovations.

Complete Convergence for Weighted Sums of Widely Acceptable Random Variables under Sublinear Expectations

Using different methods than the probability space, under the condition that the Choquet integral exists, we study the complete convergence theorem for weighted sums of widely acceptable random variables under sublinear expectation space. We proved corresponding theorem which was extended to the sublinear expectations’ space from the probability space, and similar results were obtained.

Complete Convergence for END Random Variables under Sublinear Expectations

In this paper, the complete convergence theorems of partial sums and weighted sums for extended negatively dependent random variables in sublinear expectation spaces have been studied and established. Our results extend the corresponding results of classical probability spaces to the case of sublinear expectation spaces.

Strong Limit Theorems for Dependent Random Variables

In this article We establish moment inequality of dependent random variables, furthermore some theorems of strong law of large numbers and complete convergence for sequences of dependent random variables. In particular, independent and identically distributed Marcinkiewicz Law of large numbers are generalized to the case of m₀ -dependent sequences.