The morphological diversity of the quadrate bone in squamate reptiles as revealed by high-resolution computed tomography and geometric morphometrics.

We examined the morphological diversity of the quadrate bone in squamate reptiles (i.e. lizards, snakes, amphisbaenians). The quadrate is the principal splanchnocranial element involved in suspending the lower jaw from the skull, and its shape is of particular interest because it is potentially affected by several factors, such as phylogenetic history, allometry, ecology, skull kinesis and hearing capabilities (e.g. presence or absence of a tympanic ear). Due to its complexity, the quadrate bone is also considered one of the most diagnostic elements in fragmentary fossil taxa. We describe quadrates from 38 species spread across all major squamate clades, using qualitative and quantitative (e.g. geometric morphometrics) methods. We test for possible correlations between shape variation and factors such as phylogeny, size, ecology and presence/absence of a tympanum. Our results show that the shape of the quadrate is highly evolutionarily plastic, with very little of the diversity explained by phylogenetic history. Size variation (allometric scaling) is similarly unable to explain much shape diversity in the squamate quadrate. Ecology (terrestrial/fossorial/aquatic) and presence of a tympanic ear are more significant, but together explain only about 20% of the diversity observed. Other unexplored and more analytically complex factors, such as skull biomechanics, likely play additional major roles in shaping the quadrates of lizards and snakes.

Stable invariant models via Koopman spectra.

Weight-tied models have attracted attention in the modern development of neural networks. The deep equilibrium model (DEQ) represents infinitely deep neural networks with weight-tying, and recent studies have shown the potential of this type of approach. DEQs are needed to iteratively solve root-finding problems in training and are built on the assumption that the underlying dynamics determined by the models converge to a fixed point. In this paper, we present the stable invariant model (SIM), a new class of deep models that in principle approximates DEQs under stability and extends the dynamics to more general ones converging to an invariant set (not restricted in a fixed point). The key ingredient in deriving SIMs is a representation of the dynamics with the spectra of the Koopman and Perron-Frobenius operators. This perspective approximately reveals stable dynamics with DEQs and then derives two variants of SIMs. We also propose an implementation of SIMs that can be learned in the same way as feedforward models. We illustrate the empirical performance of SIMs with experiments and demonstrate that SIMs achieve comparative or superior performance against DEQs in several learning tasks.

Sclerotic rings in mosasaurs (Squamata: Mosasauridae): structures and taxonomic diversity.

Mosasaurs (Squamata: Mosasauridae) were a highly diverse, globally distributed group of aquatic lizards in the Late Cretaceous (98-66 million years ago) that exhibited a high degree of adaptation to life in water. To date, despite their rich fossil record, the anatomy of complete mosasaur sclerotic rings, embedded in the sclera of the eyeball, has not been thoroughly investigated. We here describe and compare sclerotic rings of four mosasaur genera, Tylosaurus, Platecarpus, Clidastes, and Mosasaurus, for the first time. Two specimens of Tylosaurus and Platecarpus share an exact scleral ossicle arrangement, excepting the missing portion in the specimen of Platecarpus. Furthermore, the exact arrangement and the total count of 14 ossicles per ring are shared between Tylosaurus and numerous living terrestrial lizard taxa, pertaining to both Iguania and Scleroglossa. In contrast, two species of Mosasaurus share the identical count of 12 ossicles and the arrangement with each other, while no living lizard taxa share exactly the same arrangement. Such a mosaic distribution of these traits both among squamates globally and among obligatorily aquatic mosasaurs specifically suggests that neither the ossicle count nor their arrangement played major roles in the aquatic adaptation in mosasaur eyes. All the mosasaur sclerotic rings examined consistently exhibit aperture eccentricity and the scleral ossicles with gently convex outer side. Hitherto unknown to any squamate taxa, one specimen of Platecarpus unexpectedly shows a raised, concentric band of roughened surface on the inner surface of the sclerotic ring. It is possible that one or both of these latter features may have related to adaptation towards aquatic vision in mosasaurs, but further quantitative study of extant reptilian clades containing both terrestrial and aquatic taxa is critical and necessary in order to understand possible adaptive significances of such osteological features.

Variational Bayesian Inference Algorithms for Infinite Relational Model of Network Data.

Network data show the relationship among one kind of objects, such as social networks and hyperlinks on the Web. Many statistical models have been proposed for analyzing these data. For modeling cluster structures of networks, the infinite relational model (IRM) was proposed as a Bayesian nonparametric extension of the stochastic block model. In this brief, we derive the inference algorithms for the IRM of network data based on the variational Bayesian (VB) inference methods. After showing the standard VB inference, we derive the collapsed VB (CVB) inference and its variant called the zeroth-order CVB inference. We compared the performances of the inference algorithms using six real network datasets. The CVB inference outperformed the VB inference in most of the datasets, and the differences were especially larger in dense networks.

Convergent evolution in aquatic tetrapods: insights from an exceptional fossil mosasaur.

Mosasaurs (family Mosasauridae) are a diverse group of secondarily aquatic lizards that radiated into marine environments during the Late Cretaceous (98-65 million years ago). For the most part, they have been considered to be simple anguilliform swimmers--i.e., their propulsive force was generated by means of lateral undulations incorporating the greater part of the body--with unremarkable, dorsoventrally narrow tails and long, lizard-like bodies. Convergence with the specialized fusiform body shape and inferred carangiform locomotory style (in which only a portion of the posterior body participates in the thrust-producing flexure) of ichthyosaurs and metriorhynchid crocodyliform reptiles, along with cetaceans, has so far only been recognized in Plotosaurus, the most highly derived member of the Mosasauridae. Here we report on an exceptionally complete specimen (LACM 128319) of the moderately derived genus Platecarpus that preserves soft tissues and anatomical details (e.g., large portions of integument, a partial body outline, putative skin color markings, a downturned tail, branching bronchial tubes, and probable visceral traces) to an extent that has never been seen previously in any mosasaur. Our study demonstrates that a streamlined body plan and crescent-shaped caudal fin were already well established in Platecarpus, a taxon that preceded Plotosaurus by 20 million years. These new data expand our understanding of convergent evolution among marine reptiles, and provide insights into their evolution's tempo and mode.