A volume correspondence between anti-de Sitter space and its boundary

Let $\mathbb{H}^{n+1}_1$ be the $(n+1)$-dimensional anti-de Sitter space, in this paper we propose to extend the space by gluing it to another copy of $\mathbb{H}^{n+1}_1$ along the boundary at infinity, and denote the resulting space by \emph{double anti-de Sitter space} $\mathbb{DH}^{n+1}_1$. We introduce a volume (possibly complex valued) on polytopes in $\mathbb{DH}^{n+1}_1$ whose facets all have non-degenerate metric (called \emph{good} polytopes), and show that the volume is well defined and invariant under isometry, including the case that the good polytope contains a non-trivial portion of $\partial\mathbb{H}^{n+1}_1$. For $n$ even, the volume of a good polytope in $\mathbb{DH}^{n+1}_1$ is shown to be completely determined by its intersection with $\partial\mathbb{H}^{n+1}_1$ and induces a new intrinsic \emph{volume} on $\partial\mathbb{H}^{n+1}_1$ that is invariant under conformal symmetry, establishing a volume correspondence between $\mathbb{DH}^{n+1}_1$ and $\partial\mathbb{H}^{n+1}_1$.Comment: 38 pages, 13 figure

A Newly Discovered Late Pleistocene Lower Third Premolar and the High Frequency Occurrence of Tomes’ Root in the Human Fossil Record from China

Dental remains provide crucial evidence for interpreting a populations’ affinity as well as human evolution. Recent studies of fossil human teeth have enriched our current view of morphological variation during the Pleistocene in East Asia. In the present paper, we describe a newly discovered late Pleistocene human tooth, a lower third premolar from the Weijiadong cave in Bijie in south-western China, which is dated around 18-20Ka BP using AMS Carbon 14 dating. The tooth is identified as belonging to an early modern human based on its morphology and size. The Tomes’ root is present in this lower third premolar, one of the non-metrical dental traits developed genetically. Moreover, we examine most of the fossil lower third premolars collected from China, as well as material from several Neolithic and historical human assemblages. We find that the Tomes’ root is very common in Chinese human fossils and occurs in high frequency in Neolithic and historic human remains from China. We suggest the high frequency of Tomes’ root may serve as a non-metric dental trait to support inferences regarding regional continuity of human evolution in East Asia

FERM domain-containing unconventional myosin VIIA interacts with integrin β5 subunit and regulates αvβ5-mediated cell adhesion and migration

AbstractUnconventional myosin VIIA (Myo7a) has been known to associate with hereditary deafness. Here we present a novel function of Myo7a by identifying that Myo7a directly interacts with integrin β5 subunit and regulates cell adhesion and motility in an integrin-dependent manner. We found that Myo7a bound to the cytoplasmic tail of integrin β5. Further, we pinpointed an integrin-binding domain at F3 of the first FERM domain and F1 of the second FERM domain. Functionally, Myo7a-induced cell adhesion and migration were mediated by integrin αvβ5. These findings indicated that Myo7a interacts with integrin β5 and selectively promotes integrin αvβ5-mediated cell migration

Combating Multi-path Interference to Improve Chirp-based Underwater Acoustic Communication

Linear chirp-based underwater acoustic communication has been widely used due to its reliability and long-range transmission capability. However, unlike the counterpart chirp technology in wireless -- LoRa, its throughput is severely limited by the number of modulated chirps in a symbol. The fundamental challenge lies in the underwater multi-path channel, where the delayed copied of one symbol may cause inter-symbol and intra-symbol interfere. In this paper, we present UWLoRa+, a system that realizes the same chirp modulation as LoRa with higher data rate, and enhances LoRa's design to address the multi-path challenge via the following designs: a) we replace the linear chirp used by LoRa with the non-linear chirp to reduce the signal interference range and the collision probability; b) we design an algorithm that first demodulates each path and then combines the demodulation results of detected paths; and c) we replace the Hamming codes used by LoRa with the non-binary LDPC codes to mitigate the impact of the inevitable collision.Experiment results show that the new designs improve the bit error rate (BER) by 3x, and the packet error rate (PER) significantly, compared with the LoRa's naive design. Compared with an state-of-the-art system for decoding underwater LoRa chirp signal, UWLoRa+ improves the throughput by up to 50 times

Understand Group Interaction and Cognitive State in Online Collaborative Problem Solving: Leveraging Brain-to-Brain Synchrony Data

The purpose of this study aimed to analyze the process of online collaborative problem solving (CPS) via brain-to-brain synchrony (BS) at the problem-understanding and problem-solving stages. Aiming to obtain additional insights than traditional approaches (survey and observation), BS refers to the synchronization of brain activity between two or more people, as an indicator of interpersonal interaction or common attention. Thirty-six undergraduate students participated. Results indicate the problem-understanding stage showed a higher level of BS than the problem-solving stage. Moreover, the level of BS at the problem-solving stage was significantly correlated with task performance. Groups with all high CPS skill students had the highest level of BS, while some of the mixed groups could achieve the same level of BS. BS is an effective indicator of CPS to group performance and individual interaction. Implications for the online CPS design and possible supports for the process of online CPS activity are also discussed

Understanding binary phase separation towards Cu-C nanocrystalline-amorphous composites

The nanocrystalline-amorphous textures are commonly observed in the coatings synthesized by energetic deposition. We report a binary phase separation towards Cu-C nanocrystalline-amorphous composites by the FCVA deposition. The experimental results highlight that the average size of Cu nanocrystallines mainly depends on the C2H2 content. By performing a MD simulation using the LAMMPS, we theoretically explained how the initial reagent concentration fundamentally determines Cu nanocrystalline's final morphology and size during phase separation. This finding may give insight into the formation of nanocrystalline-amorphous structures by energetic deposition.Comment: 12 pages,5 figure

Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr