Geometrically bounding 3-manifold, volume and Betti number

It is well known that an arbitrary closed orientable $3$-manifold can be realized as the unique boundary of a compact orientable $4$-manifold, that is, any closed orientable $3$-manifold is cobordant to zero. In this paper, we consider the geometric cobordism problem: a hyperbolic $3$-manifold is geometrically bounding if it is the only boundary of a totally geodesic hyperbolic 4-manifold. However, there are very rare geometrically bounding closed hyperbolic 3-manifolds according to the previous research [11,13]. Let $v \approx 4.3062\ldots$ be the volume of the regular right-angled hyperbolic dodecahedron in $\mathbb{H}^{3}$, for each $n \in \mathbb{Z}_{+}$ and each odd integer $k$ in $[1,5n+3]$, we construct a closed hyperbolic 3-manifold $M$ with $\beta^1(M)=k$ and $vol(M)=16nv$ that bounds a totally geodesic hyperbolic 4-manifold. The proof uses small cover theory over a sequence of linearly-glued dodecahedra and some results of Kolpakov-Martelli-Tschantz [9].Comment: the latest version that adjust some figures and add more detail description

Compact hyperbolic Coxeter four-polytopes with eight facets

In this paper, we obtain the complete classification for compact hyperbolic Coxeter four-dimensional polytopes with eight facets.Comment: We corrected some textual typos about the cited authors/papers. Many thanks to Nikolay Bogache

Orientable hyperbolic 4-manifolds over the 120-cell

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume $\frac{34\pi^2}{3}\cdot 16$ by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the right-angled 120-cell up to homeomorphism; these are all with even intersection forms.Comment: In this version, we corret some drawing typos in figures of adjacent matrices of $X_{45}$, $X_{55}$, $X_{56}$ and $X_{57}$. The author are grateful to Leonardo Ferrari who pointed out the mistake

Structure and evolution patterns of contents of Chinese children's bestsellers

Children's books involve a large number of topics. This poster focuses on that in China, which is the fastest growing market for children's book in the world. This poster chose Dangdang.com, the biggest Chinese online bookstore, for data source to obtain children's bestsellers. The topic words of children's bestsellers were extracted from their brief introductions of the content on the website. With the aid of co-occurrence theory and tools of social network analysis and visualization, the distribution, correlation structures, and evolution patterns of topics were revealed and visualized. This poster shows that topics of Chinese children's bestsellers are broad and relatively concentrated, but their distribution is unbalanced. There are four distinguished topic communities (Living, Animal, World, and Child) in terms of centrality and maturity, and they all establish their individual systems and tend to be mature. The evolution of these communities tends to be stable with powerful continuity

Fast Functionalization with High Performance in the Autonomous Information Engine

Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register, or conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.Comment: 14 pages, 3 figures; all comments are welcom

Projective Synchronization of Hyperchaotic Financial Systems

Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method

A Projection-Type Method for Multivalued Variational Inequality

We propose a projection-type method for multivalued variational inequality. The iteration sequence generated by the algorithm is proven to be globally convergent to a solution, provided that the multivalued mapping is continuous with nonempty compact convex values. Moreover, we present a necessary and sufficient condition on the nonemptiness of the solution set. Preliminary computational experience is also reported

BTLA/HVEM Signaling: Milestones in Research and Role in Chronic Hepatitis B Virus Infection

B- and T-lymphocyte attenuator (BTLA) is an immune-regulatory receptor, similar to CTLA-4 and PD-1, and is mainly expressed on B-, T-, and all mature lymphocyte cells. Herpes virus entry mediator (HVEM)-BTLA plays a critical role in immune tolerance and immune responses which are areas of intense research. However, the mechanisms of the BTLA and the BTLA/HVEM signaling pathway in human diseases remain unclear. This review describes the research milestones of BTLA and HVEM in chronological order and their role in chronic HBV infection

Hepatitis B virus spliced variants are associated with an impaired response to interferon therapy

During hepatitis B virus (HBV) replication, spliced HBV genomes and splice-generated proteins have been widely described, however, their biological and clinical significance remains to be defined. Here, an elevation of the proportion of HBV spliced variants in the sera of patients with chronic hepatitis B (CHB) is shown to correlate with an impaired respond to interferon-α (IFN-α) therapy. Transfection of the constructs encoding the three most dominant species of spliced variants into cells or ectopic expression of the two major spliced protein including HBSP and N-terminal-truncated viral polymerase protein result in strong suppression of IFN-α signaling transduction, while mutation of the major splicing-related sites of HBV attenuates the viral anti-IFN activities in both cell and mouse models. These results have associated the productions of HBV spliced variants with the failure response to IFN therapy and illuminate a novel mechanism where spliced viral products are employed to resist IFN-mediated host defense. </p