Quantitative photoacoustic imaging in radiative transport regime

The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical and computational studies on the inverse problem in QPAT, however, mostly in the diffusive regime. We present in this work some numerical reconstruction algorithms for multi-source QPAT in the radiative transport regime with energy data collected at either single or multiple wavelengths. We show that when the medium to be probed is non-scattering, explicit reconstruction schemes can be derived to reconstruct the absorption and the Gruneisen coefficients. When data at multiple wavelengths are utilized, we can reconstruct simultaneously the absorption, scattering and Gruneisen coefficients. We show by numerical simulations that the reconstructions are stable.Comment: 40 pages, 13 figure

Tropicalization of classical moduli spaces

The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our primary example is the Burkhardt quartic, whose tropicalization is a 3-dimensional fan in 39-dimensional space. This effectuates a synthesis of concrete and abstract approaches to tropical moduli of genus 2 curves.Comment: 33 page

Surface location of alkaline-earth atom impurities on helium nanodroplets

There has been notable uncertainty regarding the degree of solvation of alkaline-earth atoms, especially Mg, in free He-4 nanodroplets. We have measured the electron energy dependence of the ionization yield of picked-up atoms. There is a qualitative shape difference between the yield curves of species solvated in the middle of the droplet and species located in the surface region; this difference arises from the enhanced role played by the Penning ionization process in the latter case. The measurements demonstrate that Mg, Ca, Sr and Ba all reside at or near the droplet surface.Comment: 11 pages, 3 figure

Dynamics of delay induced composite multi-scroll attractor and its application in encryption

This work was supported in part by NSFC (60804040, 61172070), Key Program of Nature Science Foundation of Shaanxi Province (2016ZDJC-01), Innovative Research Team of Shaanxi Province(2013KCT-04), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin

Classification of (n+3)(n+3)-dimensional metric nn-Lie algebras

In this paper, we focus on $(n+3)$-dimensional metric $n$-Lie algebras. To begin with, we give some properties on $(n+3)$-dimensional $n$-Lie algebras. Then based on the properties, we obtain the classification of $(n+3)$-dimensional metric $n$-Lie algebras

Size effects in multiferroic BiFeO3 nanodots: A first-principles-based study

An effective Hamiltonian scheme is developed to investigate structural and magnetic properties of BiFeO3 nanodots under short-circuit-like electrical boundary conditions. Various striking effects are discovered. Examples include (a) scaling laws involving the inverse of the dots' size for the magnetic and electric transition temperatures; (b) the washing out of some structural phases present in the bulk via size effects; (c) the possibility of tailoring the difference between the Neel and Curie temperatures, by playing with the size and electrical boundary conditions; and (d) an universal critical thickness of the order of 1.6 nm below which the dots do not possess any long-range ordering for the electrical and magnetic dipoles, as well as, for the oxygen octahedral tiltings.Comment: 3 figure

Energy-Efficient Flow Scheduling and Routing with Hard Deadlines in Data Center Networks

The power consumption of enormous network devices in data centers has emerged as a big concern to data center operators. Despite many traffic-engineering-based solutions, very little attention has been paid on performance-guaranteed energy saving schemes. In this paper, we propose a novel energy-saving model for data center networks by scheduling and routing "deadline-constrained flows" where the transmission of every flow has to be accomplished before a rigorous deadline, being the most critical requirement in production data center networks. Based on speed scaling and power-down energy saving strategies for network devices, we aim to explore the most energy efficient way of scheduling and routing flows on the network, as well as determining the transmission speed for every flow. We consider two general versions of the problem. For the version of only flow scheduling where routes of flows are pre-given, we show that it can be solved polynomially and we develop an optimal combinatorial algorithm for it. For the version of joint flow scheduling and routing, we prove that it is strongly NP-hard and cannot have a Fully Polynomial-Time Approximation Scheme (FPTAS) unless P=NP. Based on a relaxation and randomized rounding technique, we provide an efficient approximation algorithm which can guarantee a provable performance ratio with respect to a polynomial of the total number of flows.Comment: 11 pages, accepted by ICDCS'1

Hamiltonian formalism in Friedmann cosmology and its quantization

We propose a Hamiltonian formalism for a generalized Friedmann-Roberson-Walker cosmology model in the presence of both a variable equation of state (EOS) parameter $w(a)$ and a variable cosmological constant $\Lambda(a)$, where $a$ is the scale factor. This Hamiltonian system containing 1 degree of freedom and without constraint, gives Friedmann equations as the equation of motion, which describes a mechanical system with a variable mass object moving in a potential field. After an appropriate transformation of the scale factor, this system can be further simplified to an object with constant mass moving in an effective potential field. In this framework, the $\Lambda$ cold dark matter model as the current standard model of cosmology corresponds to a harmonic oscillator. We further generalize this formalism to take into account the bulk viscosity and other cases. The Hamiltonian can be quantized straightforwardly, but this is different from the approach of the Wheeler-DeWitt equation in quantum cosmology.Comment: 7 pages, no figure; v2: matches the version accepted by PR