Virtualization of 5G Cellular Networks as a Hierarchical Combinatorial Auction

Virtualization has been seen as one of the main evolution trends in the forthcoming fifth generation (5G) cellular networks which enables the decoupling of infrastructure from the services it provides. In this case, the roles of infrastructure providers (InPs) and mobile virtual network operators (MVNOs) can be logically separated and the resources (e.g., subchannels, power, and antennas) of a base station owned by an InP can be transparently shared by multiple MVNOs, while each MVNO virtually owns the entire BS. Naturally, the issue of resource allocation arises. In particular, the InP is required to abstract the physical resources into isolated slices for each MVNO who then allocates the resources within the slice to its subscribed users. In this paper, we aim to address this two-level hierarchical resource allocation problem while satisfying the requirements of efficient resource allocation, strict inter-slice isolation, and the ability of intra-slice customization. To this end, we design a hierarchical combinatorial auction mechanism, based on which a truthful and sub-efficient resource allocation framework is provided. Specifically, winner determination problems (WDPs) are formulated for the InP and MVNOs, and computationally tractable algorithms are proposed to solve these WDPs. Also, pricing schemes are designed to ensure incentive compatibility. The designed mechanism can achieve social efficiency in each level even if each party involved acts selfishly. Numerical results show the effectiveness of the proposed scheme.Comment: IEEE Transactions on Mobile Computing, under submissio

Quark Fragmentation Functions in Low-Energy Chiral Theory

We examine the physics content of fragmentation functions for inclusive hadron production in a quark jet and argue that it can be calculated in low energy effective theories. As an example, we present a calculation of $u$-quark fragmentation to $\pi^+$ and $\pi^-$ mesons in the lowest order in the chiral quark model. The comparison between our result and experimental data is encouraging.Comment: 4 (tightly packed) pages in ReVTeX and 2 PostScript figures, MIT-CTP-225

Unified Gas-kinetic Scheme with Multigrid Convergence for Rarefied Flow Study

The unified gas kinetic scheme (UGKS) is a direct modeling method based on the gas dynamical model on the mesh size and time step scales. With the implementation of particle transport and collision in a time-dependent flux function, the UGKS can recover multiple flow physics from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with direct simulation Monte Carlo (DSMC), the equations-based UGKS can use the implicit techniques in the updates of macroscopic conservative variables and microscopic distribution function. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regime. In order to further improve the computational efficiency, for the first time a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5 to 9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for a convergent steady state solution

The Dehn function of Richard Thompson's group TT

V.S.Guba had proved that the R.Thompson group $T$ satisfies polynomial isoperimetric inequality and $\Phi_T(n)\preceq n^7$, where $\Phi_T$ is the Dehn function of group $T$. In this paper, we show that $\Phi_T(n)\preceq n^5$.Comment: 9 pages, 8 figures. We correct some typos and some gramma problem

Disorder and Power-law Tails of DNA Sequence Self-Alignment Concentrations in Molecular Evolution

The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x) \propto x^{\alpha}$, with similar or apparently different negative $\alpha$s ($<-2$). The relevant fundamental processes of molecular evolution are segmental duplication and point mutation, and that recently the stick fragmentation phenomenology has been used to account the neutral evolution. However, disorder is intrinsic to the evolution system and, by freezing it in time (quenching) for the setup of a simple fragmentation model, we obtain decaying, steady-state and the general full time-dependent solutions, all $\propto x^{\alpha}$ for $x\to \infty$, which is in contrast to the only power-law solution, $x^{-3}$ for $x\to 0$ of the pure model (without disorder). %Other algebraic terms may dominate at intermediate scales, which seems to be confirmed by some species, such as rice. We also present self-alignment results showing more than one scaling regimes, consistent with the theoretical results of the existence of more than one algebraic terms which dominate at different regimes.Comment: a figure for the introductory discussion removed; less length

Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on unstructured mesh for multiscale simulation of continuum and rarefied flow. Inheriting from the multicale transport in the unified gas-kinetic scheme (UGKS), the integral solution of kinetic model equation is employed in the construction of UGKWP method to model the flow physics in the cell size and time step scales. A novel wave-particle adaptive formulation is introduced in the UGKWP method to describe the flow dynamics in each control volume. The local gas evolution is constructed through the dynamical interaction of the deterministic hydrodynamic wave and the stochastic kinetic particle. Within the resolution of cell size and time step, the decomposition, interaction, and evolution of the hydrodynamic wave and the kinetic particle depend on the ratio of the time step to the local particle collision time. In the rarefied flow regime, the flow physics is mainly recovered by the discrete particles and the UGKWP method performs as a stochastic particle method. In the continuum flow regime, the flow behavior is solely followed by macroscopic variable evolution and the UGKWP method becomes a gas-kinetic hydrodynamic flow solver for the viscous and heat-conducting Navier--Stokes solutions. In different flow regimes, many numerical test cases are computed to validate the UGKWP method on unstructured mesh. The UGKWP method can get the same UGKS solutions in all Knudsen regimes without the requirement of the time step and mesh size being less than than the particle collision time and mean free path. With an automatic wave-particle decomposition, the UGKWP method becomes very efficient. For example, at Mach number 30 and Knudsen number 0.1, in comparison with UGKS several-order-of-magnitude reductions in computational cost and memory requirement have been achieved by UGKWP

On Huang Gaoxin’s Choices in the Translation of The Canterbury Tales

As a Chinese translator, Huang Gaoxin has been devoting himself to the translation of poetry for over fifty years and has successfully translated a large number of collections of English poems into Chinese, among which The Canterbury Tales is an essential one. This paper firstly compares the translated version of The Canterbury Tales by Huang with its original version and analyzes his theory of poetry translation, and then explores the choices regarding translation text, translation methods and language style he made during his translation process, and finally offers the underlying reasons behind the choices from the perspectives of translation purpose, views towards poetry translation, qualities as a translator and audience awareness.

The semi-constrained NMSSM in light of muon g-2, LHC, and dark matter constraints

The semi-constrained NMSSM (scNMSSM) extends the MSSM by a singlet field, and requires unification of the soft SUSY breaking terms in the squark and slepton sectors, while it allows that in the Higgs sector to be different. We try to interpret the muon g-2 in the scNMSSM, under the constraints of 125 GeV Higgs data, B physics, searches for low and high mass resonances, searches for SUSY particles at the LHC, dark matter relic density by WMAP/Planck, and direct searches for dark matter by LUX, XENON1T, and PandaX-II. We find that under the above constraints, the scNMSSM can still (i) satisfy muon g-2 at 1$\sigma$ level, with a light muon sneutrino and light chargino; (ii) predict a highly-singlet-dominated 95~GeV Higgs, with a diphoton rate as hinted at by CMS data, because of a light higgsino-like chargino and moderate $\lambda$; (iii) get low fine tuning from the GUT scale with small $\mu_{\rm eff},\, M_0,\, M_{1/2},\, {\rm and}\, A_0$, with a lighter stop mass which can be as low as about 500 GeV, which can be further checked in future studies with search results from the 13~TeV LHC; (iv) have the lightest neutralino be singlino-dominated or higgsino-dominated, while the bino and wino are heavier because of high gluino bounds at the LHC and universal gaugino conditions at the GUT scale; (v) satisfy all the above constraints, although it is not easy for the lightest neutralino, as the only dark matter candidate, to get enough relic density. Several ways to increase relic density are discussed.Comment: references added including CMS report 1811.0845

The YouTube-8M Kaggle Competition: Challenges and Methods

We took part in the YouTube-8M Video Understanding Challenge hosted on Kaggle, and achieved the 10th place within less than one month's time. In this paper, we present an extensive analysis and solution to the underlying machine-learning problem based on frame-level data, where major challenges are identified and corresponding preliminary methods are proposed. It's noteworthy that, with merely the proposed strategies and uniformly-averaging multi-crop ensemble was it sufficient for us to reach our ranking. We also report the methods we believe to be promising but didn't have enough time to train to convergence. We hope this paper could serve, to some extent, as a review and guideline of the YouTube-8M multi-label video classification benchmark, inspiring future attempts and research.Comment: accepted to CVPR'17 Workshop on YouTube-8M Large-Scale Video Understanding (oral presentation); code is at https://github.com/taufikxu/youtube on branches kunxu and zh

On The Degrees of Freedom of Reduced-rank Estimators in Multivariate Regression

In this paper we study the effective degrees of freedom of a general class of reduced rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation (SURE). We derive a finite-sample exact unbiased estimator that admits a closed-form expression in terms of the singular values or thresholded singular values of the least squares solution and hence readily computable. The results continue to hold in the high-dimensional scenario when both the predictor and response dimensions are allowed to be larger than the sample size. The derived analytical form facilitates the investigation of its theoretical properties and provides new insights into the empirical behaviors of the degrees of freedom. In particular, we examine the differences and connections between the proposed estimator and a commonly-used naive estimator, i.e., the number of free parameters. The use of the proposed estimator leads to efficient and accurate prediction risk estimation and model selection, as demonstrated by simulation studies and a data example.Comment: 29 pages, 3 figure