Pathwise Performance of Debt Based Policies for Wireless Networks with Hard Delay Constraints

Hou et al have introduced a framework to serve clients over wireless channels when there are hard deadline constraints along with a minimum delivery ratio for each client's flow. Policies based on "debt," called maximum debt first policies (MDF) were introduced, and shown to be throughput optimal. By "throughput optimality" it is meant that if there exists a policy that fulfils a set of clients with a given vector of delivery ratios and a vector of channel reliabilities, then the MDF policy will also fulfill them. The debt of a user is the difference between the number of packets that should have been delivered so as to meet the delivery ratio and the number of packets that have been delivered for that client. The maximum debt first (MDF) prioritizes the clients in decreasing order of debts at the beginning of every period. Note that a throughput optimal policy only guarantees that \begin{small} \liminf_{T \to \infty} \frac{1}{T}\sum_{t=1}^{T} \mathbbm{1}\{\{client n$'s packet is delivered in frame$t} \} \geq q_{i} \end{small}, where the right hand side is the required delivery ratio for client $i$. Thus, it only guarantees that the debts of each user are $o(T)$, and can be otherwise arbitrarily large. This raises the interesting question about what is the growth rate of the debts under the MDF policy. We show the optimality of MDF policy in the case when the channel reliabilities of all users are same, and obtain performance bounds for the general case. For the performance bound we obtain the almost sure bounds on $\limsup_{t\to\infty}\frac{d_{i}(t)}{\phi(t)}$ for all $i$, where $\phi(t) = \sqrt{2t\log\log t}$

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

No association of CTLA-4 polymorphisms with susceptibility to Behcet disease

Background: Cytotoxic T lymphocyte-associated antigen 4 (CTLA-4) is a key negative regulator of T lymphocytes and has been shown to be associated with a number of autoimmune diseases. The present study was performed to assess the association between CTLA-4 polymorphisms and Behcet disease (BD) in Chinese patients. Methods: Two hundred and twenty-eight BD patients and 207 controls were analysed for four single nucleotide polymorphisms (SNPs) (21661A/G, 2318C/T, + 49G/A and CT60G/A) in the CTLA-4 gene by PCR-restriction fragment length polymorphism (RFLP) analysis. The association between SNP +49A/G and BD in Chinese population as well as other ethnic groups was analysed by meta-analysis. Results: No association could be detected between CTLA-4 SNPs or haplotypes and BD. Also, no association was observed between CTLA-4 polymorphisms and BD subgroups, stratified by clinical features. A meta-analysis showed that there was no heterogeneity between studies (p = 0.60, I-2 = 0%) and that CTLA-4 SNP + 49 was not associated with BD (overall effect: Z = 0.26, p = 0.79). Conclusion: This study and a meta-analysis failed to demonstrate any association between the tested CTLA-4 polymorphisms and B

Fourth Generation Leptons and Muon g−2g-2

We consider the contributions to $g_\mu-2$ from fourth generation heavy neutral and charged leptons, $N$ and $E$, at the one-loop level. Diagrammatically, there are two types of contributions: boson-boson-$N$, and $E$-$E$-boson in the loop diagram. In general, the effect from $N$ is suppressed by off-diagonal lepton mixing matrix elements. For $E$, we consider flavor changing neutral couplings arising from various New Physics models, which are stringently constrained by $\mu\to e\gamma$. We assess how the existence of a fourth generation would affect these New Physics models.Comment: Minor changes, with references update

First and second sound in a highly elongated Fermi gas at unitarity

We consider a Fermi gas at unitarity trapped by a highly elongated harmonic potential and solve the equations of two fluid hydrodynamics at finite temperature. The propagation of sound waves as well as the discretized solutions in the presence of weak axial trapping are considered. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both first sound and second sound solutions are calculated as a function of temperature and the role of the superfluid density is explicitly pointed out. The density fluctuations in the second sound wave are found to be large enough to be measured as a consequence of the finite thermal expansion coefficient of the gas. Emphasis is given to the comparison with recent experimental data.Comment: 15 pages, 11 figure

Demonstrating Entanglement by Testing Bell's Theorem in Majorana Wires

We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple "keyboard" gating, and projective measurement. Simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.Comment: 11 pages, 8 figures, 2 table

Wave spectra of 2D dusty plasma solids and liquids

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust thermal mode was confirmed in simulations, and a cutoff wavenumber in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), quasi-localized charged approximation (QLCA), and harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA good agreement with simulations were found in the high and low temperature limits, respectively.Comment: 26 pages, 9 figure