Generalized Semi-Holographic Universe

We study the semi-holographic idea in context of decaying dark components. The energy flow between dark energy and the compensating dark matter is thermodynamically generalized to involve a particle number variable dark component with non-zero chemical potential. It's found that, unlike the original semi-holographic model, no cosmological constant is needed for a dynamical evolution of the universe. A transient phantom phase appears while a non-trivial dark energy-dark matter scaling solution keeps at late time, which evades the big-rip and helps to resolve the coincidence problem. For reasonable parameters, the deceleration parameter is well consistent with current observations. The original semi-holographic model is extended and it also suggests that the concordance model may be reconstructed from the semi-holographic idea.Comment: 15pages,5figs. arXiv admin note: substantial text overlap with arXiv:1010.136

Conserving and Gapless Hartree-Fock-Bogoliubov theory for 3D dilute Bose gas at finite temperature

The energy spectrum for the three dimensional Bose gas in Bose-Einstein Condensation phase is calculated with Modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From Improved $\Phi -$% derivable theory, the diagrams needed to preserve Ward-Takahashi Identity are resummed in a systematic and nonperturbative way. The results show significant discrepancies with Popov theory at finite temperature. It is valid up to the critical temperature where the dispersion relation of the low energy excitation spectrum changes from linear to quadratic. Because of the repulsive interaction, the critical temperature has a positive shift from that of idea gas, which is in accordance with the result from the previous calculations in the uncondensed phase.Comment: 4pages, 5figure

Compressed Counting Meets Compressed Sensing

Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using Compressed Counting (CC). CC is a technique built on maximally-skewed p-stable random projections originally developed for data stream computations. Our recovery procedure is computationally very efficient in that it requires only one linear scan of the coordinates. Our analysis demonstrates that, when 0<p<=0.5, it suffices to use M= O(C/eps^p log N) measurements so that all coordinates will be recovered within eps additive precision, in one scan of the coordinates. The constant C=1 when p->0 and C=pi/2 when p=0.5. In particular, when p->0 the required number of measurements is essentially M=K\log N, where K is the number of nonzero coordinates of the signal

Total monochromatic connection of graphs

A graph is said to be {\it total-colored} if all the edges and the vertices of the graph are colored. A path in a total-colored graph is a {\it total monochromatic path} if all the edges and internal vertices on the path have the same color. A total-coloring of a graph is a {\it total monochromatically-connecting coloring} ({\it TMC-coloring}, for short) if any two vertices of the graph are connected by a total monochromatic path of the graph. For a connected graph $G$, the {\it total monochromatic connection number}, denoted by $tmc(G)$, is defined as the maximum number of colors used in a TMC-coloring of $G$. These concepts are inspired by the concepts of monochromatic connection number $mc(G)$, monochromatic vertex connection number $mvc(G)$ and total rainbow connection number $trc(G)$ of a connected graph $G$. Let $l(T)$ denote the number of leaves of a tree $T$, and let $l(G)=\max\{ l(T) |$ $T$ is a spanning tree of $G$ $\}$ for a connected graph $G$. In this paper, we show that there are many graphs $G$ such that $tmc(G)=m-n+2+l(G)$, and moreover, we prove that for almost all graphs $G$, $tmc(G)=m-n+2+l(G)$ holds. Furthermore, we compare $tmc(G)$ with $mvc(G)$ and $mc(G)$, respectively, and obtain that there exist graphs $G$ such that $tmc(G)$ is not less than $mvc(G)$ and vice versa, and that $tmc(G)=mc(G)+l(G)$ holds for almost all graphs. Finally, we prove that $tmc(G)\leq mc(G)+mvc(G)$, and the equality holds if and only if $G$ is a complete graph.Comment: 12 page

Total proper connection of graphs

A graph is said to be {\it total-colored} if all the edges and the vertices of the graph is colored. A path in a total-colored graph is a {\it total proper path} if $(i)$ any two adjacent edges on the path differ in color, $(ii)$ any two internal adjacent vertices on the path differ in color, and $(iii)$ any internal vertex of the path differs in color from its incident edges on the path. A total-colored graph is called {\it total-proper connected} if any two vertices of the graph are connected by a total proper path of the graph. For a connected graph $G$, the {\it total proper connection number} of $G$, denoted by $tpc(G)$, is defined as the smallest number of colors required to make $G$ total-proper connected. These concepts are inspired by the concepts of proper connection number $pc(G)$, proper vertex connection number $pvc(G)$ and total rainbow connection number $trc(G)$ of a connected graph $G$. In this paper, we first determine the value of the total proper connection number $tpc(G)$ for some special graphs $G$. Secondly, we obtain that $tpc(G)\leq 4$ for any $2$-connected graph $G$ and give examples to show that the upper bound $4$ is sharp. For general graphs, we also obtain an upper bound for $tpc(G)$. Furthermore, we prove that $tpc(G)\leq \frac{3n}{\delta+1}+1$ for a connected graph $G$ with order $n$ and minimum degree $\delta$. Finally, we compare $tpc(G)$ with $pvc(G)$ and $pc(G)$, respectively, and obtain that $tpc(G)>pvc(G)$ for any nontrivial connected graph $G$, and that $tpc(G)$ and $pc(G)$ can differ by $t$ for $0\leq t\leq 2$.Comment: 15 page

Analysis of stability of community structure across multiple hierarchical levels

The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts model. Specifically we model the Potts procedure of community structure detection by a Markov process, which has a clear mathematical explanation. Critical topological information regarding to multivariate spin configuration could also be inferred from the spectral significance of the Markov process. We test our framework on some example networks and find it doesn't have resolute limitation problem at all. Results have shown the model we proposed is able to uncover hierarchical structure in different scales effectively and efficiently.Comment: 7 pages, 3 figure

Well-posedness of the free boundary problem in incompressible elastodynamics

In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a natural stability condition, which ensures that the evolution equation describing the free boundary is strictly hyperbolic. Our result gives a rigorous confirmation that the elasticity has a stabilizing effect on the Rayleigh-Taylor instability.Comment: 20 page

Integrated Speech Enhancement Method Based on Weighted Prediction Error and DNN for Dereverberation and Denoising

Both reverberation and additive noises degrade the speech quality and intelligibility. Weighted prediction error (WPE) method performs well on the dereverberation but with limitations. First, WPE doesn't consider the influence of the additive noise which degrades the performance of dereverberation. Second, it relies on a time-consuming iterative process, and there is no guarantee or a widely accepted criterion on its convergence. In this paper, we integrate deep neural network (DNN) into WPE for dereverberation and denoising. DNN is used to suppress the background noise to meet the noise-free assumption of WPE. Meanwhile, DNN is applied to directly predict spectral variance of the target speech to make the WPE work without iteration. The experimental results show that the proposed method has a significant improvement in speech quality and runs fast

Capacity of Gaussian Channels with Duty Cycle and Power Constraints

In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio only actively transmits signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This work studies the capacity of scalar discrete-time Gaussian channels subject to duty cycle constraint as well as average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. A unique discrete input distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. Furthermore, a more realistic duty cycle constraint is studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is no longer independent over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, the distribution of which is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.Comment: 36 pages, 6 figure

Good upper bounds for the total rainbow connection of graphs

A total-colored graph is a graph $G$ such that both all edges and all vertices of $G$ are colored. A path in a total-colored graph $G$ is a total rainbow path if its edges and internal vertices have distinct colors. A total-colored graph $G$ is total-rainbow connected if any two vertices of $G$ are connected by a total rainbow path of $G$. The total rainbow connection number of $G$, denoted by $trc(G)$, is defined as the smallest number of colors that are needed to make $G$ total-rainbow connected. These concepts were introduced by Liu et al. Notice that for a connected graph $G$, $2diam(G)-1\leq trc(G)\leq 2n-3$, where $diam(G)$ denotes the diameter of $G$ and $n$ is the order of $G$. In this paper we show, for a connected graph $G$ of order $n$ with minimum degree $\delta$, that $trc(G)\leq6n/{(\delta+1)}+28$ for $\delta\geq\sqrt{n-2}-1$ and $n\geq 291$, while $trc(G)\leq7n/{(\delta+1)}+32$ for $16\leq\delta\leq\sqrt{n-2}-2$ and $trc(G)\leq7n/{(\delta+1)}+4C(\delta)+12$ for $6\leq\delta\leq15$, where $C(\delta)=e^{\frac{3\log({\delta}^3+2{\delta}^2+3)-3(\log3-1)}{\delta-3}}-2$. This implies that when $\delta$ is in linear with $n$, then the total rainbow number $trc(G)$ is a constant. We also show that $trc(G)\leq 7n/4-3$ for $\delta=3$, $trc(G)\leq8n/5-13/5$ for $\delta=4$ and $trc(G)\leq3n/2-3$ for $\delta=5$. Furthermore, an example shows that our bound can be seen tight up to additive factors when $\delta\geq\sqrt{n-2}-1$.Comment: 8 page