Lasing with cell-endogenous fluorophores: parameters and conditions

The notion of lasing with biologics has recently been realized and has since rapidly developed with the collective objective of creating lasers $\textit{in vivo}$. One limitation of achieving this goal is the requirement of exogenous laser dyes and fluorescent materials. To circumvent this, we investigate the use of cell-endogenous fluorophores - sources of cell autofluorescence - as laser gain material. In this work, we study the lasing potential and efficiency of flavins and reduced nicotinamide adenine dinucleotide (phosphate) (NAD(P)H) using a dye lasing model based on coupled rate equations. Analytical solutions for one- and two-photon pumped system were used in multi-parameter studies. We found that at physiological conditions, lasing can be supported by NAD(P)H with cavity quality factors of $10^5$. With the further consideration of damage thresholds, we recommend the use of flavins as they entail lower threshold requirements. We then identify potential parameters for engineering to make the lasing of flavins feasible even at their low physiological intracellular concentrations. We also note the higher threshold requirements and lower efficiencies of two-photon pumping, but recognize its potential for realizing lasing $\textit{in vivo}$

A note on the discrete Fourier restriction problem

In this paper, we establish a general discrete Fourier restriction theorem. As an application, we make some progress on the discrete Fourier restriction associated with KdV equation.Comment: Proc. Amer. Math. Soc. to appea

Domain structures and superdislocations of La0.7Ca0.3MnO3 thin films grown on SrTiO3 substrates

The domain structures and dislocations in epitaxial thin films of La0.7Ca0.3MnO3 grown on SrTiO3 substrates by pulsed laser deposition were investigated using Bragg-contrast diffraction and high-resolution transmission electron microscopy. It revealed that the films contained the 1/2[100]o and 1/2[10-1]o types partial threading dislocations, the 90 degree - and 120 degree - types of twin- domain boundaries, and two types 1/2[010]o, 1/2[111]o, of antiphase boundaries, which are often observed in bulk materials. In addition, two types of superdislocations were detected; one consisted of two 1/2[111]o dislocations and a 1/2[111]o antiphase boundary, and the other was composed of two 1/2[010]o dislocations and a 1/2[010]o antiphase boundary. These superdislocations, domain boundaries, and their relationships were extensively explored.Comment: 19 pages, 6 figure

L1L^1-Dini conditions and limiting behavior of weak type estimates for singular integrals

In 2006, Janakiraman [10] showed that if $\Omega$ with mean value zero on $S^{n-1}$ satisfies the condition $$\sup_{|\xi|=1}\int_{S^{n-1}}|\Omega(\theta)-\Omega(\theta+\delta\xi)|d\sigma(\theta)\leq Cn\delta\int_{S^{n-1}}|\Omega(\theta)|d\sigma(\theta),\quad 0<\delta<\frac{1}{n},\ (\ast)$$ then for the singular integral operator $T_\Omega$ with homogeneous kernel, the following limiting behavior holds: $$\lim\limits_{\lambda\rightarrow 0}\lambda m(\{x\in\mathbb{R}^n:|T_\Omega f(x)|>\lambda\})= \frac{1}{n}\|\Omega\|_{1}\|f\|_{1},\quad \text{for}\ f\in L^1(\mathbb{R}^n)\ \text{with}\ f\geq 0.\ (\ast\ast)$$ In the present paper, we prove that if replacing the condition $(\ast)$ by more general condition, the $L^1$-Dini condition, then the limiting behavior $(\ast\ast)$ still holds for the singular integral $T_\Omega$. In particular, we give an example which satisfies the $L^1$-Dini condition, but does not satisfy $(\ast)$. Hence, we improve essentially the above result given in [10]. To prove our conclusion, we show that the $L^1$-Dini conditions defined respectively via the rotation and translation on $\mathbb{R}^n$ are equivalent (see Theorem 2.5 below), which has its own interest in the theory of singular integrals. Moreover, similar limiting behavior for the fractional integral operator $T_{\Omega,\alpha}$ with homogeneous kernel is also established in this paper.Comment: 18 pages, typos are corrected, to appear in Rev. Mat. Iberoa

Weak type (1,1) bound criterion for singular integral with rough kernel and its applications

In this paper, a weak type (1,1) bound criterion is established for singular integral operator with rough kernel. As some applications of this criterion, we prove some important operators with rough kernel in harmonic analysis, such as Calder\'on commutator, higher order Calder\'on commutator, general Calder\'on commutator, Calder\'on commutator of Bajsanski-Coifman type and general singular integral of Muckenhoupt type, are all of weak type (1,1).Comment: 27 pages. To appear in Trans. Amer. Math. So

Weighted bound for commutators

Let $K$ be the Calder\'on-Zygmund convolution kernel on $\mathbb{R}^d (d\geq2)$. Define the commutator associated with $K$ and $a\in L^\infty(\mathbb{R}^d)$ by $$T_af(x)=p.v. \int K(x-y)m_{x,y}a\cdot f(y)dy.$$ Recently, Grafakos and Honz\'{\i}k [5] proved that $T_a$ is of weak type (1,1) for $d=2$. In this paper, we show that $T_a$ is also weighted weak type (1,1) with the weight $|x|^\alpha\,(-2<\alpha <0)$ for $d=2$. Moreover, we prove that $T_a$ is bounded on weighted $L^p(\mathbb{R}^d)\,(1<p<\infty)$ for all $d\ge2$.Comment: Some misprints and the reference [6] of published version are corrected. Published in J.Geom.Anal(2015

QoS-aware Full-duplex Concurrent Scheduling for Millimeter Wave Wireless Backhaul Networks

The development of self-interference (SI) cancelation technology makes full-duplex (FD) communication possible. Considering the quality of service (QoS) of flows in small cells densely deployed scenario with limited time slot (TS) resources, this paper introduces the FD communication into the concurrent scheduling problem of millimeter-wave (mmWave) wireless backhaul network. We propose a QoS-aware FD concurrent scheduling algorithm to maximize the number of flows with their QoS requirements satisfied. Based on the contention graph, the algorithm makes full use of the FD condition. Both residual self-interference (RSI) and multi-user interference (MUI) are considered. Besides, it also fully considers the QoS requirements of flows and ensures the flows can be transmitted at high rates. Extensive simulations at 60GHz demonstrate that with high SI cancelation level and appropriate contention threshold, the proposed FD algorithm can achieve superior performance in terms of the number of flows with their QoS requirements satisfied and the system throughput compared with other stateof-of-the-art schemes.Comment: 9 pages, 10 figure

Jump and variational inequalities for rough operators

In this paper, we systematically study jump and variational inequalities for rough operators, whose research have been initiated by Jones {\it et al}. More precisely, we show some jump and variational inequalities for the families $\mathcal T:=\{T_\varepsilon\}_{\varepsilon>0}$ of truncated singular integrals and $\mathcal M:=\{M_t\}_{t>0}$ of averaging operators with rough kernels, which are defined respectively by $$T_\varepsilon f(x)=\int_{|y|>\varepsilon}\frac{\Omega(y')}{|y|^n}f(x-y)dy$$ and $$M_t f(x)=\frac1{t^n}\int_{|y|<t}\Omega(y')f(x-y)dy,$$ where the kernel $\Omega$ belongs to $L\log^+\!\!L(\mathbf S^{n-1})$ or $H^1(\mathbf S^{n-1})$ or $\mathcal{G}_\alpha(\mathbf S^{n-1})$ (the condition introduced by Grafakos and Stefanov). Some of our results are sharp in the sense that the underlying assumptions are the best known conditions for the boundedness of corresponding maximal operators.Comment: 32 page

Compactness of commutators of bilinear maximal Calder\'{o}n-Zygmund singular integral operators

Let $T$ be a bilinear Calder\'{o}n-Zygmund singular integral operator and $T_*$ be its corresponding truncated maximal operator. The commutators in the $i$-$th$ entry and the iterated commutators of $T_*$ are defined by $$T_{\ast,b,1}(f,g)(x)=\sup_{\delta>0}\bigg|\iint_{|x-y|+|x-z|>\delta}K(x,y,z)(b(y)-b(x))f(y)g(z)dydz\bigg|,$$ $$T_{\ast,b,2}(f,g)(x)=\sup_{\delta>0}\bigg|\iint_{|x-y|+|x-z|>\delta}K(x,y,z)(b(z)-b(x))f(y)g(z)dydz\bigg|,$$ \begin{align*} T_{\ast,(b_1,b_2)}(f,g)(x)=\sup\limits_{\delta>0}\bigg|\iint_{|x-y|+|x-z|>\delta} K(x,y,z)(b_1(y)-b_1(x))(b_2(z)-b_2(x))f(y)g(z)dydz\bigg|. \end{align*} In this paper, the compactness of the commutators $T_{\ast,b,1}$, $T_{\ast,b,2}$ and $T_{\ast,(b_1,b_2)}$ on $L^r(\mathbb{R}^n))$ is established.Comment: New version, corrected the fomer mistake

Riesz transforms associated with higher-order Schr\"odinger type operators

In this paper, let $L=L_{0}+V$ be a Schr\"{o}dinger type operator where $L_{0}$ is higher order elliptic operator with complex coefficients in divergence form and $V$ is signed measurable function, under the strongly subcritical assumption on $V$, the authors study the $L^{q}$ boundedness of Riesz transforms $\nabla^{m}L^{-1/2}$ for $q\leq 2$ and obtain a sharp result. Furthermore, the authors impose extra regularity assumptions on $V$ to obtain the $L^{q}$ boundedness of Riesz transforms $\nabla^{m}L^{-1/2}$ for $q>2$. As an application, the main results can be applied to the operator $L=(-\Delta)^{m}-\gamma|x|^{-2m}$ for suitable $\gamma