On Gradient Solitons of the Ricci–Harmonic Flow

In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.     

Numerical study of dielectrophoresis-modified inertial migration for overlapping sized cell separation

Circulating tumor cells (CTCs) have been proven to have significant prognostic, diagnostic, and clinical values in early-stage cancer detection and treatment. The efficient separation of CTCs from peripheral blood can ensure intact and viable CTCs and can, thus, give proper genetic characterization and drug innovation. In this study, continuous and high-throughput separation of MDA-231 CTCs from overlapping sized white blood cells (WBCs) is achieved by modifying inertial cell focusing with dielectrophoresis (DEP) in a single-stage microfluidic platform by numeric simulation. The DEP is enabled by embedding interdigitated electrodes with alternating field control on a serpentine microchannel to avoid creating two-stage separation. Rather than using the electrokinetic migration of cells which slows down the throughput, the system leverages the inertial microfluidic flow to achieve high-speed continuous separation. The cell migration and cell positioning characteristics are quantified through coupled physics analyses to evaluate the effects of the applied voltages and Reynolds numbers (Re) on the separation performance. The results indicate that the introduction of DEP successfully migrates WBCs away from CTCs and that separation of MDA-231 CTCs from similar sized WBCs at a high Re of 100 can be achieved with a low voltage of magnitude 4 ×10⁶ V/m. Additionally, the viability of MDA-231 CTCs is expected to be sustained after separation due to the short-term DEP exposure. The developed technique could be exploited to design active microchips for high-throughput separation of mixed cell beads despite their significant size overlap, using DEP-modified inertial focusing controlled simply by adjusting the applied external field.     

Inertial focusing of microparticles,bacteria, and blood in serpentine glass channels

Early detection of pathogenic microorganisms is pivotal to diagnosis and prevention of health and safety crises. Standard methods for pathogen detection often rely on lengthy culturing procedures, confirmed by biochemical assays, leading to >24 h for a diagnosis. The main challenge for pathogen detection is their low concentration within complex matrices. Detection of blood-borne pathogens via techniques such as PCR requires an initial positive blood culture and removal of inhibitory blood components, reducing its potential as a diagnostic tool. Among different label-free microfluidic techniques, inertial focusing on microscale channels holds great promise for automation, parallelization, and passive continuous separation of particles and cells. This work presents inertial microfluidic manipulation of small particles and cells (1–10 μm) in curved serpentine glass channels etched at different depths (deep and shallow designs) that can be exploited for (1) bacteria preconcentration from biological samples and (2) bacteria-blood cell separation. In our shallow device, the ability to focus Escherichia coli into the channel side streams with high recovery (89% at 2.2× preconcentration factor) could be applied for bacteria preconcentration in urine for diagnosis of urinary tract infections. Relying on differential equilibrium positions of red blood cells and E. coli inside the deep device, 97% red blood cells were depleted from 1:50 diluted blood with 54% E. coli recovered at a throughput of 0.7 mL/min. Parallelization of such devices could process relevant volumes of 7 mL whole blood in 10 min, allowing faster sample preparation for downstream molecular diagnostics of bacteria present in bloodstream.     

Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes

We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with respect to one complex structure and which acts non-trivially on the corresponding symplectic form always has a fixed point locus which is complex Lagrangian with respect to one of the other complex structures, and (b) there exist Lagrangian submanifolds which are complex with respect to one complex structure and are not the fixed point locus of any involution which is anti-holomorphic with respect to one of the other complex structures.     

Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊³ × 𝕊³.     

多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题minc+tr(AX)+∑mj=1tr(BjXCjXT),s.t.XTX = Ip,其中C为常数,A∈Rpxn(n ≥ p),Bj∈Rnxn,Cj∈Rpxp为给定系数矩阵.数值实验表明已有的Majorization算法虽可行,但收敛速度缓慢且精度不高.本文从黎曼流形的角...     

基于视觉心理学的SFS流形算法研究

通过视觉方法获取形状在科学研究及工程实践中有着重要作用,灰度图像是最容易获取的视觉信息之一。目前由灰度重构的形状(SFS,shape from shading)受到了广泛的关注,但现有的算法稳定性差、效率低,一直阻碍着SFS方法的推广应用。受近期的视觉心理学研究成果的启发,针对SFS问题,从局部分析入手,即:在图像上,在每一灰度极值点附近,根据灰度单调变化的情况,形成一个椭圆形邻域,对应着表面凹凸区;在每一椭圆域上,形状可用抛物面逼近,其参数可由局部辐射度约束求解;整个图像被椭圆形邻域覆盖,这些覆盖可构成一个二维流形;借助于流形上单位分解函数,各局部抛物面粘合在一起,形成光滑的整体形状;总体形状在整幅图像的灰度约束下再进行全局优化,可得到最终的重构结果。给出了初步算例,算法的稳定性和效率均有大幅度提高。     

Growth and Spectral Properties of Yb^3＋-doped Ba3Gd（BO3）3 Crystal

Crystal of Yb3+-doped Ba3Gd(BO3)3 has been grown by the Czochralski method. The spectroscopic characterizations have been investigated at room temperature. The Yb3+:Ba3Gd(BO3)3 crystal exhibits broad absorption at 976nm with FWHM of 7nm and large overall spitting of 2F7/2 manifold (823cm-1). The absorption and emission cross sections are 5.09×10-21cm2 at 976nm and 0.97×10-21cm2 at 1040nm,respectively. The fluorescence lifetime is 2.84 ms.     

流形元法固定边界约束处理研究

在数值流形方法中,对于材料的固定边界,一般采用罚函数的方法进行处理,即在固定边界上设置刚性弹簧约束其位移来实现固定约束条件的近似满足。罚函数法在理论上不是严格的固定约束处理方法,罚弹簧的布置与弹簧刚度的大小对模拟的效果都会产生影响。基于流形单元上位移函数的组成提出了流形方法固定边界约束处理的新方法,在组成流形单元的物理覆盖上,通过取消相应的覆盖函数在流形单元位移函数中的组成来实现双向固定的约束条件,通过使用只包含单方向位移的覆盖函数使x向固定约束条件和y向固定约束条件得到实现,推导了相应固定约束条件下的流形单元刚度矩阵的数值计算格式。该方法严格满足固定约束的物理意义,简化了固定边界的处理,并经算例证明是有效和准确的,有利于数值流形方法的程序实现和工程应用。