The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Looking ahead: Joint small group detection and tracking in crowd scenes

Small group detection and tracking in crowd scenes are basis for high level crowd analysis tasks. However, it suffers from the ambiguities in generating proper groups and in handling dynamic changes of group configurations. In this paper, we propose a novel delay decision-making based method for addressing the above problems, motivated by the idea that these ambiguities can be solved using rich temporal context. Specifically, given individual detections, small group hypotheses are generated. Then candidate group hypotheses across consecutive frames and their potential associations are built in a tree. By seeking for the best non-conflicting subset from the hypothesis tree, small groups are determined and simultaneously their trajectories are got. So this framework is called joint detection and tracking. This joint framework reduces the ambiguities in small group decision and tracking by looking ahead for several frames. However, it results in the unmanageable solution space because the number of track hypotheses grows exponentially over time. To solve this problem, effective pruning strategies are developed, which can keep the solution space manageable and also improve the credibility of small groups. Experiments on public datasets demonstrate the effectiveness of our method. The method achieves the state-of-the-art performance even in noisy crowd scenes.     

小型机载激光通信系统设计与验证

针对空空宽带高速通信的需求，设计了小型化机载激光通信系统。仿真分析了300 km、2.5 Gb/s无线激光链路性能，并通过运动仿真台模拟机动环境测试了系统的跟踪与通信性能，其中粗跟踪误差为533.2 μrad(1σ)，精跟踪误差为3.6 μrad(1σ)，测试数据传输240 s，通信误码率为2.82×10-9。仿真与实验验证了该系统用于远距离空空无线激光通信的可行性。     

基于时空的弱点状运动目标检测技术

如何在复杂背景下持续有效地检测目标位置,一直是研究者们需要面对的主要挑战。本文在研究红外点状移动目标特征的基础上,根据目标无纹理,无形状的特性,提出一种改进的形态学目标增强算法,并利用目标连续时空不变性检测目标。首先,建立多尺度的图像金字塔,在每层上采用改进的形态学算法快速、粗糙定位小目标。然后进一步的根据目标在时空上的位置相关性,提出基于目标运动特征分析的精确检测方法。得到精确稳定的检测结果。最后实验结果表明与经典的形态学检测算法及其他算法相比,该技术能更有效地检测弱小目标,具有更高的鲁棒性。     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

The single-polarization filter composed of gold-coated photonic crystal fiber

A single-polarization filter comprising a gold-coated photonic crystal fiber based on surface plasmon resonance is designed and investigated. The pattern matching and coupled polarization characteristics analyzed by the full-vector finite element method (FEM) and losses at 1,540 nm are achieved to 1,016.01739 dB/cm (x-pol core mode) and 33.81917 dB/cm (y-pol core mode). The crosstalk (CT) value of the 1,540 nm band is ?853.12653 dB for fiber length $L=1,000\mathrm{\mu }\text{m}$ and the bandwidth is 850 nm. The working wavelength of the filter ranges from 1,280 nm to 1,540 nm by varying the diameter of outer air holes ($d_1$), the diameter of inner air holes ($d_4$), the metal film thickness (t), as well as the liquid refractive index (n).     

Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T₁) signals, acquired with very low flip angles that contain six times more noise than the Carr–Purcell–Meiboom–Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky–Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T₁ signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T₁, as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T₁ method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.