Attosecond Coherent Control of Symmetry Breaking and Restoration in Atoms and Molecules

Symmetry is a fundamental phenomenon in science, and symmetry breaking is often the origin of subsequent processes which are important in chemistry, physics and biology. As is well-known, a laser pulse can break the electronic symmetry in atoms and molecules by creating a superposition of electronic eigenstates with different irreducible representations, which typically initiates attosecond ultrafast charge migration. In the first part of this dissertation, an original theory of coherent laser control is proposed to induce the symmetry restoration of the electronic structure in atoms and molecules after symmetry breaking, with application to the oriented benzene molecule and to the ^{87}Rb atom. Four different strategies are proposed and corresponding sufficient conditions for symmetry restoration are derived analytically. The numerical and analytical results agree perfectly with each other. Meanwhile, the theoretical predictions for the ^{87}Rb atom have been confirmed by experimental partners in Japan, by means of high contrast Ramsey interferometry with a precision of about three attoseconds. The second part is devoted to the electronic flux during charge migration in oriented benzene molecule. Two different patterns of adiabatic attosecond charge migration are investigated by laser induced preparation of two different non-aromatic superposition states. From the knowledge of the time-dependent many-body wave functions as a linear combination of many-electron wave functions obtained from conventional quantum chemistry calculations, we derive expressions for the time-evolution of the one-electron density and the electronic flux. This allows to specify the number of electrons flowing during a given charge migration process, together with the mechanism of charge migration. In conclusion, this dissertation shows, for the first time, that the symmetry of electronic structure in atoms and molecules can not only be broken but also be restored by means of simple laser pulses. The coherent control strategies require strict control over the time-dependent phases of electronic wave functions. In practice, the precision required is few attoseconds - much shorter than the timescale of charge migration in such systems. The analysis of charge migration indicates that similar superposition states may lead to quantitative differences in the number of electrons flowing.Symmetrie ist ein fundamentales Phänomen in der Naturwissenschaft, und Symmetriebrechung kann bedeutende Folgeprozesse in der Chemie, Physik und Biologie auslösen. Insbesondere kann die elektronische Symmetrie von Atomen und Molekülen bekanntlich durch einen Laserpuls gebrochen werden, und zwar durch die Erzeugung einer Superposition von elektronischen Zuständen mit verschiedenen irreduziblen Darstellungen - dies bewirkt dann typischerweise ultraschnelle Ladungsmigration auf der Attosekundenzeit-skala. Der erste Teil dieser Dissertation entwickelt eine grundlegende Theorie der kohärenten Laserpuls-Kontrolle mit dem Ziel der Wiederherstellung der elektronischen Symmetrie in Atomen und Molekülen nach Symmetriebrechung, mit Anwendungen auf das orientierte Benzolmolekül sowie auf das ^{87}Rb Atom. Es werden insgesamt vier Strategien zur Wiederherstellung der Symmetrie vorgestellt, wobei hinreichend zielführende Bedingungen analytisch hergeleitet werden. Die analytischen Ergebnisse stimmen exzellent mit numerischen Quantendynamiksimulationen überein. Die theoretischen Vorhersagen für das ^{87}Rb Atom wurden inzwischen mit Hilfe der hoch-kontrastreichen Ramsey Interferometrie von experimentellen Partnern in Japan mit einer Genauigkeit von drei Attosekunden bestätigt. Der zweite Teil untersucht den Elektronenfluss während der Ladungsmigration in orientierten Benzolmolekülen. Dabei werden für zwei unterschiedliche nicht-aromatische elektronische Superpositionszustände verschiedene Typen der adiabatischen Ladungsmigration auf der Attosekundenzeitskala aufgezeigt. Aus der Kenntnis der zeitabhängigen Viel-Elektronen-Wellenfunktion als Linearkombination elektronischer Eigenfunktionen, die mit Hilfe konventioneller Verfahren der Quantenchemie berechnet werden, werden Ausdrücke für die Zeit-Evolution der Ein-Elektronen-Dichte und des Elektronenflusses hergeleitet. Daraus ergibt sich die jeweilige Zahl der Elektronen, die zur Ladungsmigration beitragen, sowie der Mechanismus der Ladungsmigration. Zusammenfassend zeigt diese Dissertation erstmals, dass die Symmetrie der Elektronenstruktur von Atomen und Molekülen mit Hilfe von einfachen Laserpulsen nicht nur gebrochen, sondern auch wiederhergestellt werden kann. Die Strategien der kohärenten Laserkontrolle verlangen dazu die strenge Kontrolle der zeitabhängigen Phasen der elektronischen Wellenfunktionen. Praktische Anwendungen erfordern dafür eine zeitliche Genauigkeit von wenigen Attosekunden - also noch viel genauer als die ohnehin schon ultrakurze Zeitskala der Ladungsmigration. Untersuchungen der Ladungsmigration zeigen, dass vergleichbar ähnliche Superpositionen elektronischer Wellenfunktionen zu quantitativ verschiedenen Elektronenflusszahlen führen können

Some equalities for estimations of variance components in a general linear model and its restricted and transformed models

AbstractFor the unknown positive parameter σ2 in a general linear model ℳ={y,Xβ,σ2Σ}, the two commonly used estimations are the simple estimator (SE) and the minimum norm quadratic unbiased estimator (MINQUE). In this paper, we derive necessary and sufficient conditions for the equivalence of the SEs and MINQUEs of the variance component σ2 in the original model ℳ, the restricted model ℳr={y,Xβ∣Aβ=b,σ2Σ}, the transformed model ℳt={Ay,AXβ,σ2AΣA′}, and the misspecified model ℳm={y,X0β,σ2Σ0}

Adaptive Shape Kernel-Based Mean Shift Tracker in Robot Vision System

This paper proposes an adaptive shape kernel-based mean shift tracker using a single static camera for the robot vision system. The question that we address in this paper is how to construct such a kernel shape that is adaptive to the object shape. We perform nonlinear manifold learning technique to obtain the low-dimensional shape space which is trained by training data with the same view as the tracking video. The proposed kernel searches the shape in the low-dimensional shape space obtained by nonlinear manifold learning technique and constructs the adaptive kernel shape in the high-dimensional shape space. It can improve mean shift tracker performance to track object position and object contour and avoid the background clutter. In the experimental part, we take the walking human as example to validate that our method is accurate and robust to track human position and describe human contour

Quantum Control on the Attosecond Time Scale

This article starts with an introductory survey of previous work on breaking and restoring the electronic structure symmetry of atoms and molecules by means of two laser pulses. Accordingly, the first pulse breaks the symmetry of the system in its ground state with irreducible representation IRREPg by exciting it to a superposition of the ground state and an excited state with different IRREPe . The superposition state is non-stationary, representing charge migration with period T in the sub- to few femtosecond time domains. The second pulse stops charge migration and restores symmetry by de-exciting the superposition state back to the ground state. Here, we present a new strategy for symmetry restoration: The second laser pulse excites the superposition state to the excited state, which has the same symmetry as the ground state, but different IRREPe . The success depends on perfect time delay between the laser pulses, with precision of few attoseconds. The new strategy is demonstrated by quantum dynamics simulation for an oriented model system, benzene

Filter Pruning For CNN With Enhanced Linear Representation Redundancy

Structured network pruning excels non-structured methods because they can take advantage of the thriving developed parallel computing techniques. In this paper, we propose a new structured pruning method. Firstly, to create more structured redundancy, we present a data-driven loss function term calculated from the correlation coefficient matrix of different feature maps in the same layer, named CCM-loss. This loss term can encourage the neural network to learn stronger linear representation relations between feature maps during the training from the scratch so that more homogenous parts can be removed later in pruning. CCM-loss provides us with another universal transcendental mathematical tool besides L*-norm regularization, which concentrates on generating zeros, to generate more redundancy but for the different genres. Furthermore, we design a matching channel selection strategy based on principal components analysis to exploit the maximum potential ability of CCM-loss. In our new strategy, we mainly focus on the consistency and integrality of the information flow in the network. Instead of empirically hard-code the retain ratio for each layer, our channel selection strategy can dynamically adjust each layer's retain ratio according to the specific circumstance of a per-trained model to push the prune ratio to the limit. Notably, on the Cifar-10 dataset, our method brings 93.64% accuracy for pruned VGG-16 with only 1.40M parameters and 49.60M FLOPs, the pruned ratios for parameters and FLOPs are 90.6% and 84.2%, respectively. For ResNet-50 trained on the ImageNet dataset, our approach achieves 42.8% and 47.3% storage and computation reductions, respectively, with an accuracy of 76.23%. Our code is available at https://github.com/Bojue-Wang/CCM-LRR

Components of domino tilings under flips in quadriculated cylinder and torus

In a region $R$ consisting of unit squares, a domino is the union of two adjacent squares and a (domino) tiling is a collection of dominoes with disjoint interior whose union is the region. The flip graph $\mathcal{T}(R)$ is defined on the set of all tilings of $R$ such that two tilings are adjacent if we change one to another by a flip (a $90^{\circ}$ rotation of a pair of side-by-side dominoes). It is well-known that $\mathcal{T}(R)$ is connected when $R$ is simply connected. By using graph theoretical approach, we show that the flip graph of $2m\times(2n+1)$ quadriculated cylinder is still connected, but the flip graph of $2m\times(2n+1)$ quadriculated torus is disconnected and consists of exactly two isomorphic components. For a tiling $t$, we associate an integer $f(t)$, forcing number, as the minimum number of dominoes in $t$ that is contained in no other tilings. As an application, we obtain that the forcing numbers of all tilings in $2m\times (2n+1)$ quadriculated cylinder and torus form respectively an integer interval whose maximum value is $(n+1)m$

Cross-layer protocol interactions in heterogeneous data networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 143-148).(cont.) TCP timeout backoff and MAC layer retransmissions, are studied in detail. The results show that the system performance is a balance of idle slots and collisions at the MAC layer, and a tradeoff between packet loss probability and round trip time at the transport layer. Finally, we consider the optimal scheduling problem with window service constraints. Optimal policies that minimize the average response time of jobs are derived and the results show that both the job lengths and the window sizes are essential to the optimal policy.Modern data networks are heterogeneous in that they often employ a variety of link technologies, such as wireline, optical, satellite and wireless links. As a result, Internet protocols, such as Transmission Control Protocol (TCP), that were designed for wireline networks, perform poorly when used over heterogeneous networks. This is particularly the case for satellite and wireless networks which are often characterized by high bandwidth-delay product and high link loss probability. This thesis examines the performance of TCP in the context of heterogeneous networks, particularly focusing on interactions between protocols across different layers of the protocol stack. First, we provide an analytical framework to study the interaction between TCP and link layer retransmission protocols (ARQ). The system is modelled as a Markov chain with reward functions, and detailed queueing models are developed for the link layer ARQ. The analysis shows that in most cases implementing ARQ can achieve significant improvement in system throughput. Moreover, by proper choice of protocols parameters, such as the packet size and the number of transmission attempts per packet, significant performance improvement can be obtained. We then investigate the interaction between TCP at the transport layer and ALOHA at the MAC layer. Two equations are derived to express the system performance in terms of various system and protocol parameters, which show that the maximum possible system throughput is 1/e. A sufficient and necessary condition to achieve this throughput is also presented, and the optimal MAC layer transmission probability at which the system achieves its highest throughput is given. Furthermore, the impact of other system and protocol parameters, such asby Chunmei Liu.Ph.D

Effect of regional versus general anaesthesia on postoperative opioid consumption, clinical outcomes and cognitive function in Chinese patients undergoing metastatic cancer surgery

Purpose: To compare postoperative opioid consumption, inflammatory biomarkers, cognitive function and safety profile of regional anesthesia (RA) versus general anesthesia (GA) in Chinese patients undergoing metastatic cancer surgery.Method: Chinese patients undergoing metastatic cancer surgery were enrolled and received either RA or GA) in allocation ratio of 1:1. The following efficacy variables were assessed: 1) pain score was measured on VAS scale; 2) post-operative consumption; 3) inflammatory biomarkers; 4) cognitive function; 5) clinical outcomes. Safety was also assessed.Results: Data for a total of 220 patients were analyzed. Compared to GA alone, the combination of RA and GA demonstrated significantly greater reduction in post-operative pain with decreased postoperative opioid consumption. Also, RA/GA combination inhibited inflammatory response when compared to patients who received GA only, indicating that RA + GA improved immune response in patient undergoing surgical intervention. The severity of signs and symptoms of dementia were similar at baseline visit (p > 0.05). Patients of RA/GA group had significantly greater relief in signs and symptoms of dementia/cognitive impairment, when compared to the GA-treated patients (p < 0.05). However, incidence of complications (including adverse events) was comparable for both groups (p > 0.05). Additionally, RA/GA was also associated with shorter length of hospital stay, compared to GA.Conclusion: RA/GA combination demonstrates significantly greater improvement in the level of clinical outcomes, decreases postoperative opioid consumption, and improves cognitive functions when compared to GA in Chinese patients undergoing metastatic cancer surgery