Statistical inference and computation in elliptic PDE models

Partial differential equations (PDE) are ubiquitous in describing real-world phenomena. In many statistical models, PDE are used to encode complex relationships between unknown quantities and the observed data. We investigate statistical and computational questions arising in such models, adopting an infinite-dimensional `nonparametric' framework and assuming the observed data are subject to random noise. The main PDE examples are of elliptic or parabolic type. Chapter 2 investigates the problem of sampling from high-dimensional Bayesian posterior distributions. The main results consist of non-asymptotic computational guarantees for Langevin-type Markov chain Monte Carlo (MCMC) algorithms which scale polynomially in key quantities such as the dimension of the model, the desired precision level, and the number of available statistical measurements. The bounds hold with high probability under the distribution of the data, assuming that certain `local geometric' assumptions are fulfilled and that a good initialiser of the algorithm is available. We study a representative non-linear PDE example where the unknown is a coefficient function in a steady-state Schr\"odinger equation, and the solution to a corresponding boundary value problem is observed. Chapter 3 studies statistical convergence rates for nonparametric Tikhonov-type estimators, which can be interpreted also as Bayesian maximum a posteriori (MAP) estimators arising from certain Gaussian process priors. The theory is derived in a general setting for non-linear inverse problems and then applied to two examples, the steady-state Schr\"odinger equation studied in Chapter \ref{sampling} and a model for the steady-state heat equation. It is shown that the rates obtained are minimax-optimal in prediction loss. The final Chapter 4 considers a model for scalar diffusion processes $(X_t:t\geq 0)$ with an unknown drift function which is modelled nonparametrically. It is shown that in the low frequency sampling case, when the sample consists of $(X_0,X_\Delta,...,X_{n\Delta})$ for some fixed sampling distance $\Delta>0$, under mild regularity assumptions, the model satisfies the local asymptotic normality (LAN) property. The key tools used are regularity estimates and spectral properties for certain parabolic and elliptic PDE related to $(X_t:t\geq 0)$

Switching Time Delay Optimization for “SiC+Si” Hybrid Device in a Phase-leg Configuration

Compared to SiC MOSFET, the switching loss of Si IGBT is much higher due to its slow switching speed and tail current. Si IGBT/SiC MOSFET hybrid switch device can reach to optimal performance with low static and dynamic loss, which can improve the current capacity of SiC devices and reduce the power loss of Si IGBT based converters. With the separated gate control signals, the switching moments of the two devices can be controlled independently to ensure Si IGBT under zero-voltage switching (ZVS) conditions. This measurement tends to reduce the switching loss of Si IGBT. However, the switching time delay between these two devices has significant impacts on its power loss. In this paper, the switching time delay optimization method is proposed to minimize the power loss of the hybrid switch. The static and dynamic characteristics of Si IGBT/SiC MOSFET hybrid-paralleled switch are studied, and a generalized power loss model for hybrid switch is developed. The influence of switching time delay on the characteristics of hybrid switch is analyzed and verified through double pulse tests in a phase-leg configuration. The experimental results show that the optimal turn-on delay time is that the two devices turn on at the same time and the turn-on loss can be reduced by about 73% compared with the solely Si IGBT and by about 52% compared with the solely SiC MOSFET. While the optimal turn-off sequence is that the Si IGBT turns off ahead of the SiC MOSFET. Under the proposed optimal turn-off delay time of the hybrid switch, the turn-off loss is reduced by about 61.4%. This optimization strategy is used in a Buck converter to verify the superiority of the SiC/Si hybrid switch and the optimal switching sequence. Simulation results show that the optimal switching sequence is consistent with theoretical analysis, and the efficiency is improved by 2.5% compared with Buck converter using solely Si IGBT

An optimized parameter design method of SiC/Si hybrid switch considering turn-off current spike

In order to reduce the switching loss of SiC MOSFET/Si IGBT (SiC/Si) hybrid switch, the switching mode that turn off the Si IGBT prior to the SiC MOSFET is generally adopted to achieved the zero-voltage switching operation of IGBT. The minority carrier in N-base region of the IGBT are recombined in the form of exponential attenuation due to the conductivity modulation effect. When the SiC MOSFET is turned off, if the carrier recombination process of the IGBT is not finished, it needs to bear a large collector–emitter voltage change rate, resulting in apparent current spike. This current spike will increase the current stress of the device and produce additional turn-off loss. The equivalent model of double pulse test circuit of SiC/Si hybrid switch considering parasitic parameters is established, and the turn-off transient process is given analytically. The influence of turn-off delay time, circuit parameters and working conditions on current spike are analysed quantitatively. Combined with the consideration of device stress and comprehensive turn-off loss, an optimized circuit design method of SiC/Si hybrid switch considering turn-off current peak is proposed, which provides theoretical and design guidance for high reliability and high efficiency SiC/Si-based converters

Increased inorganic aerosol fraction contributes to air pollution and haze in China

The detailed formation mechanism of an increased number of haze events in China is still not very clear. Here, we found that reduced surface visibility from 1980 to 2010 and an increase in satellite-derived columnar concentrations of inorganic precursors from 2002 to 2012 are connected with each other. Typically, higher inorganic mass fractions lead to increased aerosol water uptake and light-scattering ability in elevated relative humidity. Satellite observation of aerosol precursors of NO2 and SO2 showed increased concentrations during the study period. Our in situ measurement of aerosol chemical composition in Beijing also confirmed increased contribution of inorganic aerosol fraction as a function of the increased particle pollution level. Our investigations demonstrate that the increased inorganic fraction in the aerosol particles is a key component in the frequently occurring haze days during the study period, and particularly the reduction of nitrate, sulfate and their precursor gases would contribute towards better visibility in China.Peer reviewe

Visualizing the Zhang-Rice singlet, molecular orbitals and pair formation in cuprate

The parent compound of cuprates is a charge-transfer-type Mott insulator with strong hybridization between the Cu $3d_{\mathrm x^2-y^2}$ and O $2p$ orbitals. A key question concerning the pairing mechanism is the behavior of doped holes in the antiferromagnetic (AF) Mott insulator background, which is a prototypical quantum many-body problem. It was proposed that doped hole on the O site tends to form a singlet, known as Zhang-Rice singlet (ZRS), with the unpaired Cu spin. But experimentally little is known about the properties of a single hole and the interplay between them that leads to superconductivity. Here we use scanning tunneling microscopy to visualize the electronic states in hole-doped $\mathrm{Ca_2CuO_2Cl_2}$, aiming to establish the atomic-scale local basis for pair formation. A single doped hole is shown to have an in-gap state and a clover-shaped spatial distribution that can be attributed to a localized ZRS. When the dopants are close enough, they develop delocalized molecular orbitals with characteristic stripe- and ladder-shaped patterns, accompanied by the opening of a small gap around the Fermi level ($E_{\mathrm F}$). With increasing doping, the molecular orbitals proliferate in space and gradually form densely packed plaquettes, but the stripe and ladder patterns remain nearly the same. The low-energy electronic states of the molecular orbitals are intimately related to the local pairing properties, thus play a vitally important role in the emergence of superconductivity. We propose that the Cooper pair is formed by two holes occupying the stripe-like molecular orbital, while the attractive interaction is mediated by the AF spin background

Chronic Myeloid Leukemia Patients Sensitive and Resistant to Imatinib Treatment Show Different Metabolic Responses

The BCR-ABL tyrosine kinase inhibitor imatinib is highly effective for chronic myeloid leukemia (CML). However, some patients gradually develop resistance to imatinib, resulting in therapeutic failure. Metabonomic and genomic profiling of patients' responses to drug interventions can provide novel information about the in vivo metabolism of low-molecular-weight compounds and extend our insight into the mechanism of drug resistance. Based on a multi-platform of high-throughput metabonomics, SNP array analysis, karyotype and mutation, the metabolic phenotypes and genomic polymorphisms of CML patients and their diverse responses to imatinib were characterized. The untreated CML patients (UCML) showed different metabolic patterns from those of healthy controls, and the discriminatory metabolites suggested the perturbed metabolism of the urea cycle, tricarboxylic acid cycle, lipid metabolism, and amino acid turnover in UCML. After imatinib treatment, patients sensitive to imatinib (SCML) and patients resistant to imatinib (RCML) had similar metabolic phenotypes to those of healthy controls and UCML, respectively. SCML showed a significant metabolic response to imatinib, with marked restoration of the perturbed metabolism. Most of the metabolites characterizing CML were adjusted to normal levels, including the intermediates of the urea cycle and tricarboxylic acid cycle (TCA). In contrast, neither cytogenetic nor metabonomic analysis indicated any positive response to imatinib in RCML. We report for the first time the associated genetic and metabonomic responses of CML patients to imatinib and show that the perturbed in vivo metabolism of UCML is independent of imatinib treatment in resistant patients. Thus, metabonomics can potentially characterize patients' sensitivity or resistance to drug intervention

An Integrated Regulatory Network Based on Comprehensive Analysis of mRNA Expression, Gene Methylation and Expression of Long Non-coding RNAs (lncRNAs) in Myelodysplastic Syndromes

Myelodysplastic syndromes (MDS) are a heterogeneous group of disorders characterized by ineffective hematopoiesis, defective differentiation of hematopoietic precursors, and expansion of the abnormal clones. The prevalence of MDS has raised great concerns worldwide, but its pathogenetic mechanisms remain elusive. To provide insights on novel biomarkers for the diagnosis and therapy of MDS, we performed high-throughput genome-wide mRNA expression profiling, DNA methylation analysis, and long non-coding RNAs (lncRNA) analysis on bone marrows from four MDS patients and four age-matched healthy controls. We identified 1,937 differentially expressed genes (DEGs), 515 methylated genes, and 214 lncRNA that showed statistically significant differences. As the most significant module-related DEGs, TCL1A, PTGS2, and MME were revealed to be enriched in regulation of cell differentiation and cell death pathways. In addition, the GeneGo pathway maps identified by top DEGs were shown to converge on cancer, immunoregulation, apoptosis and regulation of actin cytoskeleton, most of which are known contributors in MDS etiology and pathogenesis. Notably, as potential biomarkers for diagnosis of MDS, four specific genes (ABAT, FADD, DAPP1, and SMPD3) were further subjected to detailed pathway analysis. Our integrative analysis on mRNA expression, gene methylation and lncRNAs profiling facilitates further understanding of the pathogenesis of MDS, and may promote the diagnosis and novel therapeutics for this disease

Dynamic residual deep learning with photoelectrically regulated neurons for immunological classification

Dynamic deep learning is considered to simulate the nonlinear memory process of the human brain during long-term potentiation and long-term depression. Here, we propose a photoelectrically modulated synaptic transistor based on MXenes that adjusts the nonlinearity and asymmetry by mixing controllable pulses. According to the advantage of residual deep learning, the rule of dynamic learning is thus elaborately developed to improve the accuracy of a highly homologous database (colorimetric enzyme-linked immunosorbent assay [c-ELISA]) from 80.9% to 87.2% and realize the fast convergence. Besides, mixed stimulation also remarkably shortens the iterative update time to 11.6 s as a result of the photoelectric effect accelerating the relaxation of ion migration. Finally, we extend the dynamic learning strategy to long short-term memory (LSTM) and standard datasets (Cifar10 and Cifar100), which well proves the strong robustness of dynamic learning. This work paves the way toward potential synaptic bionic retina for computer-aided detection in immunology

Surface acoustic wave assisted chemical reactions to produce hydrogen gas

This thesis addresses the application of Rayleigh type acoustic waves on the chemical hydrogen production reaction and studies the mechanism behind the reaction promoted by surface acoustic waves (SAW). TiO2 is the most widely used photocatalyst for the water splitting reaction to generate clean fuel of hydrogen, but the energy conversion efficiency of it is still low, mainly due to the easy recombination of photo-generated electron/hole pairs. In order to promote the efficiency of the catalyst, a device type catalyst with controllable SAW functions is designed in this experiment by employing a 128°y-cut LiNbO3 substrate to generate Rayleigh-type SAW with a frequency of 150MHz under a Pt modified TiO2 catalyst. The effect of SAW on the activation of the Pt/TiO2 catalyst for the hydrogen production from the photo-splitting of a gaseous methanol/water mixture was examined by an indirect formaldehyde production. The experimental results convincingly show that the photo-dehydrogenation of methanol is clearly enhanced by the SAW propagation on the deposited Pt/TiO2 catalyst film, and exhibits a nonlinear positive relationship with the SAW power. The mechanism of the surface acoustic wave excitation effect on the catalyst is accounted for the electric field produced by the displacement of the LiNbO3, which hinders the recombination of photo-generated electron/hole pairs. Besides the photocatalysis water splitting reaction, electrolysis of water is an attractive energy generation method to obtain hydrogen gas. However, the most efficient catalyst for this reaction is Pt, which makes this approach expensive. Thereby, there are many studies focusing on enhancing the hydrogen producing efficiency of other inexpensive catalysts. In this study, an Au electrode and Au supported Pt/TiO2 electrode were chosen as non-Pt catalyst for the electrochemical hydrogen evolution reaction (HER) in acidic solution, and a 70MHz Rayleigh type SAW was used to promote the HER. The results demonstrate that SAW application has a tunable effect on these electrodes. Under the influence of the SAW, they exhibit a better HER activity with a higher current density, whereas the promotion effect disappears immediately when the SAW is turned off. Moreover, the bigger exchange current density and the decreased overpotential indicate a better catalytic activity of these catalysts under influence of SAW, and this positively relates with the applied SAW power level. Analyzing the Tafel equation and the recorded current with/without the effect of SAW suggests that the enhanced HER activity of these catalysts can be attributed to the SAW-induced microstreaming effect, which could dissipate the electric double layer near the electrode surface, thus minimizing the required work for transferring protons through the Helmholtz layer, and finally lead to a decrease of the free energy of activation for the hydrogen evolution reaction. This study might be a first step towards extensive combination of SAW with different catalysts for the electrochemical hydrogen production.Diese Arbeit befasst sich mit der Anwendung von Rayleigh-Wellen auf die chemische Wasserstoffproduktion und untersucht den zugrunde liegenden Mechanismus Reaktion unter Beeinflussung mit akustisschen Oberflächenwellen. TiO2 ist der am weitesten verbreitete Photokatalysator für die Wasserspaltungsreaktion zur Erzeugung eines sauberen Brennstoff. Die Energieumwandlungseffizienz ist jedoch immer noch gering, hauptsächlich aufgrund der einfachen Rekombination von photoerzeugten Elektron-Loch-Paaren. Um die Effizienz des Katalysators zu erhöhen, wird in diesem Experiment ein regelbarer Katalysator entwickelt, der durch akustische Oberflächenwellen (Engl. Surface Acoustic Waves, SAW) beeinflusst wird. Hierfür wird ein LiNbO3-Substrat mit 128° y-Schnitt verwendet, um eine akustische Oberflächenwelle vom Typ Rayleigh-Welle mit einer Frequenz von 150 MHz unter einem Pt-modifizierten TiO2-Katalysator zu erzeugen. Die Wirkung von SAW auf die Aktivierung des Pt/TiO2-Katalysators für die Wasserstoffproduktion aus dem photogespalten Methanol- Wasser-Gasgemischs wurde durch eine indirekte Formaldehydproduktion quantifiziert. Die experimentellen Ergebnisse zeigen eindrucksvoll, dass die Photo-Dehydrierung von Methanol durch die SAW-Eindwirkung auf dem abgeschiedenen Pt/TiO2-Katalysatorfilm deutlich verstärkt wird und eine nichtlineare positive Beziehung zur SAW-Leistung aufweist. Der Mechanismus des Oberflächenanregungseffekts auf den Katalysator ist auf das elektrische Feld zurückzuführen, das durch die Verformung des LiNbO3 erzeugt wird und die Rekombination von durch Licht erzeugten Elektron-Loch-Paaren verhindert. Neben der Wasserspaltungsreaktion durch Photokatalyse ist die Elektrolyse von Wasser ein attraktives Verfahren zur Energieerzeugung, um Wasserstoffgas zu erhalten. Der effizienteste Katalysator für diese Reaktion ist jedoch Pt, was diesen Ansatz teuer macht. Dabei gibt es viele Studien, die sich auf die Verbesserung der Wasserstoffproduktionseffizienz anderer kostengünstiger Katalysatoren konzentrieren. In dieser Studie wurden eine Gold-Elektrode und eine Pt/TiO2-Elektrode auf einer Goldschicht als Alternative zu Pt-Katalysatoren für die elektrochemische Wasserstoffentwicklungsreaktion (Engl. hydrogen evolution reaction, HER) in saurer Lösung ausgewählt. Diese wurden mit akustischen Oberflächenwellen vom Typ Rayleigh-Welle mit einer Frequenz von 70 MHz beeinflusst um die Wasserstoffentwicklung zu steigern. Die Ergebnisse zeigen, dass SAW einen einstellbaren Effekt auf diese Elektroden ausüben. Unter dem Einfluss der SAW zeigen diese eine gesteigerte HER-Aktivität mit einer höheren Stromdichte, während der Effekt sofort verschwindet, wenn die SAW deaktiviert werden. Darüber hinaus weisen die größere Austauschstromdichte und das verringerte Überpotential auf eine bessere katalytische Aktivität dieser Katalysatoren unter dem Einfluss von SAW hin, was sich mit steigender SAW-Leistung nicht-linear zunimmt. Die Analyse der Tafel-Gleichung und des aufgezeichneten Stroms mit/ohne SAW-Einwirkung legt nahe, dass die erhöhte HER-Aktivität dieser Katalysatoren auf SAW-induzierte Mikroströmung zurückzuführen ist. Diese beeinflusst die elektrische Doppelschicht in der Nähe der Elektrodenoberfläche und könnte so die erforderliche Arbeit für den Transfer von Protonen durch die Helmholtz-Schicht und schließlich die Aktivierungsenergie für die Wasserstoffentwicklungsreaktion reduzieren. Diese Studie könnte ein erster Schritt in Richtung einer umfassenden Kombination von SAW mit verschiedenen Katalysatoren für die elektrochemische Wasserstoffproduktion sein