Accurate variational electronic structure calculations with the density matrix renormalization group

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS controls the size of the corner of the many-body Hilbert space that can be reached. Whereas the MPS ansatz will only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for other finite-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. DMRG and Hartree-Fock theory have an analogous structure. The former can be interpreted as a self-consistent mean-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-DMRG methods. Based on an approximate MPS, these methods provide improved ans\"atze for the ground state, as well as for excitations. Exponentiation of the single-particle (single-site) excitations for a Slater determinant (an MPS with open boundary conditions) leads to the Thouless theorem for Hartree-Fock theory (DMRG), an explicit nonredundant parameterization of the entire manifold of Slater determinants (MPS wavefunctions). This gives rise to the configuration interaction expansion for DMRG. The Hubbard-Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-lattice Hamiltonians allows to formulate a promising variant for MPSs.Comment: PhD thesis (225 pages). PhD thesis, Ghent University (2014), ISBN 978946197194

Audio source separation for music in low-latency and high-latency scenarios

Aquesta tesi proposa mètodes per tractar les limitacions de les tècniques existents de separació de fonts musicals en condicions de baixa i alta latència. En primer lloc, ens centrem en els mètodes amb un baix cost computacional i baixa latència. Proposem l'ús de la regularització de Tikhonov com a mètode de descomposició de l'espectre en el context de baixa latència. El comparem amb les tècniques existents en tasques d'estimació i seguiment dels tons, que són passos crucials en molts mètodes de separació. A continuació utilitzem i avaluem el mètode de descomposició de l'espectre en tasques de separació de veu cantada, baix i percussió. En segon lloc, proposem diversos mètodes d'alta latència que milloren la separació de la veu cantada, gràcies al modelatge de components específics, com la respiració i les consonants. Finalment, explorem l'ús de correlacions temporals i anotacions manuals per millorar la separació dels instruments de percussió i dels senyals musicals polifònics complexes.Esta tesis propone métodos para tratar las limitaciones de las técnicas existentes de separación de fuentes musicales en condiciones de baja y alta latencia. En primer lugar, nos centramos en los métodos con un bajo coste computacional y baja latencia. Proponemos el uso de la regularización de Tikhonov como método de descomposición del espectro en el contexto de baja latencia. Lo comparamos con las técnicas existentes en tareas de estimación y seguimiento de los tonos, que son pasos cruciales en muchos métodos de separación. A continuación utilizamos y evaluamos el método de descomposición del espectro en tareas de separación de voz cantada, bajo y percusión. En segundo lugar, proponemos varios métodos de alta latencia que mejoran la separación de la voz cantada, gracias al modelado de componentes que a menudo no se toman en cuenta, como la respiración y las consonantes. Finalmente, exploramos el uso de correlaciones temporales y anotaciones manuales para mejorar la separación de los instrumentos de percusión y señales musicales polifónicas complejas.This thesis proposes specific methods to address the limitations of current music source separation methods in low-latency and high-latency scenarios. First, we focus on methods with low computational cost and low latency. We propose the use of Tikhonov regularization as a method for spectrum decomposition in the low-latency context. We compare it to existing techniques in pitch estimation and tracking tasks, crucial steps in many separation methods. We then use the proposed spectrum decomposition method in low-latency separation tasks targeting singing voice, bass and drums. Second, we propose several high-latency methods that improve the separation of singing voice by modeling components that are often not accounted for, such as breathiness and consonants. Finally, we explore using temporal correlations and human annotations to enhance the separation of drums and complex polyphonic music signals

Accurate variational electronic structure calculations with the density matrix renormalization group

During the past fifteen years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low­-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many­-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. Whereas the MPS ansatz can only capture exponentially decaying correlation functions in the thermodynamic limit, and will therefore only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for finite­-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. For hydrogen chains, accurate longitudinal static hyperpolarizabilities were obtained in the thermodynamic limit. In addition, the low-lying states of the carbon dimer were accurately resolved. DMRG and Hartree-­Fock theory have an analogous structure. The former can be interpreted as a self­-consistent mean­-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-­DMRG methods. Based on an approximate MPS, these methods provide improved ansätze for the ground state, as well as for excitations. Exponentiation of the single­-particle excitations for a Slater determinant leads to the Thouless theorem for Hartree-­Fock theory, an explicit nonredundant parameterization of the entire manifold of Slater determinants. For an MPS with open boundary conditions, exponentiation of the single-site excitations leads to the Thouless theorem for DMRG, an explicit nonredundant parameterization of the entire manifold of MPS wavefunctions. This gives rise to the configuration interaction expansion for DMRG. The Hubbard-­Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-­lattice Hamiltonians allows to formulate a promising variant for matrix product states

Reconstruction and Estimation of Flows Using Resolvent Analysis and Data-Assimilation

A flow reconstruction methodology is presented for incompressible, statistically stationary flows using resolvent analysis and data-assimilation. The only inputs necessary for the procedure are a rough approximation of the mean profile and a single time-resolved measurement. The objective is to estimate both the mean and fluctuating states of experimental flows with limited measurements which do not include pressure. The input data may be incomplete, in the sense that measurements near a body are difficult to obtain with techniques such as particle image velocimetry (PIV), or contaminated by noise. The tools developed in this thesis are capable of filling in missing data and reducing the amount of measurement noise by leveraging the governing equations. The reconstructed flow is capable of estimating fluctuations where time-resolved data are not available and solving the flow on larger domains where the mean profile is not known. The first part of the thesis focuses on how resolvent analysis of the mean flow selects amplification mechanisms. Eigenspectra and pseudospectra of the mean linear Navier-Stokes (LNS) operator are used to characterize amplification mechanisms in flows where linear mechanisms are important. The real parts of the eigenvalues are responsible for resonant amplification and the resolvent operator is low-rank when the eigenvalues are sufficiently separated in the spectrum. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The latter is studied by considering well-known turbulent structures while the former contains a marginally stable eigenvalue which drowns out the effect of other eigenvalues over a large range of temporal frequencies. There is a geometric manifestation of this dominant mode in the mean profile, suggesting that it leaves a significant footprint on the time-averaged flow that the resolvent can identify. The resolvent does not provide an efficient basis at temporal frequencies where there is no separation of singular values. It can still be leveraged, nevertheless, to identify coherent structures in the flow by approximating the nonlinear forcing from the interaction of highly amplified coherent structures. The second part of the thesis extends the framework of Foures et al. (2014), who data-assimilated the mean cylinder wake at very low Reynolds numbers. The contributions presented here are to assess the minimum domain for successfully reconstructing Reynolds stress gradients, modifying the algorithm to assimilate mean pressure, determining whether weighting input measurements contributes to improved performance, and adapting the method to experimental data at higher Reynolds numbers. The results from data-assimilating the mean cylinder wake at low Reynolds numbers suggest that the measurement domain needs to coincide with the spatial support of the Reynolds stress gradients while point weighting has a minimal impact on the performance. Finally, a smoothing procedure adapted from Foures et al. (2014) is proposed to cope with data-assimilating an experimental mean profile obtained from PIV data. The data-assimilated mean profiles for an idealized airfoil and NACA 0018 airfoil are solved on a large domain making the mean profile suitable for global resolvent analysis. Data-assimilation is also able to fill in missing or unreliable vectors near the airfoil surface. The final piece of the thesis is to synthesize the knowledge and techniques developed in the first two parts to reconstruct the experimental flow around a NACA 0018 airfoil. Preliminary results are presented for the case where α = 0° and Re = 10250. The mean profile is data-assimilated and used as an input to resolvent analysis to educe coherent structures in the flow. The resolvent operator for non- amplified temporal frequencies is forced by an approximated nonlinear forcing. The amplitude and phase of the modes are obtained from the discrete Fourier-transform of a time-resolved probe point measurement. The final reconstruction contains less measurement noise compared to the PIV snapshots and obeys the incompressible Navier-Stokes equations (NSE). The thesis concludes with a discussion of how elements of this methodology can be incorporated into the development of estimators for turbulent flows at high Reynolds numbers.</p

Gaussian latent tree model constraints for linguistics and other applications

The relationships between languages are often modelled as phylogenetic trees whereby there is a single shared ancestral language at the root and contemporary languages appear as leaves. These can be thought of as directed acyclic graphs with hidden variables, specifically Bayesian networks. However, from a statistical perspective there is often no formal assessment of the suitability of these latent tree models. A lot of the work that seeks to address this has focused on discrete variable models. However, when observations are instead considered as functional data, the high dimensional approximations are often better considered in a Gaussian context. The high dimensional data is often inefficiently stored and so the first challenge is to project this data to a low dimension while retaining the information of interest. One approach is to use the newly developed tool named separable-canonical variate analysis to form a basis. Extending the techniques for assessing latent tree model compatibility to beyond discrete variables, the complete set of Gaussian tree constraints are derived for the first time. This set comprises equations and inequality statements in terms of correlations of observed variables. These statements must in theory be adhered to for a Gaussian latent tree model to be appropriate for a given data set. Using the separable-canonical variate analysis basis to obtain a truncated representation, the suitability of a phylogenetic tree can then be plainly assessed. However, in practice it is desirable to allow for some sampling error and as such probabilistic tools are developed alongside the theoretical derivation of Gaussian tree constraints. The proposed methodology is implemented in an in-depth study of a real linguistic data set to assess the phylogenies of five Romance languages. This application is distinctive as the data set consists of acoustic recordings, these are treated as functional data, and moreover these are then being used to compare languages in a phylogenetic context. As a consequence a wide range of theory and tools are called upon from the multivariate and functional domains, and the powerful new separable-canonical function analysis and separable-canonical variate analysis are used. Utilising the newly derived Gaussian tree constraints for hidden variable models provides a first insight into features of spoken languages that appear to be tree-compatible

Cobalts and Pyrrole-mancy: Utilizing Cooperative Strategies for Sustainable Catalysis

Metal-ligand cooperativity is ubiquitous throughout both biological and chemical catalysis, but often goes unattributed or underutilized in organic catalysis. Practically, utilizing every resource available and not discriminating metal vs. ligand is a powerful strategy to getting more tunability as well as more efficiency in any kind of chemical transformation, and nature, and an ever-increasing number of chemists, realizes this. By building in this biomimetic strategy, first row metals can also be enhanced past their native one-electron preferences, opening the door to multi-proton, multi-electron chemistry. In particular, hydrogen transfer chemistry is important due to its wide variety of applications in industrial processes and pharmaceutical development. For this reason, there has been extensive research into catalyst design for reactions involving hydrogen transfer reactivity. Homogenous catalysts are attractive for studies due to the relative ease of their characterization. However, any reaction that involves the movement of protons and electrons, even in a redox-neutral fashion, can benefit from a multifunctional ligand. In these studies, a 2,5-dihydrazonopyrrole (tBu,TolDHP) ligand scaffold, which has previously been shown to store a full H2 equivalent (in addition to any redox-capabilities of the metal center), was utilized in complexes with Co, and with these complexes alone, I show the diversity of reactivity, enhanced and altered selectivity, and broad applicability afforded by ligands as complex as the metals they bind. Not only have I demonstrated the capability of these ligands to stabilize unusual motifs, such as a rare oxidation state of TEMPOH2+ and a potassium-capped cobalt-oxido, but I have done reductive, oxidative, and redox-neutral catalysis, utilizing heat, electrochemical potential, and light to drive reactivity different directions. Specifically, I have been able to accomplish reductive hydrogenation of olefins to alkanes, with distinctive terminal selectivity and a mechanism that features ligand-based H-atom equivalents and key radical intermediates. On the oxidative side, I have been able to showcase the unusual selective formation of hydrogen peroxide from water, which can be rendered catalytic with oxidative potential (chemical or electrochemical). Lastly, I have investigated redox-neutral olefin isomerization, with the ability to use heat or light to switch between thermodynamically preferred or contra-thermodynamic products respectively. This work highlights how a proton- and electron-storing ligand can access and access broad and varied reactivity with a first-row metal and is not limited to any one class of reaction

데이터사이언스를 위한 확률과 통계

이 노트는 본저자가 2020넌 가을학기 서울대학교 데이터사이언스대학원에서 강의한 ‘데이터사이언스를 위한 확률과 통계(Probability and Statistics for Data Science)’ 과목의 강의 슬라이드를 모아서 출간한 것이

Galactic Dark Matter distribution and its implications for experimental searches

Dark Matter presents one of the key missing pieces in our understanding of the Universe. On the one hand, there is a substantial amount of independent astronomical and cosmological observations, which provide convincing evidence for its existence through various gravitational signatures. On the other hand, any non-gravitational interactions of Dark Matter remain elusive, despite more than two decades of dedicated searches in various experiments. Several of them have contended successful detection, however, such claims remain disputed, since they are in tension with null results of other related experiments and often suffer from considerable modelling uncertainties. One of the crucial unknowns entering the interpretation of direct and indirect Dark Matter searches is its distribution within galaxies. Together with rapid improvements in astronomical observations, this drives the need for accurate phase-space modelling of galactic Dark Matter distribution, which will be explored in detail throughout this thesis in various settings. First, a novel method for computing the phase-space distribution of relaxed Dark Matter component within axisymmetric systems will be presented. This method is of particular importance when addressing spiral galaxies and can have a significant impact on the interpretation of direct detection experiments, which crucially depends on the density and velocity distribution of Dark Matter in the solar neighbourhood. Therefore, the proposed phase-space distribution model will be applied to our Milky Way and carefully matched against recent measurements of the galactic kinematics. Furthermore, the corresponding impact on direct detection experiments and differences with respect to the traditional models, relying on Maxwellian velocity distribution and/or spherical symmetry, will be investigated. Regarding indirect detection, new results related to expected signals from dwarf satellite galaxies of the Milky Way will be presented, addressing the general case of velocity-dependent annihilation cross-section. Special attention will be given to a non-perturbative effect, commonly known as the Sommerfeld enhancement, which can lead to a significant boost of the annihilation signals. Similarly, as in the case of Milky Way, recent measurements of stellar kinematics within dwarf satellites will be used to bracket the astrophysical uncertainties entering the interpretation of corresponding indirect searches. Finally, a brand-new technique for detecting dark galactic subhalos will be proposed, which relies on the modern tools of machine learning and their ability to find subtle patterns in complex datasets. More precisely, the possibility of detecting tiny perturbations in stellar density and kinematics, induced by transpassing Dark Matter subhalos, will be addressed

Faculty Publications and Creative Works 2004

Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM

The Computational Attitude in Music Theory

Music studies’s turn to computation during the twentieth century has engendered particular habits of thought about music, habits that remain in operation long after the music scholar has stepped away from the computer. The computational attitude is a way of thinking about music that is learned at the computer but can be applied away from it. It may be manifest in actual computer use, or in invocations of computationalism, a theory of mind whose influence on twentieth-century music theory is palpable. It may also be manifest in more informal discussions about music, which make liberal use of computational metaphors. In Chapter 1, I describe this attitude, the stakes for considering the computer as one of its instruments, and the kinds of historical sources and methodologies we might draw on to chart its ascendance. The remainder of this dissertation considers distinct and varied cases from the mid-twentieth century in which computers or computationalist musical ideas were used to pursue new musical objects, to quantify and classify musical scores as data, and to instantiate a generally music-structuralist mode of analysis. I present an account of the decades-long effort to prepare an exhaustive and accurate catalog of the all-interval twelve-tone series (Chapter 2). This problem was first posed in the 1920s but was not solved until 1959, when the composer Hanns Jelinek collaborated with the computer engineer Heinz Zemanek to jointly develop and run a computer program. Recognizing the transformation wrought on modern statistics and communications technology by information theory, I revisit Abraham Moles’s book Information Theory and Esthetic Perception (orig. 1958) and use its vocabulary to contextualize contemporary information-theoretic work on music that various evokes the computational mind by John. R. Pierce and Mary Shannon, Wilhelm Fucks, and Henry Quastler (Chapter 3). I conclude with a detailed look into a score-segmentation algorithm of the influential American music theorist Allen Forte (Chapter 4). Forte was a skilled programmer who spent several years at MIT in the 1960s, with cutting-edge computers and the company of first-rank figures in the nascent fields of computer science and artificial intelligence. Each one of the researchers whose work is treated in these case studies—at some stage in their relationship with music—adopted what I call the computational attitude to music, to varying degrees and for diverse ends. Of the many questions this dissertation seeks to answer: what was gained by adopting such an attitude? What was lost? Having understood these past explorations of the computational attitude to music, we are better suited ask of ourselves the same questions today