25 research outputs found
Excitation dynamics in molecular systems from efficient grid-based real-time density functional theory
No full textMaking use of solar energy is a very promising approach for satisfying the energy needs of mankind. Nature has perfected its light harvesting mechanisms in plants, algae, and photosynthetic bacteria with respect to efficiency and stability. The complexes that participate in the photosynthetic process are typically aggregates of chromophores that are often anchored inside a protein scaffold. To understand the underlying processes that make natural light harvesting so efficient on the one hand and protect the participating protein-chromophore complexes from damage on the other hand is a key issue for the development of artificial light harvesting devices. Next to extensive experimental studies, this requires a detailed theoretical description on the molecular, quantum-mechanical level. Time-dependent density functional theory (TDDFT) appears as a natural choice in this respect since it combines predictive power and reliability with computational efficiency. Especially its real-space and real-time implementation is applicable to molecular systems with hundreds or even up to a few thousands of electrons. However, utilizing the theoretical potential of TDDFT requires modern, highly parallel computers and programs that are able to exploit their full computational power. One major part of this thesis is dedicated to the development of the real-space and real-time TDDFT code BTDFT. The challenges within this part include a highly scalable parallelization and the development of data structures that allow for efficient memory access while keeping the code simple and flexible. The reliable simulation of excitation-energy transfer (EET) within real-time TDDFT requires an accurate description of the relevant excited states and their nature. This includes excitation energies, oscillator strengths, and transition densities, which allow to visualize the spatial oscillations of the time-dependent electron density. A second part in this work addresses the accurate computation of these quantities from real-time TDDFT. The exchange-correlation (xc) energy, which describes the non-trivial many-particle interactions within TDDFT, has to be approximated. The size of typical light-harvesting systems requires the use of lightweight approximations to exchange and correlation. These are well established and were used in the past with great success but also have well known deficiencies. The most critical one within this work is their systematic inability to describe charge-transfer processes correctly, which results from a spurious self-interaction of an electron with its own charge density. The last part within this thesis discusses the reliability of real-time TDDFT with lightweight xc approximations for EET simulations in natural systems by means of one and two aggregated chromophores that appear in nature. Their environment, which consists of a protein scaffold and other chromophores, is included into these investigations explicitly or through an electrostatic potential. Finally, the outlook is dedicated to the general real-time simulation of energy transfer processes within real-time TDDFT
Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation
No full text2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras.
Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A!
is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k \{0}, and z, t ∈ X is satisfied in A. We prove the equivalence of the notions a binomial skew polynomial ring and a binomial solution of YBE. This implies that the Yang-Baxter algebra of such a solution is of Poincaré-Birkhoff-Witt type, and possesses a number of other nice properties such as being Koszul, Noetherian, and an Artin-Schelter regular domain.The author was partially supported by the Department of Mathematics of Harvard University, by Grant MM1106/2001 of the Bulgarian National Science Fund of the Ministry of Education and Science, and by the Abdus Salam International Centre for Theoretical Physics
(ICTP)
Propiedad Calabi-Yau para extensiones PBW torcidas graduadas
No full textGraded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition for this kind of extensions. We prove that every graded quasi-commutative skew PBW extension of an Artin-Schelter regular algebra is also an Artin-Schelter regular algebra and, as a consequence, every graded quasi-commutative skew PBW extension of a connected skew Calabi-Yau algebra is skew Calabi-Yau. Finally, we prove that graded skew PBW extensions of a finitely presented connected Auslander-regular algebra are skew Calabi-Yau.Las extensiones PBW torcidas graduadas fueron definidas por el primer autor como una generalización de las extensiones de Ore iteradas graduadas [36]. El propósito de este artículo es estudiar las condiciones Artin-Schelter regular y Calabi-Yau (torcida) para esta clase de extensiones. Demostramos que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra Artin-Schelter regular también es Artin-Schelter regular, y, como consecuencia, que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra conexa Calabi-Yau torcida es Calabi-Yau torcida. Finalmente, mostramos que las extensiones PBW torcidas graduadas de álgebras Auslander-regular finitamente presentadas y conexas son Calabi-Yau torcidas
Calabi-Yau property for graded skew PBW extensions
No full textGraded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition for this kind of extensions. We prove that every graded quasi-commutative skew PBW extension of an Artin-Schelter regular algebra is also an Artin-Schelter regular algebra and, as a consequence, every graded quasi-commutative skew PBW extension of a connected skew Calabi-Yau algebra is skew Calabi-Yau. Finally, we prove that graded skew PBW extensions of a finitely presented connected Auslander-regular algebra are skew Calabi-Yau.Las extensiones PBW torcidas graduadas fueron definidas por el primer autor como una generalización de las extensiones de Ore iteradas graduadas [36]. El propósito de este artículo es estudiar las condiciones Artin-Schelter regular y Calabi-Yau (torcida) para esta clase de extensiones. Demostramos que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra Artin-Schelter regular también es Artin-Schelter regular, y, como consecuencia, que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra conexa Calabi-Yau torcida es Calabi-Yau torcida. Finalmente, mostramos que las extensiones PBW torcidas graduadas de álgebras Auslander-regular finitamente presentadas y conexas son Calabi-Yau torcidas
Accurate Evaluation of Real-Time Density Functional Theory Providing Access to Challenging Electron Dynamics
No full textMeta-generalized gradient approximations in time dependent generalized Kohn–Sham theory: Importance of the current density correction
No full textErratum: “Linear response time-dependent density functional theory without unoccupied states: The Kohn-Sham-Sternheimer scheme revisited” [J. Chem. Phys. 149, 024105 (2018)]
No full textLinear response time-dependent density functional theory without unoccupied states: The Kohn-Sham-Sternheimer scheme revisited
No full textBlockJoin: Efficient Matrix Partitioning Through Joins
No full textLinear algebra operations are at the core of many Machine Learning (ML) programs. At the same time, a considerable amount of the effort for solving data analytics problems is spent in data preparation. As a result, end-to- end ML pipelines often consist of (i) relational operators used for joining the input data, (ii) user defined functions used for feature extraction and vectorization, and (iii) linear algebra operators used for model training and cross- validation. Often, these pipelines need to scale out to large datasets. In this case, these pipelines are usually implemented on top of dataflow engines like Hadoop, Spark, or Flink. These dataflow engines implement relational operators on row-partitioned datasets. However, efficient linear algebra operators use block-partitioned matrices. As a result, pipelines combining both kinds of operators require rather expensive changes to the physical representation, in particular re partitioning steps. In this paper, we investigate the potential of reducing shuffling costs by fusing relational and linear algebra operations into specialized physical operators. We present BlockJoin, a distributed join algorithm which directly produces block-partitioned results. To minimize shuffling costs, BlockJoin applies database techniques known from columnar processing, such as index-joins and late materialization, in the context of parallel dataflow engines. Our experimental evaluation shows speedups up to 6× and the skew resistance of BlockJoin compared to state- of-the-art pipelines implemented in Spark.Web Information System
An Intermediate Representation for Optimizing Machine Learning Pipelines
No full textMachine learning (ML) pipelines for model training and validation typically include preprocessing, such as data cleaning and feature engineering, prior to training an ML model. Preprocessing combines relational algebra and user-defined functions (UDFs), while model training uses iterations and linear algebra. Current systems are tailored to either of the two. As a consequence, preprocessing and ML steps are optimized in isolation. To enable holistic optimization of ML training pipelines, we present Lara, a declarative domainspecific language for collections and matrices. Lara's intermediate representation (IR) re ects on the complete program, i.e., UDFs, control ow, and both data types. Two views on the IR enable diverse optimizations. Monads enable operator pushdown and fusion across type and loop boundaries. Combinators provide the semantics of domainspecific operators and optimize data access and cross-validation of ML algorithms. Our experiments on preprocessing pipelines and selected ML algorithms show the effects of our proposed optimizations on dense and sparse data, which achieve speedups of up to an order of magnitude.Web Information System
