Related papers: Relations between multi-resolution analysis and qu…
We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit…
Unsupervised rationale extraction aims to extract text snippets to support model predictions without explicit rationale annotation. Researchers have made many efforts to solve this task. Previous works often encode each aspect…
We clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified. In particular, we characterize and normalize real $2$-forms with respect to the quaternionic…
We derive the multiscale entanglement renormalization ansatz (MERA) for the single impuity Kondo model. We find two types of hidden quantum entanglement: one comes from a finite-temperature effect on the geometry of the MERA network, and…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property…
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…
Hybrid question answering (HQA) aims to answer questions over heterogeneous data, including tables and passages linked to table cells. The heterogeneous data can provide different granularity evidence to HQA models, e.t., column, row, cell,…
We introduce a notion of $R$-quadratic maps between modules over a commutative ring $R$ which generalizes several classical notions arising in linear algebra and group theory. On a given module $M$ such maps are represented by $R$-linear…
The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial…
For quantum mechanics on a lattice the position (``particle number'') operator and the quasi-momentum (``phase'') operator obey canonical commutation relations (CCR) only on a dense set of the Hilbert space. We compare exact numerical…
Evaluation of QA systems is very challenging and expensive, with the most reliable approach being human annotations of correctness of answers for questions. Recent works (AVA, BEM) have shown that transformer LM encoder based similarity…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
We present a new method to obtain interaction part of a model Hamiltonian from the result of the first-principles calculation. The effective interaction contained in the model is determined based on the random phase approximation (RPA). In…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
Multiple Correspondence Analysis (MCA) is a dimension reduction method which plays a large role in the analysis of tables with categorical nominal variables such as survey data. Though it is usually motivated and derived using geometric…
Let R be the quotient of a polynomial ring over a field k by an ideal generated by monomials. We derive a formula for the multigraded Poincare' series of R, i.e., the generating function for the ranks of the modules in a minimal multigraded…
In the literature, there exist several quantum finite automata (QFA) models with both quantum and classical states. These models are of particular interest,as they show praiseworthy advantages over the fully quantum models in some…
Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…