Related papers: Comments on Omn\`es' Model for Uniqueness of Data
We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…
We consider regularization methods of Kaczmarz type in connection with the expectation-maximization (EM) algorithm for solving ill-posed equations. For noisy data, our methods are stabilized extensions of the well established…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we…
A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a…
In the present paper we introduce new optimization algorithms for the task of density ratio estimation. More precisely, we consider extending the well-known KMM method using the construction of a suitable loss function, in order to…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…
A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…
The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of…
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the…
Single molecule data made of on and off events are ubiquitous. Famous examples include enzyme turnover, probed via fluorescence, and opening and closing of ion-channel, probed via the flux of ions. The data reflects the dynamics in the…
Much recent interest has focused on the design of optimization algorithms from the discretization of an associated optimization flow, i.e., a system of differential equations (ODEs) whose trajectories solve an associated optimization…
We study local, analytic solutions for a class of initial value problems for singular ODEs. We prove existence and uniqueness of such solutions under a certain non-resonance condition. Our proof translates the singular initial value problem…
Simon's subshift conjecture states that for every aperiodic minimal subshift of Verblunsky coefficients, the common essential support of the associated measures has zero Lebesgue measure. We disprove this conjecture in this paper, both in…
An efficient approach to calculate approximate pure-state and transition reduced density matrices in the framework of the multireference relativistic Fock-space coupled cluster (FS CC) theory is proposed. The method is based on the…
Many unsupervised representation learning methods belong to the class of similarity learning models. While various modality-specific approaches exist for different types of data, a core property of many methods is that representations of…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…