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Counterfactual explanations are considered, which is to answer {\it why the prediction is class A but not B.} Different from previous optimization based methods, an optimization-free Fast ReAl-time Counterfactual Explanation (FRACE)…
In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles and approximate triples…
The relevant energy ranges for stellar nuclear reactions are introduced. Low-energy compound and direct reactions are discussed. Stellar modifications of the cross sections are presented. Implications for experiments are outlined.
The predictions of homogeneous and isotropic cosmological models with ordinary matter and gravity are off by a factor of two in the late universe. One possible explanation is the known breakdown of homogeneity and isotropy due to the…
We investigate the effects of plasma interactions on resonance-enhanced fusion rates in stars. Starting from basic principles we derive an expression for the fusion rate that can serve as a basis for discussion of approximation schemes. The…
Processes involving alpha particles and alpha-like nuclei comprise a major part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear supernovae. In an effort towards understanding alpha processes from first principles,…
A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles…
Real-time thermal field theory is used to reveal the structure of plasma corrections to nuclear reactions. Previous results are recovered in a fashion that clarifies their nature, and new extensions are made. Brown and Yaffe have introduced…
The prediction of stellar ($\gamma$,$\alpha$) reaction rates for heavy nuclei is based on the calculation of ($\alpha$,$\gamma$) cross sections at sub-Coulomb energies. These rates are essential for modeling the nucleosynthesis of so-called…
The phaseless Auxiliary Field Quantum Monte Carlo method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we apply the method to the calculation of imaginary…
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an…
This study is due to various applications in physics, chemistry and especially in biology, where both bounded configuration domain and chemical anisotropy could play a great part. In fact we generalize the well-known Berg theory, which…
The radiative neutron capture reaction rates have been studied at very low energies which are of interest for nuclear astrophysics. The rates for many of these reactions have remained independent of temperature so far. The temperature…
The abundances of the isotopes of the elements from C to Al produced by the non-explosive CNO, NeNa and MgAl modes of hydrogen burning, as well as by helium burning, are calculated with the thermonuclear rates recommended by the European…
X-ray bursts are thermonuclear flashes on the surface of accreting neutron stars and reliable burst models are needed to interpret observations in terms of properties of the neutron star and the binary system. We investigate the dependence…
We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…
We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$, as well as a minor generalisation thereof. In this case, it is possible to evaluate the scaling…
The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer…
We report the analytical nuclear gradient theory for complete active space second-order perturbation theory (CASPT2) with imaginary shift, which is commonly used to avoid divergence of the perturbation expression. Our formulation is based…