We present an extension of the Levenberg-Marquardt algorithm for fitting multichannel nuclear cross section data. Our approach offers a practical and robust alternative to conventional trust-region methods for analyzing experimental data. The CoH$_3$ code, based on the Hauser-Feshbach statistical model, involves a large number of interdependent parameters, making optimization challenging due to the presence of "sloppy" directions in parameter space. To address the uneven distribution of experimental data across reaction channels, we construct a weighted Fisher Information Metric by integrating prior distributions over dataset weights. This framework enables a more balanced treatment of heterogeneous data, improving both parameter estimation and convergence robustness. We show that the resulting weighted Levenberg-Marquardt method yields more physically consistent fits for both raw and smoothed datasets, using experimental data for ${}^{148}$Sm as a representative example. Additionally, we introduce a geometric scaling strategy to accelerate convergence -- a method based on the local geometry of the manifold.

In the study of nuclear cross sections, the computational demands of data assimilation methods can become prohibitive when dealing with large data sets. We have developed a novel variant of the data thinning algorithm, inspired by the principles of optical lensing, which effectively reduces data volume while preserving critical information. We show how it improves fitting through a toy problem and for several examples of total cross sections for neutron-induced reactions on rare-earth isotopes. We demonstrate how this method can be applied as an efficient pre-processing step prior to smoothing, significantly improving computational efficiency without compromising the quality of uncertainty quantification.

Information geometry is a study of applying differential geometry methods to challenging statistical problems, such as uncertainty quantification. In this work, we use information geometry to study how measurement uncertainties in pre-neutron emission mass distributions affect the parameter estimation in the Hauser-Feshbach fission fragment decay code, CGMF. We quantify the impact of reduced uncertainties on the pre-neutron mass yield of specific masses to these parameters, for spontaneous fission of ${}^{252}$Cf, first using a toy model assuming Poissonian uncertainties, then an experimental measurement taken from Göök et al., 2014 in EXFOR. We achieved a reduction of up to $\sim15\%$ in CGMF parameter errors, predominantly in $w_0^{(1)}$ and $w_1^{(0)}$.

The $\Lambda$ and $\Sigma$ directed flows at $\sqrt{s_{NN}}=4.5~\mathrm{GeV}$ are investigated to examine their sensitivity to the hyperon single-particle potentials. The single-particle potentials are obtained from $G$-matrix calculations with two- and three-body forces based on SU(3) chiral effective field theory. The $\Lambda+\Sigma^0$ directed flow shows sensitivity to the variation in the $\Sigma$ single-particle potential. Its effect is more pronounced for the $\Sigma^0$ directed flow.

We present extensive comparisons of $^{16}$O+$^{16}$O collisions at the center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=200$ GeV and $^{208}$Pb+$^{16}$O collisions at $\sqrt{s_{NN}}=68.5$ GeV as well as $^{20}$Ne+$^{20}$Ne collisions at $\sqrt{s_{NN}}=200$ GeV and $^{208}$Pb+$^{20}$Ne collisions at $\sqrt{s_{NN}}=68.5$ GeV based on a multiphase transport (AMPT) model. We recommend measuring the ratio of the elliptic flow to the triangular flow, which shows appreciable sensitivity to the structure of light nuclei as also found in other studies. This is especially so if the observable is measured near the target rapidity in $^{208}$Pb+$^{16}$O or $^{208}$Pb+$^{20}$Ne collisions, as originally found in the present study. Our study serves as a useful reference for understanding the structure effect on observables in collisions involving light nuclei under analysis or on the schedule.

We study the performance of the Topological Uncertainty (TU) constructed with a trained feedforward neural network (FNN) for Anomaly Detection. Generally, meaningful information can be stored in the hidden layers of the trained FNN, and the TU implementation is one tractable recipe to extract buried information by means of the Topological Data Analysis. We explicate the concept of the TU and the numerical procedures. Then, for a concrete demonstration of the performance test, we employ the Neutron Star data used for inference of the equation of state (EoS). For the training dataset consisting of the input (Neutron Star data) and the output (EoS parameters), we can compare the inferred EoSs and the exact answers to classify the data with the label $k$. The subdataset with $k=0$ leads to the normal inference for which the inferred EoS approximates the answer well, while the subdataset with $k=1$ ends up with the unsuccessful inference. Once the TU is prepared based on the $k$-labled subdatasets, we introduce the cross-TU to quantify the uncertainty of characterizing the $k$-labeled data with the label $j$. The anomaly or unsuccessful inference is correctly detected if the cross-TU for $j=k=1$ is smaller than that for $j=0$ and $k=1$. In our numerical experiment, for various input data, we calculate the cross-TU and estimate the performance of Anomaly Detection. We find that performance depends on FNN hyperparameters, and the success rate of Anomaly Detection exceeds $90\%$ in the best case. We finally discuss further potential of the TU application to retrieve the information hidden in the trained FNN.

$^{229}$Th, a crucial candidate for nuclear clocks and many other applications, is a typical heavy nucleus with an extremely low-energy isomeric state $^{229m}$Th. A detailed study of the nuclear structure of $^{229}$Th is performed here by the microscopic model of state-of-the-art projected shell model. Our calculation describes well low-energy levels of $^{229}$Th, and provides a reduced transition probability $B(M1)$ of $0.0240$ W.u. for the isomeric transition which agrees well with the radiative lifetime of $^{229m}$Th measured recently. Our result supports a small multipole mixing for the cross-band transition of the second-excited state of $^{229}$Th, suggesting that further investigations on the inconsistencies in the decay of the second-excited state should be necessary. The physics behind these properties is revealed by the analysis of the nuclear wave functions. Our findings provide a deep insight into $^{229}$Th from the microscopic nuclear structure point of view, and offer the chance for further studies for nuclear clocks and relevant topics by microscopic nuclear structure theory.

For quantifying the universal properties of the chiral phase transition in QCD through numerical calculations on a discrete space-time lattice, one needs to perform controlled extrapolations to the continuum and infinite-volume limits followed by an extrapolation to the limit of massless light quarks. We discuss here, the results on the latter two limits at still finite lattice spacings. We use here for chiral symmetry breaking, an improved order parameter free of additive and multiplicative divergences and we analyse its volume and quark mass dependence. Comparing to the expected universal behavior in the chiral limit, we quantify deviations from the universal finite-size scaling behavior as function of the light to strange quark mass ratio.

We introduce heavy-flavor energy correlators, $\langle \Psi |\mathcal{E}_{\mathcal{H}}(\vec{n}_1) \mathcal{E}_{\mathcal{H}}(\vec{n}_2)|\Psi \rangle$, as a powerful observable for profiling partonic splittings and characterizing heavy-flavor fragmentation. We present its collinear factorization, perform resummation, and demonstrate the angular distribution's sensitivity to both the heavy-quark pair splitting and their subsequent fragmentation. We then apply the heavy-flavor EEC to probe medium-induced effects, revealing its sensitivity to medium modifications to heavy-quark pair splitting functions and to the medium's spatial structure.

Color superconductivity in cold, dense quark matter is a key feature of the QCD phase diagram, whose present theoretical understanding relies predominantly on weak-coupling calculations. In this work, we revisit the evaluation of the color-superconducting gap using a renormalization group (RG) framework formulated in effective theory near the Fermi surface. By incorporating quark self-energy corrections into the RG equation, we reproduce the known weak-coupling results from the gap equation at the same perturbative order at $O(g^0)$. Within the RG approach, the angular momentum structure of the pairing channel becomes more transparent, allowing us to examine the size of the gap for various pairing patterns. We also compare our results with recent lattice QCD calculations at finite isospin density. Finally, we argue that the RG method potentially offers a simpler and more systematic route to higher-order computations of the gap, which are of order $O(g)$ and thus quantitatively important.

The exclusive production of a vector-toponium $\psi_t$ state by photon-hadron interactions is investigated considering proton-proton and proton-nucleus collisions at the Large Hadron Collider (LHC) and Future Circular Collider (FCC) energies. The scattering amplitude is calculated using the $k_T$-factorization formalism assuming that the vector-toponium state can be described by a Gaussian light-cone wave function and considering different models for the unintegrated gluon distribution. Predictions for the rapidity distributions and total cross-sections are presented.

In this work, differential cross sections of $\gamma$-ray emission produced in nuclear reactions induced by $14.1$~MeV neutrons are measured for the $4.439$~MeV line from carbon, as well as for $10$ individual $\gamma$-ray lines from aluminum, $6$ from silicon, $8$ from calcium, $16$ from titanium, $6$ from chromium, and $14$ from iron. The measurements were conducted using the tagged neutron method with four LaBr$_3$(Ce) scintillation detectors positioned at angles of $25^{\circ}$, $45^{\circ}$, $60^{\circ}$, and $70^{\circ}$ relative to the generator target -- sample center axis. A neutron generator capable of producing $16$ separate beams of tagged neutrons was employed, which, combined with the detector system, enabled the determination of differential cross-sections for $64$ distinct angle values in the range of $17^{\circ}$ to $89^{\circ}$. To simplify data visualization, the angular distributions were divided into $5^{\circ}$ intervals, with weighted mean values of the angle and differential cross-section calculated for each interval. Corrections for multiple neutron scattering and attenuation, $\gamma$-ray attenuation, and total detection efficiency, computed using GEANT4, were accounted for in the cross-section calculations. Additional measurements were performed to validate the correction calculations. The total $\gamma$-ray emission cross-sections were obtained by approximating the angular distributions with even-order Legendre polynomial expansions up to the $6$th degree, followed by integration over the full solid angle. The total systematic error for the obtained data was estimated as $9$\,\%.

The generator coordinate method (GCM) was introduced in nuclear physics by Wheeler and independently by Peierls and their collaborators in 1950's and it is still one of the mostly used approximations for treating nuclear large amplitude collective motion (LACM). GCM was inspired by similar methods introduced in molecular and condensed matter physics in the late 1920's, after the Schrödinger equation became the tool of choice to describe quantum phenomena. The interest in the 1983 extension of GCM suggested by Reinhard, Cusson and Goeke, which includes internal excitations, was revived in recent years, but unfortunately this newer version of time-dependent GCM (TDGCM) framework has flaws, which prevents it from describing correctly many anticipated features, in particular interference and entanglement, which can play an important role in fission and many-nucleon transfer reactions. I present here an alternative formulation, the enhanced GCM (eGCM), which is free of difficulties encountered in previous GCM implementations and which is relevant for fission and many-nucleon transfer in heavy-ion reactions, and which can be used in either a static or time-dependent eGCM formulations.