The determination of ground state properties of quantum systems is a fundamental problem in physics and chemistry, and is considered a key application of quantum computers. A common approach is to prepare a trial ground state on the quantum computer and measure observables such as energy, but this is often limited by hardware constraints that prevent an accurate description of the target ground state. The quantum computed moments (QCM) method has proven to be remarkably useful in estimating the ground state energy of a system by computing Hamiltonian moments with respect to a suboptimal or noisy trial state. In this paper, we extend the QCM method to estimate arbitrary ground state observables of quantum systems. We present preliminary results of using QCM to determine the ground state magnetisation and spin-spin correlations of the Heisenberg model in its various forms. Our findings validate the well-established advantage of QCM over existing methods in handling suboptimal trial states and noise, extend its applicability to the estimation of more general ground state properties, and demonstrate its practical potential for solving a wide range of problems on near-term quantum hardware.

We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scaling property suggest that the brane-brane statistical pair correlation functions divulge an asymmetric nature, in comparison with the others. This approach indicates that all above configurations are effectively attractive and stable, on an arbitrary hyper-surface of the state-space manifolds. It is nevertheless noticed that there exists an intriguing relationship between non-ideal inter-brane statistical interactions and phase transitions. The ramifications thus described are consistent with the existing picture of the microscopic CFTs. We conclude with an extended discussion of the implications of this work for the physics of black holes in string theory.

This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proof-based; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.

Depression has been associated with impaired neural processing of reward and punishment. However, to date, little is known regarding the relationship between depression and intertemporal choice for gain and loss. We compared impulsivity and inconsistency in intertemporal choice for monetary gain and loss (quantified with parameters in the q-exponential discount function based on Tsallis' statistics) between depressive patients and healthy control subjects. This examination is potentially important for advances in neuroeconomics of intertemporal choice, because depression is associated with reduced serotonergic activities in the brain. We observed that depressive patients were more impulsive and time-inconsistent in intertemporal choice action for gain and loss, in comparison to healthy controls. The usefulness of the q-exponential discount function for assessing the impaired decision-making by depressive patients was demonstrated. Furthermore, biophysical mechanisms underlying the altered intertemporal choice by depressive patients are discussed in relation to impaired serotonergic neural systems. Keywords: Depression, Discounting, Neuroeconomics, Impulsivity, Inconsistency, Tsallis' statistics

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the object and the information accounting for the remaining accidental information. There can be several ways (model classes) in which the regularity is expressed. Kolmogorov has proposed the model class of finite sets, generalized later to computable probability mass functions. The resulting theory, known as Algorithmic Statistics, analyzes the algorithmic sufficient statistic when the statistic is restricted to the given model class. However, the most general way to proceed is perhaps to express the useful information as a recursive function. The resulting measure has been called the ``sophistication'' of the object. We develop the theory of recursive functions statistic, the maximum and minimum value, the existence of absolutely nonstochastic objects (that have maximal sophistication--all the information in them is meaningful and there is no residual randomness), determine its relation with the more restricted model classes of finite sets, and computable probability distributions, in particular with respect to the algorithmic (Kolmogorov) minimal sufficient statistic, the relation to the halting problem and further algorithmic properties.

There is currently a growing interest in understanding the origins of intrinsic fluorescence as a way to design non-invasive probes for biophysical processes. In this regard, understanding how pH influences fluorescence in non-aromatic biomolecular assemblies is key to controlling their optical properties in realistic cellular conditions. Here, we combine experiments and theory to investigate the pH-dependent emission of solid-state L-Lysine (Lys). Lys aggregates prepared at different pH values using HCl and H$_2$SO$_4$ exhibit protonation- and counterion-dependent morphology and fluorescence, as shown by microscopy and steady-state measurements. We find an enhancement in the fluorescence moving from acidic to basic conditions. To uncover the molecular origin of these trends, we performed non-adiabatic molecular dynamics simulations on three Lys crystal models representing distinct protonation states. Our simulations indicate that enhanced protonation under acidic conditions facilitates non-radiative decay via proton transfer, whereas basic conditions favor radiative decay. Our combined experimental-theoretical work highlights pH and counterion identity as key factors tuning fluorescence in Lys assemblies, offering insights for designing pH responsive optical materials based on non-aromatic amino acids.

The $e-e$, $e-i$, $i-i$ and charge-charge static structure factors are calculated for alkali and Be$^{2+}$ plasmas using the method described by Gregori et al. in \cite{bibGreg2006}. The dynamic structure factors for alkali plasmas are calculated using the method of moments \cite{bibAdam83}, \cite{bibAdam93}. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the ion structure \cite{bib73}. PACS: 52.27.Aj (Alkali and alkaline earth plasmas, Static and dynamic structure factors), 52.25.Kn (Thermodynamics of plasmas), 52.38.Ph (X-ray scattering)

We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter $T$ which plays the role of the temperature in physics. We show that there is a critical value of $T$, say $T_c$, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. We have considered three models: $q=3$ ( sell, buy, wait), $q=5$ (5 states between absolutely buy and absolutely sell), and $q=\infty$. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time $t_1$ and removed at the time $t_2$. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. Many striking results are obtained. In particular we show that the price strongly fluctuates near $T_c$ and there exists a critical value $H_c$ above which the boosting effect remains after $H$ is removed. This happens only if $H$ is applied in the critical region. Otherwise, the effect of $H$ lasts only during the time of the application of $H$. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time.

A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and continuous test statistics.

The influence of static gravitational field on frequency, wave-length and velocity of photons and on the energy levels of atoms and nuclei is considered in the most elementary way. The interconnection between these phenomena is stressed.