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We investigate the dynamics of fermion localization within the framework of $f(T, B)$ gravity featuring non-minimal couplings. Starting from the Dirac action for a spin-$1/2$ fermion in a five-dimensional spacetime governed by torsional $f(T, B)$ gravity, we derive the Dirac equation and we explore its solutions under various non-minimal coupling functions. We examine two realistic forms of the torsional non-minimal coupling and reveal distinct behaviors that impact the localization of both massless and massive fermionic modes on the brane. Additionally, we employ probabilistic measurements, including Shannon entropy theory, Fisher information theory, and relative probability, to analyze the localization of these fermionic modes. The observed effects offer potential insights into probing torsional modifications.

The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers of Messier 87 galaxy and the Milky Way galaxy marks a significant step in observing the photon rings and central brightness depression that define the optical appearance of black holes with an accretion disk scenario. Inspired by this, we take into account a static and spherically symmetric magnetically charged regular black hole (MCRBH) metric characterized by its mass and an additional parameter q, which arises from the coupling of Einstein gravity and nonlinear electrodynamics (NLED) in the weak field approximation. This parameterized model offers a robust foundation for testing the coupling of Einstein gravity and NLED in the weak-field approximation, using the EHT observational results. In this study, we investigate the geodesic motion of particles around the solution, followed by a discussion of its fundamental geometrical characteristics such as scalar invariants. Using null geodesics, we examine how the model parameter influences the behavior of the photon sphere radius and the associated shadow silhouette. We seek constraints on q by applying the EHT results for supermassive black holes M87* and Sgr A*. Furthermore, it is observed that the geodesics of time-like particles are susceptible to variations in q, which can have an impact on the traits of the innermost stable circular orbit and the marginally bounded orbit. Our primary objective is to probe how the free parameter q affects various aspects of the accretion disk surrounding the MCRBH using the thin-disk approximation. Next, we discuss the physical characteristics of the thin accretion disk as well as the observed shadows and rings of the MCRBH, along with its luminosity, across various accretion models. Ultimately, variations in accretion models and the parameter q yield distinct shadow images and optical appearances of the MCRBH., Comment: 31 pages, 2 tables, 16 figures

This study delves deeply into braneworld scenarios within modified gravity models, investigating their impact on particle localization and the structure of branes. Through a comprehensive blend of numerical analyses and theoretical inquiries, we unravel a nuanced correlation between deviations from standard General Relativity (GR) and the emergence of split branes. By employing probabilistic measurements, we pinpoint stable configurations that align with brane division intervals, thus challenging prevailing assumptions regarding the gravitational framework of our universe. Furthermore, our investigation extends to the localization of fermions within the brane, exposing intricate dynamics shaped by scalar field characteristics and modifications to gravitational models. By harnessing quantum information measurements, notably Shannon entropy, we discern heightened probabilities of fermion localization within the brane as gravitational models diverge from standard paradigms. This underscores the limitations of General Relativity in comprehensively describing the complexities inherent in our universe. Lastly, our exploration of massive fermions unveils their potential to breach the confines of the brane, hinting at promising avenues for future experimental endeavors aimed at probing the nature of extra dimensions and gravitational interactions. This suggests exciting prospects for advancing our understanding of fundamental physics beyond conventional boundaries.

This study investigates the efficacy of Stochastic Hill Climbing with Random Restarts (SHC-RR) compared to Local Search (LS) strategies within the Quantum Approximate Optimization Algorithm (QAOA) framework across various problem models. Employing uniform parameter settings, including the number of restarts and SHC steps, we analyze LS with two distinct perturbation operations: multiplication and summation. Our comparative analysis encompasses multiple versions of max-cut and random Ising model (RI) problems, utilizing QAOA models with depths ranging from $1L$ to $3L$. These models incorporate diverse mixing operator configurations, which integrate $RX$ and $RY$ gates, and explore the effects of an entanglement stage within the mixing operator. We also used Quantum Fisher Information (QFI) to compare the different QAOA models, demonstrating the importance of the placement of the entanglement stage in the overall performance of QAOA. Additionally, we observed that the QFI values of previous parameters are not affected as the depth of the quantum circuit increases. Our results consistently show that SHC-RR outperforms LS approaches, showcasing superior efficacy despite its ostensibly simpler optimization mechanism. Furthermore, we observe that the inclusion of entanglement stages within mixing operators significantly impacts model performance, either enhancing or diminishing results depending on the specific problem context., Comment: 51 pages, 19 tables, 22 figures

In this research, we delve into the localization patterns of fermionic fields within a braneworld setting, employing a modified gravity model denoted as $f(Q)$. Our investigation revolves around two specific models, $f_1(Q)=Q+kQ^n$ and $f_2(Q)=Q+k_1Q^2+k_2Q^3$, where we systematically vary the parameters $n$ and $k_{1,2}$. Through an in-depth analysis encompassing the effective potential, massless, and massive modes, we elucidate how deviations from the conventional symmetric teleparallel equivalent of general relativity (STEGR) gravity impact the localization of fermionic fields. To ensure greater precision, our methodology integrates probabilistic measures such as Shannon entropy and relative probability. Moreover, we gauge the stability of these models employing differential configurational entropy (DCE), revealing a compelling correlation between the most stable configurations and the emergence of novel structures within the background scalar field. This work significantly contributes to our understanding of the gravitational modifications' intricate influence on fermionic field localization within braneworld scenarios. By shedding light on these dynamics, it advances the broader comprehension of the interplay between gravity modifications and fermionic field behaviors in these theoretical frameworks.

Existing algorithms for reinforcement learning from human feedback (RLHF) can incentivize responses at odds with preferences because they are based on models that assume independence of irrelevant alternatives (IIA). The perverse incentives induced by IIA hinder innovations on query formats and learning algorithms.

Structured light beams, in particular those carrying orbital angular momentum (OAM), have gained a lot of attention due to their potential for enlarging the transmission capabilities of communication systems. However, the use of OAM-carrying light in communications faces two major problems, namely distortions introduced during propagation in disordered media, such as the atmosphere or optical fibers, and the large divergence that high-order OAM modes experience. While the use of non-orthogonal modes may offer a way to circumvent the divergence of high-order OAM fields, artificial intelligence (AI) algorithms have shown promise for solving the mode-distortion issue. Unfortunately, current AI-based algorithms make use of large-amount data-handling protocols that generally lead to large processing time and high power consumption. Here we show that a low-power, low-cost image sensor can itself act as an artificial neural network that simultaneously detects and reconstructs distorted OAM-carrying beams. We demonstrate the capabilities of our device by reconstructing (with a 95$\%$ efficiency) individual Vortex, Laguerre-Gaussian (LG) and Bessel modes, as well as hybrid (non-orthogonal) coherent superpositions of such modes. Our work provides a potentially useful basis for the development of low-power-consumption, light-based communication devices.

In this paper, we employ PCA and t-SNE analysis to gain deeper insights into the behavior of entangled and non-entangled mixing operators within the Quantum Approximate Optimization Algorithm (QAOA) at varying depths. Our study utilizes a dataset of parameters generated for max-cut problems using the Stochastic Hill Climbing with Random Restarts optimization method in QAOA. Specifically, we examine the $RZ$, $RX$, and $RY$ parameters within QAOA models at depths of $1L$, $2L$, and $3L$, both with and without an entanglement stage inside the mixing operator. The results reveal distinct behaviors when we process the final parameters of each set of experiments with PCA and t-SNE, where in particular, entangled QAOA models with $2L$ and $3L$ present an increase in the amount of information that can be preserved in the mapping. Furthermore, certain entangled QAOA graphs exhibit clustering effects in both PCA and t-SNE. Overall, the mapping results clearly demonstrate a discernible difference between entangled and non-entangled models, quantified numerically through explained variance in PCA and Kullback-Leibler divergence (after optimization) in t-SNE, where some of these differences are also visually evident in the mapping data produced by both methods., Comment: 38 pages, 36 figures, 24 tables

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

A centerpiece of the ever-popular reinforcement learning from human feedback (RLHF) approach to fine-tuning autoregressive language models is the explicit training of a reward model to emulate human feedback, distinct from the language model itself. This reward model is then coupled with policy-gradient methods to dramatically improve the alignment between language model outputs and desired responses. In this work, we adopt a novel perspective wherein a pre-trained language model is itself simultaneously a policy, reward function, and transition function. An immediate consequence of this is that reward learning and language model fine-tuning can be performed jointly and directly, without requiring any further downstream policy optimization. While this perspective does indeed break the traditional agent-environment interface, we nevertheless maintain that there can be enormous statistical benefits afforded by bringing to bear traditional algorithmic concepts from reinforcement learning. Our experiments demonstrate one concrete instance of this through efficient exploration based on the representation and resolution of epistemic uncertainty. In order to illustrate these ideas in a transparent manner, we restrict attention to a simple didactic data generating process and leave for future work extension to systems of practical scale.

We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature related to $\lambda$ on the underlying space or, equivalently, as a Dunkl oscillator with a position-dependent mass function. This new quantum model is shown to be exactly solvable in arbitrary dimension N, and its eigenvalues and eigenfunctions are explicitly presented. Moreover, it is shown that in the two-dimensional case both the Darboux III and the Dunkl oscillators can be separately coupled with a constant magnetic field, thus giving rise to two new exactly solvable quantum systems in which the effect of a position-dependent mass and the Dunkl derivatives on the structure of the Landau levels can be explicitly studied. Finally, the whole 2D Dunkl-Darboux III oscillator is coupled with the magnetic field and shown to define an exactly solvable Hamiltonian, where the interplay between the $\lambda$-deformation and the magnetic field is explicitly illustrated.

Prevailing methods for assessing and comparing generative AIs incentivize responses that serve a hypothetical representative individual. Evaluating models in these terms presumes homogeneous preferences across the population and engenders selection of agglomerative AIs, which fail to represent the diverse range of interests across individuals. We propose an alternative evaluation method that instead prioritizes inclusive AIs, which provably retain the requisite knowledge not only for subsequent response customization to particular segments of the population but also for utility-maximizing decisions.

We develop an extension of posterior sampling for reinforcement learning (PSRL) that is suited for a continuing agent-environment interface and integrates naturally into agent designs that scale to complex environments. The approach, continuing PSRL, maintains a statistically plausible model of the environment and follows a policy that maximizes expected $\gamma$-discounted return in that model. At each time, with probability $1-\gamma$, the model is replaced by a sample from the posterior distribution over environments. For a choice of discount factor that suitably depends on the horizon $T$, we establish an $\tilde{O}(\tau S \sqrt{A T})$ bound on the Bayesian regret, where $S$ is the number of environment states, $A$ is the number of actions, and $\tau$ denotes the reward averaging time, which is a bound on the duration required to accurately estimate the average reward of any policy. Our work is the first to formalize and rigorously analyze the resampling approach with randomized exploration.

Recent investigations suggest that the use of non-classical states of light, such as entangled photon pairs, may open new and exciting avenues in experimental two-photon absorption spectroscopy. Despite several experimental studies of entangled two-photon absorption (eTPA), there is still a heated debate on whether eTPA has truly been observed. This interesting debate has arisen, mainly because it has been recently argued that single-photon-loss mechanisms, such as scattering or hot-band absorption may mimic the expected entangled-photon linear absorption behavior. In this work, we focus on transmission measurements of eTPA, and explore three different two-photon quantum interferometers in the context of assessing eTPA. We demonstrate that the so-called N00N-state configuration is the only one amongst those considered insensitive to linear (single-photon) losses. Remarkably, our results show that N00N states may become a potentially powerful tool for quantum spectroscopy, and place them as a strong candidate for the certification of eTPA in an arbitrary sample., Comment: 10 pages, 4 figures. Updated References

Intelligent learning diagnosis is a critical engine of intelligent tutoring systems, which aims to estimate learners' current knowledge mastery status and predict their future learning performance. The significant challenge with traditional learning diagnosis methods is the inability to balance diagnostic accuracy and interpretability. Although the existing psychometric-based learning diagnosis methods provide some domain interpretation through cognitive parameters, they have insufficient modeling capability with a shallow structure for large-scale learning data. While the deep learning-based learning diagnosis methods have improved the accuracy of learning performance prediction, their inherent black-box properties lead to a lack of interpretability, making their results untrustworthy for educational applications. To settle the above problem, the proposed unified interpretable intelligent learning diagnosis (UIILD) framework, which benefits from the powerful representation learning ability of deep learning and the interpretability of psychometrics, achieves a better performance of learning prediction and provides interpretability from three aspects: cognitive parameters, learner-resource response network, and weights of self-attention mechanism. Within the proposed framework, this paper presents a two-channel learning diagnosis mechanism LDM-ID as well as a three-channel learning diagnosis mechanism LDM-HMI. Experiments on two real-world datasets and a simulation dataset show that our method has higher accuracy in predicting learners' performances compared with the state-of-the-art models, and can provide valuable educational interpretability for applications such as precise learning resource recommendation and personalized learning tutoring in intelligent tutoring systems., Comment: 28 pages,5 figures

We propose a new "superpotential" and find that neither the supersymmetric energy conditions nor the associated shape invariance condition remain valid. On the other hand a new energy condition $E_{n}^{+}-E_{n}^{(-)}=2$ between the two partner Hamiltonian $H^{(\pm)}$ emerges. Mathematical proof supported the present findings with examples are presented. It is observed that, when the superpotential is associated with discontinuity or distortion, SUSY energy conditions and the shape invariance condition will no longer hold good., Comment: There are a few mistakes occurred in this work

In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN). Both the efficiency and performance of this new quantum version of the k-NN algorithm are compared to those of the classical k-NN and another quantum version proposed by Schuld et al. \cite{Int13}. Results show that the efficiency of both quantum algorithms is similar to each other and superior to that of the classical algorithm. On the other hand, the performance of our proposed quantum k-NN algorithm is superior to the one proposed by Schuld et al. and similar to that of the classical k-NN.

The machine learning algorithm is gaining prominence in traffic identification research as it offers a way to overcome the shortcomings of port-based and deep packet inspection, especially for P2P-based Skype. However,recent studies have focused mainly on traffic identification based on a full-packet dataset, which poses great challenges to identifying online network traffic. This study aims to provide a new flow identification algorithm by taking the sampled flow records as the object. The study constructs flow records from a Skype set as the dataset, considers the inherent NETFLOW and extended flow metrics as features, and uses a fast correlation-based filter algorithm to select highly correlated features. The study also proposes a new NFI method that adopts a Bayesian updating mechanism to improve the classifier model. The experimental results show that the proposed scheme can achieve much better identification performance than existing state-of-the-art traffic identification methods, and a typical feature metric is analyzed in the sampling environment. The NFI method improves identification accuracy and reduces false positives and false negatives compared to other methods.

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation parameter of underlying space and involve reflection operators. Their symmetries are obtained by the Jordan-Schwinger representations in the family of the Cayley-Klein orthogonal algebras using the creation and annihilation operators of the dynamical $sl_{-1}(2)$ algebra of the one-dimensional Dunkl oscillator. The resulting algebra is a deformation of $so_{\kappa_1\kappa_2}(4)$ with reflections, which is known as the Jordan-Schwinger-Dunkl algebra $jsd_{\kappa_1\kappa_2}(4)$. Hence, this model is shown to be maximally superintegrable. On the other hand, the superintegrability of the three-dimensional Dunkl oscillator model is studied from the factorization approach viewpoint. The spectrum of this system is derived through the separation of variables in geodesic polar coordinates, and the resulting eigenfunctions are algebraically given in terms of Jacobi polynomials., Comment: 21 pages, to appear in Journal quantum