We investigate the non-monotonic temperature sensitivity of a coherently driven two-level quantum system coupled to an Ohmic phonon environment. By employing a unitary polaron transformation, we account for phonon-induced renormalization effects that go beyond the standard weak-coupling approximations. Our analysis reveals that the Quantum Fisher Information (QFI) exhibits a prominent peak at an intermediate system-environment coupling strength, identifying an optimal regime for thermal sensing. This behavior emerges from a fundamental competition between environment-induced dissipation enhancement and the exponential suppression of system parameters due to phonon dressing. We demonstrate that while thermometric precision vanishes in both the ultra-weak and strong coupling limits, a properly tuned nonequilibrium steady state can significantly enhance sensitivity. These results suggest that environmental interactions, often viewed as detrimental decoherence sources, can be engineered as a resource to optimize the performance of solid-state quantum thermometers.

We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the external port while minimizing the standard LQR cost in the disturbance-free case. The resulting constrained optimization problem is intractable due to bilinear matrix inequalities. We analyze the set of passivating gains, showing it is unbounded, possibly nonconvex, path-connected, and contractible. We propose an indirect approach, in which the set of passivating feedback gains is inner-approximated by a compact, convex polytope. A projected gradient flow is employed to compute a gain within this polytope that minimizes the LQR cost. Numerical examples illustrate the effectiveness of the method.

We investigate the focusing and defocusing energy-critical stochastic nonlinear Schrödinger equation, subject to random perturbations in the form of either additive or multiplicative (Stratonovich) noise. We establish local well-posedness for random or deterministic initial data $u_0$ in $\dot{H}^1(\mathbb{R}^n)$ or $H^1(\mathbb{R}^n)$, depending on the noise type. In the focusing case we provide quantitative estimates regarding the existence time and probability. Moreover, we derive blow-up criteria for solutions with positive energy in both cases of noise, provided that the noise intensity is sufficiently small, showing that blow-up occurs before a certain given positive time with positive probability, thus, extending deterministic results of Kenig-Merle [24] for the energy-critical NLS equation to the stochastic setting.

We present and study the Pool model in $\mathbb{R}^2$, a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") perform continuous-time random walks and are absorbed upon entering a circular pool initially centered at the origin. Each absorbed particle increases the pool's mass, and the pool expands so that its area grows accordingly, yielding a natural mass-preserving dynamics. A central tool which is of independent interest is a version of Kurtz's theorem for this model, depicting the field of particles conditioned on the growth of the pool as an independent non-homogeneous Poisson point process.

We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying closed CRNs? While open CRNs provide the standard framework to describe out-of-equilibrium chemical systems, real systems are finite and ultimately relax to equilibrium, leaving the status of this description conceptually unresolved. Here we show that open-CRN behavior arises as an asymptotic regime of closed CRNs when two minimal and physically transparent conditions are met: a time-scale separation, whereby fast reactions effectively act as exchange mechanisms, and an abundance separation, whereby a subset of species behaves as chemostats with diverging chemical capacity. In this regime, both the stochastic dynamics and the thermodynamic structure \ -- including local detailed balance, entropy production, and free-energy balance \ -- emerge to leading order from the underlying closed CRN. Our results apply to arbitrary stoichiometries. They show that chemostats need not be introduced as external idealizations, but instead arise as emergent thermodynamic structures within closed systems, providing a unified and physically grounded foundation for the nonequilibrium thermodynamics of CRNs.

Magnetoacoustic devices that harness the strong coupling between acoustic waves and magnons have emerged as a promising platform for energy-efficient spintronics. Laser-generated pulsed surface acoustic waves (SAWs) are particularly attractive for such applications, offering broadband frequency content up to the gigahertz (GHz) range, remote excitation without lithographic patterning, and surface localization for efficient on-chip integration. In this work, we present a comprehensive experimental study of laser-generated SAW pulses in the Fe49Rh51/MgO(001) system. A thin film of the near-equiatomic FeRh alloy serves both as an opto-acoustic transducer and as a mechanical load that modulates SAW propagation. The antiferromagnetic to ferromagnetic phase transition in FeRh, occurring slightly above room temperature, is accompanied by abrupt changes in its elastic properties, enabling controlled modification of the SAW excitation efficiency and dispersion characteristics by tuning the sample temperature and laser fluence. Using 160 fs laser pulses for excitation and time-resolved Sagnac interferometry for detection, we evaluated key SAW parameters, including amplitude, spectral content, phase and group velocities, and their in-plane anisotropy. Particular emphasis is placed on the dispersion relation and its anisotropy, which govern the coherent interaction between phonons and magnons and are determined primarily by the FeRh film.

This paper investigates non-intrusive occupancy detection methods for residential buildings using environmental sensor data from the KTH Live-In Lab in Stockholm, Sweden. Three machine learning approaches, namely, logistic regression (LR), support vector machines (SVM), and long short-term memory (LSTM) network enhanced with an attention mechanism, are evaluated in terms of predictive performance and computational complexity. The analysis considers the trade-off between sensor availability (investment cost) and prediction accuracy in real applications, as well as the models' cross-apartment generalizability. Hyperparameters for both the SVM and LSTM models are optimized using Bayesian optimization. All three models are evaluated on data collected from apartments not used during training, and on data generated from a calibrated digital model of the testbed. Results show that all models achieve comparable performance on the same-apartment test data (accuracy of approximately 0.83, F1 score of approximately 0.86). When assessed on cross-apartment data, the LSTM model demonstrates the strongest generalization capability (accuracy of 0.84, F1 score of 0.85), while LR provides a competitive, low-complexity alternative for applications that do not require cross-apartment generalization.

We study the minimization problem for eigenvalues of the Dirac operator within a fixed conformal class on a closed spin Riemannian manifold. We establish a criterion for the existence of a minimizer for this variational problem, focusing specifically on the case of closed surfaces. Furthermore, we apply our results to derive isoperimetric inequalities for the Dirac operator on the two-dimensional sphere, providing a complete characterization of its conformal spectrum.

Recent advancements in multimodal recommendations, which leverage diverse modality information to mitigate data sparsity and improve recommendation accuracy, have gained significant attention. However, existing multimodal recommendations overlook the critical role of user representation initialization. Unlike items, which are naturally associated with rich modality information, users lack such inherent information. Consequently, item representations initialized based on meaningful modality information and user representations initialized randomly exhibit a significant semantic gap. To this end, we propose a Semantically Guaranteed User Representation Initialization (SG-URInit). SG-URInit constructs the initial representation for each user by integrating both the modality features of the items they have interacted with and the global features of their corresponding clusters. SG-URInit enables the initialization of semantically enriched user representations that effectively capture both local (item-level) and global (cluster-level) semantics. Our SG-URInit is training-free and model-agnostic, meaning it can be seamlessly integrated into existing multimodal recommendation models without incurring any additional computational overhead during training. Extensive experiments on multiple real-world datasets demonstrate that incorporating SG-URInit into advanced multimodal recommendation models significantly enhances recommendation performance. Furthermore, the results show that SG-URInit can further alleviate the item cold-start problem and also accelerate model convergence, making it an efficient and practical solution for multimodal recommendations.

Modern communication networks demand ever-increasing transmission bandwidth, placing stringent requirements on low-cost, high-performance electro-optic modulators. Substantial advances have been made in integrated photonics employing lithium niobate on insulator. In contrast, photonic integrated circuits based on lithium tantalate -- a material already commercially adopted for wireless filters -- have been developed, offering reduced DC drift, higher optical power handling, and lower birefringence. These advantages enable more complex and dense photonic integrated circuits, and make lithium tantalate a promising material platform for next-generation integrated electro-optic modulators. However, in contrast to the extensively studied thin-film lithium niobate platform, thin-film lithium tantalate modulators have only been explored on silicon substrates. Here, we report the first fabrication and characterization of thin-film lithium tantalate electro-optic modulators manufactured on a 4-inch (100 mm) fused-silica substrate for adapting a low-loss slow-wave microwave electrode to improve the electro-optic bandwidth. By employing a slow-wave electrode design to achieve velocity matching between microwave and optical signals, the demonstrated modulator achieves a 3-dB electro-optic bandwidth of 64 GHz with a low half-wave voltage of 1.53 V, with potential to operate at the measured 100 GHz electrical bandwidth, if the employed spectral biasing is removed. The modulator moreover exhibits low bias drift, with a constant switching voltage down to 10 mHz. This performance enables high-speed data transmission comparable to state-of-the-art lithium niobate modulators fabricated on quartz substrates. Using the fabricated devices, a net single lane data rate of 440.6 Gbps is achieved using PAM8 signaling.

Singular Lagrangian fibrations arising from three-degree-of-freedom integrable Hamiltonian systems remain largely unexplored. While several results describe the global structure of large classes of systems with two degrees of freedom, only a few examples are understood in higher dimensions. We present a three-degree-of-freedom system derived from the two-spin Tavis-Cummings model whose singular Lagrangian fibration exhibits a topology that has not been observed in other physical models. We show that the most degenerate singular fiber is homeomorphic to $\mathbf{S}^2\times\mathbf{S}^1$ with a singularity of $A_2$ type. We further describe the bifurcation diagram and the global topology of the fibration, and we compute its Hamiltonian monodromy.

Large Language Models have shown great success in recommender systems. However, the limited and sparse nature of user data often restricts the LLM's ability to effectively model behavior patterns. To address this, existing studies have explored cross-domain solutions by conducting Cross-Domain Recommendation tasks. But previous methods typically assume domains are overlapped and can be accessed readily. None of the LLM methods address the privacy-preserving issues in the CDR settings, that is, Privacy-Preserving Cross-Domain Recommendation. Conducting non-overlapping PPCDR with LLM is challenging since: 1)The inability to share user identity or behavioral data across domains impedes effective cross-domain alignment. 2)The heterogeneity of data modalities across domains complicates knowledge integration. 3)Fusing collaborative filtering signals from traditional recommendation models with LLMs is difficult, as they operate within distinct feature spaces. To address the above issues, we propose SF-UBM, a Semantic-enhanced Federated User Behavior Modeling method. Specifically, to deal with Challenge 1, we leverage natural language as a universal bridge to connect disjoint domains via a semantic-enhanced federated architecture. Here, text-based item representations are encrypted and shared, while user-specific data remains local. To handle Challenge 2, we design a Fact-counter Knowledge Distillation module to integrate domain-agnostic knowledge with domain-specific knowledge, across different data modalities. To tackle Challenge 3, we project pre-learned user preferences and cross-domain item representations into the soft prompt space, aligning behavioral and semantic spaces for effective LLM learning. We conduct extensive experiments on three pairs of real-world domains, and the experimental results demonstrate the effectiveness of SF-UBM compared to the recent SOTA methods.

Recommender systems on social media increasingly mediate how users encounter mental health content, yet it remains unclear whether they distinguish help-seeking from distress expression. We conduct a controlled 7-day audit of TikTok's "For You" page using 30 fresh accounts and LLM-guided agents that vary initial search framing (distress- vs. help-initiated) and interaction strategy (engaged, avoidant, passive). Across 8,727 recommended videos, interaction behavior dominates exposure outcomes: engagement rapidly saturates feeds with mental health content (~45% of daily recommendations), while avoidance and passive viewing reduce but do not eliminate exposure (~11-20%). Search framing mainly shifts composition rather than volume--help-initiated searches yield more potentially supportive material, yet potentially harmful content persists at low but non-zero levels, including content in the Suicide/Self-Harm category. These findings suggest limited sensitivity to user intent signals in TikTok's recommendations and motivate context-aware safeguards for sensitive topics.

In this systematic density functional theory study, we compare a standard gradient corrected functional (PBE) with a long-range hybrid functional (HSE06), with and without correction for the dispersion forces, relatively to their ability to correctly reproduce structural and electronic properties of different bulk 3D C3N4 phases, encompassing diamond- and graphitic-like models. Corrugation is found to provide further stabilization to the layered structures with all methods. We observe that HSE06-D3 method provides results in good agreement with experimental data and with more sophisticated G0W0 calculations. Based on that, we exploited the method to investigate the nature of the bulk triplet excitons in these C3N4 structures to evaluate the S0-T1 energy difference, the selftrapping triplet exciton energy and the photoluminescence emission energy, since this is a promising vis-light photocatalyst. Nanostructuring (0D and 2D) is another relevant aspect of these materials in practical applications, therefore we have considered the effect of single or multilayer exfoliation or space confinement in nanoparticles. Finally, we also discuss how the introduction of extrinsic dopants (e.g. S atoms) in the nanostructures modifies the atomic and electronic structure.

The response of a complex system to a slow varying external force often displays a jump discontinuity in the order parameter near the critical point. However, this discontinuity is not usually a single jump but rather breaks into smaller jumps which makes it difficult to locate the critical point on approaching its vicinity based only on simulations, in the absence of exact results. Our work is a small effort in understanding these breaks in jump through the hysteretic response of a classical Ising spin system to an external field, $h$, in the context of a nonequilibrium zero-temperature random field Ising model on dilute systems. We consider a Bethe lattice with coordination number, $z = 4$, and dilute a fraction $(1-c)$ of the sites. Therefore the lattice now consists of sites with varying $z = 4, 3, 2, 1$ and possibly few isolated sites $(z=0)$, depending on the concentration $c$. We obtain the exact solution of the magnetization curve, $m(h)$ vs $h$, for the entire lattice as well as for each sublattice of different $z$ coordinated sites, $m_4(h), m_3(h), m_2(h), m_1(h), m_0(h)$. The discontinuity in total magnetization is the result of the superposition of the jumps of different $z$ coordinated sites and observed at the same value of external field, $h_{crit}$. The dominant contribution to the jump comes from those sites with higher concentration and larger $z$. However, the triggering sites responsible for large jumps are mostly $z\ge3$. We test this on cubic lattices as well, where exact results are not available. We hope our analysis will help in understanding fluctuations around a jump in numerical simulations as well as experiments.

A. Albouy and R. Moeckel in 2000 found some interesting inequalities related to the inverse problem for collinear (Moulton) central configurations: the Pfaffian of a certain matrix is positive since all coefficients of some polynomials are positive, for the Newtonian (interaction potential $1/r$ and $n\leq 6$). They conjectured that for all $n$ such Pfaffians, for the Newtonian case, are positive. In this article we analyze further the problem, and we prove that such inequalities hold true in more general cases (potentials with log-convex derivative, such as those with homogeneity parameters $α>0$, for all even $n\leq 14$).

Weyl conformal gravity was originally proposed in the early twentieth century as an attempt to unify gravitation and electromagnetism. Since 1989, renewed interest in this fourth-order theory of gravity has emerged following the discovery of several exact black hole solutions. In this work, we investigate the timelike circular geodesics of a spherically symmetric Weyl black hole. The effective potential, the circular geodesics and their Jacobi and Lyapunov stability are discussed. Our analysis provides new insights into the stability properties of Weyl black holes and the role of the free parameters appearing in their solutions.

Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of $\mathcal{G}(F)$. We first construct a type for each Bernstein component attached to a principal series representation of $\mathcal{G}(F).$ We then use these types and the local Langlands correspondence for principal series representations defined in [Sol25] to verify the formal degree conjecture. Our approach follows a similar strategy to [Ric25], reducing the problem to the case of unipotent representations of some other quasi-split group.

Similar to microspheres, thin-walled microbubble resonators support whispering gallery modes (WGMs) that combine ultrahigh Q-factors and small effective mode volumes. In contrast, their hollow nature enables enhanced interactions with encapsulated materials and lower spectral mode density due to the tight radial confinement of the optical modes. However, the existence of a high axial-mode density still leads to significant mode mixing and modal interference that can complicate spectral shift measurements, thereby limiting sensing applications. To address this limitation, we have fabricated geometric filters directly on the surface of microbubbles using focused ion beam (FIB) milling. Based on numerical calculations, we first designed and then fabricated large tapered patterns, such as circular surface dips or holes, that could effectively filter modes while minimizing optical scattering losses. Local lateral mode confinement and partial recovery of high Q-factors were experimentally achieved by adding shallow slit patterns. Using few-mode engineered microbubble resonators, we subsequently demonstrated pressure sensing and wide spectral tuning of WGMs free from mode-mixing artifacts. This precision engineering approach promises improved mode isolation, tunable directional emission, and ultrasensitive measurements in microbubble resonator devices.

We present a study of the melting dynamics of a two-phase eutectic solid. In situ, thin-sample experiments using a transparent eutectic alloy and two-dimensional phase field simulations calibrated for the very same alloy are combined to assess pattern formation during directional melting in a temperature gradient. Depending on the melting velocity $V_m$ and the spacing $λ$ of the pre-solidified lamellar microstructure, an unexpectedly rich diversity of melting patterns is observed, with good agreement between experiments and simulations. We unravel the different physical mechanisms leading to this diversity, and establish the scaling behaviors of (i) the penetration of the liquid along the solid-solid interface at large $V_m$, (ii) the thickening of the primary-phase fingers at low $V_m$, and (iii) a period-doubling instability for small $λ$ values. Our study provides a fundamental basis for further investigations of eutectic melting, including additive manufacturing during which melting/solidification cycles take place.

Resolving real-world software engineering (SWE) issues with autonomous agents requires complex, long-horizon reasoning. Current pipelines are bottlenecked by unoptimized demonstration data, sparse execution rewards, and computationally prohibitive inference scaling, which collectively exacerbate token bloat, reward hacking, and policy degradation. We present SWE-TRACE (Trajectory Reduction and Agentic Criteria Evaluation), a unified framework optimizing the SWE agent lifecycle across data curation, reinforcement learning (RL), and test-time inference. First, we introduce an LLM multi-task cascading method, utilizing stepwise oracle verification to distill a 60K-instance Supervised Fine-Tuning (SFT) corpus strictly biased toward token-efficient, shortest-path trajectories. Second, to overcome the instability of sparse outcome rewards, we design a MemoryAugmented Agentic RL pipeline featuring a Rubric-Based Process Reward Model (PRM). An auxiliary Rubric-Agent provides dense, fine-grained heuristic feedback on intermediate steps, guiding the model through long-horizon tasks. Finally, we bridge training and inference by repurposing the PRM for heuristic-guided Test-Time Scaling (TTS). By dynamically evaluating and pruning action candidates at each step, SWE-TRACE achieves superior search efficiency without the latency overhead of standard parallel sampling. Extensive experiments on standard SWE benchmarks demonstrate that SWE-TRACE significantly advances the state-of-the-art, maximizing resolution rates while drastically reducing both token consumption and inference latency.

Safe navigation for an ego vehicle in uncertain environments characterized by dynamic obstacles with unknown nonlinear dynamics is a challenging problem of significant practical interest. Existing approaches in the literature either lack formal safety guarantees, require full model knowledge, or fail to account for the risk associated with the vehicle's exact body geometry and the temporal evolution of uncertainty between sampling instants. In this paper, we propose a data-driven observer for the unknown obstacle dynamics that generates an alpha-confidence set flow, which is exactly transformed into a Control Barrier Function (CBF) to enforce (1-alpha)-probability safety. The proposed framework accommodates nonlinear ego vehicle dynamics of arbitrary relative degree, as demonstrated through case studies involving first- and second-order dynamics of an unmanned surface vehicle.

Magnetic tunnel junction (MTJ) is the key component to enable information access and increasing number of MTJs is integrated to develop high-density spintronic devices. However, continuous miniaturization of the conventional MTJs is hindered by stray magnetic fields. Altermagnets, combining the advantages of both ferromagnets and antiferromagnets, provide a promising alternative to fabricate versatile MTJs with exotic properties, such as giant spin splitting, high intrinsic frequency, and absence of stray fields. Inspired by the altermagnetic metal candidate KV2Se2O reported recently, we design an altermagnetic tunnel junction (AMTJ) based on KV2Se2O/SrTiO3/KV2Se2O. Using density functional theory combined with non-equilibrium Green's function, we investigate the layer-dependent quantum transport properties and the tunneling magnetoresistance (TMR) of such AMTJ device. Our calculated results reveal that the transmission of the AMTJ device exhibits a pronounced oscillation behavior dependent on the number of layers of the SrTiO3 semiconductor, which is attributed to the interface configuration determined by parity of the layer number. In odd-layer devices, the electron-rich O-Se interface exhibits a smooth effective potential and enables transverse momentum (k||) transport channels, leading to enhanced transmission. In contrast, in even-layer devices, the Ti-Se interface presents a steeper effective potential, impeding quantum transport through transverse momentum (k||) channels. A giant TMR of 4.6*10^7% is predicted to be realized by using a 4-layer SrTiO3. Our findings not only provide physical understanding relevant to the quantum transport in AMTJs, but also unveil that the barrier interface engineering is a strategy to tune the magnetoelectric performance.

We investigate near-threshold $J/ψ$ photoproduction off the nucleon, focusing on hadronic rescattering effects induced by open-charm meson-baryon intermediate states. Beyond the conventional Pomeron-exchange mechanism, the $\bar D^0Λ_c^+$ and $\bar D^{*0} Λ_c^+$ channels are incorporated within an effective Lagrangian framework. The relevant production amplitudes are evaluated at tree level from $t$-, $s$-, and $u$-channel diagrams in a gauge-invariant manner. The resulting total and $t$-dependent differential cross sections are compared with recent near-threshold data from the GlueX, $J/ψ$-007, and CLAS experiments at Jefferson Lab. We find that the open-charm rescattering contributions significantly improve the description of the data, particularly at large momentum transfer, and naturally generate cusp-like structures near the $\bar D^0 Λ_c^+$ and $\bar D^{*0} Λ_c^+$ thresholds in the GlueX data. We further present predictions for the associated open-charm processes $γp \to \bar D^{(*)0} Λ_c^+$, whose cross sections are estimated to be of the order of 5 nb.

This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue analysis, distinguishing this problem from the classical complex case. We use spectral norm inequalities for partitioned quaternionic matrices and apply them to quaternionic block matrices associated with monic matrix polynomials. By analyzing the structure of powers of these companion matrices we derive progressively sharper bounds for the right eigenvalues. Consequently, these bounds give bounds for the zeros of quaternionic polynomials.

We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant. The resulting hierarchy of equations defining the perturbative corrections is governed by a gauge-rotated Hamiltonian of the unperturbed system and leads to closed-integral expressions for the time-dependent corrections based on Duhamel's formula. This closed-integral structure of corrections is a hallmark of time-independent logarithmic perturbation theory and is preserved in the present extension. This structure, in particular, provides a computable expression for the instantaneous energy shift. Furthermore, dynamic energy shifts arise naturally within this framework in the form of time-averaged expectation values of pseudopotentials and can be related, for example, to AC Stark shifts and electric polarizabilities. As an illustration, we apply the method to the harmonic oscillator and the hydrogen atom, both driven by a time-dependent laser field. The harmonic oscillator provides a proof of principle for which the exact solution is recovered, while the hydrogen atom illustrates the method applied to atomic systems. Supported by numerical simulations, we demonstrate the applicability to obtain relevant physical observables with high accuracy. The present approach offers a promising alternative for analytical studies of time-dependent multi-photon processes in the perturbative regime.

In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the initial curve, we establish the long-time existence of the flow and prove that, as $t \to +\infty$, the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of $\mathrm{SL}(2)$.

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a general family of (inexact) SQP-type methods can benefit from AA and introduce a simple heuristic to alleviate slower convergence farther from the solution. The method is implemented in the software framework acados. Numerical examples from optimal control illustrate consistent improvements in convergence of different SQP-type methods.

Quantum coherence is a fundamental issue in quantum mechanics and quantum information processing. We explore the coherence dynamics of the evolved states in HHL quantum algorithm for solving the linear system of equation $A\overrightarrow{x}=\overrightarrow{b}$. By using the Tsallis relative $α$ entropy of coherence and the $l_{1,p}$ norm of coherence, we show that the operator coherence of the phase estimation $P$ relies on the coefficients $β_{i}$ obtained by decomposing $|b\rangle$ in the eigenbasis of $A$. We prove that the operator coherence of the inverse phase estimation $\widetilde{P}$ relies on the coefficients $β_{i}$, eigenvalues of $A$ and the success probability $P_{s}$, and it decreases with the increase of the probability when $α\in(1,2]$. Moreover, the variations of coherence deplete with the increase of the success probability and rely on the eigenvalues of $A$ as well as the success probability.

In the 4FGL-DR4 point-source catalog of the Large Area Telescope (LAT) onboard NASA's Fermi Gamma-ray Observatory (Fermi-LAT), around a third of the sources are still unidentified (unIDs). In this work, we perform a detailed study of one of them, namely 4FGL J2112.5-3043. Only gamma-ray emission has been detected from this unidentified source, with no counterpart observed at any other wavelength as of today. Together with its high detection significance, this makes 4FGL J2112.5-3043 a particularly compelling target for further investigation. The results of our spectral and spatial analyses show that the source photon spectrum is better described with a subexponential cutoff power-law spectral model, with no significant flux variability over time, and a morphology consistent with being a point-like source. We investigate and discuss the characterized emission within the context of both conventional and exotic astrophysics, namely a pulsar origin or potential dark matter (DM) annihilations in a nearby Galactic subhalo. Although our results are inconclusive and neither confirm a DM origin nor firmly establish an astrophysical nature, we find a spectral preference for the $b\bar{b}$ and $c\bar{c}$ DM annihilation channels over a pulsar origin, thus making this unID a particularly intriguing candidate for next multiwavelength observations.