Advances in nanotechnology now allow the creation of artificial atoms - engineered structures whose electronic states closely mimic those of real atoms. Understanding how these artificial atoms interact and bond is key to designing new materials with tailored electronic properties. Here, we use scanning tunnelling microscopy to visualise the bound states of nanostructures patterned in a two-dimensional molecular film featuring a parabolic band with multiple partial energy gaps. The lowest-energy states split off from the bottom of the band and resemble the familiar $s$ and $p$ orbitals of natural atoms, even bonding in the same way. Yet, artificial atoms go beyond this analogy: the gapped two-dimensional vacuum in which they reside gives rise to entirely new orbitals with no counterparts in real atoms. These quasi-one-dimensional localised states enrich the orbital vocabulary of chemistry, adding a new class of orbitals that are predominantly shaped by the surrounding electronic vacuum.

To meet the urgent demands for spectral efficiency and multi-user access in high-frequency application scenario for the sixth-generation wireless communication, this paper investigates a rate splitting multiple access (RSMA) system assisted by pinching antennas (PAs) with multiple waveguides and multiple carriers, aiming to maximize the overall system sum rate. To address the high sensitivity of high-frequency signals to PA movement in the overloaded scenarios, a two-stage PA position optimization method based on both path loss and phase shift error minimization is proposed under RSMA framework. Specifically, the first step is to perform coarse adjustment by minimizing large-scale path loss. Then, based on the derivation of a closed-form solution for the ideal phase shift in a single-user single-carrier case, the fine-grained positions of PAs are optimized via a one-dimensional line search to minimize the composite phase shift error across all users and carriers. In order to meet the quality of service requirements, the Lagrange dual method is employed to obtain the closed form of beamforming vectors after the PA positions are determined. Simulation results demonstrate that the proposed scheme achieves significant improvement in sum rate and confirm that RSMA exhibits stronger robustness to inaccurate PA positions caused by both discrete position channel estimation and physical hardware compared to other multiple-access techniques in PA-assisted systems. Furthermore, the results validate that fine-grained PA position adjustment is particularly crucial in high-frequency bands.

Indirect long range interactions between localized magnetic moments are in metals mediated by itinerant electrons. In insulators and semi-conductor, such interactions need to be small, if not negligible, due to the absence of mediating carriers. The existence of magnetically ordered insulators, for instance, metal-oxides, is therefore an everlasting source for proposals of various mechanisms that may support the order. Here, phonon mediated interactions between localized magnetic moments is considered as a mechanism that can provide quantifiable symmetric and anti-symmetric anisotropic spin-spin interactions. It is demonstrated that while a symmetric anisotropic interaction exists for all types of phonons, the existence of anti-symmetric anisotropic interactions requires broken inversion symmetry. The latter mechanism may explain the weak ferromagnetic order observed in chiral, e.g., CuO and CoO compounds. Furthermore, the interaction is nearly independent of the temperature at low temperature while approaches a linear growth at high. Spatially, the interactions have an oscillatory power law decay with the inter-nuclei distance.

A novel approach for measuring the electrical resistivity of non-magnetic materials using magnetic force microscopy (MFM) is discussed. In this method, MFM detects magnetic fields generated by eddy currents induced by the oscillation of a magnetized probe tip. To enhance measurement sensitivity, it is essential to increase the magnitude of these eddy currents. It is discussed that introducing controlled sample vibration amplifies eddy current generation by increasing the relative velocity between the probe tip and the sample surface. Theoretical analysis predicts increase of the phase shift by sample vibration, and experimental validation using a modified MFM system confirms the improvement in sensitivity. The calculated and experimental results exhibit relatively good agreement, establishing that sample vibration excitation is an effective strategy for high-sensitivity resistivity measurements.

Arbitrary Detuning ASynchronous OPtical Sampling (ADA-SOPS) is an emerging technique for extending standard pump--probe experiments performed with two femtosecond lasers to multitimescale experiments, which are of great interest for the study of complex systems. Although no specific requirements are needed for laser repetition rates, their ratio determines the achievable delay distribution and therefore is strongly related to the temporal resolution of the technique. We report a detailed theoretical analysis of measurement performances with respect to laser repetition rates, and we validate our model with experimental data. In the case of amplified laser systems, we demonstrate that achieved delays are inherently correlated to the time interval between amplified pulses, which affects the pulse energy and can generate artifacts. Nevertheless, a deep understanding of the origin of such artifacts allows to suggest several compensation strategies, either during data analysis or at the conception of the experimental setup. Finally we present a new algorithm integrated into the ADASOPS device: by selecting pairs of probe pulses having the same elapsed time with respect to the previous pulse, it automatically compensates any effect of energy fluctuation.

The Casimir-Polder (CP) effect -- the force between a neutral atom and an uncharged conducting plate in empty space -- is an intriguing consequence of quantum vacuum fluctuations. The typically attractive CP potential crosses over from a scaling of $z^{-3}$ at short separations to $z^{-4}$ at long distances, where retardation effects due to the finite speed of light become important. At intermediate distances, where the atom--surface separation is of the order of the wavelength of the dominant atomic transition, experiments have so far relied on indirect methods, such as diffraction or quantum reflection, to observe the CP effect. Here, we directly reveal the CP force between strontium atoms and a dielectric surface via the induced shifts in the atomic energy levels in the intermediate regime. We spectroscopically probe the CP-induced kHz-frequency shift of ultracold atoms confined by a magic-wavelength optical lattice at 189(2)~nm from the surface -- on the scale of the dominant 461-nm transition. Our measurements agree well with QED calculations and differ from the short-range approximation, while excluding the long-distance one. This paves the way for studying the CP effect across various surface properties and geometries, as well as exploring the tensor nature of the atom-surface potential -- all important for the development of hybrid atomic optical-magnetic quantum devices.

BESIII has accumulated 4.5 fb$^{-1}$ of $e^+e^-$ collision data in the 4.6 to 4.7 GeV energy range, corresponding to the world's largest sample of $Λ_c^+\barΛ_c^-$ pairs. This paper summarizes recent BESIII results on charmed-baryon decays, including the observation of the rare semi-leptonic decay $Λ_c^+\to ne^+ν_e$ using a Graph Neural Network, the first measurement of the decay asymmetry in the pure $W$-exchange decay $Λ_c^+\toΞ^0K^+$, and branching fraction measurements of the inclusive decays $Λ_c^+\to Xe^+ν_e$ and $\barΛ_c^-\to \bar{n}X$. We also report partial wave analyses of $Λ_c^+\toΛπ^+π^0$ and $Λ_c^+\toΛπ^+η$, measurements of Cabibbo-suppressed decays such as $Λ_c^+\to pπ^0$, and studies of $K_S^0-K_L^0$ asymmetries in $Λ_c^+$ decays.

On generalized Heisenberg-type groups $\mathbb{G}(2n,m,\mathbb{U},\mathbb{W})$, we give uniform volume estimates for the ball defined by a large class of Carnot-Carathéodory distances, and establish weak (1, 1) $O(C^m \, n)$-estimates for associated centered Hardy-Littlewood maximal functions, extending the results in \cite{BLZ25}. As a by-product, we establish uniformly volume doubling property on Heisenberg groups for a class of left-invariant Riemannian metrics.

In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike robustness, which evaluates how well a system satisfies a specification under a given disturbance, resilience measures the maximum disturbance a system can tolerate from a given initial state while maintaining specification satisfaction. We first derive bounds on the perturbed trajectories and then use them to formulate a computational method based on scenario optimization to efficiently compute the maximum admissible disturbance. We validate our approach through case studies, including dc motor, temperature regulation, a nonlinear numerical example, and a vehicle collision avoidance case.

The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal covariance and interference-plus-noise covariance (INC) matrices, considering a general-rank signal model. First, the corresponding minimax SINR problem is reformulated as a convex optimization problem. In particular, this problem becomes a semidefinite programming (SDP) problem when the uncertainty sets can be represented by finitely many linear matrix inequality constraints. It is then shown that, for a general-rank signal model, the maximin and minimax SINR problems are equivalent when the uncertainty sets are convex and closed, in the sense that they share the same optimal value and the same set of optimal solutions. The requirement of closedness is weaker than the compactness assumption previously used to establish the equivalence between minimax and maximin SINR problems for the rank-one signal model, a state-of-the-art result reported approximately two decades ago. Consequently, an optimal solution to the minimax SINR problem is also globally optimal for the maximin SINR problem, and this solution can be obtained by solving the equivalent SDP of the minimax problem in a single step. In contrast, existing iterative approximation algorithms for the maximin SINR problem yield only locally optimal solutions. Simulation results demonstrate that these approximation algorithms return suboptimal values that can be strictly smaller than the optimal value of the minimax problem, and that the beamformer output SINR obtained via the minimax formulation is higher than that achieved by beamformers derived from the maximin problem using approximation algorithms.

We study global transonic solution for a relativistic, magnetized, viscous advective accretion flow around a rotating black hole, incorporating the effects of mass and angular momentum loss through winds. Our model considers dominant toroidal magnetic fields with synchrotron radiation as the primary cooling mechanism. To self-consistently model mass loss, the mass accretion rate is prescribed to decrease inward as a power-law with disk radius. With this, we solve the governing equations that describe the accretion flows in presence of winds and obtain the flow structure in terms of the inflow parameters (energy $\mathcal{E}$, angular momentum $λ$, plasma-$β$, accretion rate $\dot{m}$, and viscosity $α_{\rm B}$), the wind parameters ($p$, governing mass loss; and $l$, governing angular momentum transport by winds), and the black hole spin ($a_{\rm k}$). Our analysis reveals that winds substantially modify the accretion flow leading to a significant decrease in disk luminosity. We specifically identify global solutions that admit standing shocks and find that winds profoundly alter shock properties, such as the shock radius ($x_{\rm s}$), compression ratio ($R$), and shock strength ($S$). Furthermore, we determine the critical wind parameter $p^{\rm crit}$ beyond which steady shock solutions cease to exist. We demonstrate that increased viscosity and strong angular momentum extraction by winds lead to reduce $p^{\rm crit}$. These findings evidently highlight a complex interplay between viscosity and winds in governing the dynamics of shock formation in accretion disks.

We prove existence, uniqueness and structure results for complete noncompact 7-dimensional G2-holonomy metrics with ALC (asymptotically locally conical) asymptotics. We regard such spaces as G2-analogues of ALF gravitational instantons in 4-dimensional hyperkähler geometry. Our main results include the existence of a G2-analogue of the Atiyah-Hitchin metric in 4-dimensional hyperkähler geometry, the existence of a good moduli theory for ALC G2-holonomy metrics and rigidity results for ALC G2-metrics in terms of the symmetries of their asymptotic model. The analytic toolkit needed to prove all these results is a robust Fredholm theory for the natural geometric linear elliptic operators on ALC spaces. We provide a self-contained derivation of this Fredholm theory for arbitrary Riemannian manifolds with ALC asymptotics. Since our ALC Fredholm theory does not rely on imposing any holonomy reduction or curvature conditions it may also be of utility beyond the setting of ALC special holonomy metrics. As one such application of our general Fredholm theory we prove some Hodge-theoretic results on general ALC spaces.

Topology optimization is a computational method used to determine the optimal material distribution within a prescribed design domain, aiming to minimize structural weight while satisfying load and boundary conditions. For critical infrastructure applications, such as structural health monitoring of bridges and buildings, particularly in digital twin contexts, low-latency energy-efficient topology optimization is essential. Traditionally, topology optimization relies on finite element analysis (FEA), a computationally intensive process. Recent advances in deep neural networks (DNNs) have introduced data driven alternatives to FEA, substantially reducing computation time while maintaining solution quality. These DNNs have complex architectures and implementing them on inference-class GPUs results in high latency and poor energy efficiency. To address this challenge, we present a hardware accelerated implementation of a topology optimization neural network (CRONet) on the AMD Versal AI Engine-ML (AIE-ML) architecture. Our approach efficiently exploits the parallelism and memory hierarchy of AIE-ML engines to optimize the execution of various neural network operators. We are the first to implement an end-to-end neural network fully realized on the AIE-ML array, where all intermediate activations and network weights reside on-chip throughout inference, eliminating any reliance on DRAM for intermediate data movement. Experimental results demonstrate that our implementation achieves up to 2.49x improvement in latency and up to 4.18x improvement in energy efficiency compared to an inference-class ML-optimized GPU in the same power budget (Nvidia T4) after scaling for technology node. These results highlight the potential of Versal AIE-ML based acceleration for enabling low-latency energy-efficient topology optimization.

Using the first data release of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) All-Sky HI survey (FASHI), we compile a catalogue of 70 dark galaxy candidates (DGCs) within 50 Mpc. We select DGCs without an identified optical counterpart at a limiting g-band magnitude of ~ 28 mag arcsec^-2 in the DESI Legacy Survey, using both automatic cross-checking with optical catalogues and visual inspection of the colour images. After validating our DGCs, excluding potential spurious detections, issues in the registered position of the HI sources, and possible Radio Frequency Interferences (RFIs), we analyse their distribution over the surveyed sky, HI mass, linewidths, and inferred distance. They appear evenly distributed across the surveyed area, with no apparent bias to isolation. We did not find any DGC within the Local Volume (11 Mpc) in the sky surveyed by this first release of FASHI. We compare the observed properties of DGCs with those of galaxies with optical counterparts, finding that DGCs tend to have higher linewidths for a given HI mass. We discuss our DGCs in light of theoretical works, and compare them with other observational samples from previous HI surveys. This work presents a catalogue of dark galaxy candidates, which can serve as a basis for follow-up studies.

Ensuring the reproducibility of physics results is one of the crucial challenges in high-energy physics (HEP). In this study, we develop a proof-of-concept system that uses large language models (LLMs) to extract analysis procedures from HEP publications and generate executable analysis code for reproducing published results. Our method consists of two stages. In the first stage, open-weight LLMs extract event selection criteria, object definitions, and other relevant analysis information from a target paper and, when necessary, from its referenced publications, and then produce a structured selection list. In the second stage, the structured selection list is used to generate analysis code, which is then executed and validated iteratively. As a benchmark, we use the ATLAS $H \to ZZ^{*} \to 4\ell$ analysis based on proton-proton collision data recorded in 2015 and 2016 and released as ATLAS Open Data. This benchmark allows direct comparison between the generated results and the published analysis, as well as comparison with a manually developed baseline implementation. We separately evaluate selection extraction and code generation in order to clarify the current capabilities and limitations of open-weight LLMs for HEP analysis reproduction. Our initial results show that recent open-weight models can recover many documented selection criteria from papers and references, and that in some runs they can generate event selections fully matching a baseline implementation at the event level. At the same time, stochasticity, hallucination, and execution failure remain significant challenges. These results suggest that LLMs are already promising as human-in-the-loop tools for reproducibility support, although they are not yet reliable as fully autonomous HEP analysis agents. In this paper, we report the design of the prototype system and its initial performance evaluation.

Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems and lead to the emergence of many-body localization (MBL) is a challenging open frontier. We study the level statistics of a variant of the spin-$1/2$ Haldane-Shastry model with $1/r^α$ interactions, where $α{\geq}0$ parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this long-range interacting system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the $SU(2)$ symmetry, the strength of the position disorder, $δ$, appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter, $αδ$.

Encoding models enable measurement of how our brains represent sensory inputs using electro-and magneto-encephalography (MEEG). Evaluating how closely encoding models reflect the underlying brain functions is a crucial premise for model interpretation and hypothesis testing. However, the ground-truth neural activity is unknown, preventing model evaluation with respect to the target neural signal. Existing evaluation metrics must therefore relate model's predictions to noisy MEEG measurements, where most variance is stimulus-unrelated. Here, I introduce an evaluation framework where model predictions are compared to a ground-truth approximation, obtained by aligning MEEG signals with predictions using canonical correlation analysis and via participant averaging. The resulting metric (CPA-PA) yields single-participant evaluations outperforming conventional scores by 300-1000% on synthetic EEG data and 250% on 34 real MEEG datasets (818 datapoints). These gains reflect increased sensitivity to stimulus-relevant neural activity and reduced dependence on SNR, establishing ground-truth approximation as a robust framework for evaluating encoding models.

The 2023/24 NICER monitoring campaign of the 7 Crab bright black hole X-ray binary Swift J1727.8-1613 covered the outburst in almost all accretion states. High-quality data are available in the high-Eddington-fraction hard-intermediate state, hard-to-soft transition, the soft state, and the poorly studied back-transition to the dim hard state, making it an ideal dataset to compare the accretion flow at vastly different accretion rates. We apply disk continuum fitting techniques to investigate the evolution of the inner disk radius throughout the outburst. Taking a temperature-dependent color-correction factor into account, we see evolution of the disk inner radius by a factor of a few comparing the hard states to the thermal/soft state. We tentatively detect an onset of disk truncation in the soft-to-hard transition, right after the source leaves the soft state. After accounting for model systematics, we find the disk to be more truncated in the high-luminosity bright hard state compared to the low-luminosity dim hard state.

Communication is pivotal in LLM training, and a thorough analysis of the communication efficiency of AI data center (AIDC) network is essential for guiding the design of these capital-intensive clusters. However, conventional metrics are inadequate for such analysis, as they do not directly link network activity to computational progress and lack granularity to diagnose the impact of different network design patterns. To address this, we introduce a metric framework, the Switching Efficiency Framework, whose core metric - Switching Efficiency ($η$) - quantifies computationally effective data throughput per unit switching capacity. We further decompose $η$ into three factors - Data, Routing Efficiency, and Port Utilization to facilitate analysis of distinct communication bottlenecks. Using this metric framework, we demonstrate how the symmetric, distributed switching of 3D-Torus and the centralized, hierarchical switching of Rail-Optimized architecture align with sparse or imbalanced LLM training traffic, and show that All-to-All traffic from Mixture-of-Experts models severely degrades their port utilization and routing efficiency. Our analysis also demonstrates how key design choices - such as adjusting switching resource allocation, expanding server size, adopting in-network computing, and multi-plane design - positively influence distinct facets of communication efficiency. Ultimately, the Switching Efficiency Framework provides an analytical tool for analyzing efficiency bottlenecks, thereby informing the design of future-generation AIDC networks.

This paper explores an integrated sensing and communication (ISAC) system with backscattering RFID tags. In this setup, an access point employs communication beams to serve communication users while leveraging a sensing beam to interrogate RFID tags. Under the total transmit power constraint of the system, our objective is to design a joint sensing and communication beamforming codebook by considering the tag interrogation and communication requirements. To lay a foundation for the codebook design problem, we first study the beamforming design problem in a single-tag scenario and investigate two approaches: (i) a zero-forcing approach with optimized sensing/communication power allocation, for which a closed-form solution is derived under a dominant sensitivity condition, and (ii) a joint sensing and communication beamforming design obtained by transmit power minimization. Then, we investigate the codebook design problem in a multi-tag scenario. To resolve this, we propose a sector-based joint sensing and communication beamforming codebook that scans the region of interest. For each sector, semidefinite relaxation and generalized Benders decomposition are employed to handle the resulting optimization. The simulation results show that the proposed joint beamforming designs can effectively mitigate the mutual interference between sensing and communication functionalities, thus enhancing the interrogation range of the tags with minimized transmit power. Also, the efficacy of the proposed sector-based codebook design has been demonstrated in terms of interrogation success rate, offering a promising approach for the ISAC-backscattering systems.

Freeze-in of multi-component dark sectors is governed not only by the interaction with the thermal plasma, but also by their internal dynamics. Full thermalisation within the dark sector is not guaranteed, raising the question of impact of departures from local thermal equilibrium onto the evolution and ultimately relic abundance and momentum distribution of dark matter. In this work we explore this question in a minimal two-scalar model, which can give rise to observable signatures in indirect detection and long-lived particle searches at forward physics experiments. Focusing on the phenomenologically viable regions, we analyse the impact of non-thermal evolution on the dark matter abundance, finding deviations of up to an order of magnitude between the full phase-space treatment and the traditional number-density approach. Our results highlight the importance of phase-space level computation for accurate freeze-in predictions and further motivate dedicated numerical tools for studying the evolution of multi-component dark sectors at the phase space level.

For a given graph \( G \), let \( G^{(j)} \) denote the graph obtained by the deletion of vertex \( v_j \) from \( G \). The difference \( \mathscr{E}(G) - \mathscr{E}(G^{(j)}) \) quantifies the change in the energy of \( G \) upon the removal of \( v_j \), termed as the local energy of \( G \) at vertex $v_j$, as defined by Espinal and Rada in 2024. The local energy of $G$ at vertex $v$ is denoted by \(\mathscr{E}_G(v)\). The local energy of the graph \( G \), therefore, is the summation of these vertex-specific local energies across all vertices in \( V(G) \), expressed by \( e(G) = \sum \mathscr{E}_G(v) \). Two graphs of the same order are defined as locally equienergetic if they have identical local energy. In this paper, we have investigated several pairs of locally equienergetic graphs.

Provenance-based intrusion detection has emerged as a promising approach for analyzing complex attack behaviors through system-level provenance graphs. However, existing defense methods face an inherent granularity limitation. Node-centric detectors, which evaluate anomalies using entities' attributes and local structural patterns, may misclassify benign behavioral changes or configuration modifications as suspicious. In contrast, edge-centric detectors, which focus more on interactions, may lack sufficient contextual awareness of the involved entities, leading to missed detections when compromised entities perform seemingly ordinary operations. These analytical biases highlight a persistent gap between node-centric and edge-centric analyses. To mitigate this gap, we present PROVFUSION, a multi-view detection framework that integrates anomaly signals from three distinct views (i.e., attribute, structure, and causality). The framework fuses heterogeneous anomaly signals through lightweight fusion schemes and determines the final anomaly decisions through a voting-based integration process, providing a more consistent and context-aware assessment of system behavior. This design enables PROVFUSION to capture both entity level deviations and interaction-level anomalies within a consistent analytic pipeline. Experiments on nine widely used benchmark datasets demonstrate that PROVFUSION achieves higher detection accuracy and lower false-positive rates than single node- and edge-centric baselines, maintaining stable performance across scenarios. Overall, the results suggest that our multi-view anomaly fusion together with voting-based decision aggregation offers a practical and effective direction for advancing provenance-based intrusion detection.

Given a classical gas described by the truncated correlation functions of all orders, we prove convergence of an expansion of the pair interaction part of the (unknown) potential in terms of the truncated correlation functions of all orders, at infinite volume.

Electroforming of metal-oxide-metal memristors is generally attributed to the creation of oxygen-vacancy filaments within the oxide, with noble metal electrodes such as Pt and Au remaining chemically inert. Here, we demonstrate that electroforming and subsequent operation of Pt/NbOx/Nb2O5/Pt devices can induce an unexpected and highly correlated redistribution of both oxygen and platinum. Time-of-flight secondary ion mass spectrometry reveals a filamentary pathway characterized by micrometer-scale oxygen enrichment extending from the Nb2O5 layer through NbOx and deep into the Pt top electrode. Surprisingly, this is accompanied by the formation of a Pt-rich filament penetrating the oxide stack along the same filamentary path. Finite-element and lumped-element modelling show that current-controlled negative-differential-resistance operation produces localized Joule heating and high-frequency thermal cycling, which strongly enhances oxygen migration and enables thermally assisted Pt diffusion along vacancy-rich pathways. These findings reveal a previously unrecognized metal-ion transport mechanism in NbOx memristors and highlight the critical role of post-forming electrical dynamics in determining filament chemistry, stability, and device reliability.

Exceptional points (EPs) have attracted extensive research interest due to their intriguing properties. One of the hallmarks of EP physics is that dynamically encircling the EPs induces chiral mode switching, arising from the breakdown of adiabaticity due to the presence of a complex spectrum in the system's Hamiltonian. While such chiral mode behavior has been widely observed experimentally, achieving truly adiabatic, and thus symmetric, state transfer, regardless of the winding direction, in time-modulated non-Hermitian systems has remained elusive. In this work, we demonstrate that this long-sought adiabatic state dynamics can indeed be restored. By steering a two-mode photonic setup along specifically designed trajectories in parameter space, we realize conditions where the associated non-Hermitian evolution operator acquires a purely real spectrum. Moreover, our experimental platform enables controlled switching between symmetric (adiabatic) and chiral (non-adiabatic) state-transfer regimes for the same set of initial modes, thus effectively implementing a universal symmetric-asymmetric two-mode switch. Our results therefore open new avenues for harnessing unique topological spectral properties of non-Hermitian systems, paving the way for the practical design of versatile optical wave-manipulation devices and for advancing both classical and quantum information technologies.

In the classical online model, the maximum independent set problem admits an $Ω(n)$ lower bound on the competitive ratio even for interval graphs, motivating the study of the problem under additional assumptions. We first study the problem on graphs with a bounded independent kissing number $ζ$, defined as the size of the largest induced star in the graph minus one. We show that a simple greedy algorithm, requiring no geometric representation, achieves a competitive ratio of $ζ$. Moreover, this bound is optimal for deterministic online algorithms and asymptotically optimal for randomized ones. This extends previous results from specific geometric graph families to more general graph classes. Since this bound rules out further improvements through randomization alone, we investigate the power of randomization with access to geometric representation. When the geometric representation of the objects is known, we present randomized online algorithms with improved guarantees. For unit ball graphs in $\mathbb{R}^3$, we present an algorithm whose expected competitive ratio is strictly smaller than the deterministic lower bound implied by the independent kissing number. For $α$-fat objects and for axis-aligned hyper-rectangles in $\mathbb{R}^d$ with bounded diameters, we obtain algorithms with expected competitive ratios that depend polylogarithmically on the ratio between the maximum and minimum object diameters. In both cases, the randomized lower bound implied by the independent kissing number grows polynomially with the ratio between the maximum and minimum object diameters, implying substantial performance guarantees for our algorithms.

Ionization balance in the intergalactic medium (IGM) is central to the interpretation of quasar absorption spectra, linking observed ionic columns to the underlying gas density, temperature, metallicity, and ionizing radiation field. Because ionization, recombination, and cooling timescales can be comparable to the timescales over which the ultraviolet background (UVB) and gas thermodynamic state evolve, ion populations may retain a strong memory of their past history. To this end, we present a fast, metals-inclusive, zero-dimensional framework for modeling the redshift evolution of the IGM. The model follows the coupled thermal and ionization evolution of a Lagrangian gas parcel in a redshift-dependent UVB, solving stiff, time-dependent rate equations for H, He, and 107 metal ions while self-consistently evolving the temperature through photoheating and standard cooling processes. We validate the framework against full three-dimensional hydrodynamical non-equilibrium calculations and find that it reproduces the thermal and ionization histories of the IGM with good accuracy over a wide redshift range, including the heating associated with $\rm He_{\,\rm II}$ reionization. As an application, we predict the cosmic $\rm C_{\,\rm IV}$ density parameter, $Ω_{\rm CIV}$, and use it to infer the origin of metal ions in the IGM and the corresponding metallicities from observational measurements, obtaining values broadly consistent with literature constraints. The framework is well suited for rapid parameter studies of how reionization timing, UVB spectral hardness, self-shielding, and UVB inhomogeneity shape the thermal and ionization history of the IGM and the resulting metal-line observables.

Utilizing the Weierstrass representation for embedded doubly periodic minimal surfaces with parallel ends, we construct entire singly periodic graphs of spacelike maximal surfaces with isolated cone-like singularities in the Lorentz-Minkowski 3-space.

In the context of the hierarchical formation of galaxies, we investigated the role played by mergers in shaping the scale relations of galaxies, that is the projections of their Fundamental Plane onto the \IeRe, \IeSig, \MRa\ and \Lsig\ planes. To this aim, we developed a simple model of multiple dry mergers among galaxies by suitably combing the formalism and properties of the so-called infall models of galaxy formation and evolution with the formalism of the scalar Virial Theorem. In this context, we mimicked the hierarchical formation of galaxies and generated simple models of galaxies undergoing a number mergers in the course of their evolution. The results are used to interpret the large scale simulations and the companion scale relations from observational and theoretical perspectives. The aim is to interpret the observational data of the MANGA and WINGS samples and the results of theoretical detailed numerical cosmo-hydro-dynamical simulations, such as Illustris-TNG100. In this context, we derived the above scale relations for our theoretical models and compared them with the observational counterparts from the MANGA and WINGS database, (and indirectly the large scale simulations of Illustris-TNG100). The multiple dry merging mechanism is able to explain all the main characteristics of the observed scale relations of galaxies, such as slopes, scatters, curvatures and zones of exclusion. The distribution of galaxies in these planes is continuously changing across time because of the merging activity and other physical processes, such as star formation, quenching, energy feedback, and so forth.} The precision of the present simple merger theory is comparable with that obtained by the modern cosmo-hydro-dynamical simulations, with the advantage of providing a rapid exploratory response on the consequences engendered by different physical effects.