We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most importantly the Bruhat decomposition of the group generated by the \(\mathtt{cx}\) gates. These circuits require a number of qubits that scale logarithmically with the permutation dimension, and are therefore employable in near-term applications. We further augment the circuits with ancilla qubits to enlarge their span, and with these we build ansatze to tackle permutation-based optimization problems such as quadratic assignment problems, and graph isomorphisms. The resulting quantum algorithm, \textsc{QuPer}, is competitive with respect to classical heuristics and we could simulate its behavior up to a problem with $256$ variables, requiring $20$ qubits.

Firms increasingly delegate decisions to learning algorithms in platform markets. Standard algorithms perform well when platform policies are stationary, but firms often face ambiguity about whether policies are stationary or adapt strategically to their behavior. When policies adapt, efficient learning under stationarity may backfire: it may reveal a firm's persistent private information, allowing the platform to personalize terms and extract information rents. We study a repeated screening problem in which an agent with a fixed private type commits ex ante to a learning algorithm, facing ambiguity about the principal's policy. We show that a broad class of standard algorithms, including all no-external-regret algorithms, can be manipulated by adaptive principals and permit asymptotic full surplus extraction. We then construct a misspecification-robust learning algorithm that treats stationarity as a testable hypothesis. It achieves the optimal payoff under stationarity at the minimax-optimal rate, while preventing dynamic rent extraction: against any adaptive principal, each type's long-run utility is at least its utility under the menu that maximizes revenue under the principal's prior.

The intergalactic medium (IGM) underwent intense heating that resulted in pressure disequilibrium in the wake of ionization fronts during cosmic reionization. The dynamical relaxation to restore pressure balance may have driven small-scale turbulence and, hence, the amplification of intergalactic magnetic fields. We investigate this possibility for the first time using a suite of $\approx 100$ pc resolution radiation-hydrodynamics simulations of IGM gas dynamics. We show that as the spatial resolution improves beyond that achieved with most prior studies, much of the IGM becomes turbulent unless it was pre-heated to $\gg 100~$K before reionization. In our most turbulent simulations, we find that the gas energy spectrum follows the expected $k^{-5/3}$ Kolmogorov scaling to the simulation's resolution, and the eddy turnover time of the turbulence is $< 1$ Gyr at $k \approx 1 ~$kpc$^{-1}$. Turbulence will grow magnetic fields, and we show that the fields grown by reionization-driven turbulence could explain lower limits on the strength of volume-filling B-fields from observations of TeV blazars. As reionization sweeps over the cosmos, this mechanism could create turbulence throughout the cosmic volume with a character that only depends on the amount of IGM preheating.

Avoided crossings are fundamental phenomena in quantum mechanics and photonics that originate from the interaction between coupled energy levels and have been extensively studied in linear dispersive dynamics. Their manifestation in open, driven-dissipative systems, however, where nonlinear dynamics of quantum fluctuations come into play, remains largely unexplored. In this work, we analyze the hitherto unexplored occurrence of avoided and genuine crossings in the spectrum of quantum noise. We demonstrate that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the associated singular vectors and suggesting the presence of genuine crossings (diabolical points) in nearby systems. We show that these spectral features can be deliberately designed, highlighting the possibility of programming the quantum noise response of photonic systems. As a notable example, such control can be exploited to generate broad, flat-band squeezing spectra - a desirable feature for enhancing degaussification protocols. Our analysis is based on a detailed study of the Analytic Bloch-Messiah Decomposition (ABMD), which we use to characterize the parameter-dependent behavior of singular values and their corresponding vectors. This study provides new insights into the structure of multimode quantum correlations and offers a theoretical framework for the experimental exploitation of complex quantum optical systems.

We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria for homological dimensions. Under such finiteness conditions, our main result is a new duality for certain Ext modules when tensored by canonical modules.

We present late-time optical and infrared (IR) observations of a sample of nine extragalactic luminous red novae (LRNe) discovered in the past three decades. In all of these cases, the LRN survivors fade below the pre-outburst luminosity of the progenitors in the optical region. However, they remain visible in the near-IR (NIR) and bright in the mid-IR (MIR) domains for years. We recover AT 1997bs in Spitzer images from 2004, and a residual source is visible in HST and JWST NIR images 27 years after the outburst. The spectral energy distribution (SED) of AT 1997bs is consistent with that of an orange giant star with a photospheric temperature of 3750-4250 K and a radius of 120-150 $R_{\odot}$, without a significant circumstellar dust attenuation. Similarly, the SED of AT 2019zhd after three years is compatible with a red supergiant star with $T_{ph}=3100\pm100$ K and $R=350\pm50$ $R_{\odot}$. Another LRN, AT 2011kp, is detected by JWST 12.5 years after the outburst. Its SED, with two excesses at 1.8 and 7.7 $μ$m, can be explained by a cold ($T\sim450$ K) dusty shell composed of amorphous carbon surrounding a cold expanded source, plus emission from the Pa$α$ line. We constructed the [3.6]-[4.5] colour curves extending up to more than 7 years for six LRNe, which show a similar evolution: The MIR colour is $\sim-0.5$ mag before the optical maximum light, it becomes bluer after around one year, and then it gradually turns to redder colours before reaching $\sim+1.0$ mag after 7 years. We also estimated the masses and the temperatures of newly formed dust years after the LRN onset. We find that LRNe produce dust masses of the order of (1-5)x$10^{-4}$ (and up to 2x$10^{-3}$) $M_{\odot}$ between 7 and 13 years after the outbursts. Finally, we find that the remnants of LRNe detected years or decades after the merger are expanded and cool objects, similar to red supergiant stars.

Large sinusoidal variations in the radio light curves of the blazars PKS J0805$-$0111 and PKS 2131$-$021 have recently been discovered with an 18-year monitoring programme at the Owens Valley Radio Observatory, making these systems strong supermassive black hole binary (SMBHB) candidates. The sinusoidal variations in PKS 2131$-$021 dominate its light curves from 2.7 GHz to optical frequencies. We report sinusoidal variations observed in both objects with the Atacama Cosmology Telescope (ACT) at 95, 147 and 225 GHz consistent with the radio light curves. The ACT 95 GHz light curve of PKS 2131$-$021 agrees well with the contemporaneous 91.5 GHz ALMA light curve and is comparable in quality, while the ACT light curves of PKS J0805$-$0111, for which there are no ALMA or other millimetre light curves, show that PKS 2131$-$021 is not an isolated case, and that this class of AGN exhibits the following properties: (a) the sinusoidal pattern dominates over a broad range of frequencies; (b) the amplitude of the sine wave compared to its mean value is monochromatic (i.e., nearly constant across frequencies); (c) the phase of the sinusoid phase changes monotonically as a function of frequency; (d) the sinusoidal variations are intermittent. We describe a physical model for SMBHB systems, the modified Kinetic Orbital model, that explains all four of these phenomena. Monitoring of ${\sim}8000$ blazars by the Simons Observatory over the next decade should provide a large number of SMBHB candidates that will shed light on the nature of the nanohertz gravitational-wave background.

We examine the ideal $I=(x_1^2, \dots, x_n^2, (x_1+\dots+x_n)^2)$ in the polynomial ring $Q=k[x_1, \dots, x_n]$, where $k$ is a field of characteristic zero or greater than $n$. We also study the Gorenstein ideal $G$ linked to $I$ via the complete intersection ideal $(x_1^2, \dots, x_n^2)$. We compute the Betti numbers of $I$ and $G$ over $Q$ when $n$ is odd and extend known computations when $n$ is even. A consequence is that the socle of $Q/I$ is generated in a single degree (thus $Q/I$ is level) and its dimension is a Catalan number. We also describe the generators and the initial ideal with respect to reverse lexicographic order for the Gorenstein ideal $G$.

The correlations of certain entangled states can be perfectly simulated classically via a local model. Hence such states are termed Bell local, as they cannot lead to Bell inequality violation. Here, we show that Bell nonlocality can nevertheless be activated for certain Bell-local states via a catalytic process. Specifically, we present a protocol where a Bell-local state, combined with a catalyst, is transformed into a Bell-nonlocal state while the catalyst is returned exactly in its initial state. Importantly, this transformation is deterministic and based only on local operations. Moreover, this procedure is possible even when the state of the catalyst is itself Bell local, demonstrating a new form of superactivation of Bell nonlocality, as well as an interesting form of quantum catalysis. On the technical level, our main tool is a formal connection between catalytic activation and many-copy activation.

The evolution of galaxies is known to be connected to their position within the large-scale structure and their local environmental density. We investigate the relative importance of these using the underlying dark matter density field extracted from the Constrained Simulations in BORG (CSiBORG) suite of constrained cosmological simulations. We define cosmic web environment through both dark matter densities averaged on a scale up to 16 Mpc/h, and through cosmic web location identified by applying DisPerSE to the CSiBORG haloes. We correlate these environmental measures with the properties of observed galaxies in large surveys using optical data (from the NASA-Sloan Atlas) and 21-cm radio data (from ALFALFA). We find statistically significant correlations between environment and colour, neutral hydrogen gas (HI) mass fraction, star formation rate and Sérsic index. Together, these correlations suggest that bluer, star forming, HI rich, and disk-type galaxies tend to reside in lower density areas, further from filaments, while redder, more elliptical galaxies with lower star formation rates tend to be found in higher density areas, closer to filaments. We find analogous trends with the quenching of galaxies, but notably find that the quenching of low mass galaxies has a greater dependence on environment than the quenching of high mass galaxies. We find that the relationship between galaxy properties and the environmental density is stronger than that with distance to filament, suggesting that environmental density has a greater impact on the properties of galaxies than their location within the larger-scale cosmic web.

Consider the underdamped Langevin process $(q(t),p(t))_{t\geq0}$ in $\R^d\times\R^d$. We derive the low-temperature asymptotic of its mean-transition time between basins of attraction for a double-well potential. This asymptotic is called Eyring-Kramers law and often relies in the literature on Potential theory tools which are ill-defined for hypoelliptic processes like the underdamped Langevin process. In this work, we implement a novel approach which circumvents the use of these traditional methods.

This study explores the thermodynamic and geometric properties of phantom BTZ black holes within a noncommutative spacetime framework, where noncommutativity is implemented through Lorentzian smearing of mass and charge distributions. The resulting metric exhibits significant modifications in curvature and horizon structure, particularly in the near-horizon regime. We perform a comparative thermodynamic analysis between phantom and Maxwell field cases, calculating quantities such as Hawking temperature, entropy, heat capacity, and Gibbs free energy. Our findings reveal that noncommutative corrections strongly affect phase transitions and stability conditions. Furthermore, we model the black hole as a heat engine and compute its efficiency, showing how noncommutative effects enhance or suppress energy extraction. This work underscores the interplay between spacetime fuzziness and exotic field dynamics in lower-dimensional gravity, offering new insights into quantum-modified black hole thermodynamics.

Context: Despite more than half a century of research, the dominant radiation mechanism of gamma-ray burst (GRB) prompt emission remains unsolved. Some progress has been made through the analyses of the observational spectra of Swift/BAT, Konus/Wind, and Fermi/GBM, as well as the spectra of the photosphere or synchrotron models, but it is still insufficient to pin down the answer. Aims: Combining the spectral and polarization observations, we seek new criteria for model evaluation. Methods: We thoughtfully investigate the polarization samples of POLAR and AstroSAT, combining the light curve, the spectral and the polarization parameters. Results: The power-law shape of the X-ray afterglows, the $T_{90} \propto (L_{\text{iso}})^{-0.5}$ correlation, and the hard low-energy spectral index $α$ are revealed, thus supporting the photosphere origin. Furthermore, we discover the positive correlation of the $α$ and the polarization degree (PD), which can be consistently explained by the photosphere polarization scenario involving the jet asymmetry from a moderate viewing angle of $θ_{v}$=0.015.

We propose a predator-prey model with an age-structured predator population that exhibits a functional role reversal. The structure of the predator population in our model embodies the ecological concept of an "ontogenetic niche shift," in which a species' functional role changes as it grows. This structure adds complexity to our model but increases its biological relevance. The time evolution of the age-structured predator population is motivated by the Kermack-McKendrick Renewal Equation (KMRE). Unlike KMRE, the predator population's birth and death rate functions depend on the prey population's size. We establish the existence, uniqueness, and positivity of the solutions to the proposed model's initial value problem. The dynamical properties of the proposed model are investigated via Latin Hypercube Sampling in the 15-dimensional space of its parameters. Our Linear Discriminant Analysis suggests that the most influential parameters are the maturation age of the predator and the rate of consumption of juvenile predators by the prey. We carry out a detailed study of the long-term behavior of the proposed model as a function of these two parameters. In addition, we reduce the proposed age-structured model to ordinary and delayed differential equation (ODE and DDE) models. The comparison of the long-term behavior of the ODE, DDE, and the age-structured models with matching parameter settings shows that the age structure promotes the instability of the Coexistence Equilibrium and the emergence of the Coexistence Periodic Attractor.

We describe the general shift orbifold of a Narain CFT and use this to investigate decompactification limits in the heterotic Narain moduli space. We also comment on higher rank theories and describe some applications to the CFT based on the Leech lattice and its shift orbifolds.

The Sachdev--Ye--Kitaev (SYK) model is a prominent model of strongly interacting fermions that serves as a toy model of quantum gravity and black hole physics. In this work, we study the Trotter error and gate complexity of the quantum simulation of the SYK model using Lie--Trotter--Suzuki formulas. Building on recent results by Chen and Brandão (arXiv:2111.05324), we derive bounds on the first- and higher-order Trotter error of the SYK model, and subsequently find near-optimal gate complexities for simulating these models. For the $k$-local SYK model on $n$ Majorana fermions, at time $t$, our gate complexity estimates for the first-order Lie--Trotter--Suzuki formula scales with $\tilde{\mathcal{O}}(n^{k+\frac{5}{2}}t^2)$ for even $k$ and $\tilde{\mathcal{O}}(n^{k+3}t^2)$ for odd $k$, and the gate complexity of simulations using higher-order formulas scales with $\tilde{\mathcal{O}}(n^{k+\frac{1}{2}}t)$ for even $k$ and $\tilde{\mathcal{O}}(n^{k+1}t)$ for odd $k$. Given that the SYK model has $Θ(n^k)$ terms, these estimates are close to optimal. These gate complexities can be further improved upon in the context of simulating the time evolution of an arbitrary fixed input state $|ψ\rangle$, leading to a $\mathcal{O}(n^2)$-reduction in gate complexity for first-order and $\mathcal{O}(\sqrt{n})$-reduction for higher-order formulas. Regarding the sparse SYK model, which is a simplified variant of the SYK model obtained by deleting all but a $Θ(n)$ fraction of the terms in a uniformly i.i.d. manner, our average gate complexity estimates for higher-order formulas scale as $\tilde{\mathcal{O}}(n^{1+\frac{1}{2}} t)$ for even $k$ and $\tilde{\mathcal{O}}(n^{2} t)$ for odd $k$. Similar to the full SYK model, we obtain a $\mathcal{O}(\sqrt{n})$-reduction simulating the time evolution of an arbitrary fixed input state $|ψ\rangle$.

We investigate the time evolution of relative elemental abundances in the context of the first ionization potential effect focusing on an active region. Our aim is to characterize this evolution in different types of solar active region structures as well as in different atmospheric layers. We wish to assert how the measured changes relate to different magnetic topologies by computing abundance enhancement in different conditions using the ponderomotive force model. Leveraging spectroscopic observations from the Spectral Imaging of the Coronal Environment instrument on board Solar Orbiter, we use extreme ultraviolet lines from ions formed across a broad temperature range--from the upper chromosphere to the low corona--and we perform relative abundance ratios following differential emission measure analysis. This methodology yields relative abundance maps from low, intermediate, and high first ionization potential elements. We obtain the temporal evolution of a number of abundance ratios for different structures on the Sun. We compare these results with the outcomes of the ponderomotive force model. We find good correlation between the model and our results, suggesting an Alfvén-wave driven fractionation of the plasma. Fan loops, loop footpoints and active region boundaries exhibit coronal abundances, while the active region core shows more photospheric-like composition. A slow and steady increase in the magnesium to neon relative first ionization potential bias values is observed, starting around 1.5 and increasing by about 50\% after two days. The sulfur to oxygen evolution coupled with the model brings evidence of resonant waves fractionating the plasma in transition region structures.

We review the main achievements regarding the interactions between gem theory (which makes use of edge-colored graphs to represent PL-manifolds of arbitrary dimension) and both the classical representation of PL 4-manifolds via Kirby diagrams and the more recent one via trisections. Original results also appear (in particular, about gems representing closed 4-manifolds which need 3-handles in their handle decomposition, as well as about trisection diagrams), together with open problems and further possible applications to the study of compact PL 4-manifolds.

This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode non-parallelizability. The reduction leads to algorithms for circuit optimization by adopting any vertex coloring solver as an optimization backend. The approach is validated by numerical experiments as well as applications to known quantum circuits, including finite field multiplication and QFT-based addition.

We lay some mathematically rigorous foundations for the resolution of differential equations with respect to semi-classical bases and topologies, namely Freud-Sobolev polynomials and spaces. In this quest, we uncover an elegant theory melding various topics in Numerical and Functional Analysis: Poincaré inequalities, Sobolev orthogonal polynomials, Painlevé equations and more. Brought together, these ingredients allow us to quantify the compactness of Sobolev embeddings on Freud-weighted spaces and finally resolve some differential equations in this topology. As an application, we rigorously and tightly enclose solutions of the Gross-Pitaevskii equation with sextic potential.

We propose two medium-baseline, kiloton-scale neutrino experiments to study neutrinos from LHC proton-proton collisions: SINE, a surface-based scintillator panel detector observing muon neutrinos from the CMS interaction point, and UNDINE, a water Cherenkov detector submerged in lake Geneva observing all-flavor neutrinos from LHCb. Using a Monte Carlo simulation, we estimate millions of neutrino interactions during the high-luminosity LHC era. We show that these datasets can constrain neutrino cross sections, charm production in $pp$ collisions, and strangeness enhancement as a solution to the cosmic-ray muon puzzle. SINE and UNDINE thus offer a cost-effective medium-baseline complement to the proposed short-baseline forward physics facility.

We report the X-ray spectral and timing analysis of the high mass X-ray binary EXO 2030+375 during the 2021 type-II outburst based on the Insight-HXMT observations. Pulsations can be detected in the energy band of 1-150 keV. The pulse profile shows energy and luminosity dependence and variability. We observed transitions in the pulse profile shape during the rising and the decaying phase of the outburst. The pulse fraction exhibits an anti-correlation with luminosity and a non-monotonic energy dependence, with a possible dip near 30 keV during the outburst peak. The hardness-intensity diagrams (7-10 keV/4-7 keV) suggest state transitions during the early and late phases of the outburst. These transitions are consistent with the luminosity at which the pulse profile shape changes occur, revealing the source reaching the critical luminosity and transitioning between super-critical and sub-critical accretion regimes. We performed the average and phase-resolved spectral analysis, where the flux-resolved average spectra show a stable spectral evolution with luminosity. The phase-resolved spectral analysis reveals that the dependence of spectral parameters on the pulse phase varies with different luminosities.

We present the Metadetection weak lensing galaxy shape catalogue from the six-year Dark Energy Survey (DES Y6) imaging data. This dataset is the final release from DES, spanning 4422 deg$^2$ of the southern sky. We describe how the catalogue was constructed, including the two new major processing steps, cell-based image coaddition and shear measurements with Metadetection. The DES Y6 Metadetection weak lensing shape catalogue consists of 151,922,791 galaxies detected over riz bands, with an effective number density of $n_{\rm eff}$ =8.22 galaxies per arcmin$^2$ and shape noise of $σ_e$ = 0.29. We carry out a suite of validation tests on the catalogue, including testing for PSF leakage, testing for the impact of PSF modeling errors, and testing the correlation of the shear measurements with galaxy, PSF, and survey properties. In addition to demonstrating that our catalogue is robust for weak lensing science, we use the DES Y6 image simulation suite (Mau, Becker et al. 2025) to estimate the overall multiplicative shear bias of our shear measurement pipeline. We find no detectable multiplicative bias at the roughly half-percent level, with m = (3.4 $\pm$ 6.1) x $10^{-3}$, at 3$σ$ uncertainty. This is the first time both cell-based coaddition and Metadetection algorithms are applied to observational data, paving the way to the Stage-IV weak lensing surveys.

We explore models where single new exotic states interact with the Standard Model through an asymmetric Standard Model portal with couplings to at least one quark and one lepton. All effective operators up to dimension six where such interactions couple the SM to spin 0 and spin 1/2 particles are written down, and the exotic states accessible through the portal are identified. We note interactions that couple the SM to new particles with exotic combinations of baryon and lepton numbers, states of higher electric charge, and particles with unusual SM charge, including states in higher-dimensional representations of both SU(3) and SU(2). Finally, we discuss the phenomenology of these interactions, including novel particle decays, and we classify some of the collider production modes for exotic states at the LHC, LHeC and muon colliders.

The initial mass function (IMF) of stars and the corresponding cloud mass function (CMF), traditionally considered universal, exhibit variations that are influenced by the local environment. Notably, these variations are apparent in the distribution's tail, indicating a possible relationship between local dynamics and mass distribution. Our study is designed to examine how the gas PDF , the IMF and the CMF depend on the local turbulence within the interstellar medium (ISM). We run hydrodynamical simulations on small star-forming sections of the ISM under varying turbulence conditions, characterized by Mach numbers of 1, 3.5, and 10, and with two distinct mean densities. This approach allowed us to observe the effects of different turbulence levels on the formation of stellar and cloud masses. The study demonstrates a clear correlation between the dynamics of the cloud and the IMF. In environments with lower levels of turbulence likely dominated by gravitational collapse, our simulations showed the formation of more massive structures with a powerlaw gas PDF, leading to a top-heavy IMF and CMF. On the other hand environment dominated by turbulence result in a lognormal PDF and a Salpeter-like CMF and IMF. This indicates that the turbulence level is a critical factor in determining the mass distribution within star-forming regions.

We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.

We study the statistical properties of the anisotropy in the gravitational wave (GW) background originating from supermassive black hole (SMBH) binaries. We derive the distribution of the GW anisotropy power spectrum coefficients, $C_{l\geq1}/C_0$, in scenarios including environmental effects and eccentricities of the SMBH binaries. Although the mean of $C_{l\geq1}/C_0$ is the same for all multipoles, we show that their distributions vary, with the low $l$ distributions being the widest. We also find a strong correlation between spectral fluctuations and the anisotropy in the GW signal. We show that the GW anisotropy can break the degeneracy between the scenarios including environmental effects or eccentricity. In particular, we find that existing NANOGrav constraints on GW anisotropy begin to constrain SMBH scenarios with strong environmental effects.

In this paper, we introduce a new technique to study the distribution in residue classes of sets of integers with digit and sum-of-digits restrictions. From our main theorem, we derive a necessary and sufficient condition for integers with missing digits to be uniformly distributed in arithmetic progressions, extending previous results going back to the work of Erdős, Mauduit and Sárközy. Our approach utilizes Markov chains and does not rely on Fourier analysis as many results of this nature do. Our results apply more generally to the class of multiplicatively invariant sets of integers. This class, defined by Glasscock, Moreira and Richter using symbolic dynamics, is an integer analogue to fractal sets and includes all missing digits sets. We address uniform distribution in this setting, partially answering an open question posed by the same authors.

Galaxy mergers are a key driver of galaxy formation and evolution, including the triggering of AGN and star formation to a still unknown degree. We thus investigate the impact of galaxy mergers on star formation and AGN activity using a sample of 3,330 galaxies at $z = [4.5, 8.5]$ from eight JWST fields (CEERS, JADES GOODS-S, NEP-TDF, NGDEEP, GLASS, El-Gordo, SMACS-0723, and MACS-0416), collectively covering an unmasked area of 189 arcmin$^2$. We focuses on star formation rate (SFR) enhancement, AGN fraction, and AGN excess in major merger ($μ> 1/4$) close-pair samples, defined by $Δz < 0.3$ and projected separations $r_p < 100$ kpc, compared to non-merger samples. We find that SFR enhancement occurs only at $r_p < 20$ kpc, with values of $0.25 \pm 0.10$ dex and $0.26 \pm 0.11$ dex above the non-merger medians for $z = [4.5, 6.5]$ and $z = [6.5, 8.5]$. No other statistically significant enhancements in galaxy sSFR or stellar mass are observed at any projected separation or redshift bin. We also compare our observational results with predictions from the SC-SAM simulation and find no evidence of star formation enhancement in the simulations at any separation range. Finally, we examine the AGN fraction and AGN excess, finding that the fraction of AGNs in AGN-galaxy pairs, relative to the total AGN population, is $3.25^{+1.50}_{-1.06}$ times greater than the fraction of galaxy pairs relative to the overall galaxy population at the same redshift. We find that nearly all AGNs have a companion within 100 kpc and observe an excess AGN fraction in close-pair samples compared to non-merger samples. This excess is found to be $1.26 \pm 0.06$ and $1.34 \pm 0.06$ for AGNs identified via the inferred BPT diagram and photometric SED selection, respectively.

Understanding the emergence of cooperation in social networks has advanced through pairwise interactions, but the corresponding theory for group-based public goods games (PGGs) remains less explored. Here, we provide theoretical conditions under which cooperation thrives in PGGs on arbitrary population structures, which are accurate under weak selection. We find that a class of networks that would otherwise fail to produce cooperation, such as star graphs, are particularly conducive to cooperation in PGGs. More generally, PGGs can support cooperation on almost all networks, which is robust across all kinds of model details. This fundamental advantage of PGGs derives from self-reciprocity realized by group separations and from clustering through second-order interactions. We also apply PGGs to empirical networks, which shows that PGGs could be a promising interaction mode for the emergence of cooperation in real-world systems.