We show that a large class of non-abelian monoidal categories can be realized as subcategories of tilting objects in abelian monoidal categories with a highest weight structure. The construction relies on a monoidal enhancement of Brundan-Stroppel's semi-infinite Ringel duality and applies to many of Sam-Snowden's triangular categories and Knop's tensor envelopes of regular categories. We also explain how monoidal Ringel duality gives rise to monoidal structures on categories of representations of affine Lie algebras at positive levels.

This paper addresses precoder design for secure multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) systems. We introduce a MIMO channel with a multiple-antenna eavesdropper and a multiple-antenna sensing receiver (MIMO-ME-MS) and analyze the fundamental performance limits of this tripartite tradeoff. Using sensing mutual information, we formulate the precoder design as a nonconvex weighted sum rate maximization problem. A high signal-to-noise ratio analysis based on a subspace decomposition characterizes the maximum weighted degrees of freedom. This analysis reveals the structure of a quasi-optimal precoder that must span the ``useful subspace'' and demonstrates the inadequacy of extending known schemes from simpler wiretap or ISAC channels. To solve this nonconvex problem, we develop a practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program. We demonstrate that the proposed method captures the desirable precoder structure identified in our analysis and achieves substantial performance gains in the MIMO-ME-MS channel.

Quantum simulation is central to understanding and designing quantum systems across physics and chemistry. Yet it has barriers to access from both computational complexity and computational perspectives, due to the exponential growth of Hilbert space and the complexity of modern software tools. Here we introduce{\cinzel El Agente Cuántico}, a multi-agent AI system that automates quantum-simulation workflows by translating natural-language scientific intent into executed and validated computations across heterogeneous quantum-software frameworks. By reasoning directly over library documentation and APIs, our agentic system dynamically assembles end-to-end simulations spanning state preparation, closed- and open-system dynamics, tensor-network methods, quantum control, quantum error correction, and quantum resource estimation. The developed system unifies traditionally distinct simulation paradigms behind a single natural-language interface. Beyond reducing technical barriers, this approach opens a path toward scalable, adaptive, and increasingly autonomous quantum simulation, enabling faster exploration of physical models, rapid hypothesis testing, and closer integration between theory, simulation, and emerging quantum hardware.

Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.

We propose that spacetime dynamics can be organized by a Planck-scale bookkeeping rule, written using a modular-parameter normalization of size $2π$, that balances the geometric entropy increment $δA/4G$ against a reversible modular-energy flow $δ\!\langle K\rangle$ and an irreversible Landauer--Bennett cost $\ln 2\,δN_c$, where $K\equiv K_σ$ is the (dimensionless) modular Hamiltonian of the chosen region defined relative to a fixed reference state $σ$, and $N_c$ counts logically irreversible one-bit record updates (e.g. coarse-grained overwrites or registrations) on that screen. This ``information--geometry ledger'' is consistent with the Bekenstein--Hawking area law and, when enforced on small causal screens under the standard entanglement-equilibrium assumptions, recovers the full nonlinear Einstein equation. In FLRW cosmology, the same bookkeeping motivates a two-component vacuum sector $ρ_{\rm vac}=ρ_Λ+3\varepsilon H^{2}/8πG$ when a constant inefficiency parameter $\varepsilon$ is assumed.

Dense tracking environments in experiments at CERN's High-Luminosity LHC and future FCC experiments call for an increased use of timing information in addition to the position measurement of pixel detectors. This adds one dimension to the information available, and is essential for pile-up mitigation at high luminosity. The CASSIA sensor project (CMOS Active SenSor with Internal Amplification) focuses on the development of pixel matrices with internal charge multiplication based on monolithic CMOS sensor technologies suitable for application as charged particle tracking and timing detectors. CMOS sensors with in-pixel internal amplification would result in higher signal amplitudes having an improved signal-to-noise ratio, better time resolution and increased sensitivity, making them attractive for high-radiation environments. Their monolithic integration in small pixels reduces the input capacitance of a front-end amplifier and power dissipation making it suitable for fine-pitch low-power detectors. Fast signal rise time due to internal charge amplification improves the response time and timing resolution, all of which makes such a technology attractive for future 4D tracking applications in HEP experiments. This paper presents the first results of the CASSIA sensor, a novel MAPS which uses gain layers fully integrated in a 180nm imaging process to achieve internal signal amplification. In the first measurements presented here we demonstrate the gain behaviour of different pixel implant designs and show that the sensor can be operated with low gain proportional mode as LGAD sensor at lower voltages and as SPAD sensor at higher voltages.

We study the smallest area $A(M,g)$ of a 2-dimensional stationary integral varifold in a closed Einstein 4-manifold $(M^4,g)$ with $Ric_g = λg, |λ|\leq 3, Vol(M,g)\geq v>0, diam(M,g)\leq D, H_1(M;\mathbb{Z})=0.$ Building on the previous work on homological filling functions, we show that for every $(M^4,g)$ in this Einstein class, there is an upper bound $A(M,g)\leq F_{Ein}(v,D),$ where $F_{Ein}$ depends only on $(v,D)$ and on quantitative Sobolev and $\varepsilon$-regularity constants for Einstein metrics.

Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates required to realize such an advantage remain uncertain; resource estimates for ground-state electronic structure span orders of magnitude, and no quantum-native method has been validated at a commercially relevant scale. Here we address this uncertainty by executing the iterative qubit coupled-cluster (iQCC) algorithm, designed for fault-tolerant quantum hardware, at unprecedented scale using a quantum solver on classical processors, enabling simulations of transition organo-metallic complexes requiring hundreds of logical qubits and millions of entangling gates. Using this approach, we compute the lowest triplet excited state (T$_1$) energies of Ir(III) and Pt(II) phosphorescent organometallic compounds and show that iQCC achieves the lowest mean absolute error (0.05 eV) and highest R$^2$ (0.94) relative to experiment, outperforming leading classical methods. We find these systems remain classically tractable up to $\sim$200 logical qubits, establishing the threshold at which quantum advantage in computational chemistry may emerge and clarifying resource requirements for future quantum computers.

We consider Bernoulli percolation on $\mathbb Z^d$ with $d>6$. We prove an up-to-constant estimate for the critical two-point function restricted to a half-space. This completes previous results of Chatterjee and Hanson (Commun. Pure Appl. Math., 2021), and Chatterjee, Hanson, and Sosoe (Commun. Math. Phys., 2023), and solves a question asked by Hutchcroft, Michta, and Slade (Ann. Probab., 2023).

Computer-generated hologram (CGH) allows for the on-demand scaling and projection of artificially designed target patterns, while incorporating benefits such as a lensless setup and high-frame-rate operation. In this work, we actively control the projection pattern using CGH and integrate two typical single-pixel imaging (SPI) schemes, thereby implementing a ghost imaging (GI) scheme with flexibly tunable properties. Specifically, various reference signals from computational holography and the corresponding bucket signals are used in the intensity correlation algorithm. Accordingly, those GI results enable the parallel presentation of the outcomes from these two SPI schemes. In the experiment, two types of target patterns, intensity-squared chaotic speckle and artificially designed sparse matrix, are used to perform GI. Those imaging results indicate a significant improvement in ghost image visibility, irrespective of whether the reference signal is the reconstruction or target pattern of computational holography. Furthermore, we realize positive and negative copies of ghost image via holographic projection in which symmetrical mirror target patterns are artificially designed. Thus, by integrating these two SPI schemes, the lensless GI scheme based on CGH not only advances towards the visibility requirements for practical applications but also enables a high-frame-rate projection scheme essential for multi-frame intensity correlation measurements.

We analytically derive, and illustrate with a population synthesis model, the maximum offset of binary neutron star mergers ejected from their host galaxies. This approximate maximum offset is 300 kpc $\times\ (v_\mathrm{esc} / 500\ \mathrm{km}\ \mathrm{s}^{-1})^{-7}$, where $v_\mathrm{esc}$ is the escape velocity from the host galaxy. Massive hosts with high escape velocities are unlikely to yield very large offsets. This maximum offset should inform the host associations of mergers that are not coincident with galaxies. We also discuss potential correlations between offsets and system masses, and possibly the duration of the gamma-ray burst accompanying the merger.

This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a trivalent vertex, which results in a standalone framework for computations that supersedes the underlying Schwinger-boson framework. To that end, we present a partial summary of the commutation relations and use it to evaluate the result of applying any gauge-invariant operator on the LSH basis states introduced in Part I (arXiv:2407.19181). Classical calculations in the LSH basis run significantly faster than equivalent calculations performed using Schwinger bosons. A companion code script is provided, which implements the derived formulas and aims to facilitate rapid progress towards Hamiltonian-based calculations of quantum chromodynamics.

Effective code retrieval is indispensable and it has become an important paradigm to search code in hybrid mode using both natural language and code snippets. Nevertheless, it remains unclear whether existing approaches can effectively leverage such hybrid queries, particularly in cross-language contexts. We conduct a comprehensive empirical study of representative code models and reveal three challenges: (1)insufficient semantic understanding; (2) inefficient fusion in hybrid code retrieval; and (3) weak generalization in cross-language scenarios. To address these challenges, we propose UniCoR, a novel self-supervised framework designed to learn Unified Code Representations that are semantically robust, modally collaborative, and language-agnostic. Firstly, we design a multi-perspective supervised contrastive learning module to enhance semantic understanding and modality fusion. It aligns representations from multiple perspectives, including code-to-code, natural language-to-code, and natural language-to-natural language, enforcing the model to capture a semantic essence among modalities. Secondly, we introduce a representation distribution consistency learning module to improve cross-language generalization, which explicitly aligns the feature distributions of different programming languages, enabling language-agnostic representation learning. Extensive experiments on both an empirical benchmark and a large-scale benchmark show that UniCoR outperforms all baseline models, achieving an average improvement of 8.64% in MRR and 11.54% in MAP over the best-performing baseline. Furthermore, UniCoR exhibits stability in hybrid code retrieval and generalization capability in cross-language scenarios.

The process of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ is among the most favored modes for searching for bottom-charm baryons. However, its branching fraction has never been studied in theory. In this work, we investigate the branching fraction of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ in the final-state-interaction approach, as it is dominated by the color-suppressed non-factorizable contributions. A similar process, $Λ_{b}^{0}\to Λ^0 J/ψ$, is used as a control mode to fix the model parameter. Consequently, the branching fraction of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ is predicted to be $(1.55_{-0.42}^{+0.50})\times10^{-4}$. With the production rate of bottom-charm baryons and the detection efficiencies of the final states, it is expected for considerable signal events to observe $Ξ_{bc}^+$ in the near future.

We present a new model of quantum computation rooted in the representation theory of the mass less sector of unitary irreducible representations of the extended Poincare group developed in [1].

Bimetric MOND (BIMOND) is used as a platform for variable-$G$ theories that have MOND-specific idiosyncrasies. E.g., MOND premises dictate return to standard dynamics in the high-acceleration limit, predicting the standard value of $G$ for high-acceleration systems. This automatically ensures compliance of such theories with all the constraints on inconstancy of $G$ that emerge from the study of high-acceleration systems: geophysics, solar system, pulsars, supernovae, stellar evolution, emission of gravitational waves, etc. In MOND, constraints deduced from such phenomena have no bearing on possible $G$ variability in cosmology. My guiding motivation is to see if such theories may account for some roles of dark matter in cosmology; e.g., in accounting for the expansion history of the Universe in the matter-dominated era, by having a $G_e\approx 2πG$ govern the later stages of the expansion, instead of invoking matter density $\approx 2π\times$ baryon density. Without adding degrees of freedom, or new dimensionful constants, BIMOND can be extended to a class of theories that entail what is best described as phenomenon-dependence of Newton's constant, $G$. I cannot yet present a consistent model that complies with all the observations in cosmology, including the expansion history, with all its details. Instead, I describe some examples of theories in the class that predict different values of $G_e$ in different circumstances, including one where $G$ takes its standard value for all subcosmological systems -- even if they are deep in the MOND regime. I also discuss scenarios in which $G_e\approx G$ in the early Universe, as required by constraints from big-bang nucleosynthesis, but with $G_e> G$ setting in at later times, where it can affect the expansion history during the matter-dominated era.

We analyze the decay of $η\rightarrow \ell^+\ell^-(\ell=e, μ)$ via $J/ψ\rightarrowγη'$ and $η'\rightarrowπ^+π^-η$, based on (10087 $\pm$ 44) $\times$ 10$^{6}$ $J/ψ$ events collected with the BESIII detector at the BEPCII storage rings. The branching fraction of $η\rightarrowμ^+ μ^-$ is measured to be $(5.8 \pm 1.0_{\rm stat} \pm 0.2_{\rm syst}) \times 10^{-6}$, which is consistent with the previous measurements and theoretical expectations. In addition, no significant $η\to e^+e^-$ signal is observed in the $e^+ e^-$ invariant mass spectrum, and an improved upper limit of ${\cal B}(η\to e^+ e^-) < 2.2 \times 10^{-7}$ is set at 90\% confidence level.

The rotation of a planet located in the habitable zone of a solar-type star can be reversed by a smooth process associated with the formation of its atmosphere and the increase of stronger torques, opposite to normal tidal torques. Our understanding of the rotational dynamics of Venus is revisited to analyze what might happen to exoplanets in the habitable zone of a solar-type star. The creep tide theory is used to calculate the gravitational tidal torque. Mathematical analysis is used to study the differential equation resulting from the combined effects of tidal torque and atmospheric torque. It shows that no collision with other bodies or critical planetary perturbations is necessary to convert the rotation of an Earth or super-Earth with a significant atmosphere formed during its evolution into a retrograde rotation. The reversal of a planet's rotation is not an exceptional event and may have occurred many times among known exoplanets in the habitable zone. It is sufficient for the planet to be at a sufficiently short distance from its host star to allow tidal torques to nearly synchronize the planet's rotation before most of its atmosphere forms (but not so close that stellar radiation destroys the formed atmosphere). When atmospheric torques become more important than tidal torques, a pitchfork bifurcation occurs: the synchronous attractor bifurcates into two asynchronous attractors, and the system evolves toward one of the asynchronous attractors. If it evolves toward the subsynchronous branch, the rotation may subsequently become retrograde. Venus's rotation is an example. None of these processes is catastrophic. Planetary atmosphere formation is a continuous and smooth process, which may be more or less efficient, but it is not a low-probability event.

This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|^alpha / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in R^N \ {0}, where N >= 1, lambda > 0, p > 0, alpha > -2 and F in R are constants. We study positive rupture solutions with rupture point at the origin (u(0)=0). Our main emphasis is on asymptotic radial rupture solutions: we prove the existence of both radial and non-radial solutions, characterize their asymptotic behavior near the origin, and obtain a full asymptotic expansion of arbitrary order.

In this paper, we review and compare some geometric frameworks for dissipation in non-equilibrium thermodynamics. We start with a brief overview of classical irreversible thermodynamics and gradient dynamics. Then we discuss several specific frameworks including Rayleigh dissipation potential and the dissipative d'Alembert framework, showing their relations with gradient dynamics. Finally, we discuss frameworks for dissipative evolution generated from Poisson brackets.

Kaonic atoms, formed when a negatively charged kaon replaces an electron, provide a sensitive probe of the low-energy strong interaction via precision X-ray spectroscopy. The SIDDHARTA-2 experiment at the DA$Φ$NE collider employs high-performance Silicon Drift Detectors (SDDs) optimized for the 4-12 keV range to study light kaonic systems. In preparation for the EXKALIBUR phase, which targets heavier kaonic atoms, new 1 mm-thick SDDs have been developed with Politecnico di Milano and Fondazione Bruno Kessler. Their increased thickness enhances the quantum efficiency by a factor of about two at 30 keV while preserving excellent energy resolution. These detectors are also intended for VIP-3, the next-generation test of the Pauli Exclusion Principle (PEP). Building on VIP-2, which set the most stringent limits on PEP-violating $K_α$ transitions in copper, VIP-3 will extend the search to heavier elements such as Ag, Sn, and Zr. Preliminary measurements demonstrate efficient detection up to 30 keV, supporting future high-precision studies of the kaon-nucleon interaction and PEP in heavier systems.

Spin-torque and spin-Hall oscillators (SHOs) have emerged as promising candidates for building blocks in neuromorphic computing due to their ability to synchronize mutually, a process that can be mediated by propagating spin waves. We demonstrate a SHO that takes advantage of a low-damping magnetic garnet with dominant perpendicular magnetic anisotropy (PMA), namely gallium-substituted yttrium-iron-garnet (Ga:YIG). In-plane magnetized Ga:YIG allows for the operation at a high efficiency level while also enabling resonant spin-wave emission. A nonlinear self-localization of the excitation is avoided by exploiting the positive nonlinear frequency shift, which facilitates a current-controlled frequency of the emitted spin waves. Via micro-focused Brillouin light scattering spectroscopy, we investigate the properties of the local auto-oscillation and its spin-wave emission. Multiple modes are excited and compete internally, with two propagating modes detected up to distances larger than 10 $μ$m. Their frequencies combine to an extended frequency bandwidth of approximately 1.6 GHz. The experimentally observed two-mode system and its transition to a single mode at higher currents are reproduced via micromagnetic simulations, which account for spatial variation of the PMA arising due to the microstructures on Ga:YIG. Our results propose a promising platform for hosting SHOs, interconnected via propagating spin waves with particular relevance to neuromorphic computing.

Nonparametric regression and regression-discontinuity designs suffer from smoothing bias that distorts conventional confidence intervals. Solutions based on robust bias correction (RBC) are now central to the economist's toolbox. In this paper, we establish a novel connection between RBC methods and bootstrap prepivoting. Revisiting RBC through the lens of bootstrapping allows us to develop a novel bias correction procedure which delivers improved nonparametric inference. The resulting confidence intervals are 17% shorter than the usual intervals employed in curve estimation and regression discontinuity designs, without compromising asymptotic coverage. This holds regardless of evaluation point location, bandwidth choice, or regressor and error distribution.

Warm Inflation is a scenario in which the inflaton field dissipates its energy during inflation to maintain a subdominant constant radiation bath. Two of its remarkable features are (i) inflation can be realized even by very steep potentials and (ii) such a scenario doesn't call for a separate post-inflation reheating phase. We exploit the first feature to show that Warm Inflation can successfully take place on the very steep left wing of the Witten-O'Raifeartaigh potential while remaining in excellent agreement with current cosmological data (joint analysis of Planck, ACT and DESI). The Witten-O'Raifeartaigh potential has a flatter right wing as well, which opens up the possibility of dark energy when the field rolls along this wing. However in order to successfully realize quintessential inflation one needs to (i) normalize the two wings of the Witten-O'Raifeartaigh potential differently in order to bridge between the two extreme energy scales of inflation and dark energy, (ii) allow the quintessence field to be dissipative, which is consistent with the presence of a dissipative term in warm inflation. The dissipative dynamics of the quintessence field is needed in order to sustain slow-roll in the right wing. With these modifications, we demonstrate that the Witten-O'Raifeartaigh potential can give rise to a unified model of warm inflation (on the left wing) and transient dark energy (on the right wing).

We investigate how the newly obtained static black hole in bumblebee gravity affects the behavior of accreting matter and its observable signatures. The Lorentz-violating parameter that characterizes this geometry modifies photon trajectories and shifts the location of the critical curve that defines the shadow. Using ray tracing, we examine light deflection, the structure of direct emission, lensing rings, and photon rings, and we explore three thin-disk emission models--starting at the ISCO, at the photon sphere, and at the event horizon--together with static and infalling spherical accretions. Larger values of this parameter enlarge the shadow, move all optical features outward, and suppress the observed intensity through gravitational redshift, with additional dimming produced by Doppler effects for infalling matter

We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable $W^{1, p}$-Sobolev energy can always be strongly approximated by smooth maps, giving a counterpart of Hang's density result in $W^{1, 1}$ for the Sobolev space $W^{1, p}$ with integer $p \ge 2$. Our result extends to higher-order Sobolev spaces and is straightforward in fractional Sobolev spaces. We also provide a proof based on the weak continuity of Jacobians in the cases where the cohomological criterion of Bethuel, Demengel, Colon and Hélein applies.

Gravitational wave interferometers have studied compact object mergers and solidified our understanding of strong gravity. Their increasing precision raises the possibility of detecting new physics, especially in a neutron star binary system that may contain hidden-sector particles. In particular, a new vector force between binary constituents, giving rise to dark electromagnetic phenomena, could measurably alter the inspiral waveforms and thus be constrained by gravitational wave observations. In this work, we critically examine the mechanisms for neutron stars to acquire enough hidden-sector particles with requisite couplings to furnish a detectable signature from dark electromagnetism. We demonstrate that the repulsive nature of vector forces imposes stringent constraints on any putative particle physics model or astrophysical environment which could give rise to such gravitational signatures. We argue that absent an extreme fine-tuning of parameters, such signatures are well out of reach of any current or near-future gravitational wave observatory.

We introduce and study block-separated overpartitions, a constrained family of overpartitions in which no two consecutive distinct part-blocks are both overlined. This local restriction produces a new sequence that naturally interpolates between classical partitions and unrestricted overpartitions. We show that the internal decoration of distinct part-blocks is governed by Fibonacci-type combinatorics: once the set of distinct part-sizes is fixed, the admissible overlining patterns are counted by Fibonacci numbers. This leads to a symmetric-function expansion of the generating function and a two-state transfer-matrix formulation. After extracting the Euler product, we obtain normalized recurrences, second-order scalar recurrences, determinantal representations, and a continued-fraction description of finite truncations. Finally, we determine the asymptotic growth of the counting function, and prove that block-separated overpartitions share the same exponential scale as ordinary partitions, with a modified subexponential constant.

We extend the probabilistic approach for constructing Kahler-Einstein metrics on log Fano manifolds X - involving random point processes - to the case of non-discrete automorphism groups, by breaking the symmetry using a moment map constraint. In particular, an algebraic notion of Gibbs polystability is introduced, ensuring that the corresponding point processes on X are well-defined. We conjecture that the Gibbs polystability of X is equivalent to the existence of a Kahler-Einstein metric and that the unique such metric with vanishing moment emerges when sampling a large number of N points on X. The definition of Gibbs polystability involves a limit of log canonical thresholds on the GIT semistable locus of the N-fold products of X, that we conjecture coincides - as N tends to infinity - with an analytic reduced stability threshold, encoding the coercivity of the K-energy functional modulo automorphisms. These conjectures follow from an overarching conjectural Large Deviation Principle for the large N-limit. We prove several of our conjectures on log Fano curves and derive a strengthened form of the sharp logarithmic Hardy-Littlewood-Sobolev (HLS) inequality on the two-sphere, under a moment constraint. It yields quantitative stability results for the sharp logarithmic HLS inequality with optimal stability constants. Furthermore, we show that any log Fano manifold that is strongly uniformly Gibbs polystable admits a Kahler-Einstein metric. In companion papers we will present applications to Onsager's point vortex model on the two-sphere and the AdS/CFT correspondence.

The JUNO experiment has recently released its first measurement results based on 59.1 days of data, achieving unprecedented precision in measuring the lepton mixing angle $θ_{12}$. This significant improvement places stringent constraints on certain neutrino mass models and flavor mixing patterns. In this work, we examine the impact of the latest JUNO results on the two trimaximal (i.e., TM1 and TM2) mixing patterns. They are two well-motivated variants of the tri-bimaximal mixing pattern and predict specific correlations between $θ_{12}$ and $θ_{13}$. After taking into account the first JUNO results, the TM1 mixing pattern sits on the edge of the experimentally allowed $1σ$ region, while the TM2 mixing pattern lies outside the $3σ$ region. To reconcile these TM mixing patterns with the latest experimental data, we further investigate the renormalization group (RG) running effects on them in the both Majorana and Dirac neutrino cases. Our analytical and numerical results show that RG corrections can bring the two TM mixing patterns into excellent agreement with the latest JUNO data if neutrino masses are quasi-degenerate. However, the Majorana case faces severe constraints from neutrinoless double beta decay limits, and particularly, the TM2 mixing pattern with Majorana neutrinos has been essentially ruled out. In the Dirac case, the TM1 mixing pattern is fully consistent with current data including beta decay results, whereas the TM2 pattern is strongly constrained by the KATRIN limit and even could be largely ruled out if the KATRIN experiment reaches its final sensitivity without any discovery. Future high-precision measurements of lepton mixing parameters and absolute neutrino masses in both oscillation and non-oscillation experiments will provide decisive tests of these mixing patterns.