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We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle of the Stochastic Heat Equation (SHE). The logarithm of the minimizer of the variational problem gives the most probable shape of the solution of the Kardar--Parisi--Zhang equation conditioned on achieving certain unlikely values. Taking the SHE with the delta initial condition and conditioning the value of its solution at the origin at a later time, under suitable scaling, we prove that the logarithm of the minimizer converges to an explicit function as we tune the value of the conditioning to 0. Our result confirms the physics prediction Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson, and Sasorov (2016). 

We consider the n-point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations and a wide range of scaling regimes that allows time to be short, unit-order, and long. We prove the n-point large deviation principle and characterize, with proof, the corresponding spacetime limit shape. Our proof is based on the results—from the companion paper (Tsai in High moments of the SHE in the clustering regimes, 2023)—on moments of the stochastic heat equation and utilizes ideas coming from a tree decomposition. Behind our proof lies the phenomenon where the major contribution of the noise concentrates around certain corridors in spacetime, and we explicitly describe the corridors. 

Many Gram-negative bacterial pathogens rely on the secretion system to inject effectors into their host cells, thereby suppressing host immunity and subsequently leading to diseases. In a recent Science paper, Miao et al. identified a plant secondary metabolite that dismantles type III injectisome by targeting the conserved HrcC protein within the secretion apparatus. 

We analyze the high moments of the Stochastic Heat Equation (SHE) via a transformation to the attractive Brownian Particles (BPs), which are Brownian motions interacting via pairwise attractive drift. In those scaling regimes where the particles tend to cluster, we prove a Large Deviation Principle (LDP) for the empirical measure of the attractive BPs. Under the delta(-like) initial condition, we characterize the unique minimizer of the rate function and relate the minimizer to the spacetime limit shapes of the Kardar–Parisi–Zhang (KPZ) equation in the upper tails. The results of this paper are used in the companion paper [75] to prove an n-point, upper-tail LDP for the KPZ equation and to characterize the corresponding spacetime limit shape. 

With its extreme axial tilt, Uranus' radiant energy budget (REB) and internal heat flux remain among the most intriguing mysteries in our solar system. By combining observations with modeling, we present the global REB over a complete orbital period (1946–2030), revealing significant seasonal variations. Despite these fluctuations, the global average emitted thermal power consistently exceeds absorbed solar power, indicating a net energy loss. Assuming no significant seasonal variation in emitted power, we estimate an internal heat flux of 0.078 ± 0.018 W/m2 by analyzing the energy budget over one orbital period. The combination of internal heat and radiant energies indicates substantial global and hemispheric imbalances, with excesses or deficits exceeding 85% of emitted power at the hemispheric scale. These findings are crucial for understanding Uranus' interior and atmosphere. A future flagship mission to Uranus would provide critical observations to address more unresolved questions of this enigmatic ice giant. 

We extend the construction of the semigroup of the two-dimensional delta-Bose gas in [20] (based on [22, 16]) to a weighted L2 space that allows exponentially growing functions. We further show that the semigroup of the mollified delta-Bose gas converges strongly to that of the delta-Bose gas. 

To scale out the massive metadata access, the Ceph distributed file system (CephFS) adopts adynamic subtree partitioningmethod, splitting the hierarchical namespace and distributingsubtreesacross multiple metadata servers. However, this method suffers from a severe imbalance problem that may result in poor performance due to its inaccurate imbalance prediction, ignorance of workload characteristics, and unnecessary/invalid migration activities. To eliminate these inefficiencies, we propose Lunule, a novel CephFS metadata load balancer, which employs animbalance factor modelfor accurately determiningwhento trigger re-balance and tolerate unharmful imbalanced situations. Lunule further adopts aworkload-aware migration plannerto appropriately select subtree migration candidates. Finally, we extend Lunule to Lunule⁺, which models metadata accesses into matrices, and employs matrix-based formulas for more accurate load prediction and re-balance decision. Compared to baselines, Lunule achieves better load balance, increases the metadata throughput by up to 315.8%, and shortens the tail job completion time by up to 64.6% for five real-world workloads and their mixture, respectively. Besides, Lunule is capable of handling the metadata cluster expansion and the workload growth, and scales linearly on a 16-node cluster. Compared to Lunule, Lunule⁺achieves up to 64.96% better metadata load balance, and 13.53-86.09% higher throughput. 

Quantum ghost imaging (QGI) leverages correlations between entangled photon pairs to reconstruct an image using light that has never physically interacted with an object. Despite extensive research interest, this technique has long been hindered by slow acquisition speeds, due to the use of raster-scanned detectors or the slow response of intensified cameras. Here, we utilize a single-photon-sensitive time-stamping camera to perform QGI at ultra-low-light levels with rapid data acquisition and processing times, achieving high-resolution and high-contrast images in under 1 min. Our work addresses the trade-off between image quality, optical power, data acquisition time, and data processing time in QGI, paving the way for practical applications in biomedical and quantum-secured imaging.