Dark matter much heavier than the weak scale remains a comparatively unexplored frontier. This review surveys theoretical and experimental developments on very heavy dark matter, including composite and dissipative formation mechanisms, multiscatter detection, and astrophysical searches.

We determine the large-genus limiting distribution of the 4-rank of the Picard group of hyperelliptic curves over a fixed finite field $\mathbb F_q$ of odd characteristic. This is a function field analogue of a result of Fouvry and Klüners. Our computation agrees with (the Picard group analogue of) the Cohen--Lenstra--Gerth heuristics in the case $q \equiv 3\pmod{4}$, i.e., in the absence of roots of unity in the base field. When roots of unity are present, the result is of the same form as conjectured distribution for class groups of quadratic extensions of number fields containing roots of unity. The limiting distribution does not change when imposing finitely many conditions on the ramification behavior of the curves. In the process, we determine the rank distribution of a certain class of random matrix ensembles over finite fields determined by symmetry conditions.

We prove two "Singularity removal rigidity theorems" for minimal hypersurfaces with isolated singularities in manifolds of nonnegative scalar curvature (Theorems \ref{thm: rigidity for minimal surface} and \ref{thm: georch free of singularity}). In particular, we observe a new phenomenon that the extremal scalar curvature condition forces smoothness, which reveals a kind of positive effect of minimal hypersurface singularities in scalar curvature geometry. As an application, we obtain a direct proof of the positive mass theorem (PMT) for asymptotically flat $8$-manifolds with arbitrary ends (Theorem \ref{thm: pmt8dim}), without using N. Smale's generic regularity theorem. A key ingredient is a new spectral version of PMT for AF manifolds with arbitrary ends, whose proof relies on PMT for asymptotically locally flat (ALF) manifolds with $\mathbf{S}^1$-symmetry.

In this paper, we introduce and explore the concepts of strongly LU-E-preinvex (SLUEP), pseudo strongly LU-E-preinvex (PSLUEP) and strongly LU-E-invex (SLUEI) functions. To illustrate and validate these definitions, we provide several non-trivial examples. Additionally, we extend the idea of strongly-G invex sets to the context of interval-valued functions. The epigraph of a SLUEP function is derived, and a relationship between SLUEP and PSLUEP functions have been explored. A key contribution of this work is the identification of a significant connection between weakly-strongly E-invex functions and SLUEP functions. As an application, we consider a nonlinear programming problem involving SLUEP functions. Under certain conditions, we prove that a local minimum of the problem is also a global minimum. Moreover, the sufficiency of Karush-Kuhn-Tucker (KKT) optimality conditions by considering the objective and constraint functions are SLUEI and SEI respectively. The theoretical results are validated through illustrative examples and counterexamples.

Time-Sensitive Networking (TSN) is a set of standards aiming to enable deterministic and predictable communication over Ethernet networks. However, as the standards of TSN do not specify how to schedule the data streams, the main open problem around TSN is how to compute schedules efficiently and effectively. In this paper, we solve this open problem for no-wait schedules on the daisy-chain topology, one of the most commonly used topologies. Precisely, we develop an efficient algorithm that optimally computes no-wait schedules for the daisy-chain topology, with a time complexity that scales polynomially in both the number of streams and the network size. The basic idea is to recast the no-wait scheduling problem as a variant of a graph coloring problem where some restrictions are imposed on the colors available for every vertex, and where the underlying graph is an interval graph. Our main technical part is to show that this variant of graph coloring problem can be solved in polynomial time for interval graphs, though it is NP-hard for general graphs. Evaluations based on real-life TSN systems demonstrate its optimality and its ability to scale with up to tens of thousands of streams.

Driven by the widespread deployment of distributed energy resources, local energy markets (LEMs) have emerged as a promising approach for enabling direct trades among prosumers and consumers to balance intermittent generation and demand locally. However, LEMs involve processing sensitive participant data, which, if not protected, poses privacy risks. At the same time, since electricity is exchanged over the physical power network, market mechanisms should consider physical constraints and network-related costs. Existing work typically addresses these issues separately, either by incorporating grid-related aspects or by providing privacy protection. To address this gap, we propose a privacy-preserving protocol for LEMs, with consideration of network fees that can incite participants to respect physical limits. The protocol is based on a double-auction mechanism adapted from prior work to enable more efficient application of our privacy-preserving approach. To protect participants' data, we use secure multiparty computation. In addition, Schnorr's identification protocol is employed with multiparty verification to ensure authenticated participation without compromising privacy. We further optimise the protocol to reduce communication and round complexity. We prove that the protocol meets its security requirements and show through experimentation its feasibility at a typical LEM scale: a market with 5,000 participants can be cleared in 4.17 minutes.

Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

Motivated by the construction of optimal locally repairable codes, we introduce the new finite geometric concept of a \emph{local arc} which is defined as a collection $\mathcal{S}$ of disjoint point sets $S_{i}$ in $\mathrm{PG}(2,q)$ such that $S_{i} \cup S_{j}$ is an arc for any $S_{i}, S_{j} \in \mathcal{S}$. We focus on the upper and lower bounds on the sizes of maximum $k$-uniform local arcs. For $q=p^m$ with $p$ prime, we construct $k$-uniform local arcs in $\mathrm{PG}(2,q)$ of size $Ω(q^{d})$ where $d$ is between $1.1167$ and $1.25$ depending only on $m$. For $k=4$, this implies the existence of optimal locally repairable codes (LRCs) with minimum distance 6, locality 3, and disjoint repair groups, whose length is superlinear in $q$--a significant improvement over the previously known $O(q)$ constructions for such LRCs.

Guided by first-principles calculations, we demonstrate superconductivity in the ternary perovskite hydride SrPdH$_{3-x}$, synthesized at low pressure. Structural characterization via neutron diffraction reveals the near-stoichiometric composition SrPdD$_{2.9(2)}$ with 96\% deuterium site occupancy. Subsequent transport and magnetic susceptibility measurements establish onset superconducting transitions at $T_\text{c} = \SI{2.1}{K} $ (H) and $T_\text{c} = \SI{2.2}{K} $ (D), exhibiting an inverse isotope effect that our first-principles calculations attribute predominantly to quantum zero-point motion. The excellent agreement between theory and experiment with respect to thermodynamic stability and superconducting properties provides important validation for theory-guided superconductor discovery. This work establishes superconductivity in the perovskite hydride structural prototype -- expanding the limited family of experimentally realized ternary hydride superconductors -- and demonstrates the importance of quantum nuclear motion on the accurate theoretical treatment of low-pressure hydride superconductors.

Liquid foams are archetypal athermal amorphous solids whose elasticity arises from the jamming of densely packed bubbles. We investigate the stress relaxation of non-ageing liquid foams following flow cessation, using fast X-ray tomo-rheoscopy. Thanks to in situ, time-resolved measurements, we uncover robust linear affine relationships between shear stress, plastic activity, and coordination number throughout the relaxation toward a residual stress state below the yield value. In contrast to previous studies on amorphous solids, we observe an exponential relaxation governed by the duration of individual plastic events, rather than by cascades of correlated ones associated with much longer, shear-rate-dependent timescales or power-law relaxations. Our results are consistent with a recent theoretical framework proposed by Cuny et al., suggesting that residual stress originates from the orientation of the stress tensor.

Imaging the full-field microvibration of extended targets remains a formidable challenge for conventional remote sensing. Traditional array-based sensors are often severely constrained by data throughput and sensitivity limits when scaling to high spatial resolutions, while point-scanning interferometric systems lack the instantaneous full-field capability required to capture transient, spatially coupled vibration modes. To overcome these limitations, we propose a Coherent Detection-Ghost Imaging (CD-GI) framework that synergizes the spatial multiplexing capability of single-pixel imaging with the high-dimensional sensitivity of coherent detection. We establish a comprehensive mathematical model that describes the coupling mechanism of the target's spatial distribution and temporal micro-dynamics within a 1D bucket detector signal. To resolve the resulting inverse problem, we develop a frequency-channel self-calibration scheme. This approach effectively decouples the micro-Doppler signatures from spatial speckle patterns without requiring prior knowledge of the vibration frequency. Experimental results demonstrate that our system successfully reconstructs the spatially resolved microvibration patterns of adjacent targets with a frequency difference as small as 1 Hz, achieving sub-wavelength vibration sensitivity. This work bridges the gap between computational imaging and coherent metrology, offering a robust solution for non-invasive, high-precision structural health monitoring.

Sustaining the effectiveness of behavior change technologies remains a key challenge. AI self-modeling, which generates personalized portrayals of one's ideal self, has shown promise for motivating behavior change, yet prior work largely examines short-term effects. We present one of the first longitudinal evaluations of AI self-modeling in fitness engagement through a two-stage empirical study. A 1-week, three-arm experiment (visual self-modeling (VSM), auditory self-modeling (ASM), Control; N=28) revealed that VSM drove initial performance gains, while ASM showed no significant effects. A subsequent 4-week study (VSM vs. Control; N=31) demonstrated that VSM sustained higher performance levels but exhibited diminishing improvement rates after two weeks. Interviews uncovered a catalyst effect that fostered early motivation through clear, attainable goals, followed by habituation and internalization which stabilized performance. These findings highlight the temporal dynamics of personalized nudging and inform the design of behavior change technologies for long-term engagement.

We present a comprehensive search for non-thermal high-energy $γ$-ray emission from the nearby merging galaxy cluster Abell~119 ($z=0.044$) using archival observations spanning over seven decades in photon energy. Our analysis combines hard X-ray data from INTEGRAL/ISGRI (30--100~keV), MeV $γ$-ray observations from COMPTEL (0.75--30~MeV), and GeV--TeV data from the DArk Matter Particle Explorer (DAMPE; 3~GeV--1~TeV). No statistically significant emission is detected at the cluster position in any energy band. In the hard X-ray regime, we derive a $3σ$ upper limit of $F_{30-100\,\mathrm{keV}} \lesssim 8.5 \times 10^{-11}$~erg~cm$^{-2}$~s$^{-1}$ from ISGRI mosaic imaging. Reanalysis of archival COMPTEL data yields 95\% confidence-level upper limits ranging from $\sim 9 \times 10^{-11}$ to $\sim 8 \times 10^{-10}$~erg~cm$^{-2}$~s$^{-1}$ across 0.75--30~MeV. In the GeV--TeV range, DAMPE constrains the differential energy flux to $\sim 10^{-12}$--$10^{-10}$~erg~cm$^{-2}$~s$^{-1}$ (95\% confidence level). These results provide independent multi-band constraints on the reported GeV excess from recent Fermi-LAT studies. While our DAMPE limits do not exclude the flux levels claimed in those analyses, the absence of confirmation across keV--MeV--GeV bands indicate that any non-thermal emission from Abell~119 remains tentative.

Magnetic reconnection in partially ionized plasmas plays a crucial role in a wide range of solar, astrophysical, and laboratory environments. While reconnection in such plasmas is commonly characterized by the ion-neutral coupling strength and the ionization fraction $χ=n_{i}/(n_{i}+n_{n})$, most previous studies have focused primarily on the former. A systematic exploration of the ionization fraction, particularly in combination with ion-neutral coupling, is still lacking. This study presents the first systematic scan of the two-dimensional parameter space defined by ion-neutral collisionality and ionization fraction, enabling investigation of the transition from strongly coupled reconnection to faster, decoupled reconnection. To achieve this, we employ a new three-fluid, five-moment numerical model that treats electrons, ions, and neutrals as separate species on an equal footing. We find that in the strongly coupled regime, the reconnection rate is consistent with a $χ^{1/4}$ scaling. As collisionality decreases, the system transitions to a fast, ionization-independent regime. On the other hand, in all simulations, the current sheet thins down to the ion inertial length di, rather than the expanded hybrid scale $d_{i}χ^{-1/2}$ predicted by analytic fluid theories. The identified critical thickness and the resulting onset of fast reconnection agree reasonably well with recent fully kinetic simulations and laboratory experiments. In addition, we show that, over a wide range of coupling strengths, the ion outflow velocities remain Alfvénic, scaling with the appropriate ion or hybrid Alfvén speed, while the hybrid outflow velocity scales as $χ^{1/2}$ when normalized by ion Alfvén speed.

A novel effect involving the formation of a stable kink-like torsion deformation in a magnetoactive elastomer (MAE) beam subjected to a uniform magnetic field is theoretically predicted and experimentally confirmed. The phenomenon was demonstrated using an elastomer beam containing soft magnetic carbonyl iron microparticles within a silicone matrix. The torsion kink acts as a transition boundary between two undeformed homogeneous states of the beam. We show that the elastic moment is compensated by a magnetoelastic moment in the kink region, where the local magnetization of the beam is non-collinear to the applied magnetic field due to shape anisotropy. We It is established that within the kink region, the MAE beam exists in a non-uniformly elastically deformed, low-symmetry magnetic state. Outside the kink, the beam's magnetization is collinear with the magnetic field, corresponding to an undeformed, high-symmetry homogeneous magnetic state.

Despite being well established in cuprates, an intrinsic translational symmetry-breaking charge order has not been clearly identified in iron-based superconductors. Using spectroscopic-imaging scanning tunneling microscopy on epitaxial Ca(Fe1-xCox)2As2 (x = 0 ~ 0.055) thin films, we observe smectic, near-commensurate charge-stripe order in the underdoped regime that intervenes between the nematic parent phase and optimally doped superconductivity. Distinct from the bidirectional checkerboard-like order in cuprates, these charge stripes are unidirectional along the antiferromagnetic Fe-Fe bond direction and are accompanied by a van Hove singularity near the Fermi level, inherited from the Fermi surface reconstruction driven by intertwined antiferromagnetic and nematic correlations. Both local and global suppression of the charge-stripe instability enhance superconductivity, tunable via epitaxial strain and Co doping. These results establish charge-stripe order as an intermediate electronic phase in iron pnictides and reveal a coherent pathway from nematicity to superconductivity. Our findings highlight charge ordering as a unifying element across different families of high-temperature superconductors.

Mg$_2$IrH$_6$ is a metastable complex metal hydride with a predicted superconducting transition temperature as high as 170 K at ambient pressure. Following the synthesis of isomorphic, insulating Mg$_2$IrH$_5$ at low pressure, higher-pressure studies were conducted to investigate the phase behavior and compound formation in this system. X-ray diffraction and Raman spectroscopic measurements indicate that cubic Mg$_2$IrH$_7$ is stabilized above ca. 40 GPa and coexists with a related hexagonal hydride with likely composition near Mg$_2$IrH$_5$. Electrical transport measurements show that the cubic Mg$_2$IrH$_7$ is insulating, in agreement with ab initio predictions, and persists during room-temperature decompression until $\sim$20 GPa before reverting back to the cubic Mg$_2$IrH$_5$. The experimental results confirm ground-state structure predictions in the Mg-Ir-H system, and the formation of two nearly identical phases with surrounding compositions opens new opportunities to access superconducting Mg$_2$IrH$_6$ through non-equilibrium processing pathways.

In this paper, we present development of a portable cosmic muon tracker tailored for both on-site measurements of cosmic muon flux as well as for outreach activities. The tracker comprises of two 70 mm x 70 mm plastic scintillators, wavelength shifting (WLS) fibers, and Hamamatsu made Silicon Photomultipliers (SiPM) S13360-2050VE. The detector uses plastic scintillator panels optically coupled to WLS fibers, which transmit scintillation light to the SiPMs. SiPM signals are routed to an electronics board equipped with op-amp amplifiers and a peak-hold circuit connected to an ESP32 microcontroller module. When muons traverse through both scintillators the light emitted is collected by the SiPMs, and thus generating signals proportional to the incident light intensity. These signals are then amplified and the pulse peak is held for 500 us. A high speed discriminator is used to generate trigger logic signals. The peak analog voltage is digitized using the onboard ADC of the ESP32 when a coincident trigger occurs. The SiPMs are powered by a High Voltage bias supply module while an onboard BMP180 module measures temperature and pressure. For real-time event tagging, a GPS module is interfaced with the ESP-32. Housed within an acrylic box measuring 100 mm x 100 mm x 100 mm the detector can be powered using a 5V 1A USB power bank. An open source mobile application was used for real-time monitoring. This versatile and cost-effective portable detector facilitates cosmic muon research in various experimental settings. Its portability and low power requirements enable on-site measurements in environments such as tunnels, caves as well as high altitudes.

Using the Spitzer and WISE images, we discovered 42 mid-IR luminous dusty supernovae with local integral-field spectroscopy data. The observed mid-IR emission indicates the presence of newly formed dust, or pre-existing dust heated by the radiation from the supernovae or circumstellar medium interactions. We carried out a systematic analysis of the supernova host environments and their dust properties, for understanding the dust-veiled exploding stars, and whether such an intense dust production process is associated with their local environments. We find that dusty supernovae prefer the locations with higher EW(Hα), lower metallicity, and heavier host extinctions compared to typical SN types, and they show the same increasing sequence in the values of EW(Hα) and oxygen abundance from hydrogen-rich, type IIn and hydrogen-poor dusty supernovae. These differences in environmental properties of different dusty SN types indicate the diversity of their progenitors. We also found that one marginal correlation is a negative correlation between the SN dust mass and star formation rate. This means that SNe would be more mid-IR luminous and more dust-rich at the region with lower star formation rate. However, the SN dust mass show no correlation with the metallicity and the host extinction, which were thought to be key factors affecting the mass-loss history of progenitors and the CSM environment of SNe. Therefore, the dust formation process in SNe might be insensitive to metallicity and the dust condition of their host environments.

Modern recommendation systems primarily rely on attention mechanisms with quadratic complexity, which limits their ability to handle long user sequences and slows down inference. While linear attention is a promising alternative, existing research faces three critical challenges: (1) temporal signals are often overlooked or integrated via naive coupling that causes mutual interference between temporal and semantic signals while neglecting behavioral periodicity; (2) insufficient positional information provided by existing linear frameworks; and (3) a primary focus on short sequences and shallow architectures. To address these issues, we propose FuXi-Linear, a linear-complexity model designed for efficient long-sequence recommendation. Our approach introduces two key components: (1) a Temporal Retention Channel that independently computes periodic attention weights using temporal data, preventing crosstalk between temporal and semantic signals; (2) a Linear Positional Channel that integrates positional information through learnable kernels within linear complexity. Moreover, we demonstrate that FuXi-Linear exhibits a robust power-law scaling property at a thousand-length scale, a characteristic largely unexplored in prior linear recommendation studies. Extensive experiments on sequences of several thousand tokens demonstrate that FuXi-Linear outperforms state-of-the-art models in recommendation quality, while achieving up to 10$\times$ speedup in the prefill stage and up to 21$\times$ speedup in the decode stage compared to competitive baselines. Our code has been released in a public repository https://github.com/USTC-StarTeam/fuxi-linear.

We demonstrate an efficient circuit to prepare a quantum state with amplitudes proportional to a harmonic sequence. We do this by first preparing a large quantum state with linearly related amplitudes and then applying a quantum Fourier transform; this has a direct analogy to the fact that the Fourier coefficients of a sawtooth wave follow a harmonic sequence. We then consider an extension of this problem by block-encoding a matrix with a harmonic sequence along its diagonal. The cost of both circuits is dominated by the costs associated with the quantum Fourier transform.

Large-scale 3D geospatial data visualization has become increasingly critical for the development of the digital society infrastructure in Japan. This study conducted a comprehensive performance evaluation of two major WebGL-based web mapping libraries, CesiumJS and MapLibre GL JS, using large-scale 3D point-cloud data from the VIRTUAL SHIZUOKA and PLATEAU building models. The research employs standardized 3D Tiles 1.1, and Mapbox Vector Tiles (MVT) formats, comparing performance across different data scales (2nd and 3rd grid levels) using Core Web Vitals metrics, including First Contentful Paint (FCP), Largest Contentful Paint (LCP), Speed Index, Total Blocking Time (TBT), and Cumulative Layout Shift (CLS). The results demonstrate that MVT-based building visualization with MapLibre GL JS achieves optimal performance (FCP 0.8s, TBT 0ms), whereas MapLibre GL JS combined with deck.gl shows superior performance for large-scale point cloud processing (TBT: 3ms, CesiumJS: 21,357ms). This study provides data-driven selection guidelines for appropriate technology choices according to use cases, establishing reproducible performance evaluation frameworks for 3D web mapping technologies during the WebGPU and OGC 3D Tiles 1.1 standardization era.

In an age of financial system digitisation and the increasing adoption of digital currencies, Central Bank Digital Currencies (CBDCs) have emerged as a focal point for technological innovation. Privacy compliance has become a key factor in the successful design of CBDCs, extending beyond technical requirements to influence legal requirements, user trust, and security considerations. Implementing Privacy-Enhancing Technologies (PETs) in CBDCs requires an interdisciplinary approach, however, the lack of a common understanding of privacy and the essential technological characteristics restricts progress. This work investigates: (1) How privacy can be defined within the framework of CBDCs and what implications does this definition have for CBDCs design? and (2) Which PETs can be employed to enhance privacy in CBDC design? We propose a comprehensive definition for privacy that is mapped to the cryptographic landscape for feature implementation. The research is validated against case studies from 20 current CBDCs. The study shows that comprehensive privacy can be designed in the proposal stage, but that privacy does not reach the launched version of the CBDC.

Structured x-rays carrying an orbital angular momentum break spatial inversion symmetry and have been proposed as a means to probe chirality. We theoretically investigate twisted non-resonant x-ray diffraction from chiral molecules and demonstrate that no dichroic signal can arise from randomly oriented molecules, irrespective of the beam spatial profile. However, a dichroic response is found to emerge if the molecule is oriented. Our results establish the beam and sample conditions for which a measurable dichroic scattering signal survives axial and focal averaging.

Binary convolutional coding (BCC) has been a cornerstone of the IEEE 802.11 wireless LAN standard since its inception, and it remains relevant today across the full generational arc from the legacy 802.11a/g through Wi-Fi 6 (802.11ax) and into the forthcoming Wi-Fi 8 (802.11bn). Although low-density parity-check (LDPC) codes now dominate high-throughput applications, BCC is mandatory for backward compatibility and continues to serve as the default forward-error-correction scheme in bandwidth-constrained and cost-sensitive deployments: 20 MHz-only devices, Internet-of-Things nodes, and other implementations where LDPC's decoder complexity is prohibitive. Critically, BCC at rate 1/2 is the coding scheme used throughout the packet preamble in every IEEE 802.11-compliant frame, making it indispensable regardless of which data-field code is selected. Furthermore, the new Enhanced Long Range (ELR) packet format introduced in the 802.11bn/UHR amendment mandates rate-1/2 BCC for the data portion of the frame, reinforcing the continued importance of this code in next-generation deployments. The performance of BCC under Viterbi decoding is governed by the distance spectrum of the convolutional code. This note explains how to compute that spectrum exactly for the IEEE 802.11 mother code (rate 1/2, K=7, generators octal 133 / octal 171) and its three standard punctured derivatives (rates 2/3, 3/4, 5/6) obtained via rate-compatible puncturing. Union-bound BEP and FER curves are derived for AWGN with BPSK/QPSK and Gray-coded M-QAM modulation and validated against Monte Carlo simulation. Python, Julia, and C++ implementations are openly available at https://github.com/geekymode/bcc_spectrum.

Binary neutron star mergers are thought to produce hot, rapidly rotating neutron stars with masses that can far exceed their Tolman-Oppenheimer-Volkoff mass. The gravitational-wave emission from such remnants provides a unique opportunity to measure the nuclear equation of state at densities and temperatures not available to terrestrial experiments. Current detector design is informed by gravitational-wave signals from general relativistic hydrodynamics simulations of neutron star mergers, typically with hybrid thermal treatments for the equation of state, where a cold equation of state is modified by adding a thermal component. We use realistic equations of state based on the relativistic mean field model with consistent treatment of thermal effects to compute the distribution of expected peak gravitational-wave frequencies. Marginalising over equation of state and progenitor neutron star masses, we show the peak frequency of emission ranges from $\sim2.5$ to 4 kHz. The width of this distribution suggests the need for broadband observatories with kHz sensitivity, and calls into question some of the so-called post-merger optimised configurations. We show the proposed KAGRA high-frequency design is well-suited to measuring post-merger remnants when compared to the KAGRA broadband design.

In this work, the particle number projection at finite temperature is incorporated into self-consistent Skyrme density functional calculations. In particular, the energies of compound nuclei as a function of deformations are calculated rigorously based on projected densities. Results show that the even-odd staggering effect in partition function gradually diminishes as the system approaches the critical temperature. The obtained fission barriers are similar to that without projection at finite temperature, although projected energies are different. The nuclear level density at the ground state and the barrier are also studied using the projection method and the discrete Gaussian method.

The solar cycle - most notably characterized by its sunspot activity patterns - serves as a cornerstone of heliospheric physics. This research uncovers a fundamental magnetic dichotomy in the Sun's full-disk field, identifying two functionally separate populations: the Strong-Field Group (SG) and Weak-Field Group (WG). The solar cycle exhibits a dual nature, much like Janus, with the SG and WG operating in opposing phases regardless of low or high latitudes. The SG-dominated cycle represents one facet of this duality and is visually prominent at the solar surface. It is well-established that this component synchronizes with the sunspot cycle at low latitudes but operates in anti-phase at high latitudes. In contrast, the WG-driven cycle acts as its hidden counterpart, functioning in opposition to the SG at both high and low latitudes -- a behavior that had not been identified until now. Influenced by these magnetic field groups, this dual nature permeates the entire solar atmosphere, revealing that the full-disk solar activity is globally modulated by the Janus cycle.

While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal identification assumptions. When these assumptions do not hold, sensitivity analysis methods can be used to characterize how different violations may change our inferences. The Bayesian approach to sensitivity analyses in causal inference has unique advantages as it allows users to encode subjective beliefs about the direction and magnitude of assumption violations via prior distributions and make inferences using the updated posterior. However, uptake of these methods remains low since implementation requires substantial methodological knowledge. Moreover, while implementation with publicly available software is possible, it is not straight-forward. At the same time, there are few papers that provide practical guidance on these fronts. In this paper, we walk through four examples of Bayesian sensitivity analyses: 1) exposure misclassification, 2) unmeasured confounding, and missing not-at-random outcomes with 3) parametric and 4) nonparametric Bayesian models. We show how all of these can be done using a unified Bayesian "missing data" approach. We also cover implementation using Stan, a publicly available open-source software for fitting Bayesian models. To the best of our knowledge, this is the first paper that presents a unified approach with code, examples, and methodology in a three-pronged illustration of sensitivity analyses in Bayesian causal inference. Our goal is for the reader to walk away with implementation-level knowledge.

Generative Recommendation (GR) has become a promising paradigm for large-scale recommendation systems. However, existing GR models typically perform single-pass decoding without explicit refinement, causing early deviations to accumulate and ultimately degrade recommendation quality. To tackle this problem, we propose GRC, which is, to our knowledge, the first structured reflection-correction framework for GR that extends standard decoding into a Generation-Reflection-Correction (GRC) process. Concretely, GRC introduces a supervised reflection-correction template that decomposes the decoding process into initial draft generation, multi-granular reflection, and reflection-guided correction, thereby enabling structured reflection and correction in the semantic token space. To further explore the enlarged refinement space introduced by the GRC process, we optimize the entire GRC trajectory with GRPO-based reinforcement learning, under a carefully designed reward function with token-level and trajectory-level signals. For efficient online serving, we propose an Entropy-Guided Reflection Scheduling (EGRS) strategy that dynamically allocates more correction budget to high-uncertainty decoding trajectories during beam search. Extensive experiments on real-world datasets show that GRC consistently outperforms six state-of-the-art baselines by up to 15.74%, and online A/B tests demonstrate its substantial practical value in large-scale industrial recommendation, delivering a 1.79% lift in advertising revenue with only modest latency overhead.