The nature of dark matter remains a central problem in cosmology. A compelling possibility is that dark matter is macroscopic, consisting of composite objects formed in the early Universe. We introduce the QCD-AQN framework, a well-motivated scenario in which dark matter is composed of dense aggregates of quark and antiquark matter stabilised by axion domain walls. The framework proposes a unified explanation for both dark matter and the observed matter-antimatter asymmetry. Particular emphasis is placed on existing observational constraints and on observational tests. Finally, we explore a possible QCD-based scenario for dark energy.

Existing GPU spatial sharing systems face a three-way tradeoff: resource utilization, performance isolation, and semantic determinism. Hardware partitioning suffers from hardware under-utilization. Hardware multiplexing fails to avoid performance interference. Recently proposed software-based GPU kernel slicing reshapes floating-point reduction orders, destroying semantic determinism and inducing catastrophic token drift in generative models. We present CoGPU, a transparent spatial sharing system that resolves this trilemma. CoGPU introduces \emph{GPU coroutine}, a novel abstraction that enables logical-to-physical resource decoupling. By dynamically mapping immutable virtual contexts to mutable physical resource via lightweight cooperative migration, CoGPU enables extensible, workload-aware scheduling without altering kernel semantics. Evaluations demonstrate CoGPU simultaneously achieves high utilization, strong isolation, and absolute semantic determinism (guaranteeing zero token mismatch). In multi-tenant co-location, it improves training throughput by up to 79.2\% over temporal sharing and reduces P99 inference tail latency by 15.1\%. Its pluggable architecture supports custom policies; compared to the default policy, a \textsc{TPOT-FIRST} policy further reduces SLO violations by 21.2\% under dynamic traffic.

Precise characterization of the local spin environment of single diamond nitrogen-vacancy (NV) centers is crucial for advancing quantum sensing, quantum networking, and the optimization of quantum materials. However, single NV center fluorescence measurements requires long averaging times to obtain clean data that is suitable for conventional model fitting, and that constitutes a key experimental bottleneck for high-throughput characterization. To address this, we introduce \textsc{NVRNet}, a physics-informed simulation-to-reality machine learning pipeline that maps minimal-sweep, noisy Ramsey data to a denoised waveform while directly estimating the hyperfine coupling to proximal ${}^{13}\mathrm{C}$ nuclear spins. The pipeline's denoiser utilizes a two-stage time-frequency U-Net and an attention-augmented time-domain U-Net, pretrained on Hamiltonian-based spin-dynamics simulations with experimentally calibrated noise. To effectively bridge the simulation-to-reality gap, parameter-efficient adapters are attached to the backbone and fine-tuned on targeted experimental data. Across three distinct NV centers, this experimentally fine-tuned model reduces the median reconstruction error on held-out, few-sweep traces to $0.44\text{-}0.67\times$ of the raw experimental noise level. Subsequently, a transformer-based estimator extracts the underlying hyperfine parameters. Forward reconstructions derived from these inferred parameters faithfully reproduce the dominant experimental time- and frequency-domain features, yielding representative normalized fast Fourier transform (FFT) reconstruction errors of $0.10\text{-}0.19$. By reducing both the required data volume and acquisition time, \textsc{NVRNet} enables up to $\sim 40\times$ acceleration of the measurement process, establishing a fast, hardware-compatible pathway for robust hyperfine inference and autonomous qubit characterization.

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.

This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application of symmetric polynomials (Waring's formulas) to the classical Binet's formula. Particular attention is given to the binomial expansion for the generalized Fibonacci sequence, which structurally combines two adjacent binomial coefficients from Pascal's triangle.

Genetic analyses indicate minimal gene flow across the so-called Eastern Pacific Barrier (EPB) in larvae of the reef-building coral \emph{Porites lobata}. Notably, Clipperton Atoll, situated on the eastern side of the EPB, is the only site that exhibits detectable genetic connectivity with the Line Islands, which lie to the west of the EPB. To elucidate the relationship between this genetic signal and large-scale Pacific Ocean circulation, we analyze historical trajectories of surface-drifting buoys from the Global Drifter Program (GDP). We first discretize the GDP drifter trajectories into a Markov chain representation and subsequently apply transition path theory (TPT) in combination with Bayesian inference. The TPT analysis identifies reactive trajectories -- pathways that connect the Line Islands to Clipperton Atoll with minimal detours -- whose travel times do not exceed 5 months, which is taken as an upper bound for the larval survival time of \emph{P. lobata}. Consistently, the posterior distribution of transport from Pacific islands west of the EPB to Clipperton Atoll attains a local maximum in the Line Islands at a travel time of approximately 2.5 months. Our probabilistic characterization of the Lagrangian dynamics therefore supports a scenario of weak, but non-negligible, permeability of the EPB, in agreement with the genetic evidence, and it motivates a refined dynamical definition of the EPB based on the remaining duration of reactive trajectories. Furthermore, our results indicate that the connectivity between the Line Islands and Clipperton Atoll is governed primarily by the seasonal modulation of the North Equatorial Countercurrent, rather than by the phase of the El Niño--Southern Oscillation (ENSO). Finally, Clipperton Atoll's role as a terminal sink for trajectories is relevant to the planned mining operations.

We revisit and extend the construction of bulk local states in flat holography, focusing on the induced representation obtained from the flat limit of the AdS highest-weight conditions. In three dimensions we clarify the scaling mismatch between bra and ket states in the flat basis and resolve it by introducing a dual basis, which yields a smooth flat limit and reproduces the correct Green's function. For higher dimensions we construct bulk local states explicitly, both in the momentum basis and in an alternative tilde basis. The flat limit of the AdS$_{d+1}$ construction is shown to be non-uniform in the descendant level and the Riemann-sum treatment over the scaling window $n\sim l$ converts the discrete descendant expansion into the continuum momentum representation, recovering the massive propagator. The tilde basis generalizes seamlessly to any dimension and is related to the three-dimensional flat basis by a sign factor. These results establish the induced representation as the correct algebraic foundation for bulk reconstruction in flat holography and provide a unified framework valid for arbitrary dimension.

We analyze many-body entanglement in interacting fermionic systems by using the $M$-body reduced density matrix. We demonstrate that if a particle number conserving fermionic Hamiltonian contains only up to $M$-body interaction terms, then its $N$-particle ground state cannot be maximally $M$-body entangled. As a key step in the proof, we show that the energy expectation value of a maximally $M$-body mixed state is equal to the spectral mean of the Hamiltonian on the corresponding $N$-particle subspace. We further demonstrate that the many-body entanglement structure of a ground state can place quantitative constraint on the interaction strength of its parent Hamiltonian. We illustrate the theorem and its implications in Hubbard and extended SYK models. Going beyond ground states, we analyze entanglement generation under unitary dynamics from Slater-determinant initial states in these models. We determine early-time growth and estimate entanglement saturation times. Finally, we derive explicit symmetry-refined saturation upper bounds for $M$-body entanglement in the presence of an Abelian symmetry.

We present SpectralUnmix, an R package for regularized non-negative matrix factorization (NMF), implemented in torch with optional GPU acceleration. The package estimates low-rank non-negative representations through proximal-gradient updates and allows smoothness regularization along the spectral axis. As a compact demonstration, we apply the method to a subset of stellar spectra and compare the recovered NMF components with principal-component directions and representative stellar spectra. The package is released under the MIT license at \href{https://rafaelsdesouza.github.io/SpectralUnmix/}{this repository}.

We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm's output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an $(\varepsilon,0)$-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every $(\varepsilon,δ)$-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.

The recent release of high-precision cosmological data, particularly the small-scale cosmic microwave background (CMB) measurements from ACT and baryon acoustic oscillation (BAO) data from DESI, has opened a new landscape for probing the neutrino mass. In this work, we present updated constraints on the total neutrino mass, $\sum m_ν$, and its hierarchy within the $Λ$CDM, $w$CDM, holographic dark energy (HDE), and $w_0w_a$CDM models, using the latest ACT DR6, DESI DR2, and DESY5 datasets. We find that the upper limits on $\sum m_ν$ are critically governed by the evolutionary behavior of the dark energy equation of state. Specifically, models exhibiting early-time quintessence features (e.g., HDE) yield the most stringent constraints, whereas those allowing for early-time phantom behavior (e.g., $w_0w_a$CDM) result in significantly looser bounds. Despite these model-dependent variations, we observe a robust hierarchy dependence across all scenarios, where the inverted hierarchy consistently yields weaker constraints and the degenerate hierarchy consistently yields tightest constraints. Our analysis demonstrates that the improved small-scale CMB information from ACT, combined with high-precision BAO data, systematically tightens the limits on $\sum m_ν$, providing a crucial benchmark for future neutrino mass measurement.

We introduce and study strongly vertex dismissible, vertex dismissible, and scalable simplicial complexes as non-pure extensions of vertex decomposability and shellability. Strong vertex dismissibility is defined recursively by relaxing the shedding vertex condition, while vertex dismissibility and scalability are determined by the initial dimension skeleton. These classes form a strict hierarchy in which strong vertex dismissibility implies vertex dismissibility, which in turn implies scalability, and scalability implies initially Cohen-Macaulayness. On the algebraic side, we define strongly vertex divisible ideals, vertex divisible ideals, and ideals with degree quotients, and show that they are precisely the Alexander duals of the corresponding topological classes. This perspective yields a unified topological and homological structure together with skeletal characterizations that recover several classical results. For complexes of initial dimension one and the independence complexes of co-chordal and certain cycle graphs, this chain collapses to the purely combinatorial condition of weak connectedness.

Let $f_θ$ be the joint density of a random sample $X$. A frequently used criterion asserts that a statistic $T(X)$ is minimal sufficient if, for any sample points $x$ and $y$, $T(x) = T(y)$ exactly when there exists a finite constant $h_{xy} > 0$, independent of $θ$, such that $f_θ(y) = f_θ(x)h_{xy}$ for all $θ$. We show that this criterion is false in general via a counterexample exploiting the non-uniqueness of versions of Radon--Nikodym derivatives. Although Sato (1996) established sufficient regularity conditions for the validity of this criterion, these conditions are frequently intractable to verify in practice. We resolve this limitation by introducing a version-robust method applicable whenever sufficiency is known. Moreover, our method allows us to generalize Sato's approach from Euclidean settings to arbitrary analytic Borel sample spaces and separable measurable statistic spaces. We also obtain a method for exponential-family densities under verifiable hypotheses. Taken together, these results clarify when pointwise likelihood-ratio arguments for minimal sufficiency are mathematically sound in irregular settings. Finally, we construct a counterexample demonstrating that a distinct criterion for minimal sufficiency due to Pfanzagl (1994, 2017) similarly fails in the absence of supplementary hypotheses. Identifying minimal sufficient statistics is important not only for parsimonious data reduction but also because, in models admitting complete sufficiency, such statistics provide a practical route to the complete sufficient structure underlying optimal estimation and prediction.

This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous inclusions remains a key challenge for various practical applications. For problems involving a large number of scatterers, the number of iterations in Krylov subspace methods is known to increase significantly. This occurs even when using second-kind boundary integral equations, which are typically recognized for their rapid convergence. We consider a fast direct solver as an alternative, an approach that has been less commonly explored for transmission problems with disjoint multiple inclusions. The low-rank approximation based on the proxy method achieve speedup by calculating interactions between disjoint scatterers without the terms derived from the internal integral representation. Notably, this advantage applies to the Poggio--Miller--Chang--Harrington--Wu--Tsai (PMCHWT) formulation but breaks down in the Burton--Miller case. Numerical examples demonstrate that the proposed solver can compress the system of linear algebraic equations to a size of $O(ωD)$, where $ω$ is the frequency of the incident wave and $D$ is the diameter of the (smallest) bounding box enclosing the multiple inclusions. The total computational cost scales as $O(N^{1.5})$ $(= O(\sqrt{N}^3))$ at most for a fixed $ω$ when the inclusions are arranged on a grid. Moreover, the PMCHWT formulation, that omits the interior term in the proxy method, is approximately six times faster than the Burton--Miller formulation when treating each inclusion as a cell. Furthermore, in the same setting, the former can compress the size of the system of linear algebraic equations by half compared to the latter.

In this paper, we study the asymptotic behaviour of the product tail probability $ \mathbb{P}(ξ_1\cdotsξ_N \geqslant n), $ where $\{ξ_1,\ldots,ξ_N\}$ is a finite collection of independent Poisson random variables with positive parameters $λ_1,\ldots,λ_N$. We derive a refined Laplace-type asymptotic formula for the tail probability, based on Stirling's logarithmic approximation, a constrained saddle-point method, the Lambert function, and a careful evaluation of the constrained Gaussian prefactor. This yields an explicit approximation with an $O(\log n)$ remainder term in the exponent.

We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the form E(t)u_t, which introduces a nonstandard feedback structure coupling the dynamics and the energy functional. Weak solutions are constructed via Galerkin approximations, with the passage to the limit relying on uniform energy estimates and compactness arguments. Special attention is devoted to the critical nature of the nonlinearity, where concentration phenomena prevent purely energy-based methods from yielding refined spacetime control. This difficulty is resolved by incorporating nonhomogeneous Strichartz estimates together with smoothly truncated spectral approximations, ensuring uniform bound at the dispersive level. Finally, we establish polynomial decay rates for the energy by adapting Nakao's method to the present nonlinear dissipative framework. The results highlight the stabilizing effect of the energy-dependent damping and its interaction with the critical wave dynamics.

Josephson junction (JJ) chains combine the coherence of superconductivity with the controllability of microwave-frequency circuits, making them a powerful platform for circuit quantum electrodynamics. In this work we consider a long JJ chain that effectively realizes a multi-mode cavity with nonlinear dispersion and additional multi-mode interactions. Individual modes appearing due to the finite size of the chain can be experimentally probed via microwave spectroscopy, both in equilibrium and in driven far-from-equilibrium settings. We study the role of multi-mode interactions in degrading internal coherence -- observable as excess linewidth -- in both equilibrium and driven regimes. Focusing on two-into-two mode scattering as the leading relaxation process, we classify the relevant scattering processes and derive their expected temperature- and frequency-scaling under equilibrium conditions. For experimentally relevant parameters, we show that the equilibrium decay rate is dominated by non-resonant processes, however weakly driving a particular set of modes out of equilibrium enhances resonant scattering, leading to observable signatures in the distribution function and linewidth. Finally, in the strong non-equilibrium regime we report a crossover to a qualitatively different non-equilibrium steady state.

We study ultra-Planckian $2\to2$ scattering in an Abelian gauge theory coupled to agravity, the scale-free and renormalizable realization of quadratic quantum gravity. Focusing on charged fermions and scalars interacting with the photon and the higher-derivative graviton, we present compact analytic expressions for the unpolarized squared matrix elements for a broad set of tree-level processes, including photon--photon, fermion--fermion, fermion--photon, scalar--fermion, scalar--photon, scalar--scalar, and annihilation channels. In contrast to purely graviton-mediated analyses, we retain systematically the photon--graviton interference contributions and verify explicitly the independence of the results on the gravitational gauge-fixing parameter. The amplitudes display characteristic forward/backward enhancements associated with small momentum transfer, amplified by the $1/p^{4}$ graviton propagator, while their high-energy scaling reflects the underlying dimensionless gravitational couplings. Moreover, for all channels analyzed the corresponding differential cross sections exhibit the universal ultra-Planckian scaling $dσ/dΩ\propto 1/s$, where $s$ is the Mandelstam invariant (the squared center-of-momentum energy). Our results furnish a unified amplitude-level description of how higher-derivative gravity reshapes familiar QED scattering at ultra-Planckian energies and provide analytic building blocks for further studies of IR definitions and UV consistency in agravity with matter.

We have successfully developed and implemented an entire and compact table-top high-order harmonics generation (HHG) setup from monochromatic and intense femtosecond ($10^{-15}$ s) laser pulses launched in a target composed of a high-purity monoatomic noble gas specie, which can be Argon or Helium, distinctively. Its frequency arrangement is distributed both in the full eXtreme UltraViolet (XUV, $22-124$ eV) spectral region and in the bottom part of the Soft-X Ray range (SXR, $124-132$ eV), at once. Specifically, the core of this coherent secondary light source is based solely on a homemade, modular, affordable, though sturdy, design. We take advantage of this opportunity to present our design guidance of the XUV generation from a hollow capillary waveguide apparatus, and our simple recipe regarding the alignment process of the latter, which is easily carried out thanks to our adjustable design. Then, a comprehensive description of our entire XUV beamline is described, and participate in adding essential contents to the existing literature. Concurrently, we conducted theoretical studies, in order to anticipate or explain our experimental results. Overall, we found very good consistency between the experimental and cost-effective time-consuming numerical results. Finally, our setup provides very good vacuum performance under high gas load pressures, to a few atmospheres. All of these attributes fulfill the requirements regarding ultrafast time-resolved pump-probe configuration in table-top element-sensitive spectroscopy of complex and integrated optoelectronic devices made of magnetic materials.

Event cameras emit asynchronous brightness-change events where each pixel triggers an event when the last event exceeds a threshold, yielding a history-dependent measurement model. We address online maximum-likelihood identification of continuous-time dynamics from such streams. The latent state follows a Neural ODE and is mapped to predicted log-intensity through a differentiable state-to-image model. We model events with a history-dependent marked point process whose conditional intensity is a smooth surrogate of contrast-threshold triggering, treating the contrast threshold as an unknown parameter. The resulting log-likelihood consists of an event term and a compensator integral. We propose a receding-horizon estimator that performs a few gradient steps per update on a receding horizon window. For streaming evaluation, we store two scalars per pixel (last-event time and estimated log-intensity at that time) and approximate the compensator via Monte Carlo pixel subsampling. Synthetic experiments demonstrate joint recovery of dynamics parameters and the contrast threshold, and characterize accuracy--latency trade-offs with respect to the window length.

This paper introduces the concepts of the augmented Zarankiewicz number $z_A(m,n)$ and the limited augmented Zarankiewicz number $z_L(m,n)$, which are natural combinatorial extensions of the classical Zarankiewicz number. These numbers arise from augmented bipartite graphs that may contain both standard edges (1-edges) and pairs of edges representing squares of binomials (2-edges). The main theoretical result establishes the inequality chain $\operatorname{BSR}(m, n) \geq z_A(m, n) \geq z_L(m, n) \geq z(m, n)$, linking the maximum biquadratic sum-of-squares (SOS) rank to these extremal graph parameters. We determine the exact values of $z_L(m, n)$ for the cases $(m,2)$, $(3,3)$, $(4, 3)$ and $(4,4)$, and provide new lower bounds for the cases $(5,3)$, $(5,4)$, and $(5,5)$. These results yield improved lower bounds for the maximum SOS rank of biquadratic forms, demonstrating that $z_L(m,n)$ can exceed the classical Zarankiewicz number, thereby offering a refined combinatorial perspective on the SOS rank problem.

We infer the age of the R127 and R128 clusters in the Large Magellanic Cloud (LMC) using Strömgren photometry from the literature and the age-dating algorithm, Stellar Ages. Analysis using single-star evolutionary models shows a substantial discrepancy between the relative numbers of bright blue stars and lower-mass stars as compared to expectations from a Salpeter mass function, and yields a younger age for the brightest blue stars than for the rest of the cluster. This inconsistency reflects an emerging trend among young clusters in the Local Group. In general, the resolution may be binary evolution or very rapid rotation, although in the specific case of the R127 and R128 clusters, unknown incompleteness in the data may also affect the relative numbers of low- and high-mass stars. The discrepancy grows toward fainter magnitudes, suggesting that the dataset is likely incomplete. However, when the five brightest stars are excluded, the observed and expected counts become consistent, demonstrating that the brightest stars are peculiar. These findings have direct implications for the luminous blue variable (LBV) R127, which is the only confirmed LBV in the LMC located within a young stellar cluster. LBVs have traditionally been considered products of single-star evolution, although there is growing recognition that binary interactions may play a critical role in their evolution. A more complete dataset, particularly deeper imaging with the Hubble Space Telescope, is needed to confirm whether the apparent absence of coeval stars arises solely from observational incompleteness or the broader trend of inconsistency in young cluster modeling.

We report the discovery of a Lyman-alpha emitter (LAE) protocluster at z = 4.90 in the COSMOS field, comprising four distinct overdensity peaks spanning ~65 x 36 cMpc$^2$, with the primary concentration exhibiting a 4-fold surface density enhancement relative to the field within a 1.5 proper Mpc (pMpc) radius. Using SILVERRUSH narrowband survey data combined with JWST COSMOS-Web imaging, we perform a first systematic rest-frame optical and UV morphological comparison of protocluster versus field LAEs at this redshift using JWST NIRCam rest-frame UV (F150W, ~2540 Angstrom) and optical (F277W, ~4700 Angstrom) imaging. Sersic profile fitting for 16 protocluster members and 23 field LAEs reveals a size difference: protocluster LAEs are $\sim$40% larger in rest-optical (median $R_e = 0.81_{-0.04}^{+0.26}$ kpc vs. $0.58_{-0.04}^{+0.11}$ kpc, $p = 0.041$) with no significant difference in rest-UV ($p = 0.51$) or Sersic index. At fixed stellar mass, protocluster LAEs are offset by $+0.12$~dex ($\simeq$31%) in rest-optical size from the field size-mass relation (68% CI: $[+0.08, +0.21]$; Mann-Whitney $p = 0.033$), with 75% exhibiting positive size residuals compared to 44% of field LAEs. This wavelength-dependent environmental signature suggests that protocluster environments at $z \simeq 5$ preferentially affect extended stellar populations, possibly through tidal interactions, with no significant environmental difference detected in rest-UV sizes, providing observational evidence for environmental influences on the structure of LAEs during the early build-up phase of cosmic star formation.

Restaurants, cafes, pubs, and takeaways are among the most visible markers of neighborhood change, yet whether their arrival is capitalised into nearby housing values remains empirically unsettled. We assemble a London-wide panel linking Land Registry prices, non-domestic EPC lodgement timings for food-and-drink establishments, and neighborhood amenity measures at the LSOA level. Our preferred annual event-study design defines treatment as the first clean-onset year in which an LSOA records at least two eligible EPC lodgements for food-and-drink establishments, after a two-year lookback with no prior entries. In this specification, pre-trend tests are not rejected in either the stacked or Sun-Abraham estimators, and log house prices rise gradually from about 0.5% in the event year to roughly 3.4--3.7% by years four and five. The results are consistent with local amenity capitalization following commercial entry, while remaining appropriately cautious about endogenous siting and concurrent redevelopment.

While real quantum devices have been increasingly used to conduct research focused on achieving quantum advantage or quantum utility in recent years, executing deep quantum circuits or performing quantum machine learning with large-scale data on current noisy intermediate-scale quantum devices remains challenging, making classical simulation essential for quantum machine learning research. However, such classical simulation often suffers from the cost of gradient calculations, requiring enormous memory or computational time. To address these problems, we propose a method to fuse multiple consecutive gates in each of the forward and backward paths to improve throughput by minimizing global memory accesses. As a result, we achieved approximately $20$ times throughput improvement for a Hardware-Efficient Ansatz with $12$ or more qubits, reaching over $30$ times improvement on a mid-range consumer GPU with limited memory bandwidth. By combining our proposed method with gradient checkpointing, we drastically reduced memory usage, making it possible to train a large-scale quantum machine learning model, a $20$-qubit, $1{,}000$-layer model with $60{,}000$ parameters, using $1{,}000$ samples in approximately $20$ minutes per epoch. This implies that we can train the model on large datasets, comprising tens of thousands of samples, like MNIST or CIFAR-10, within a realistic time frame (e.g., $20$ hours per epoch). Thus, our proposed method significantly accelerates such classical simulations, making a significant contribution to advancing research in quantum machine learning and variational quantum algorithms, such as verifying algorithms on large datasets or investigating learning theories of deep quantum circuits like barren plateaus.

Photomultiplier tubes (PMTs) are used in Imaging Atmospheric Cherenkov Telescopes (IACTs) to detect Cherenkov light produced by air showers induced by gamma rays in the atmosphere. The afterpulsing rate of the PMTs for the Large-Sized Telescopes (LSTs) of the Cherenkov Telescope Array Observatory (CTAO) was found to increase if they were kept unused in storage. In contrast, PMTs that had been operated in the first LST showed a slight decrease in the rate. This decrease could be explained by a reduction of residual gas caused by ion feedback, although the detailed mechanism remained unclear. In this study, to investigate factors responsible for the evolution in the afterpulsing rate, we operated several PMTs under different high voltage and light illumination conditions. We monitored their rate daily for three weeks to compare their evolution under different conditions. We found that the reduction of afterpulses require both illumination and high-voltage operation. Notably, the reduction strongly depends on the applied high voltage and is closely correlated with the integrated anode current. Therefore, we conclude that the reduction of residual gas is mainly caused by ionization occurring at later dynodes of the PMTs, and the ions are trapped by the dynodes. We also discuss a possible explanation of the reduction of afterpulsing rate by later dynodes.

The Weiner's theory (WT) is developed on the basis of the exactly solvable Schrödinger equation with trigonometric double-well potential (TDWP). The symmetric case of TDWP is considered. This modified version of WT (mWT) enables one to eliminate some severe approximations of the original Weiner's approach and to obtain more accurate results. An analytic formula is derived which provides the calculation of the proton transfer rate with the help of elements implemented in {\sl {Mathematica}}. We exemplify the application of mWT by calculating the proton transfer rate constant in the hydrogen bond of the proton-bound ammonia dimer cation ${\rm{N_2H_7^{+}}}$ (${\rm{H_3N\cdot\cdot\cdot H^{+} \cdot\cdot\cdot NH_3}}$). The parameters of the model for this object are extracted from available literature data on IR spectroscopy and quantum chemical calculations. The approach yields the transition from the Arrhenius-like exponential temperature dependence characteristic of thermal activation to that of quantum tunneling. Besides it is well suited for describing the phenomenon of vibrationally enhanced tunnelling.

Twist-stacked graphene with a twist angle $θ$ of $\sim 5^\circ$--$30^\circ$ retains two-dimensional monolayer graphene-like Dirac states near the Dirac point. In three-dimensional nanoporous graphene (3D-NPG), curvature inherently produces twist-stacking and topological defects required to form a porous network. When regions with $θ\ge 5^\circ$ dominate, Dirac states in individual layers are expected to persist, allowing the Dirac-electron behavior to be tuned through coupling to the 3D curved geometry. However, predicted band gap formation or localized states have remained unobserved. Here we report that 3D-NPG maintains monolayer-like Dirac electronic states while simultaneously exhibiting insulating behavior near the Dirac point. Raman G-band softening confirms these monolayer-like states, and an Arrhenius-type temperature-resistance trend coexisting with weak localization near the Dirac point indicates partially insulating states induced by topological defects. These findings demonstrate that 3D-NPG hosts distinctive Dirac electronic states coupled to 3D curvature, providing a platform for developing new functionalities in 3D graphene-based electronics and energy devices.

The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors), is a well-studied question in the case where the distances are in fact deterministically contracted by the drift (global dissipativity condition) or in the case $p=1$ (with reflection couplings). This work focuses on the non-globally dissipative case with $p>1$. This situation was previously considered in \cite{MonmarcheBruit}, but only for elliptic processes, and with a restriction on the diffusivity coefficient (which had to be large enough). Here, we extend this analysis to non-elliptic processes and provide sharper conditions to get contractions along synchronous coupling, including negative results, lower bounds and a characterization (at least in dimension 1) in terms of the maximal eigenvalue of a Feynman-Kac operator.

A wide range of numerical and semi-analytical approaches has been developed for optical modeling of photonic-crystal surface-emitting lasers (PCSELs). However, a systematic framework for comparing their predictive capabilities and identifying their respective validity limits remains largely unexplored. In this work, we introduce a comparative methodology in which four representative methods-including rigorous numerical and effective-index-based approaches-are analyzed and partially hybridized within a coupled-wave-theory framework. Using single- and double-lattice PCSELs as representative models, we demonstrate that this approach not only reveals fundamental differences between predictions of rigorous methods and the coupled-wave-theory framework, but also captures leaky and symmetry-broken phases of bound states in the continuum (BICs) relevant for laser operation.