We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing equations for probability distributions and probability generating functions which involve fractional derivatives of different orders. Closed form expressions for probability distributions and probability generating functions are also provided for several considered models.

A major challenge in computational models of cardiac electromechanics is the reconstruction of myocardial fiber architecture, as direct in vivo measurements of fiber orientation are not feasible. Consequently, rule-based methods are commonly adopted as surrogates. This study investigates the respective roles of macroscopic fiber architecture and microscopic fiber disarray in cardiac electromechanical simulations. A high-fidelity biventricular electromechanical model of a murine heart was developed using a high-resolution myocardial fiber field obtained via mesoscopic optical imaging, which serves as a reference ground truth. A spatial smoothing strategy is introduced to decouple macroscopic fiber organization from local disarray, and the resulting responses are also compared with those obtained using a rule-based fiber field. The results show that passive mechanics and electrophysiological activation are only weakly affected by fiber disarray, with global chamber compliance and activation times remaining largely unchanged across different fiber descriptions. In contrast, active mechanics is highly sensitive to fiber architecture. Moderate regularization of the experimentally measured fiber field enhances the ventricular pumping efficiency of the computational model by reducing microscopic disarray while preserving the macroscopic helical organization, whereas excessive smoothing or rule-based fiber reconstructions lead to unphysiologically strong or inefficient contraction. Within this framework, two commonly adopted surrogate strategies to account for fiber disarray are investigated: a reduction of the effective cross-bridge stiffness in the active tension model, and the introduction of controlled misalignment between active tension and the local fiber direction. Overall, the results reveal important limitations of commonly adopted surrogate approaches for modeling fiber disarray.

Microscopic description of two-neutron ($2n$) halo candidates $^{31}$F and $^{39}$Na has been realized from nuclear structure to reaction observables for the first time. The reliability of the Glauber reaction model has been confirmed by exactly reproducing the momentum distributions of the benchmark $2n$ halo nucleus $^{11}$Li, with the identical structural inputs from the former work. Combined with the structure from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), the Glauber model is applied to predict the reaction observables, including the reaction cross sections (RCSs) for the fluorine and sodium isotopes bombarding a carbon target at 240~MeV/A and the longitudinal momentum distributions of the fragments after $2n$ knockout reactions. It turns out that the calculated RCSs agree well with the available experimental data and a pronounced increase occurs to $^{29, 31}$F + $^{12}$C and $^{37, 39}$Na + $^{12}$C, which deviate from the original trend of their neighbours. Furthermore, the narrower longitudinal momentum distributions of the fragments after $2n$ knockout reactions demonstrate that $^{31}$F and $^{39}$Na have the dilute $2n$ halo structure. Such a new combination is promising to suggest new $2n$ halo candidates for future measurements.

Bergeron and Ceballos defined a Hopf algebra structure on equivalence classes of subword complexes. We introduce a category of subword complexes, endow it with a proto-exact-like structure, and show that the corresponding dual Hall Hopf algebra is isomorphic to the algebra of Bergeron-Ceballos. We prove that the full subcategory of root-independent objects is proto-abelian in the sense of Dyckerhoff. We give a categorical lift of flips in subword complexes. We consider a version of a category of formal direct sums of subobjects for a root-independent subword complex and interpret it in terms of quivers. If the corresponding quiver is a tree, the category is endowed with a proto-exact structure. We show that its Hall algebra is isomorphic to the Hall algebra of the category of representations of this quiver over $\mathbb{F}_1$. Under certain conditions, a flip corresponds to changing a proto-exact structure while keeping the category the same up to isomorphism, which corresponds to a non-trivial automorphism of the Hall algebra. In type $A$, this leads to a realization of the nilpotent part of the universal enveloping algebra and its automorphisms.

The waiting time statistics of solar flares provides clues for the underlying physical mechanisms. However, flares occurring on the far-side have been missing in the statistics. In the 2024 May and June, the Solar Orbiter (SolO) spacecraft orbiting behind the Sun, together with near-Earth spacecrafts, provides a unique opportunity to study one of the most flare-productive active regions, NOAA \sar, over its lifetime, as well as the flare occurrence over the entire solar globe. Derived from time intervals between flare peak times, the waiting time distribution (WTD) is fitted by exponential, log-normal, power-law, and \levy functions with the maximum likelihood estimation method. The goodness of fit is evaluated by the Kolmogorov-Smirnov test, and the statistical models are discriminated by information criteria. The major statistical results are: the WTD of flares in the \sar leans towards the log-normal function, while that in the `normal' \rar towards the \levy function; the WTD of global flares defies the local Poisson hypothesis, and its overall profile cannot be reasonably fitted by any of the four candidate distributions, but its power-law tail $Δt^{-α}$ is steeper ($α>3$) than the theoretical expectations ($α\le3$), due to the decreased number of long waiting times ($>10^4$ s) and the increased number of shorter waiting times when the far-side flares are taken into account. These results highlight the importance of studying the flare WTD from a global perspective, and suggest that the long-range magnetic connections in the corona may play a role in the flare occurrences.

We present a comprehensive 20-year multiwavelength variability study of the blazar PKS 2155-304, one of the most luminous and extensively monitored high-frequency-peaked BL Lac objects in the southern hemisphere. Using Fermi-LAT $γ$-ray data together with Swift-XRT and UVOT observations spanning 2005-2024, we trace the long-term evolution of its flux, interband correlations, and spectral behaviour across the optical, X-ray, and $γ$-ray bands. All flux distributions are compatible with log-normality. Interestingly, the optical domain exhibited a notable baseline change around 2009, but this has no strong influence on the fit of the flux distribution. While interband flux-flux correlations are found, no stable temporal lags emerge. This implies varying correlation patterns between epochs. The X-ray emission displays a robust harder-when-brighter trend, however with epoch-dependent slopes, while the $γ$-ray spectra show only mild flux dependence. The fractional variability increases systematically with energy within a given radiation component. No direct correlation of the year-wise fractional variability with the corresponding average flux could be found. Interestingly, a pronounced X-ray spectral upturn, detected during a low state in 2012, points to an additional radiative component. As the connection from this upturn to the $γ$-ray spectrum is not smooth, it probably is not the onset of the inverse-Compton component, but more likely points either to a hadronic contribution or an additional spatially-separate emission zone. These findings reveal the complexity of variability patterns in PKS 2155-304 and the non-uniform nature of its particle acceleration and emission processes.

A system of three or four particle can be entangled in a number of different ways. It may be the case that only subsets of the particles are entangled, and these subsets are not entangled with each other. It may also be the case that the state is the sum of states in which entanglement only exists within subsets. If this is not the case, the state is said to be genuinely entangled. GHZ states, for example, are genuinely entangled. Deciding whether a state is genuinely entangled is not simple, but conditions do exist to detect it. Here we would like to propose additional sufficient conditions based on one for bipartite entanglement.

Societies and organizations often fail to surface latent consensus because individuals fear social censure. A manager might suspect a silent majority would offer a criticism, support a change, report a risk, or endorse a policy -- if only it were safe. Likewise, individuals with beliefs they think are rare and controversial might stay quiet for fear of consequences at work or an online mob. In both cases pluralistic ignorance produces a public discourse misaligned with privately-held beliefs. Social assurance contracts unlock latent consensus, making the public discussion more accurately reflect the underlying distribution of actual beliefs. They are akin to an open letter that publishes only when a stated threshold number of private signatures is reached. If it is not reached, nothing is revealed and no one is exposed. Whereas a single hand raised in dissent might get cut off, a thousand can be raised safely together. I build a formal model and derive rules for choosing the threshold. The mechanism (i) induces participation from those willing to speak if assured of company, resolving the core coordination problem in pluralistic ignorance; (ii) makes the threshold a transparent policy lever -- sponsors can maximize success, maximize public-coalition revelation, or hit a desired success probability; and (iii) turns success into information: meeting the threshold publicly reveals hidden agreement and can widen the range of views that can be expressed in public. I consider robustness to mistrust, organized opposition, and network structure, and outline low-trust implementations like cryptographic escrow. Applications include employee voice, safety and compliance, whistleblowing, and civic expression.

We develop a geometric formulation of peak statistics in cosmological density fields based on optimal transport and entropy. In this framework, the density field is treated as a probability measure, and its local structure is characterized by the Hessian of the log-density, which arises as the local response of an entropy functional in Wasserstein space. Peaks are thereby defined as positive-curvature stationary points, and their number density is expressed as a curvature-conditioned point process. In the linear Gaussian limit, the joint distribution of local variables closes in terms of a finite set of spectral moments, recovering the standard theory of peak statistics, known as BBKS. This clarifies that BBKS corresponds to a solvable limit of a more general structure combining probability distributions, curvature constraints, and geometric measure. The framework extends naturally beyond Gaussianity and linearity. Deviations from Gaussianity are incorporated as deformations of the joint distribution of curvature variables, while nonlinear structures are described through the curvature of the log-density. We further derive the two- and three-point peak statistics as curvature-conditioned $n$-point measures, and show that the full hierarchy of peak statistics can be organized as response functions to long-wavelength background modes. In this formulation, the conventional peak bias appears as the lowest-order response coefficient, with higher-order correlations arising as its natural extensions. This work embeds peak theory into a unified geometric framework and provides a systematic basis for incorporating nonlinearity, non-Gaussianity, and higher-order statistics, with direct relevance for observational applications.

Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the between-set correlation matrix. The canonical analysis provides a low-rank approximation to the between-set correlation matrix that is optimal in a generalised least squares sense. This article proposes to adjust the between-set correlation matrix using either a single scalar effect, or column and/or row effects. An alternating generalised least squares algorithm is proposed to obtain optimal adjustments and low-rank factorisations. The adjustment leads to a better approximation of the between-set correlation matrix that achieves a lower root mean squared error in comparison with the classic canonical analysis. The results of the adjusted analysis can be efficiently visualised using biplots, with a minimal change in interpretation rules that only affects the biplot origin. Biplot calibration is used to enhance the visualisation of the results of the adjusted analysis. Some examples with publicly available data sets from social science, geochemistry and medical science illustrate the proposed improvement. Software for carrying out the adjusted canonical analysis in the R environment is provided.

Prion-like propagation of misfolded proteins is a key mechanism underlying the progression of neurodegenerative diseases such as Alzheimer's disease. In previous work, we introduced the HeMiTo framework, describing these prion-like dynamics for a class of heterodimer models in terms of three phases: the healthy (He), mixed (Mi), and toxic (To) phases. While the He-phase was characterised analytically, the Mi-phase was described numerically and the To-phase was inferred from linear stability arguments. In this work, we provide a complete analytical characterisation of the Mi- and To-phases for our class of heterodimer models. We derive exact inner solutions governing the Mi-phase and match them with outer solutions from the He-phase, explaining the concave-like behaviour of the healthy species and establishing explicit conditions for exponential growth of the toxic species with a mechanistically interpretable growth rate. Furthermore, we formalise a quasi steady-state reduction near the toxic steady state and show that the dynamics reduce to a logistic growth equation, linking exponential growth to saturation. Together, these results provide a unified and mechanistic description of prion-like dynamics across all phases of disease progression and establish a foundation for predictive modelling of biomarker trajectories.

The weakly first-order nature of the two-dimensional 5-state ferromagnetic Potts model poses challenges for numerical study. Using density-matrix and tensor-network renormalization group methods, we investigate these transitions of the Potts-$q$ model via the Klein bottle ratio $g$ on original and dual lattices. Finite-size scaling of $g$ as a function of transverse system size $L_y$ accurately locates the critical points for $q = 4, 5, 6$. We further examine the transfer-matrix spectra and entanglement entropy, extracting central charges through toroidal and Klein bottle boundary conditions. For $q = 5$, the extracted central charge ($c \approx 1.14811$) is close to the real part of the theoretical value $c_{5\text{-Potts}} = 1.1375 \pm 0.0211 i$ predicted by complex conformal field theories. The observed drift in the scaling exponent $b$ effectively distinguishes the continuous transition from the weakly first-order regime. Furthermore, the extrapolated divergence of $g$ confirms the first-order nature of the $q=5$ Potts model.

Workplace stress is often addressed through visual or auditory interventions, yet these modalities can compete with attention and contribute to sensory overload. We explore olfaction as an alternative ambient medium for representing stress-related physiological signals in office settings. We present AuraDesk, an olfactory data physicalization system that translates wearable-derived physiological cues into situated scent expressions at the workstation. The system combines local physiological state inference with a constrained actuation strategy to produce temporally regulated and spatially localized scent output suitable for everyday work environments. To examine the feasibility and experiential qualities of this approach, we conducted a one-day in-situ field deployment with 25 knowledge workers at their actual workstations. Our findings show that participants often interpreted the scent output not as an explicit alert, but as a subtle atmospheric cue that supported momentary awareness, micro-break taking, and perceived environmental attunement. At the same time, participants raised important concerns regarding scent preference, habituation, and contextual appropriateness in shared offices. This work contributes (1) an olfactory interface for physiologically driven ambient feedback in the workplace, (2) a hybrid mapping approach for coupling continuous biosignal interpretation with constrained scent actuation, and (3) empirical insights into how workers perceive, negotiate, and appropriate ambient olfactory feedback in real office contexts. Rather than claiming therapeutic efficacy, we position AuraDesk as a probe into the design space of olfactory data physicalization for workplace wellbeing and attention-sensitive interaction.

In the neutrinophilic Higgs doublet framework, the neutrino Dirac Yukawa couplings can be sizable because of the small vacuum expection value of the extra Higgs doublet, even for a low seesaw scale. Due to this structure, the neutrinophilic charged Higgs bosons, once created, decay dominantly into heavy neutral leptons (HNLs) and charged leptons. This is a new mechanism to produce a gauge singlet HNL without suppressed cross sections. In the standard seesaw, one HNL can be long-lived, when the lightest neutrino is sufficiently light. We investigate displaced vertex signatures of the long-lived HNLs produced from the decays of the charged Higgs pair at the high luminosity LHC. We consider one displaced vertex as well as two displaced vertices signatures and perform a dedicated simulation to identify the displaced leptons. We find that high statistical significance can be achieved for the observation of one displaced vertex for charged Higgs pair production cross section $>\mathcal{O}(1)$ fb. On the other hand, the observation of two displaced vertices is challenging even for charged Higgs pair production cross section of $\mathcal{O}(10)$ fb.

With the rapid expansion of low-altitude economy (LAE) services and the growing demand for integrated sensing and communication (ISAC) in air-ground networks, reliable direction-of-arrival (DOA) estimation has become essential for both directional communication and sensing functions. DOA underpins beam alignment, spatial-reuse scheduling, and ISAC-critical tasks such as airspace situational awareness and multi-target monitoring. Hybrid analog-digital (HAD) architectures have emerged as a practical solution for large-aperture directional operation under stringent radio frequency (RF), analog-to-digital converter (ADC), and size, weight, and power (SWaP) constraints. However, HAD compresses antenna-domain observations through analog combining, fundamentally reshaping the measurement model and introducing new algorithmic and system-level challenges for DOA estimation. This article first reviews the principles and representative architectures of HAD, highlighting their advantages for scalable beam-centric and ISAC-oriented operation in LAE scenarios. We then provide a structured overview of HAD-enabled DOA estimation methodologies, including spatial covariance matrix (SCM) reconstruction, multi-combiner scan-based acquisition, and pilot-aided estimation, along with key design tradeoffs. Finally, we discuss open challenges and outline reliability-driven research directions toward robust, deployable HAD-enabled DOA solutions for practical ISAC-enabled low-altitude environments.

We develop a unified Fisher-information framework for localization in environments with both Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) paths, focusing on diffraction-dominated NLOS propagation characteristic of Outdoor-to-Indoor (O2I) signal propagation. The model couples anchor geometry with a physically grounded path-loss law that is continuous across the LOS/NLOS boundary and serves as an optimization objective for our optimal anchor placement problem. As the first step, we analyze single-target anchor placement and derive the classical A-, D-, and E-optimality criteria. Under a specific path-loss assumption, these criteria collapse to a polygon-closure condition in the complex plane: A-, D-, and E-optimal designs coincide, yielding necessary and sufficient conditions for optimal placement. Next, we extend the notion of optimal anchor placement with respect to a single target to optimality over a feasible region (multi-target setting) using a general formulation that explicitly includes a realistic path loss model. This is achieved by recasting the anchor placement as a combinatorial anchor-selection problem with provable guarantees. Next, we specify E- and D-optimal objectives over multiple targets in a predefined feasible target region and show that E-optimality straddles A-optimality (within a constant factor), while D-optimality provides looser bounds. These insights yield two practical algorithms, both mixed-integer second-order cone programs (MISOCP) with exact E-optimal and exact D-optimal objectives that produce robust, region-wide designs under mixed LOS/NLOS conditions.

A sensitivity study for the measurement of $\bar{K}_1(1270)$ decay modes is performed using semileptonic $D$-meson decays. The BESIII experiment is taken as a case study, where a simultaneous analysis of $\bar{K}_1(1270)$ decays to the four thee-body final states $K^-π^+π^-$, $K^-π^+π^0$, $K_S^0π^+π^-$, and $K_S^0π^-π^0$ is presented and a model-independent determination of \mbox{$\mathcal{B}(\bar{K}_1(1270)\to \bar Kππ)$}, without requiring detailed knowledge of intermediate resonant contributions, is proposed.

We study a paradigm of coding for compression of the natural numbers via the zeta distribution and develop a statistical-mechanical interpretation, both in terms of Hagedorn systems and a Bose gas with energy levels given by logarithms of prime numbers. We also propose a simple coding scheme for the zeta distribution that nearly achieves the ideal code length. For block coding of vectors of natural numbers, we derive the micro-canonical entropy function and demonstrate its asymptotic linearity implying that its behavior is analogous to that of a Hagedorn system. We also derive the large deviations rate function, and provide a formula for the best coding parameter in the large deviations sense. We show that due the Hagedorn-type phase transition there is only partial equivalence of ensembles, due to the degeneration of the domain of the partition function.

Deaf and hard of hearing (DHH) students often experience communication barriers in higher education, which are particularly acute in experiential learning environments such as laboratories. Traditional accessibility services, such as interpreting and captioning, often require DHH students to divide their attention between critical tasks, potential safety hazards, instructional materials, and access providers, creating trade-offs between safety and equitable communication. These demands can disrupt task engagement and increase cognitive load in settings that require sustained visual focus, highlighting the limitations of current approaches. To address these challenges, this study investigates Augmented Reality Real-Time Access for Education (ARRAE), an ecosystem based on augmented reality (AR) smart glasses, as a potential intervention for laboratory-based environments. By overlaying interpreters or captions directly into a student's field of view, AR enables the integration of accessibility into hands-on learning without compromising safety or comprehension. Through an empirical study with 12 DHH participants, we evaluate how AR-mediated access influences visual attention patterns and perceived cognitive load during hands-on tasks. The findings suggest that AR-mediated communication shows strong potential to improve attention management and communication accessibility in experiential learning environments, though participants emphasized that accessibility preferences are highly context-dependent. Participants also identified several design and ergonomic challenges, including display positioning, visual fatigue, and compatibility with hearing devices. Together, these results highlight both the promise of AR for supporting accessible participation in visually demanding environments and key design considerations for future systems.

Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing time-decomposition methods as contraction mappings that converge in a finite number of iterations. We derive a finite-time guarantee linking the initial error, convergence rate, and iteration count, defined via a geometric outer--inner-ball condition. We apply this framework to Parareal, deriving explicit estimates for the convergence factor $β$ on nonlinear problems and showing it scales as $\mathcal{O}(h^2)$ when the macroscopic time grid is uniformly refined. Further, we address the failure of standard convergence criteria in chaotic regimes by introducing a proximity function. This chaos-aware criterion weighs solution discontinuities by the system's Lyapunov exponent (or the solver's Lipschitz constant), allowing the algorithm to converge to the correct statistical attractor without enforcing futile pointwise accuracy on divergent trajectories. Numerical experiments on the Logistic, Lorenz, and Lorenz-96 systems demonstrate that this approach decouples the iteration count from the total simulation time. By isolating the intrinsic mathematical bounds from hardware-dependent overheads, we establish that the method is strictly algorithmically scalable.

A folklore conjecture states that the Nahm sum associated with a pair of Dynkin diagrams of type $ADET$ is a modular function. In this paper, we extend this conjecture to Dynkin diagrams of type $ABCDEFGT$ in the context of generalized Nahm sums. The modular Nahm sums are closely related to the characters of 2d rational conformal field theories. In this work, we identify many specific generalized Nahm sums with characters of some well-studied 2d CFTs. For example, we find that the generalized Nahm sums associated with $(T_1, C_r)$ and $(T_1,D_r)$ correspond to the supersymmetric Virasoro minimal models $\mathrm{SM}(4r+6, 4)$ and $\mathrm{SM}(8r+4, 2)$, respectively.

The assessment of unwanted radiated emissions from Active Antenna Systems (AAS) has become a critical issue in adjacent-band coexistence scenarios. In this paper, we establish the existence of a deterministic spatial upper bound on the radiated power of active antenna arrays. We show that the maximum radiated power always occurs in the boresight direction, irrespective of frequency or signal nature (useful signal, nonlinear distortion, or noise), or instantaneous beamforming configuration, thereby defining a conservative spatial upper bound whose angular envelope is solely determined by the elementary radiating building block of the antenna architecture, i.e., the element or sub-array radiation pattern. Starting from a two-element array with third-order nonlinearities, we derive the spatial envelope and extend the result to realistic AAS architectures. The theoretical findings are validated by over-the-air (OTA) measurements performed on a 3.5 GHz Massive Multiple-Input Multiple-Output (MIMO) antenna. The proposed approach offers a simple, robust, and measurement-oriented methodology for coexistence assessments involving beamformed radio systems.

We derive spectral sum rules for inverse powers of the eigenvalues of the Helmholtz equation on a $d$-sphere in the presence of an arbitrary density. By adopting a rigorous renormalization scheme, we remove the divergent contributions of the zero mode and obtain exact expressions for the sum rules without requiring an explicit determination of the eigenvalues, which is generally impossible. As an application, we derive explicit sum rules for the density $Σ(Ω) = 1 + κY_{1,\vec{0}}(Ω)$ in $d=3,4,5$ dimensions and compare them with numerical estimates obtained by approximating the low-lying part of the spectrum with the Rayleigh--Ritz method and the high-energy part with Weyl's formula.

We present a methodological study of quantum simulation of cranking in a Nilsson $+$ pairing Hamiltonian on a fixed deformation grid. The many-body Routhian is mapped to qubits via the Jordan--Wigner transformation and minimized using the Variational Quantum Eigensolver (VQE) in a truncated active space $(M)$. We employ a structured, number-conserving singles-and-doubles ansatz: double excitations implement pair transfer, while singles are restricted to the nonzero Coriolis-coupling graph of the active Nilsson basis. For $M=8$, this yields 42 parameters while preserving particle number exactly. Exact number conservation enforces $\langle P_k \rangle = 0$, so the conventional pairing gap $Δ_κ\propto G\left|\sum_k \langle P_k \rangle\right|$ vanishes identically. We instead introduce a fixed-$N$ pairing-coherence diagnostic, \[ Δ_{\mathrm{coh}} = G \sqrt{\sum_{k \neq l} \left| \langle P_k^\dagger P_l \rangle \right|}, \] used as a scalar measure of off-diagonal pair coherence rather than a BCS gap. We study even-even $^{80,82,84}$Zr. $^{80}$Zr shows a stable oblate minimum at $δ^\ast \approx -0.25$; $^{82}$Zr exhibits the strongest rotational evolution; $^{84}$Zr retains a robust prolate minimum with the largest neutron pairing coherence. These results reflect the present truncated model rather than converged spectroscopy. A cranked BCS calculation on the same grid serves as a qualitative baseline. Comparisons between $M=6$ and $M=8$ show stable trends but visible shifts, so no active-space convergence is claimed. The structured fixed-$N$ ansatz thus captures consistent isotope trends and provides a practical framework to analyze pairing via $Δ_{\mathrm{coh}}$.

Accurate prediction of acid dissociation constants (p$K_{\rm a}$) and the determination of dominant protonation states is critical in drug discovery, influencing molecular properties such as solubility, permeability, and protein-ligand binding. We present Acep$K_{\rm a}$, an advanced application integrated into the PlayMolecule AI platform. Acep$K_{\rm a}$ is built upon the theoretically rigorous Uni-p$K_{\rm a}$ framework, which unifies statistical mechanics with representation learning. By modeling the complete protonation ensemble rather than treating p$K_a$ as a scalar regression target, Acep$K_{\rm a}$ ensures thermodynamic consistency across coupled ionization sites. We describe the application's enhanced architecture, which features a retrained Uni-Mol backbone achieving state-of-the-art performance on standard benchmarks. Furthermore, we detail critical engineering advancements. These include AceConfgen, a proprietary GPU-accelerated conformer generator that achieves a ~40x speed-up compared to NVIDIA's nvmolkit, a streamlined inference engine to directly protonate molecules, and a 3D-aware modality for applying protonation states to bound ligand poses. Finally, we discuss the integration of Acep$K_{\rm a}$ into the PlayMolecule AI ecosystem, a modern AI-assisted environment for molecular modelling and drug discovery.

We develop a continuous-time model for the long-term dynamics of adaptive stochastic optimization, focusing on bias-corrected Adam-type methods. Starting from a finite-sum setting, we identify a canonical scaling of learning rates, decay parameters, and gradient noise that yields a coupled, time-inhomogeneous stochastic differential equation for the parameters $x_t$, first-moment tracker $z_t$, and second-moment tracker $y_t$. Bias correction persists via explicit time-dependent coefficients, and the dynamics becomes asymptotically time-homogeneous. We analyze the associated Fokker-Planck equation and, under mild regularity and dissipativity assumptions on $f$, prove existence and uniqueness of invariant measures. Noise propagation is governed by $A(x)=\mathrm{Diag}(\nabla f(x))H_f(x)$. Hypoellipticity may fail on $\mathcal D_A\times\mathbb R^m\times(\mathbb R_+)^m$, where \[ \mathcal D_A=\{x\in\mathbb R^m:\exists j,\ e_j^\top A(x)=0\}\subset\{x:\det A(x)=0\}=\mathcal D_A^\dagger, \] and critical points of $f$ lie in $\mathcal D_A$. We show $\mathcal D_A^\dagger\neq\mathbb R^m$ and use this to prove exponential convergence of the Markov semigroup $μ_0P_t$ to a unique invariant measure, uniformly in $μ_0$. The proof uses a Harris-type argument, minorization on Lyapunov sublevel sets, control constructions, and hypoellipticity on $(\mathbb R^m\setminus\mathcal D_A)\times\mathbb R^m\times(\mathbb R_+)^m$. This provides a transparent continuous-time view of Adam-type dynamics.

We present micromagnetic simulations and experiments on voltage-assisted field switching in perpendicular magnetic tunnel junctions (MTJs) with a synthetic antiferromagnetic (SAF) free layer, where the magnetic state of one sublayer is detected via tunneling magnetoresistance (TMR). Simulations reveal that local modulation of perpendicular magnetic anisotropy (PMA) in one SAF sublayer leads to distinct switching characteristics. The switching field varies linearly with the anisotropy field, indicating voltage-controlled magnetic anisotropy (VCMA)-dominated dynamics similar to single free-layer devices. We then experimentally study the magnetic switching field of MTJ devices with SAF free layers under applied gate voltage. By varying the MgO tunnel barrier thickness to systematically modulate the resistance-area (RA) product, we enable quantitative separation of spin-transfer torque (STT), VCMA, and Joule heating contributions. Our findings indicate that VCMA dominates in devices with a high RA product, while low-RA devices exhibit nonlinear switching behavior due to enhanced contributions from STT and Joule heating. Furthermore, the effective fields derived from STT, VCMA, and Joule heating contributions under various gate voltages show minimal dependence on device critical dimensions, indicating favorable scaling behavior. This work presents a unified framework analyzing the roles of STT, VCMA, and Joule heating in SAF-based voltage-gated spin-orbit torque (SOT) MRAM, offering key insights for the optimization of performance, energy efficiency, and scalability in SOT-MRAM technologies.

Altermagnets (AMs), characterized by zero net magnetization and momentum-dependent spin splitting, are anticipated to hold significant potential for generating multiple exotic and uncommon superconducting states. However, superconductivity has not yet been realized in AMs to date. Recently, two-dimensional (2D) V$_2$Ch$_2$O (Ch = Se, Te) monolayers, as well as AV$_2$Ch$_2$O (A = K, Rb, Cs) crystals containing [V$_2$Ch$_2$O]$^{δ-}$ building layers, have been predicted and/or demonstrated to be promising altermagnetic materials. Our preliminary attempts to explore superconductivity in these materials by applying pressure or chemical doping were unsuccessful. Here we report the discovery of superconductivity at a relatively high transition temperature of ~ 16.3 K in a newly synthesized layered compound, Na$_{2-x}$V$_2$Se$_2$O, a variant of AV$_2$Ch$_2$O. In this structure, the [V$_2$Ch$_2$O]$^{δ-}$ layers are interspersed with double layers of Na$^+$ instead of a single layer of A$^+$, with sodium sites being only half-filled. This new family of layered vanadium oxychalcogenides, lacking inversion symmetry, represents an intriguing platform for exploring altermagnetic superconductors, and holds the potential to reveal novel phenomena, such as topological states, van Hove singularities, and finite-momentum superconductivity. Furthermore, this material acts as a "bridge" between the cuprate/nickelate and iron-pnictide high temperature superconductors, providing new hope and opportunity to expand the category of layered superconductors with higher critical temperatures (T$_c$) and enhancing our understanding of the underlying mechanisms in these systems.

Topological interlocking assemblies (TIA) are arrangements of blocks such that rigid-body motions of the blocks are fully constrained by their neighbours and a fixed frame. In this work, we investigate tubular interlocking structures derived from the sine curve and parametrised by several geometric design parameters. We analyse the behaviour of these parametrised tubular interlockings under various boundary conditions and examine how our proposed parameters influence the mechanical response. For this purpose, we first develop a simplified multibody dynamics formulation that enables an efficient exploration of how the design parameters of the block influence the load transfer within the assembly. To further corroborate these results, we perform several finite element simulations, which give insights into the mechanical behaviour of our proposed TIA. Our results show that the block geometry plays a decisive role in the mechanical performance of the corresponding TIA. We additionally discuss the problem of exploding TIAs and demonstrate that the TIA resulting from our Sine Block does not exhibit this behaviour. Lastly, we provide evidence that non-exploding TIAs possess better mechanical properties than exploding ones.

Microscopic description of one neutron ($1n$) halo candidates $^{40,42}$Al, with particular triaxial shape, is presented by combining the triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc) with the Glauber reaction model for the first time. In this scheme, the reaction cross sections of aluminum isotopes on a carbon target at 240 and 900 MeV/A are calculated, which exhibit a pronounced increase for $^{40,42}$Al + $^{12}$C deviating from the systematic trend of their neighbours. Furthermore, the predicted longitudinal momentum distributions of the residues after $1n$ removal reactions for $^{40,42}$Al + $^{12}$C are narrower than those for $^{36,38}$Al + $^{12}$C, which suggest halo structure with spatially extended density distribution. Based on the large occupation probabilities of $p$-wave valence neutrons, we identify $^{40,42}$Al as the first triaxially deformed $1n$ $p$-wave halo candidates. This work cast a new light on the search for the heavier halo nuclei for future experiments in the mass region of $A\approx40$, through theoretical predictions from triaxial structure to reaction observables.