This paper establishes the projective equivalence between the Knizhnik-Zamolodchikov connection and the Hitchin connection in genus 0 with at least 3 marked points. The Knizhnik-Zamolodchikov connection is defined on the sheaf of conformal blocks in the Tsuchiya-Ueno-Yamada model of conformal field theory. The Hitchin connection is defined on the Verlinde bundle via geometric quantisation of the moduli space of flat connections. Pauly's isomorphism establishes the equivalence of these two vector bundles. The main theorem of this paper is that the isomorphism intertwines these two connections up to a scalar-valued one-form. In addition, this theorem is used to construct a Hitchin connection through an auxiliary metaplectic correction. As a corollary of the main theorem, this construction of the Hitchin connection is projectively unique and projectively flat.

The Green-Kubo lattice thermal conductivity computed using the full classical heat current of a crystalline solid is compared with results obtained from the quadratic component of the heat current and from the commonly used Peierls heat current. In addition, thermal conductivity within the relaxation time approximation is evaluated. Three crystalline systems are investigated: solid argon, a model of solid argon with alternating masses, and $α$-quartz. For all materials considered, the thermal conductivities calculated using the quadratic and Peierls heat currents differ only slightly. In the case of $α$-quartz, the optical phonon contribution to the thermal conductivity is found to exceed that of the acoustic modes. The relaxation time approximation systematically underestimates the thermal conductivity in all three systems.

Co-adsorption of Bi and Sb on Ag(111) at room temperature yields a single-layer Bi(1-x)Sb(x) alloy with a rectangular 3xsqrt(3) structure containing four atoms per unit cell (2/3 ML total coverage) and lacking long-range chemical order. We present an electronic structure study of this system combining angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations. To investigate the effect of inversion symmetry breaking induced by substituting a heavier atom (Bi) with a lighter isoelectronic one (Sb) within a fixed crystallographic framework, we focused on a Bi-rich composition. ARPES measurements reveal four surface-state bands, in good agreement with DFT calculations based on a rectangular four-atom overlayer unit cell. DFT calculations further show that Sb incorporation induces both in-plane and out-of-plane asymmetries in the electronic potential, leading to sizable spin splitting and spin polarization of the overlayer bands. Although these effects are partially reduced by interaction with the substrate, they remain significant. Our work illustrates, through a concrete model system, a general principle: incorporating a lighter isovalent element can significantly enhance spin polarization, potentially offering a useful design guideline for understanding and engineering Rashba-related systems.

Most of the laws of Nature involve derivatives up to the second order. Ostrogradski was the first to seek a formulation of the equations of higher-order derivatives. He extended Hamilton's equations by considering Lagrangians that depend on higher-order derivatives of generalized coordinates. The Hamilton-Ostrogradski formulation served as the basis for later studies with higher-order derivatives. However, the Hamilton-Ostrogradski formalism is rarely discussed in textbooks or the pedagogical literature. This motivated us to show how the Hamilton-Ostrogradski formalism can be applied it to the Pais-Uhlenbeck oscillator. We hope that the approach presented in this work can serve as a basis for discussion in advanced classical mechanics courses.

A polygon is equable if its area is equal to its perimeter. A pair of polygons is an amicable pair if the area of the first is equal to the perimeter of the second, and vice versa. A polygon is a lattice polygon if its vertices lie on the integer lattice. We show that amicable lattice rhombuses are actually equable.

Weakly almost i.i.d. quantum sources are sequences of multipartite states whose fixed-size marginals converge, on average, to tensor powers of a reference state, while allowing arbitrary global correlations and entanglement. We establish two concentration principles for such sources: a noncommutative weak law of large numbers for empirical observables, and a universal entropy-concentration principle showing asymptotic concentration on subspaces of exponential dimension governed by the von Neumann entropy of the reference state. These concentration principles provide a unified and conceptually transparent approach to several information-theoretic applications beyond the i.i.d. setting, including direct proofs of universal compression within classes of weakly almost i.i.d. sources sharing a common reference state, asymmetric quantum hypothesis-testing bounds, concentration results for macroscopic observables in quantum many-body systems including generalized Gibbs ensembles and for repeated local measurement statistics, as well as bounds on smooth- and spectral entropy quantities.

Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of quantitative error bounds, which in turn play a key role in guaranteeing the safety of learned controllers and related learning-based algorithms. However, these error bounds rely on a particular property of the target function -- its reproducing kernel Hilbert space (RKHS) norm -- which is usually impossible to obtain in practice. Motivated by this severe shortcoming, we present a novel sampling-based RKHS norm estimation approach with a solid theoretical foundation, leveraging very recent advances in the theory of superconvergence in kernel methods. Our method is applicable to a broad range of practically relevant function classes and requires only reasonable prior knowledge about the target function. Extensive numerical experiments demonstrate the efficacy and practical applicability of the proposed method. By providing a reliable RKHS norm estimation approach, we remove a major obstacle to the practical deployment of learning-based control algorithms.

For $α\ge 0$, let $\mathcal{W}(α)$ be the class of all analytic functions in the unit disk $\mathbb{D}$ with normalization $f(0) = 0 $ and $ f'(0) = 1 $ that satisfy the relation $Re\,\{f'(z) + αz f''(z)\} > 0$. This article aims to establish sharp bounds for logarithmic coefficients $γ_1$, $γ_2$ and $γ_3$ and logarithmic inverse coefficients $Γ_1$, $Γ_2$ and $Γ_3$ of functions in $\mathcal{W}(α)$. The sharp upper and lower bounds for $\bigl|\,γ_2 \,\bigr|-\bigl|\,γ_1\,\bigr|$ and $\bigl|\,Γ_2 \,\bigr|-\bigl|\,Γ_1\,\bigr|$ have been obtained for the class $\mathcal{W}{(α)}$. In addition, we establish sharp inequality for the second Hankel determinant of the logarithmic and inverse logarithmic coefficients for the class $\mathcal{W}{(1)}$.

Steady-state density functional theory, called i-DFT, is employed to compute spectral and transmission properties of general interacting nanoscale regions coupled to electronic reservoirs. Exchange-correlation functionals are constructed for different interactions and coupling geometries. The potential of the method is illustrated by applications to various multiple quantum dots from the Coulomb blockade to the Kondo regime, capturing phenomena such as quantum phase transitions. The results are in excellent agreement with many-body approaches at a fraction of the computational cost.

Explainable AI (XAI) is often criticized for failing to satisfy broad desiderata (e.g., fairness, accountability) and for limited practical value to stakeholders. This challenge partly arises because researchers across disciplines prioritize different sets of desiderata that remain underspecified and context-dependent, yet expect XAI to satisfy them simultaneously, resulting in fragmented and sometimes incompatible operationalizations. We argue that many desiderata are not independent, but instead form dependency structures in which higher-level goals (\emph{e.g.}, trust, accountability) rely on more foundational properties (\emph{e.g.}, faithfulness, robustness). Some desiderata are multi-faceted and are best understood within these structures. In particular, instead of addressing all desiderata at once, we focus on subsets of dependency structures and translate them into concrete XAI tasks, thereby decomposing research questions into benchmarkable and solvable units. To this end, we propose a three-axis taxonomy (\emph{target}, \emph{functional role}, and \emph{mode of justification}) and a three-step framework for deriving well-scoped, benchmarkable XAI tasks. Our approach builds on a systematic literature review and conceptual analysis, and supports clarifying desiderata, identifying dependencies, scoping feasibility, and delimiting the design space to derive concrete XAI tasks from abstract desiderata. We illustrate its utility through two explanatory cases, showing how the taxonomy and framework guide systematic task design and evaluation in XAI. {\color{red}{This is a preprint of a paper that will appear in AISoLA 2026.}}

We present the discovery and characterization of TIC 295741342, a triply-eclipsing triple star system with a giant tertiary. The eclipsing binary consists of two similar main-sequence stars in a 4.75-day orbit. The binary is in a 412.8-day orbit with the giant tertiary. We found two degenerate solutions for the system: one where the tertiary is ascending the Red Giant Branch (RGB), and the other where the tertiary is on the Horizontal Branch (HB) and will eventually ascend the Asymptotic Giant Branch (AGB). In both solutions, the system is near-perfectly coplanar. In TESS Sector 33, the binary passes behind the giant tertiary, producing a distinctive "head-and-shoulders" eclipse that directly constrains the relative flux contributions and radii of all three stars. We modeled the system using a comprehensive spectro-photodynamical model that simultaneously fits the TESS lightcurve, eclipse times, spectral energy distribution, and radial velocities from 48 TRES spectra obtained over four years of observation resolving all three components. Evolutionary analysis using MIST tracks indicates that, in both solutions, the tertiary will overflow its Roche lobe, one in the RGB and the other in the AGB. The Roche lobe overflow will initiate either a stable mass transfer to the binary or a common envelope evolution that will likely result in ejections and/or mergers. Our models predict the midpoint of the next outer eclipse will occur on September 1, 2026 and we encourage follow-up observations with a $\pm$3 day window to observe the full event and further constrain the system parameters.

Digital quantum simulation offers a promising route for studying quantum dynamics, but efficient operator representations and circuit depth remain key challenges for near-term hardware. We investigate one-dimensional wave packet dynamics using a grid-based encoding of the wave function onto qubit registers. Time evolution is implemented via split-operator approach, with kinetic energy operator applied using Quantum Fourier Transform (QFT) with polynomial scaling and potential energy operator expressed through commuting Pauli-Z gates, improving accuracy and enabling incorporation of arbitrary discretized potentials. While the full Pauli decomposition of Hamiltonian scales exponentially as O(4^n ), the present approach reduces the operator scaling to O(2^n) for n qubits. We benchmark this approach on classical simulators and quantum hardware (IBM Quantum and IonQ) for two- to five-qubit implementations. For two- and three-qubit cases, all platforms qualitatively reproduce the benchmarked dynamics; at larger qubit counts, the IBM results deviate more strongly, whereas IonQ remains closer to the benchmark.

Quantum Key Distribution (QKD) provides secure keys for classical communications through one-time-pad (OTP) encryption with physical-law security. Advanced PON-based Classical Access Networks (CANs) support up to 256 users with a total rate of 10 Gbps (10-Gbps @ 256-users). The equivalent rate demand of OTP encryption requires QKD Access Networks (QANs) to reach comparable performance, yet state-of-the-art PON-based QANs remain far from this standard. To address this gap, we propose a passive Thermal-State QAN (TS-QAN) distributing polychromatic quantum randomness from a single thermal source and supporting 304 users with an aggregate secret key rate (SKR) of 13 Gbps (13-Gbps @ 304-users). This performance is enabled by three features. First, broadband thermal states with Bose-Einstein statistics can be represented, through the Glauber-Sudarshan representation, as high-bandwidth Gaussian coherent-state ensembles across frequency modes, eliminating many active modulators and quantum random number generators (QRNGs). Second, Electro-Optic (EO) comb beacons provide time-varying polychromatic phase tracking, so each frequency-mode thermal signal can be coherently measured with a Local Local Oscillator (LLO) aided by its beacon, without large-scale phase-locking networks. Third, state broadcasting allows each user to obtain independent final keys via reverse reconciliation after accounting for residual broadcast-induced correlations, expanding network capacity with small SKR losses. Experimentally, we verify a 13-Gbps @ 304-users TS-QAN using Continuous-Variable QKD (CV-QKD) under covariance-matrix-based network security analysis including multimode Holevo leakage and broadcast correlations. This work meets the SKR and capacity demands from CAN to QAN: 13-Gbps @ 304-users satisfies the 10-Gbps @ 256-users benchmark and provides a scalable solution for modern telecommunication systems.

In this paper we propose a novel unified cosmological model that connects a pre-inflationary epoch, starting at the Planckian time, with the onset of inflation within a single scalar-field framework. The pre-inflationary phase is characterized by a decelerated expansion with an increasing comoving Hubble horizon, followed by a gradually transition to an accelerated inflationary regime. This early dynamics leads to a modified causal structure that naturally accounts for the suppression of large-angle $(θ\gtrsim 60^\circ)$ correlations in the cosmic microwave background (CMB) reported by the satellite PLANCK. We study the quantum fluctuations of the scalar field using the Mukhanov-Sasaki formalism and a canonical quantization procedure based on energy minimization. We find that the vacuum state is well-defined only for sub-horizon modes at the onset of inflation, which induces a natural cutoff in the primordial power spectrum. The resulting spectrum exhibits a suppression at large scales while remaining nearly scale-invariant at small scales. In the appropriate limit, the model recovers the standard de Sitter result, in agreement with current observational constraints. These results highlight the relevance of pre-inflationary dynamics for addressing large-scale anomalies within a consistent inflationary framework.

We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a Lyapunov transform and rescaling, we enlarge the class of nonlinear systems that can be efficiently simulated on quantum computers. For systems that exhibit stability in the shifted coordinates, we establish long time convergence of the truncated Carleman embedding. We prove that the truncation order scales only logarithmically with the simulation time and target precision, and we derive end-to-end quantum query complexity bounds for preparing a state proportional to the final solution. By introducing a modified nonlinearity condition, this framework entirely removes the conventional lower bound requirement on the initial condition. For more general systems that remain unstable after shifting, we provide short time convergence guarantees that are similarly free from the initial condition constraints. Numerical experiments on the logistic and the Lotka-Volterra equations demonstrate that an appropriate pivot choice improves stability and accuracy, and yields exponential error decay with truncation order. These results show that pivot shifting provides a practical and theoretically justified route for extending Carleman-based quantum algorithms to a broader class of nonlinear dynamical systems.

The seminal work of Roth, Sönmez, & Ünver shows that the Edmonds-Gallai structure theorem for non-bipartite matching can be leveraged to yield a randomized algorithm to match patient-donor pairs in kidney exchange with extraordinarily strong properties. This breakthrough led to randomized polynomial-time algorithms to find a maximum-cardinality matching maximizing individual fairness objectives--measured by the probability that nodes are matched--such as Nash social welfare. But the exchanges allowed in practice go beyond cardinality matching, generalizing to weighted variants and allowing structures such as paths and 3-cycles. We show that strongly polynomial algorithms guaranteeing the same fairness properties can be obtained in weighted settings for matching and 2-paths. While even maximum cardinality coverage with cycles and paths of length at least three is NP-hard, we provide a general result showing that any optimization subroutine (for whichever structure is allowed) can be bootstrapped using a polynomial number of calls to yield a mechanism that has analogous fairness properties to those obtained for matching. We complement these theoretical results with computational results, both on well-studied synthetic data-sets and on samples drawn from real data, that demonstrate the striking advantages of adding fairness considerations to more general kidney-exchange mechanisms.

The coherent nonlinear dynamics between collective excitations, such as magnons and phonons, drive emergent phenomena in quantum materials, yet their direct observation remains a central challenge. Here, using double-terahertz-pump optical-probe spectroscopy, we report the direct observation of coherent magnon-phonon three-wave mixing in the layered antiferromagnetic insulator FePS$_{3}$. We resolve both second- and third-order nonlinear responses of antiferromagnetic magnons and identify a suite of nonlinear couplings in two-dimensional (2D) coherent spectra, including definitive sum- and difference-frequency generation between magnons and phonons. These results lay the groundwork for exploiting coherent nonlinearities to entangle magnetic and vibrational excitations, opening avenues for quantum control and hybrid quantum technologies in the terahertz regime.

Determining the dynamics of interacting integrable many-particle quantum systems at finite times after homogeneous quantum quenches is a long-standing challenge. We present a Monte Carlo sampling scheme that numerically evaluates the Lehmann representation for time-dependent expectation values of local operators, allowing us to access system sizes and times significantly beyond the reach of existing methods. The approach accommodates both the full Lehmann sum and the Quench Action formalism. We benchmark against exact results for non-interacting lattice and continuum models and short-time results at weak interactions, finding excellent agreement. We apply the method to quantum quenches from a Bose-Einstein condensate in the repulsive Lieb-Liniger model and determine the time evolution of the order parameter for a wide range of interaction strengths. We discuss the emergence of a "sign problem" for more general dynamical correlators and setups.

The article deals with the role of gravitational radiation energy in the large-scale dynamics of the universe. Motivated by the observed accelerated expansion, we investigate whether gravitational energy, treated as a well-defined physical quantity within the teleparallel equivalent of general relativity, contributes to cosmological acceleration through its associated energy flux. Using radiative space-times described by the Bondi--Sachs framework, we analyze the total gravitational energy and the corresponding energy flux evaluated in asymptotic regions. Particular emphasis is placed on the cumulative character of gravitational radiation over long time scales and on the fact that gravitational energy in this formulation is not positively definite. The present analysis provides a consistent theoretical basis for assessing the relevance of gravitational radiation energy and its flux in cosmological contexts.

We develop a Galois descent approach to finite-field Fourier spectra over an arbitrary finite base field. Let $\mathbb K=\mathbb F_q$ and $\mathbb L=\mathbb F_{q^m}$. If a Fourier transform is applied to a $\mathbb K$-valued vector, then its spectrum is not an arbitrary element of $\mathbb L^n$: it satisfies the Frobenius consistency relation \[ V_s^q=V_{qs \bmod n}. \] We prove a general Galois-descent theorem for Fourier transforms on finite abelian groups, characterize the one-dimensional spectra as products of subfields indexed by $q$-cyclotomic classes, and show that the orbit-seed representation is optimal in base-field coordinates. For arbitrary vectors in $\mathbb L^n$, we study a two-stage representation $g=f+h$, where $f$ is class-consistent and $h$ is a residual. The residual optimization separates over cyclotomic classes. We give exact support minimization, a symbol weight enumerator for the class-consistent code, recovery guarantees, global covering-radius formulas, random residual tail bounds, and entropy-type lower bounds. We also discuss implementation consequences for trace decompositions, normal bases, canonical subfield embeddings, and sparse-polynomial residual backends.

Recent results from the Dark Energy Spectroscopic Instrument (DESI) provide evidence for a dynamical dark-energy component, whose equation of state appears to have recently crossed the phantom divide. In this Letter, we present an interacting dark-energy model, grounded in field theory, that naturally accommodates such a double crossing. In our framework, fermionic dark matter is coupled via a Yukawa interaction to a tachyonic scalar field governed by Born-Infeld dynamics. The phantom crossing arises at the level of the effective dark-energy equation of state, while the underlying scalar-field dynamics remains nonphantom and well bounded. We confront our model with data including BAO from the DESI (DR2) survey, CMB distance priors from Planck 2018, and the latest Type Ia supernovae compilations, obtaining robust constraints across the different data combinations and reconstructing a recent double crossing of the phantom divide. Furthermore, under naturalness assumptions, the model expects an ultralight fermionic dark matter mass of order $1.9\times10^{-3}\,\mathrm{eV}$, suggesting a possible connection with new light particles in the dark sector and motivating future tests with cosmological perturbations.

Considering systematically derived energy-transfer-dependent effective electron-electron interactions leads to the appearance of secondary phase and amplitude modes in isotropic superconductors in the intermediate-to-strong-coupling regime. We study the implications of such interactions on Bravais lattices by computing the corresponding response functions using the iterated equations of motion (iEoM) approach. In the weak-coupling regime, we find the conventional, primary amplitude and phase modes at $ω=2Δ$ and $ω=0$, respectively. For intermediate coupling, the amplitude mode detaches from the quasiparticle continuum towards lower energies. Increasing the coupling further leads to additional, long-lived secondary collective excitations below the continuum. This phenomenon is largely independent of the underlying lattice and the specific Fermi level. The amplitude and phase modes couple if the system is not particle-hole symmetric. Additionally, we extend the method to compute eigenoperators, i.e., linear combinations of operators that excite each secondary mode specifically. We identify nodal structures in the coefficients for these eigenoperators reminiscent of wave functions in the Hydrogen problem.

We revisit the renormalisation of models with two U(1) gauge symmetries, in a formulation with non-canonical gauge kinetic terms which is covariant under field reparametrisations among the two gauge bosons. This approach is convenient to study the appearance of kinetic mixing in scale evolution, because a coupling matrix is attributed to the gauge kinetic terms. We obtain simple MSbar renormalisation group equations up to two-loop, which can be solved to give effective millicharges at low energy which depend on the running couplings and heavy mass scales of the model. This formulation allows to construct ``invariants'' out of running Lagrangian parameters, which are invariant under generic gauge field reparametrisations, including rescalings, and which can be related directly to observables such as the millicharge.

Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the derivation of core mathematical principles, such as Peano's axioms (excluding induction), and serves as a foundation for the Abella interactive proof assistant. However, integrating this equality into automated proof search remains challenging. We present a proof search procedure that extends unification to handle the complexities of quantifier alternation and equations that occur in both positive and negative occurrences. While established logical frameworks such as $λ$Prolog and LF lack direct support for this kind of equality, our procedure enables a lightweight logical framework that addresses this gap. Our system enables unification-aware proof search across a diverse range of first-order sequent calculi that can directly use this form of equality.

Let \(A\) be a central simple algebra over a field \(F\) with index \(n\) and let \(\mathrm{SB}_r(A)\) denote the \(r\)-th generalized Severi--Brauer variety associated with \(A\). We prove that the Chow group of zero cycles of degree zero \(\mathrm{A_0}(\mathrm{SB}_r(A))\) is \((d, n/d)\)-torsion where \(d = (r,n)\). Our approach reduces the general case to division algebras of prime power index and yields several new instances in which \(\mathrm{A_0}\) is trivial, together with sharper torsion bounds in general.\\ We also show that if \(F\) is a local or global field, then \(\mathrm{A_0}(\mathrm{SB}_r(A))=0\). Since Severi--Brauer flag varieties are stably birational to generalized Severi--Brauer varieties, these results extend to them, yielding corresponding torsion bounds and vanishing results for \(\mathrm{A_0}(X)\), where \(X\) is stably birational to \(\mathrm{SB}_r(A)\).

AI infra has become a shared execution layer for model training, deployment, and agent orchestration. Because many projects reimplement similar model-centric workflows, a vulnerability disclosed in one repository can recur as a variant in another repository with a related design. Yet the prevalence and detectability of these variants remain poorly understood. This paper presents a measurement study of vulnerability variants in AI infra. Analyzing 688 GitHub repositories and 251 publicly disclosed vulnerabilities, we find that AI infra projects frequently share overlapping functionality and recurrent vulnerable patterns, creating a concrete basis for cross-repository variants. Building on this finding, we study how to automatically identify such variants from known disclosures. We propose INFRASCOPE, a reference-driven multi-agent framework that extracts transferable vulnerability semantics from known cases and uses them to locate and validate variants in new repositories. Evaluating INFRASCOPE on 20 real-world AI infra repositories, we uncover over 20 vulnerabilities, including 11 acknowledged cases and 4 cases that have been assigned CVEs so far.

Template histograms are the foundation of statistical inference at the Large Hadron Collider. The HistFactory likelihood encodes template uncertainty through per-bin Barlow-Beeston gamma factors for Monte Carlo statistical error and through interpolation-based modifiers for systematic shape variations. These two mechanisms scale with the number of bins, which becomes problematic for multi-dimensional analyses and for templates constructed from limited Monte Carlo samples. We propose the use of eigenmode decomposition for efficiently estimating statistical and systematic uncertainties when replacing histogram templates with smooth functional representations derived from log-Gaussian Cox process posteriors fitted to the Monte Carlo data. The posterior covariance, augmented by rank-1 updates for each systematic shape variation, provides a unified eigenmode basis that encodes both statistical and systematic template uncertainty. Truncating to the leading eigenmodes replaces the full set of per-bin gamma factors and interpolation parameters with a small number of Gaussian-constrained amplitudes. We prove that this construction contains Barlow-Beeston as a limiting case and that the Gaussian Process posterior variance is bounded above by the Barlow-Beeston variance at every bin.

Cryptographic algorithms such as AES-128 and SHA-256 are fundamental to ensuring data security and integrity. Although these algorithms are computationally efficient, their performance is often constrained by the processor-centric architectures (e.g., CPUs, GPUs), primarily due to the memory bottleneck. This constraint leads to increased latency and higher energy consumption, particularly when handling large volumes of data. To overcome these challenges, Processing-in-Memory (PIM) has emerged as a promising architectural paradigm, allowing computation to occur directly within or near memory units. By minimizing data movement between the processor and memory units, PIM can significantly accelerate cryptographic algorithms while improving energy efficiency. Several pieces of prior work have demonstrated the effectiveness of PIM at fundamentally accelerating cryptographic algorithms. However, none of the prior works have extensively demonstrated the potential of a real-world PIM system. In this paper, we want to investigate the potential and limitations of real-world PIM in accelerating cryptographic algorithms. As part of our methodology, the UPMEM PIM architecture is used to assess the scalability of cryptographic algorithms. When these algorithms operate on a single rank, their performance remains below that of modern CPUs. However, distributing the computation across multiple ranks significantly enhances performance. When all available ranks are utilized, real-world PIM can accelerate cryptographic algorithms more effectively.

In the present work we investigate the multiscale dynamics of enstrophy in homogeneous isotropic turbulence by exploiting the two-point formalism provided by the Kármán-Howarth-Monin-Hill approach. The study is conducted on direct numerical simulations with a Taylor-based Reynolds number in the range of $140 \lesssim Re_λ \lesssim 400$. The two-point enstrophy budget at scales $r > 10 η$ appears to be entirely determined by production via vortex stretching, which balances enstrophy destruction, and to be dominated by the diffusive transport at smaller scales, thus preventing the emergence of a range dominated by the inertial transport of enstrophy. The decomposition in longitudinal and transverse contributions also highlights a dual nature of the inertial enstrophy flux. In particular, enstrophy appears to be transferred across scales through a non-trivial combination of direct and reverse interscale transfer. It is shown that the dual nature of this transfer is strictly related to the vortex stretching mechanism, which, in addition to producing enstrophy through vorticity amplification, also transfers longitudinal vorticity towards larger scales (by stretching the vortical elements) and transverse vorticity towards smaller scales (by contracting these vortical elements in the radial direction). The sum of these two contributions results in an overall transfer of enstrophy from large towards small scales. We propose the use of the pressure transport term as a proxy to obtain some information on the dynamics of relevant events of inertial energy and enstrophy transport. The new findings highlight the relevance of inertial compression events in longitudinal energy transport. At the same time, a good correlation between transverse energy transport events and the radial contraction of vortical elements due to vortex stretching mechanisms is also found.

This paper studies the Chow and cohomology rings of the Hacking moduli stack $\mathcal{P}^{\mathrm{H}}$ of plane quartics. We construct a smooth proper Deligne--Mumford stack resolving the Calabi--Yau wall crossing between the KSBA and K-moduli compactifications for plane quartics via stack-theoretic weighted blowups. Its coarse moduli space is, up to normalization, the fiber product of the natural diagram relating the KSBA, K-moduli, and boundary polarized Calabi--Yau compactifications. From this, we compute the Poincaré polynomial of $\mathcal{P}^{\mathrm{H}}$, show that the cycle class map is an isomorphism with rational coefficients, and determine generators and relations for its Chow ring in terms of tautological classes. Analogous results are established for the GIT and K-moduli stacks.