We investigate the geometric behavior of $τ(E)$ for bounded finite-perimeter sets $E \subset \mathbb R^n$, where $τ(E)$ is the trace constant introduced by Figalli--Maggi--Pratelli [Invent. Math. 2010]. This quantity is a key ingredient in proving a quantitative isoperimetric inequality with the optimal exponent. We first show that for every $ε>0$ one can find a bounded open set $Ω\subset \mathbb R^n$ that is very close to the unit ball $\mathbb B^n$ in the sense that $$ τ(\mathbb B^n)>τ(Ω)>τ(\mathbb B^n)-ε\quad \text{and} \quad P(ΩΔ\mathbb B^n)\le C(n)ε, $$ while at the same time the complement of $Ω$ has infinitely many connected components. Thus, $τ(Ω)$ can be made arbitrarily close to $τ(\mathbb B^n)$ even when $Ω$ has highly intricate geometry. We then establish, under a mild additional hypothesis, the equivalence between a condition formulated in terms of $τ$ and two classical criteria from the literature for open sets that admit trace inequalities. As a consequence, we obtain the John-type characterization of domains that support a trace inequality, assuming the ball separation property.

Many real-world problems are naturally formulated as higher-order optimization (HUBO) tasks involving dense, multi-variable interactions, which are challenging to solve with classical methods. Quantum optimization offers a promising route, but hardware constraints and limitations to quadratic formulations have hampered their practicality. Here, we develop a distributed quantum optimization framework (DQOF) for dense, large-scale HUBO problems. DQOF assigns quantum circuits a central role in directly capturing higher-order interactions, while high-performance computing orchestrates large-scale parallelism and coordination. A clustering strategy enables wide quantum circuits without increasing depth, allowing efficient execution on near-term quantum hardware. We demonstrate high-quality solutions for HUBOs up to 500 variables within 170 seconds, significantly outperforming conventional approaches in solution quality and scalability. Applied to optical metamaterial design, DQOF efficiently discovers high-performance structures and shows that higher-order interactions are important for practical optimization problems. These results establish DQOF as a practical and scalable computational paradigm for large-scale scientific optimization.

We investigate the regularity of local weak solutions to evolution equations of the form \[ \partial_{t}u\,=\,\sum_{i=1}^{n}\,\partial_{x_{i}}\left[a_{i}(x,t)\,(\vert\partial_{x_{i}}u\vert-δ_{i})_{+}^{p_{i}-1}\,\frac{\partial_{x_{i}}u}{\vert\partial_{x_{i}}u\vert}\right]\,\,\,\,\,\,\,\,\,\,\mathrm{in}\,\,\,Ω_{T}\,=\,Ω\times(0,T)\,, \] where $Ω$ is a bounded domain in $\mathbb{R}^{n}$ with $n\geq2$, the coefficients $a_{i}$ are measurable and bounded, $p_{i}>1$ and $δ_{i}\geq0$ are fixed parameters. Under suitable assumptions on the exponents $p_{i}$, we first show that the local boundedness of weak solutions follows from their membership in an appropriate non-homogeneous parabolic De Giorgi class. We then establish the existence of semicontinuous representatives for local weak sub(super)-solutions. Our analysis extends analogous results available for less degenerate operators and generalizes the local boundedness results obtained in [7] to fully anisotropic, widely degenerate parabolic PDEs with non-smooth coefficients depending additionally on the space-time variables $(x,t)$, whose growth is governed by a family of exponents $p_{i}$ rather than by a single exponent.

The co-segregation of impurities in multicomponent alloys has been widely recognized as an effective strategy for tailoring material properties. However, quantitative predictions of co-segregation behavior remain a significant challenge for alloy design in systems containing multiple solute species. In this work, we develop an extended dual-solute (DS) segregation framework to quantitatively predict co-segregation behavior with solute-solute interactions, including both homoatomic and heteroatomic contributions. A machine-learning workflow is first established to predict the pairwise segregation energy to construct the DS segregation energy spectra that intrinsically include solute-solute interactions. The resulting spectral information is then utilized to determine the upper and lower bounds of segregation for individual solutes. When applied to magnesium-based multicomponent systems constructed by alloying Mg with any two of the 11 candidate solute species, the extended DS segregation framework is successfully validated by hybrid molecular dynamics/Monte Carlo simulations and experimental results available in existing literature. Furthermore, we introduce a design strategy to promote co-segregation by incorporating additional solute species that exhibit attractive interactions with existing solutes, thereby enabling enhanced segregation even in the presence of strong site competition. These results underscore the critical role of solute-solute interactions in governing co-segregation behavior and provide a predictive pathway for the design and optimization of multicomponent alloys.

We develop a theory for the second-order time-reversal-odd ($\mathcal{T}$-odd) angular-momentum current, incorporating both spin and orbital components. We reveal that besides spin and orbital Berry curvature dipoles, $\mathcal{T}$-odd nonlinear angular-momentum current can originate from disorder-induced mechanisms including coordinate shift, side-jump spin and orbital currents, anomalous scattering amplitude, and skew scattering. A general scaling relation is derived to help distinguish some of these contributions in experiments. Model calculations demonstrate that the orbital component can be comparable to and much larger than the spin component. Our theory lays the groundwork for $\mathcal{T}$-odd nonlinear spin and orbital transport.

A skew morphism of a finite group $B$ is a permutation of $B$ fixing the identity and satisfying $φ(xy) = φ(x)φ^{i_x}(y)$ for some integers $i_x$ indexed by $x \in B$. The enumeration of skew morphisms of finite cyclic groups remains an open problem. The most substantial progress to date concerns cyclic $p$-groups with $p$ odd, for which a full classification and enumeration was obtained by Kovács and Nedela. In this paper we treat the remaining case $p = 2$, giving a complete classification and enumeration of skew morphisms of finite cyclic $2$-groups. Writing $\mathrm{Skew}(n)$ for the number of skew morphisms of $\mathbb{Z}_n$, we prove that $\mathrm{Skew}(2^e) = 4\,\mathrm{Skew}(2^{e-1}) - 4$ for each $e \geq 4$, and that $\mathrm{Skew}(2^e) = (7 \cdot 4^{e-2} + 8)/6$ for each $e \geq 3$. This completes the enumeration of skew morphisms for all cyclic $p$-groups.

We study the edge-expansion of the graph of a random $0/1$ polytope $P^d_p$, defined as the convex hull of a random subset of the points in $\{0,1\}^d$ where every point is retained independently and with probability $p$. This problem was introduced more than twenty years ago in a work of Gillmann and Kaibel, and has been extensively studied ever since. We prove that, for every fixed $\varepsilon>0$ and every $p\in(0,1-\varepsilon]$, with high probability the graph of $P^d_p$ has edge-expansion $Θ(d)$. This improves the previously best known bound due to Ferber, Krivelevich, Sales and Samotij, and verifies, in a strong form, the celebrated Mihail-Vazirani conjecture for random $0/1$ polytopes. Although the expansion factor $Θ(d)$ is typically best possible for $p\ge 1/2+\varepsilon$, we also show that the behaviour changes drastically at $p=1/2$. Namely, for every fixed $\varepsilon>0$ and every integer $k\ge 2$, if $p\le 1/2-\varepsilon$, then with high probability the graph of $P^d_p$ has edge-expansion $Ω(d^k)$. Thus, random $0/1$ polytopes exhibit an interesting phase transition at $p=1/2$.

Let H(k) be the smallest N such that every finite coloring of [N] contains a monochromatic or rainbow k-term arithmetic progression. Erdős and Graham asked whether $H(k)^{1/k}/k \to \infty$ (Problem #190 of the Erdős Problems database). We prove that there is an absolute constant $k_0 \ge 2$ such that for all $k \ge k_0$, \[ H(k)^{1/k}/k \ge (1/e - \varepsilon(k)) \cdot k/\log k, \qquad \varepsilon(k) = O(k^{-0.475} \log k) \to 0 \text{ as } k \to \infty; \] in particular $H(k)^{1/k}/k = Ω(k/\log k)$ and $\lim_{k\to\infty} H(k)^{1/k}/k = \infty$, resolving the positive direction of the Erdős-Graham question. The argument combines three standard ingredients -- the symmetric Lovász Local Lemma applied to the k-AP hypergraph on $[N]$, the restricted form of the Blankenship-Cummings-Taranchuk recurrence, and the Baker-Harman-Pintz prime-gap theorem -- together with the pigeonhole reduction $H(k) \ge W(k-1,k)$, and uses BHP as the only analytic black box. Previous applications of Erdős-Lovász had fixed $r$; the improvement here is that the $r^{k-1}$ base dominates once one allows the color count $r_0 = \lfloor k / \log k \rfloor$ to grow with $k$. No matching upper bound on $H(k)^{1/k}/k$ is known.

Checking whether database transactions adhere to isolation levels is a crucial yet challenging problem. We present Boomslang, the first general-purpose checking framework capable of verifying configurations that were previously uncheckable. Boomslang advances beyond prior work in three key aspects: (1) it supports arbitrary operation types provided by modern transactional key-value stores, (2) it requires no knowledge of database internals, and (3) it offers a modular, extensible pipeline amenable to customization and optimizations. Boomslang adopts a front-/back-end separation. As the front-end, it parses a database trace into an Abstract Semantic Graph, which is then lowered -- via semantic analysis -- into a low-level intermediate representation (IR). The back-end converts this IR to a set of constraints for SMT solving. This design is enabled by a key abstraction in the IR, called superpositions, which capture the uncertainty and complexity caused by arbitrary operations and missing information. Our experiments show that with just 271--386 lines of code, the core logic of three prior checkers can be reimplemented as Boomslang modules, achieving comparable or superior performance. Using Boomslang, we also identify a new bug in TiDB, audit the metadata layer of the JuiceFS file system, check vendor-specific behavior in MariaDB, support five previously unchecked isolation levels, and confirm a theoretical result on the correctness of strict serializability.

We present a non-Abelian model for magnetic monopoles in inhomogeneous media, based on a generalization of the standard 't~Hooft-Polyakov model. The medium is described by spatially dependent couplings in the gauge and scalar sectors, constrained by $P(|Φ|,r)M(|Φ|,r)=1$ so that the Bogomol'nyi-Prasad-Sommerfield (BPS) bound is preserved. For static spherically symmetric configurations, we study the first-order monopole equations for the class of generalized permeabilities $M(H,r)=f(r)/H^α$. For the power-law profile $f(r)=r^β$, we determine the domain in the $(α,β)$ plane where regular BPS solutions exist. On the line $α=1$, the system becomes exactly integrable, with closed-form monopole solutions in an inhomogeneous background. Away from this analytical sector, the solutions are constructed numerically. The model supports a rich spectrum of configurations, including effectively point-like monopoles, compact-core monopoles, hollow monopoles, shell-like structures, and multi-shell monopoles characterized by multiple concentric peaks in the energy density.

Wavefront engineering for applications in near-field wireless connectivity is gradually becoming common ground. In this landscape, beams that propagate on bent paths are ideal candidates for dynamic blockage avoidance and suppression of potential eavesdropping. In this work we study the physical layer security offered by bending beams, and we demonstrate their capabilities for line-of-sight and non-line-of-sight eavesdropping. We analyze the dependencies between the possible locations of an eavesdropper and the design parameters of such beams, and we introduce metrics to assess their physical layer security performance. Our results demonstrate their superiority with respect to beams generated with conventional beam-forming.

Low-scale leptogenesis scenarios, such as the resonant or ARS leptogenesis, typically require a highly degenerate mass spectrum of right-handed neutrinos (RHNs). This requirement can be circumvented by extending the seesaw framework with a scalar singlet $S$ that couples to RHNs via the $S N^{}_I N^{}_J$ terms (with $I \neq J$), which opens up new decay channels $N^{}_I \to N^{}_J S$ and provides additional sources of CP violation, thereby enabling successful leptogenesis at the TeV scale without the need for mass degeneracy. In this work, we point out that the flavon fields, which are introduced in many flavor-symmetry neutrino mass models to be responsible for the generation of RHN masses through the acquisition of non-zero vacuum expectation values, serve as ideal candidates for the $S$ field. Taking as an example a flavor-symmetry neutrino mass model that naturally realizes the experimentally allowed TM1 mixing pattern and has the attractive features that only one flavon field plays the role of $S$ and that it couples to only two RHNs, we demonstrate that the observed neutrino masses and mixing angles can be consistently reproduced, while the observed baryon asymmetry can be achieved within a parameter space compatible with current experimental constraints.

Laddering is the propagation of a topological defect in an everyday-life material: weft knitted fabrics, following a broken thread or a dropped stitch. What is a minor frustration when damaging a pair of tights is a more serious issue for industrial-scale production, but might inspire new solutions to limit and mitigate damage to architected materials. In this work, laddering is investigated in a pre-stressed model knit through experiments and Discrete Element Rod simulations. The control parameter is the initial tension applied on the fabric. A force threshold due to the stitch's natural curvature is evidenced. It controls both the propagation onset and arrest, as tension is relaxed by the thread length freed by ladder growth, and enables damage prediction at moderate tension. Furthermore, we uncovered that the laddering velocity is of the order of the velocity of bending waves and exhibits an unexpected linear scaling with the fabric tension, that arises from a complex combination of elastic and friction forces. Finally, we discuss the implications of our results from the perspective of damage control and mitigation.

We present formulations of effective potentials suitable for approximating general relativistic effects in Newtonian simulations of core-collapse supernovae. Assuming a spherically symmetric spacetime and a stress-energy tensor that includes both fluid and neutrino contributions, Eulerian and Lagrangian projections of the Einstein equations are made to determine general relativistic corrections to the Newtonian gravitational potential. We implement the effective potentials in both the Chimera and Flash-X codes, and perform a series of adiabatic and core collapse simulations. The results are compared to Newtonian and fully general relativistic simulations, as well as another widely used effective potential formulation. We find close agreement between our new effective potentials and the fully general relativistic results from multiple other codes.

Let \(G\) be a finite simple graph and let \(T\) be its Hashimoto operator on the directed-edge space. We show that edge reversal induces a canonical symmetric/antisymmetric splitting under which \(T\) acquires an explicit \(2\times 2\) block form. The diagonal blocks are \(\tfrac12 L(G)\) and \(-\tfrac12 A(G)\), where \(L(G)\) is the line-graph adjacency and \(A(G)\) is the antisymmetric line-graph adjacency, while the off-diagonal block is the mixed incidence product \(M=|D|^\top D\). This identifies the ordinary and antisymmetric line-graph sectors as the two canonical diagonal sectors of Hashimoto theory and isolates a mixed sector linking them. A Schur-complement argument then gives a factorization \[ \det(I-wT)=\det\!\bigl(I-\tfrac w2 L(G)\bigr)\,C_G(w), \] where \(C_G(w)\) is an explicit correction determinant built from the antisymmetric and mixed sectors. We show that the trivial roots \(w=\pm1\) localize on canonical edge subspaces, and that for line-graph-cospectral pairs all remaining Ihara separation is forced into the correction sector. Although the raw mixed block \(M\) depends on edge orientation, its natural gauge-invariant shadows, including \(MM^\top\), \(M^\top M\), and \(M^\top L^kM\), define a canonical matrix package attached to the graph. In the regular case these collapse to adjacency-side data, but in the irregular case they need not. As an application, we exhibit irregular non-isomorphic graphs that are adjacency-cospectral and line-graph-cospectral yet are separated by the correction sector, and we find further examples where the gauge-invariant mixed shadows separate even when the scalar Ihara polynomial does not. This isolates new irregular edge-space invariants in Hashimoto--Ihara theory.

As DRAM scaling exacerbates RowHammer, DDR5 introduces per-row activation counting (PRAC) to track aggressor activity. However, PRAC indiscriminately increments counters on every activation -- including benign refreshes -- while relying solely on explicit RFM operations for resets. Consequently, counters saturate even in an idle bank, triggering cascading mitigations and degrading performance. This vulnerability arises from a fundamental mismatch: PRAC tracks the aggressor but aims to protect the victim. We present Per-Victim-row hAmmered Counting (PVAC), a victim-based counting mechanism that aligns the counter semantics with the physical disturbance mechanism of RowHammer. PVAC increments the counters of victim rows, resets the activated row, and naturally bounds counter values under normal refresh. To enable efficient victim-based updates, PVAC employs a dedicated counter subarray (CSA) that performs all counter resets and increments concurrently with normal accesses, without timing overhead. We further devise an energy-efficient CSA layout that minimizes refresh-induced counter accesses. Through victim-based counting, PVAC supports higher hammering tolerance than PRAC while maintaining the same worst-case safety guarantee. Across benign workloads and adversarial attack patterns, PVAC avoids spurious Alerts, eliminates PRAC timing penalties, and achieves higher performance and lower energy consumption than prior PRAC-based defenses.

Device-independence is the gold standard of quantum cryptography. To meet this standard, a central assumption is that no information leakage occurs during protocol execution. We relax this assumption by analyzing CHSH-based randomness certification and key distribution with partial leakage of the inputs, modeled in terms of a noisy channel. Our results quantify the certifiable local randomness and the secret key rate as a function of the magnitude of the input leakage.

Let $n\ge 25$ be an integer. In this paper, we construct a smooth metric $g_{0}$ on $\mathbb{S}^n$ with the property that the set of metrics in the conformal class of $g_{0}$ having positive scalar curvature and positive constant quotient $Q/R$ is non-compact. Equivalently, we construct families of solutions exhibiting blow-up behavior for the following equation \begin{align*} P _{g_{0}}u- \frac{ (n+2 )(n-4 )}{4} u^{ \frac{2}{n-4}} L_{g_{0}}u^{ \frac{n-2}{n-4}} =0, \quad u>0\quad\text{on} \ \mathbb{S}^{n}, \end{align*} where $P _{g_{0}}$ is the Paneitz operator and $ L_{g_{0}}=-Δ_{g_{0}} +\frac{n-2}{4(n-1 )}R_{g_{0}} $ is the conformal Laplacian of $ g_{0}$.

The equilibrium shape of a thin, elastic, inextensible ribbon minimizes its bending energy. It has been shown that, as the width of the ribbon tends to zero, the bending energy Gamma-converges to the so called Sadowsky functional. In this paper we consider geometrically frustrated anisotropic ribbons with a possibly curved reference configuration. We prove that the Gamma-convergence remains valid under prescribed affine boundary conditions, including, in particular, those satisfied by a Möbius strip.

We classify unitary highest weight modules with a given integral infinitesimal character for the real Lie algebras $\mathfrak{su}(p,q)$ and $\mathfrak{so}^*(2n)$. We treat both regular and singular cases. For $\mathfrak{su}(p,q)$ we identify the unitarizable modules in the Hasse diagrams of the highest weight orbit. Analogous results for the other Hermitian Lie algebras were given in our earlier publications.

Fix a 3-manifold $Y$ with boundary $F\amalg F$ and an orientation-preserving involution $τ: Y\to Y$ exchanging the boundary components, with nonempty fixed set. To an appropriate kind of Heegaard diagram for $Y$, we describe how to associate a module over the bordered Heegaard Floer algebra of $F$. These modules satisfy a gluing, or pairing, theorem, and extend the "hat" variant of Guth-Manolescu's real Heegaard Floer homology, $\widehat{HFR}(Y,τ)$. Using these modules, we give a practical algorithm to compute $\widehat{HFR}(Y,τ)$ for real 3-manifolds $(Y,τ)$ with connected fixed set.

We investigate the topology of the different phases of the extended Su-Schrieffer-Heeger (eSSH) model, which includes hopping processes between translationally inequivalent atoms beyond nearest neighbors. Exact analytical expressions for the edge states of a semi-infinite eSSH chain are derived, with wave functions that decay exponentially from the boundary with a unit-cell decay factor z. From the winding number of the bulk Hamiltonian under periodic boundary conditions, we determine the topological phase diagram and establish the bulk-boundary correspondence: changes in the winding number coincide with bulk gap closings and with the condition |z|=1 for the edge-state solutions. For finite chains, we further obtain analytical, approximate expressions for the low-energy edge states, which are shown to be highly accurate.

High-energy photonuclear ($γ+A$) scattering in ultra-peripheral heavy-ion collisions provides a unique probe of nuclear structure. This Letter studies the dependence of $γ+A$ jet production in ultra-peripheral Pb+Pb collisions at $\sqrt{s_{_\text{NN}}} = 5.02$ TeV on the presence of forward neutron emission from either nucleus. The data was taken in 2018 with the ATLAS detector at the LHC and corresponds to an integrated luminosity of $1.72$ nb$^{-1}$. The kinematics of the hard $γ+A$ processes, expressed via the particle-level photon ($z_{-}$) or nuclear parton ($x_{+}$) momentum fractions, are determined from $R = 0.4$ jets reconstructed using the anti-$k_t$ algorithm. At lower $z_{-}$, where the non-diffractive component dominates, the nuclear parton distribution can be cleanly probed in collisions that leave the struck nucleus essentially intact. Such collisions are expected to probe larger impact parameters ($b_\text{A}$) within the target. The shape of the $γ+A$ cross-section as a function of $x_{+}$ in such collisions is found to differ from that in $γ+A$ collisions accompanied by forward neutron emission, with an observed significance of $6.0σ$. These results are consistent at large $x_{+}$ with large $b_\text{A}$ collisions exhibiting no modifications to the parton distributions that are usually observed in hard scattering processes involving nuclei, relative to collisions with smaller $b_\text{A}$. Thus, these measurements provide an experimental observation that the modifications to nuclear parton distributions vary with impact parameter.

Scanning transmission electron microscopy (STEM) is widely used tool for materials characterisation. However, being a scanned technique, STEM is susceptible to sample, stage or beam drift, manifesting as distortions within images or movement in the field-of-view during multi-frame imaging. Often this is corrected post-acquisition using image registration of multiple frames, but drift reduces the usable area common to all frames. Here we present a method to mitigate sample drift by analysing past frames to predict the sampling-grid points for the immediately future frame. We present this correction across two time-scales and two lengthscales. By offsetting the scan-grid framewise we remove long-range drift, and offsetting pixelwise we minimise intra-image warping. Examples are presented for both atomic-resolution imaging and lower-magnification in-situ video capture. The framework is general to raster, serpentine, interlaced and other scan patterns, as well as sequential or scan-rotation series STEM.

We propose an enhanced Chase-Pyndiah decoder that scales extrinsic messages based on decoder confidence of the component decoder, achieving a 0.1 dB gain over the original with negligible complexity increase.

We construct examples of abelian categories with no non-zero injective (or projective) objects satisfying Grothendieck's AB5 condition. The procedure combines Rickard's examples of AB5 categories without products but some non-trivial injectives (also addressing an apparent gap in the literature) with a 2-functorial construct attaching to any category $\mathcal{C}$ that of $\mathcal{C}$-objects equipped with set-indexed families of endomorphisms.

Modern distributed systems produce massive, heterogeneous logs essential for reliability, security, and anomaly detection. Converting these free-form messages into structured templates (log parsing) is challenging due to evolving formats and limited labeled data. Machine-learning-based parsers like Drain are fast but accuracy often degrades on complex variables, while Large Language Models (LLMs) offer better generalization but incur prohibitive inference costs. This paper presents DeepParse, a hybrid framework that automatically mines reusable variable patterns from small log samples using an LLM, then applies them deterministically through the Drain algorithm. By separating the reasoning phase from execution, DeepParse enables accurate, scalable, and cost-efficient log structuring without relying on brittle handcrafted rules or per-line neural inference. Across 16 benchmark datasets, DeepParse achieves higher accuracy in variable extraction (97.6% average Parsing Accuracy) and better consistency than both heuristic and LLM-only baselines. Integrating DeepParse into an anomaly detection pipeline reduced false alarms by over 30% and reduced inference latency by 36% compared to heuristic baselines.

Polytropic models of stellar winds remain to be useful tools because they allow for a simple description of the energy balance of the expanding plasma without explicitly specifying potentially complex energy transport processes like, e.g., heat conduction or extended wave heating. Among recent applications to stellar winds and to the solar wind was a study of the consequences of strongly localized heating in the latter, possibly due to acoustic waves. Such 'nonuniform' heating can result from a time- and space-localized damping of wave modes and allows, as an extreme case, an adiabatic expansion of particular wind streams outside the heating region. The present study generalizes the modeling from the first analytical as well as numerical studies, that were limited to this extreme case, towards a more realistic non-adiabatic behaviour. The additional energy due to heating is demonstrated to be in a plausible range in view of typical flare energies and low compared to the gravitational energy of the plasma in this region. The corresponding solutions may be of interest for stellar winds, in general, and w.r.t. recent observations made with the Parker Solar Probe, which revealed strongly varying wind streams and the presence of acoustic waves near the Sun, for the solar wind, in particular. Potential observational evidence for the solar wind is discussed.

We establish the homogenization results for a class of nonlocal operators of convolution type with integrable jumping kernel $p$ multiplied by rapidly oscillating periodic or locally periodic coefficients. The associated measure $p(z)dz$ is assumed to belong to the domain of attraction of a symmetric $α$-stable law. We also assume that $p$ satisfies a pointwise Lévy type lower bound and an averaged annular upper bound for points bounded away from the origin, and that the local $L^1$ oscillation of $p$ decays faster at infinity than its local $L^1$-norm. Under these assumptions, we prove the resolvent convergence of the nonlocal operators and explicitly determine the corresponding homogenized nonlocal operator, which is shown to be comparable to the fractional Laplacian. The proof relies on compactness arguments and a refined analysis based on the annular integral upper bound and an $\varepsilon$-cube decomposition.

Amorphous grain boundary complexions have been shown to be radiation tolerant interfaces that can also reduce grain boundary embrittlement, marking them as favorable microstructural features. However, the incorporation of these features into new alloy systems is often a slow and arduous process based on trial and error. Here, a computational framework for alloy design is presented which enables the selection of dopants that promote the formation of amorphous grain boundary complexions. This framework is primarily built on density functional theory calculations and is demonstrated for W-rich binary and ternary alloys, which represent a promising target for fusion energy materials. Our framework first evaluates the grain boundary segregation tendency of dopants and then the energy penalty for amorphization alongside targeted interfacial energy comparison, with the end goal of identifying the best dopants. For a W base, Y and some transition metals such as Co and Ni are found to significantly lower these energetic barriers. Electronic structure analysis, local lattice distortion, and charge density distributions are calculated and used to provide mechanistic explanations for these dopant selections. Finally, the framework is validated by comparing with experimental literature for W alloys and a refractory complex concentrated alloy, showing a strong correlation between our dopant selections and low sintering onset temperatures that have been attributed to activated sintering. As a whole, this work establishes a transferable pipeline for designing alloys with grain-boundary complexions across diverse alloy systems.