Fermion condensate inflation, where inflation emerges from four-fermion interactions induced by spacetime torsion, removes the need for additional scalar fields beyond the Standard Model. In this framework, the fermion field can be decomposed into two distinguished sectors, each giving rise to bound states. After integrating out fermions, the bound fields play the roles of the inflaton and the auxiliary fields, resembling hybrid inflation with a waterfall mechanism. The inclusion of an axial chemical potential naturally introduces a mechanism to end inflation and trigger instant preheating. During the waterfall phase, the effective potential of the fermion condensate supports the formation of non-topological solitons such as Q-balls, which act as seeds of primordial black holes. This model is intrinsically connected to Chern-Simons gravity, which implies a parity-violating universe. Consequently, both the primordial black hole (PBH) dark-matter abundance and parity-violation signatures could provide observational tests of the model.

Recently, the observation of superconductivity (SC) with $T_c$ $\approx$ 3.6 K in the pressurized 1313 La$_3$Ni$_2$O$_7$ has attracted considerable interest. Here, we systematically investigate the electronic properties and superconducting mechanism of 1313 La$_3$Ni$_2$O$_7$ using density functional theory plus dynamical mean-field theory (DFT+DMFT) and random phase approximation (RPA). Our DFT+DMFT calculations reveal that the single-layer (SL) subsystem exhibits nearly insulating behavior, with the $d_{z^2}$ orbital showing Mott physics, while the trilayer (TL) subsystem remains metallic. This indicates that SC primarily resides in the TL subsystem, whose Ni-$e_g$ orbitals are found to be hole-doped relative to bulk La$_4$Ni$_3$O$_{10}$. Based on DFT+DMFT-derived low-energy Hamiltonian, RPA-based analysis yields an $s^{\pm}$-wave pairing symmetry within the TL subsystem. Importantly, we identify two key factors that contribute to the significant suppression of $T_c$ in 1313 La$_3$Ni$_2$O$_7$ compared to bulk La$_4$Ni$_3$O$_{10}$. First, the hole doping in the TL subsystem, as established by DMFT, leads to a decreased pairing strength, as confirmed by RPA calculations -- a trend resembling that in bulk La$_4$Ni$_3$O$_{10}$. Second, the SL subsystem acts as a bridge connecting adjacent superconducting TL subsystems, thereby forming an S-N-S Josephson junction. The resulting interlayer Josephson coupling governs the phase coherence between TL subsystems and further suppresses the global $T_c$. Combinedly, our findings suggest that the high-$T_c$ phase in the RP La$_3$Ni$_2$O$_7$ family should be attributed to the 2222 La$_3$Ni$_2$O$_7$ rather than the 1313 La$_3$Ni$_2$O$_7$.

The aim of this paper is to demonstrate some interesting and useful approaches for writing a program in the assembly language. In order to demonstrate the possibilities of the assembly language, a project called "Arkanoid" was created. This project is written in assembly language and it presents few interesting algorithms. Assembly language, which is used for designing the game is x86 Assembly language, which produces object code for the x86 class of processors. As a working environment is chosen Visual Studio 2015, because it gives the useful tools for debugging and testing of the created software (game). Execution of the program results in a "Arkanoid" game, placed in Windows OS Console.

We study the kernel complexity of constraint satisfaction problems over a finite domain, parameterized by the number of variables, whose constraint language consists of two relations: the non-equality relation and an additional permutation-invariant relation $R$. We establish a conditional lower bound on the kernel size in terms of the largest arity of an OR relation definable from $R$. Building on this, we investigate the kernel complexity of uniformly rainbow free coloring problems. In these problems, for fixed positive integers $d$, $\ell$, and $q \geq d$, we are given a graph $G$ on $n$ vertices and a collection $\cal F$ of $\ell$-tuples of $d$-subsets of its vertex set, and the goal is to decide whether there exists a proper coloring of $G$ with $q$ colors such that no $\ell$-tuple in $\cal F$ is uniformly rainbow, that is, no tuple has all its sets colored with the same $d$ distinct colors. We determine, for all admissible values of $d$, $\ell$, and $q$, the infimum over all values $η$ for which the problem admits a kernel of size $O(n^η)$, under the assumption $\mathsf{NP} \nsubseteq \mathsf{coNP/poly}$. As applications, we obtain nearly tight bounds on the kernel complexity of various coloring problems under diverse settings and parameterizations. This includes graph coloring problems parameterized by the vertex-deletion distance to a disjoint union of cliques, resolving a question of Schalken (2020), as well as uniform hypergraph coloring problems parameterized by the number of vertices, extending results of Jansen and Pieterse (2019) and Beukers (2021).

In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted graph $G$ is a straightforward concept, yielding a graph on the same set of nodes, and an edge exists in $\bar G$ if and only if it is not present in $G$. In contrast, a weighted complement graph cannot be uniquely determined. However, if we consider PTNs with travel times as edge weights, there are physical constraints on the possible weight ranges. We propose a method to construct weighted complement graphs of operational PTN graph representations based on the geographical distances between nodes (representing stops) and assign weights to edges based on distance, combined with network-specific distributions of effective velocities and waiting times. We observe that the most central nodes in the weighted complement graph do not correspond to the least central nodes in the original network but are, remarkably, those in the geographical centre of the network that lack topological connectedness. Testing against null models on a dataset of 31 metro networks worldwide confirms that this is a fundamentally spatial effect.

In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions without requiring second-order information. We develop one-step, two-step, and three-step iterative schemes (denoted by SS1, SS2, and SS3) and establish that these methods achieve higher-order convergence of orders two, four, and six, respectively. Despite their high convergence rates, the computational complexity of the proposed methods remains comparable to existing gradient-based methods, with a cost of $\mathcal{O}(n^2)$ per iteration. The proposed methods are simple to implement and do not require complicated line-search procedures. Their effectiveness is demonstrated through extensive numerical experiments on a wide range of problems, including large-scale and ill-conditioned cases. The results show that the proposed methods significantly outperform classical methods, such as the Barzilai-Borwein method and other gradient-based approaches, in terms of iteration count and computational efficiency. Finally, the numerical results are consistent with the theoretical analysis, confirming the stability of the proposed schemes for test optimization problems.

The internal low-energy symmetry of the massless Lorentz-invariant Dirac Hamiltonian in $2+1$ dimensions is known to be $O(2N)$, where $N$ is the number of two-component Dirac fermions. Here we point out that there exists an analogous internal symmetry of the single-particle quadratic-band-touching Hamiltonian in two spatial dimensions, and it is the unitary symplectic group, $USp(2N)$. All fermionic bilinears belong to one of the three small irreducible representations of this group. The interacting theory that respects the $USp(2N)$ symmetry and the spatial rotations is constructed and found to allow two independent interaction terms. When these interactions are infrared-relevant the symplectic symmetry either remains preserved or becomes spontaneously broken to $USp(N) \times USp(N)$. The symmetry in the lattices such as honeycomb to infinite order in the dispersion's expansion in powers of local momentum is given by the overlap of the symplectic and the orthogonal groups. We show that this overlap is $O(2N) \bigcap USp(2N) = U(N)$.

We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_2(ω, θ,ϕ)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames.

We construct the first smooth embedded compact special Legendrian surfaces in \(\mathbb S^5\) of genus greater than one. More precisely, for every sufficiently large integer \(k\), we construct an embedded special Legendrian surface whose conformal structure is the Fermat curve of degree \(k\) and genus \(\tfrac12(k-1)(k-2)\). Our approach combines an elementary implicit function theorem with the description of special Legendrian surfaces via loop algebra-valued meromorphic connections and a characterization of the unitarizability locus in the ${SL}_{3}(\mathbb C)$-character variety of the thrice-punctured sphere.

The rapid expansion of blockchain and digital asset ecosystems has intensified the challenge of translating academic research into deployable systems and regulatory frameworks. While advances in cryptography, consensus, digital assets, and governance are substantial, institutional mechanisms that sustain research-to-deployment translation at ecosystem scale remain comparatively under-theorized. This paper examines the architectural and coordination patterns that enable such translation, using the University Blockchain Research Initiative (UBRI) network as a representative case of long-term academic and industry collaboration. Drawing on research outputs and convenings from 2022 to 2025, we synthesize recurring design tensions across technical and institutional domains, including scalability versus security, decentralization versus governance, and privacy versus compliance. Rather than cataloging individual projects, we abstract system-level themes that connect research contributions to deployment constraints and policy adaptation, providing a structured lens for understanding how academic research informs production architectures, regulatory development, and ecosystem resilience in emerging decentralized infrastructures.

JWST has revealed a population of super-luminous early galaxies with a volume density in excess of most expectations. The spectra reveal diverse properties: while some reveal strong emission lines characteristic of galaxies in the midst of strong bursts, others show weak emission lines that could reflect old stellar populations, large escape fractions, or post-burst star formation histories. Through the JWST Cycle 4 large program SPURS, we have obtained ultra-deep (29 hr) rest-frame UV spectroscopy of a z=9.3 super-luminous ($M_{\rm UV}=-21.66$) galaxy with large assembled stellar mass (1.6$\times$10$^9$ $M_\odot$) and extremely weak emission lines (H$β$ EW $\approx25$~Å). The strong stellar wind features and rest-optical line ratios suggest the galaxy is already significantly enriched, with a metallicity of 0.4--0.7~Z$_\odot$. The interstellar absorption lines reveal outflows ($v\simeq -161$~km~s$^{-1}$) with a large neutral gas covering fraction, suggesting that the weak emission lines are not due to large escape fractions. The combination of the Balmer break, weak emission lines, and stellar wind features constrains the star formation history, indicating a recent burst of star formation lasting 10--20 Myr followed by a downturn over the last 10~Myr. The observations suggest that $z\gtrsim 9$ weak emission line galaxies such as this source can be explained by stochastic star formation, provided that the downturns in star formation are recent (i.e., <10 Myr prior to observation). The ultra-deep grating spectrum enables the IGM damping wing to be characterized, decoupling the effects of local absorption. The smooth Ly$α$ break indicates that this source, one of the most massive galaxies known at z>9, is likely situated in a small ionized bubble ($0.29_{-0.09}^{+0.11}$~pMpc), as is common at large neutral hydrogen fractions ($\bar{x}_{\rm HI}=0.81_{-0.21}^{+0.14}$).

We study bubbling for sequences of Yang-Mills connections on closed four-manifolds and we derive a compatibility of Pohozaev type between the weak limit connection and the bubble formed at a concentration point, involving the Weyl tensor of the background metric. This yields obstruCtions to bubbling extending earlier results of Yin beyond the locally conformally flat case. As an application, we rule out certain bubbling configurations on CP2.

We show that all existing methods quantifying rotational motion in molecular fluids eventually fail in systems undergoing complex rotational motion characterised by slow, heterogeneous, or intermittent dynamics. This impacts in particular the study of rotational dynamics in molecular supercooled liquids near their glass transition, as well as discussions of the decoupling between rotational and translational motion and violations of the Debye-Stokes-Einstein relation. We present a brief overview of existing methods and explain why none of them can accurately capture the evolution of rotational dynamics from a diffusive fluid to an arrested solid, thus resolving inconsistent literature results. We then introduce an empirical method that efficiently solves all issues. We benchmark our method devising a family of continuous time random walk models for rotational dynamics. Our method correctly quantifies the statistics of free and caged rotational motion, as well as non-Gaussian and non-Fickian rotational dynamics, and should allow a better characterisation of dynamic heterogeneity in the rotational motion of supercooled molecular fluids.

The generalized second laws of quantum thermodynamics are usually formulated in terms of Rényi divergences and the associated family of generalized free energies. In catalytic thermal transformations, this framework typically certifies the existence of a suitable catalyst but does not make the catalytic contribution explicit in the resulting system-level inequalities. Here we develop a complementary formulation based on non-additive divergences, whose pseudo-additive structure yields a family of generalized free energies with an explicit catalyst-dependent correction term. For uncorrelated catalytic thermal transformations, we show that this leads to non-additive second-law relations that make the catalytic contribution explicit and provide nontrivial constraints on admissible catalysts when the catalyst is returned only approximately. We also analyze correlated catalytic thermal transformations and show, through explicit finite-dimensional examples, that reduced-state data are generally insufficient to characterize thermodynamic accessibility: the thermo-majorization behavior of the joint transformation can change while the system and catalyst marginals remain fixed, and even states with identical marginals and the same mutual information can exhibit different thermo-majorization accessibility. Our results show that non-additivity can be thermodynamically informative in uncorrelated catalysis, whereas correlated catalysis generally requires a genuinely joint-state-sensitive description beyond reduced-state monotones.

For $0<δ,τ<1$ and $1\le s\le \frac{n}{n-δ}$, we prove that for a given $s$-John domain $Ω\subset \mathbb{R}^n$, the following Boxing inequality holds for every Lebesgue measurable set $U\subsetΩ$ with $|U|/|Ω|\leγ<1$: \[ \mathcal{H}^{s(n-δ)}_{\infty}(U\setminus\mathcal{N}_U)\le C(1-δ)\int_Ω\int_{|x-y|<τ\operatorname{dist}(y,\partialΩ)}\frac{|χ_U(x)-χ_U(y)|}{|x-y|^{n+δ}}\,dx\,dy, \] where $\mathcal{H}^{s(n-δ)}_{\infty}(U)$ denotes the $s(n-δ)$-dimensional Hausdorff content of $U$, $\mathcal{N}_U$ is a set of Lebesgue measure zero and the constant $C$ depends only on $n,τ,s,γ$, the John constant and the diameter of $Ω$. Moreover, we establish the functional formulation of the above Boxing inequality and discuss the equivalence between these two formulations. Based on the Boxing inequality, we prove the fractional Poincaré--Wirtinger trace inequality on $s$-John domains, of which the fractional Sobolev--Poincaré inequality and fractional Hardy-type inequality are special cases. Notably, we prove all of the aforementioned inequalities with the Bourgain--Brezis--Mironescu (BBM) factor $1-δ$. Furthermore, with the aid of the Bourgain--Brezis--Mironescu formula, we recover the Poincaré--Wirtinger trace inequality. Finally, by showing that, under the separation property, any domain supporting the Boxing inequality is necessarily a John domain, we conclude that the John domain condition is essentially sharp for the above inequalities. All the above inequalities with the BBM factor are new even for Lipschitz domains.

Software requirement ambiguity is ubiquitous in real-world development, stemming from the inherent imprecision of natural language and the varying interpretations of stakeholders. While Large Language Models (LLMs) have demonstrated impressive capabilities in generating code from precise specifications, such ambiguity poses a significant obstacle to reliable automated code generation. Existing benchmarks typically assume clear and unambiguous requirements, leaving an empirical gap in understanding how LLMs behave when faced with the inherent uncertainty of real-world software requirements. In this paper, we introduce Orchid, the first code generation benchmark specifically designed with ambiguous requirements. It comprises 1,304 function-level tasks covering four distinct types of ambiguity: lexical, syntactic, semantic, and vagueness. Leveraging this dataset, we conduct the first systematic empirical study to evaluate the impact of requirement ambiguity on LLM-based code generation. Our results demonstrate that ambiguity consistently degrades the performance of all evaluated LLMs, with the most pronounced negative effects observed in highly advanced models. Furthermore, we observe that LLMs frequently produce functionally divergent implementations for the same ambiguous requirement and lack the capability to identify or resolve such ambiguity autonomously. These findings reveal a significant performance gap between clear and ambiguous requirements, underscoring the urgent need for ambiguity-aware techniques in the next generation of automated software engineering tools. The Orchid benchmark is publicly available at https://huggingface.co/datasets/SII-YDD/Orchid.

We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional to the product of endpoint weights. We adopt a temporal viewpoint, adding edges to the graph one at a time up to a fixed time horizon, and allowing for self-loops or duplicate edges in the first stage. Then, the simple projection of the resulting multigraph recovers exactly the simple Norros--Reittu random graph, whose expected degrees match the prescribed targets under mild conditions. Building on this representation, we develop an exact generator based on \textit{edge-arrivals} for expected-degree random graphs with running time $O(n+m)$, where $m$ is the number of generated edges, and hence proportional to the output size. This removes the typical vertex sorting used by widely-used fast generator algorithms based on \textit{edge-skipping} for rank-1 expected-degree models, which leads to a total running time of $O(n \log n + m)$. In addition, our algorithm is simpler than those in the literature, easy to implement, and very flexible, thus opening up to extensions to directed and temporal random graphs, generalization to higher-order structures, and improvements through parallelization.

The radioisotope $^{125}\text{Xe}$ is a short-lived ($T_{1/2}\sim16.9 h$) activation product of the neutron calibrations performed in the LUX-ZEPLIN experiment. Subsequently, $^{125}$Xe decays primarily ($>99\%$) via electron capture, but positron emission has been confirmed by direct measurement to at least the 243 keV level of $^{125}\text{I}$. An additional decay to the 188keV level is expected from triple-coincident measurements of the annihilation and relaxation $γ$ rays, but has not been directly confirmed. By utilizing multiple-scatter event analysis and the pre-activation data to constrain backgrounds, this work reports positron emission with a statistical significance of 5.5$σ$. This corresponds to a total branching ratio of $0.29\pm0.08_{\text{stat.}}\pm0.04_{\text{sys.}}$ %, and is the first constraint to the individual branching levels of $^{125}\text{I}$.

Miniaturized, ultra-sensitive and easily integrable magnetometers are needed for many applications, like space exploration or health monitoring. Achieving this goal requires a magnetic sensor with high sensitivity and low noise. High sensitivity (>1000 %/mT) can be obtained by integrating high gain permalloy flux concentrators (FC). And reducing the magnetic 1/f noise can be realized by increasing the number of magnetic tunnel junctions (MTJs) in the air-gap of the FC. However, this is obtained at the expense of a wider air-gap and consequently a decrease of the magnetic gain and thus of the sensitivity. In this paper, we explore a design optimization scheme in order to find the best trade-off between high FC gain and low magnetic noise. To model the gain of the flux concentrator, we propose two complementary approaches; one is based on finite elements simulations of the FC gain where the influence of geometrical parameters of the air-gap is investigated. Then, in a second step, we propose an analytical formula consistent with all our simulations results and based on magnetic reluctance. Finally, we derive an analytical model of the sensor detectivity from which we can extract the optimal sensor design which allows an improvement by three orders of magnitude of the performances compared to a single junction.

The intermediate state of type-I superconductors presents a classic paradigm of modulated pattern formation, arising from the competition between short-range attractive and long-range repulsive vortex-vortex interactions. However, direct visualization and, more importantly, active control over the topology and dynamics of these flux structures have remained significant challenges, limiting our ability to manipulate them for fundamental studies and potential applications. Here, using low-temperature magnetic force microscopy, we achieve direct imaging and controllable manipulation of the flux structures in a high-purity tantalum single crystal. We systematically track the evolution of flux morphology - from tubes to stripes - during flux penetration and expulsion, revealing a pronounced topological hysteresis originating from the geometric barrier. Furthermore, we demonstrate precise local control by using the magnetic tip to drag and merge individual flux tubes and to reconfigure entire stripe domains. Under global alternating current (AC) excitation, we discover a reversible stripe-grid-stripe transition, a dynamic reorganization driven by current-induced flux penetration and pinning effects. The corresponding phase diagram shows that the threshold current decreases with magnetic field but increases with AC frequency. Our work establishes a pathway for active flux manipulation in type-I superconductors, revealing rich dynamics and paving the way for flux-based superconducting devices.

Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the design of assistive technologies. We analyze experimental data in which blind, low-vision, and sighted participants performed spatial updating tasks under five sensory conditions, with signed angular error as the response. To model these data, we propose a nonparametric circular regression framework that accommodates both continuous and categorical predictors via a product-kernel estimator. Bandwidth selection is crucial in this setting, yet developing practical data-driven methods remains challenging. We derive asymptotic bias and variance expressions for the estimator, though these results do not directly lead to a feasible plug-in bandwidth selector. To address this, we develop a bootstrap bandwidth selection criterion tailored to the cosine loss and compare it with cross-validation and rule-of-thumb approaches in simulation studies. Applied to the spatial updating data, the proposed framework reveals nonlinear, condition-specific patterns and quantifies uncertainty via simultaneous bootstrap confidence bands. Across the scenarios considered, the proposed bootstrap selector achieves a favorable bias-variance trade-off and yields stable inference relative to the competing methods. An implementation is available in the R package circMixedReg.

We present the first high-resolution X-ray spectral analysis of Cygnus X-1 using XRISM. The observation was carried out from April 7 to 10, 2024, covering the orbital phase range 0.65--0.17 during its low/hard state. Taking advantage of the exceptional energy resolution of the Resolve instrument, we examined highly ionized iron absorption lines and characterized the ionization states, column densities, and line-of-sight velocities of the absorbing plasma. Spectral analysis revealed an ionization parameter of approximately 3, column densities of a few times 10^21 cm^-2, and a blueshifted velocity of approximately 100 km s^-1. The observation was divided into two phases: before and after orbital phase phi_orb = 0.9, corresponding to non-dipping and dipping intervals. While only weak absorption features were present before phi_orb = 0.9, strong absorption by He-like and H-like Fe appeared during the dipping phase. We measured equivalent widths of 2.3 eV, 0.4 eV, and 1.2 eV for He-like Fe K-alpha, and H-like Ly-alpha1 and Ly-alpha2, respectively, demonstrating the capability of XRISM Resolve to securely detect narrow absorption features of only a few eV. These measurements trace the motion of the absorbing material and offer insight into the kinematics and spatial distribution of the wind in the vicinity of the black hole. These findings enhance our understanding of wind-fed accretion in Cygnus X-1 and highlight the importance of continued high-resolution X-ray observations to further constrain the physical properties of winds and accretion flows in high-mass X-ray binaries.

Covalent Organic Frameworks (COFs) are versatile two-dimensional (2D) materials for flexible electronics, catalysis, and sensing, owing to their tunable architectures and large surface areas. However, like most materials, COFs inevitably contain synthesis-induced defects, which-similar to graphene-can strongly influence intrinsic properties, such as thermal transport and mechanical strength. To address this challenge, we have assessed the performance of a set of machine learning interatomic potentials (MLIP) capable of efficient large-scale simulations of COFs with quantum accuracy. In doing so, QCOF models (Quantum COF) were developed by tuning the state-of-the-art MACE architecture on an extensive dataset of non-equilibrium COF conformations generated from high-fidelity density functional theory calculations. The accuracy, computational efficiency, memory footprint, and transferability to unseen chemical environments of these models were benchmarked against general-purpose MACE models and their fine-tuned variants. Our results show that an invariant QCOF model with a small descriptor dimensionality and cutoff outperforms all other models in most validation tasks, including scalability to large systems, force prediction in defective COFs, and phonon dispersion calculations. The best-performing QCOF model was then used to run large-scale simulations of thermal conductivity for defective CTF-1 and COF-LZU1 systems via non-equilibrium MD, revealing a more pronounced sensitivity of CTF-1 to structural defects. Stress-strain curves were also investigated, showing that the mechanical response remains nearly invariant at low defect densities, while asymmetric behaviour emerges at large strains. This work thus provides a foundation for the design of robust quantum-informed MLIP for large-scale property simulations of defective of extended network materials.

We study a minimal framework that naturally yields viable Dark Matter, a strong first-order electroweak phase transition and low-scale resonant leptogenesis. Augmenting the Standard Model with three heavy Majorana neutrinos, we study the corresponding neutrino-extended Standard Model Effective Field Theory, including operators upto mass-dimension six. The pure Higgs operator provides the dominant enhancement required for a strong first-order electroweak phase transition, while the remaining operators yield subleading effects consistent with electroweak precision constraints. The signal for the stochastic gravitational-wave background is dominated by sound waves in the plasma, with magnetohydrodynamic turbulence providing a subleading contribution. Low-scale resonant leptogenesis is realized through tiny mass splittings among quasi-degenerate heavy neutrinos, dynamically generated in the symmetric phase by the combined effect of one-loop RG-induced corrections and finite-temperature contributions. Solving the Boltzmann equations, we show that the observed baryon asymmetry of the Universe can be reproduced while remaining consistent with neutrino oscillation data and charged-lepton-flavor-violation constraints. One of the heavy neutrinos is stabilized by a discrete symmetry thereby acting as a fermionic dark matter candidate. Its interactions with the Standard Model arise from dimension-five and dimension-six effective operators, leading to viable annihilation, elastic scattering, and indirect detection phenomenology compatible with current experimental bounds. The dark matter sector remains decoupled from the dynamics of the electroweak phase transition and leptogenesis, allowing all three phenomena to be consistently realized within a unified effective field theory framework.

Differential privacy (DP) is a mathematical framework that guarantees individual privacy; however, systematic evaluation of its impact on statistical utility in survival analyses remains limited. In this study, we systematically evaluated the impact of DP mechanisms (Laplace mechanism and Randomized Response) with data-driven clipping bounds on the Cox proportional hazards model, using 5 clinical datasets ($n = 168$--$6{,}524$), 15 levels of $\varepsilon$ (0.1--1000), and $B = 1{,}000$ Monte Carlo iterations. The data-driven clipping bounds used here are observed min/max and therefore do not provide formal $\varepsilon$-DP guarantees; the results represent an optimistic lower bound on utility degradation under formal DP. We compared three types of input perturbations (covariates only, all inputs, and the discrete-time model) with output perturbations (dfbeta-based sensitivity), using loss of significance rate (LSR), C-index, and coefficient bias as metrics. At standard DP levels ($\varepsilon \leq 1$), approximately 90% (90--94%) of the significant covariates lost significance, even in the largest dataset ($n = 6{,}524$), and the predictive performance approached random levels (test C-index $\approx 0.5$) under many conditions. Among the input perturbation approaches, perturbing only covariates preserved the risk-set structure and achieved the best recovery, whereas output perturbation (dfbeta-based sensitivity) maintained near-baseline performance at $\varepsilon \geq 5$. At $n \approx 3{,}000$, the significance recovered rapidly at $\varepsilon = 3$--10; however, in practice, $\varepsilon \geq 10$ (for predictive performance) to $\varepsilon \geq 30$--60 (for significance preservation) is required. In the moderate-to-high $\varepsilon$ range, false-positive rates increased for variables whose baseline $p$-values were near the significance threshold.

These years, kagome materials with 1:1 stoichiometry have garnered increasing attention, among which FeSn, CoSn, and FeGe have been the focus of current studies. However, all of them are antiferromagnetic, thereby hindering the observation of superconductivity and other novel physical properties. Here, we predict a novel 1:1 kagome metal VSn, which is an intrinsic charge density wave (CDW) material. Interestingly, with increasing pressure or doping concentration, the CDW order is progressively suppressed, followed by the emergence of superconductivity characterized by a non-monotonic transition temperature that exhibits a rare anti-dome-shaped dependence. Above a critical threshold, a reentrance of the CDW phase occurs. The anti-dome superconductivity originates from the first hardening and then softening of phonon modes, together with band reconstruction. Crucially, VSn retains nontrivial topological properties across the entire superconducting regime, a feature of paramount importance for realizing robust topological superconductivity. These intertwined CDW, superconductivity, and topological phenomena elucidate the correlations among multiple quantum states in VSn. Therefore, this research paves the way for for designing 1:1 kagome superconducting topological metals and establishes a platform for exploring the interplay of multiple phases in kagome systems.

Brain-inspired non-Boolean computing offers intrinsic error tolerance and parallelism, but its practical deployment is limited by the lack of compact, energy-efficient spiking hardware compatible with large-scale integration. Mott phase-transition materials provide a promising route, as their abrupt insulator-to-metal transitions enable neuron-like thresholding and oscillatory dynamics in compact devices. Among these, vanadium dioxide (VO$_2$) stands out for its near-room-temperature transition, fast switching, and scalability. However, existing VO$_2$-based neuristors rely on discrete components, limiting integration density and system applicability. Here, we report monolithic back-end-of-the-line (BEOL) integration of one-transistor-one-VO2-memristor (1T-1MR) spiking neurons on CMOS-compatible platforms. VO$_2$ nanosheet devices are fabricated by pulsed-laser deposition below 430 °C on dielectrically isolated silicon-on-insulator (SOI) p-type junctionless field-effect transistors (JLFETs) in a compact 1T-1MR configuration. The architecture exhibits gate-tunable oscillations from 40 to 410 kHz in 60 nm-thick VO$_2$ devices with an active area of 6 $μ$m$^2$, achieving energy consumption as low as 18 pJ per spike at room temperature, with memristor power dissipation of 8 $μ$W and potential scaling toward sub-3 $μ$W operation. We further uncover a non-monotonic dependence of oscillation frequency on current and temperature, along with bias-dependent stochastic firing dynamics, highlighting the rich behavior of integrated VO$_2$ memristor systems. Finally, we demonstrate voltage-controlled oscillator functionality and actively tunable resistive coupling of two nano-oscillators mediated by a JLFET. These results establish a pathway toward dense, energy-efficient, and monolithically integrated Mott-based neuromorphic hardware compatible with CMOS technology.

A $k$-regular graph of girth $g$ is called vertex-girth-regular if every vertex is contained in the same number of cycles of length $g$. For integers $n, k, g$ and $λ$, we denote such a graph on $n$ vertices in which every vertex lies on exactly $λ$ cycles of length $g$ by a $\text{vgr}(n,k,g,λ)$-graph. It is well-known that any vertex-girth-regular graph satisfies $λ\le \frac{k(k-1)^{\left\lfloor \frac{g}{2} \right\rfloor}}{2}$. Graphs for which $λ$ is close to this bound are of particular interest in connection with the cage problem, since requiring many girth cycles through every vertex is a natural way to isolate highly structured candidates for small regular graphs of prescribed girth. In this paper, we prove that for every $k\ge 3$ and every integer $0< \varepsilon \leq \frac{k-1}{2}$, there does not exist a $\text{vgr}(n,k,5,\frac{k(k-1)^2}{2}-\varepsilon)$-graph. Previous non-existence results had already settled all odd girths at least $7$ and very recently also girth $3$, leaving girth $5$ as the only girth for which no non-trivial non-existence result was known. Thus, our result resolves the final remaining case and completes the picture for odd girths.

Interferometry provides highly sensitive access to optical phase and is central to much of modern metrology and phase imaging methods. Conventional implementations, however, often face trade-offs between mechanical stability and experimental or computational complexity. Here, we present a general framework for designing custom interferometers within a single optical beam by exploiting structured light. This approach yields compact, robust common-path configurations that bypass the need for complex post-processing and can easily be integrated into existing setups. We demonstrate the versatility of this concept by designing a range of interferometers, each tailored by the structured mode, and implement them through active and passive modal conversion optics, proving its adaptability to different experimental requirements. To showcase the practical utility of our framework, we apply it to quantitative phase imaging over a variety of physical samples, showing excellent agreement with atomic force microscopy benchmarks. Furthermore, we emphasise the flexibility of our structured light interferometers by mapping phase objects to a choice of either amplitude or polarisation, the latter providing a direct route toward real-time phase-retrieval. This cost-effective approach offers a practical, high-throughput solution for phase-sensitive metrology across fields such as fundamental physics, biology, and material science.

We present a lightweight and interpretable decision framework for dynamic edge server selection in latency-critical applications that explicitly accounts for tail risk and switching stability. Each candidate server is characterised by predictive mean and uncertainty summaries of network latency, which are used to estimate the risk of service-level objective (SLO) violations and to guide selection. Risk is evaluated using a tight Normal approximation complemented by a conservative Cantelli bound, while percentile-based scoring coupled with hysteresis stabilizes decisions and suppresses oscillatory switching under short-lived network fluctuations. Experimental results on a multi-server edge testbed with a strict SLO of $τ= 0.5$\,s show that the proposed approach reduces the deadline-miss rate from 39\% to 34\% compared to a mean-only baseline, while reducing switching frequency from 46\% to 5.5\% ($\approx$88\% reduction) and maintaining sub-SLO average latency ($\approx$0.45\,s). These results demonstrate that explicit risk evaluation combined with stability-preserving control enables practical and robust adaptive server selection in dynamic edge environments.