Given a simple, finite, nonempty graph $G=(V(G),E(G))$, a vertex subset $D\subseteq V(G)$ is said to be a dominating set if every vertex $v\in V(G)-D$ is adjacent to a vertex in $D$. The independent domination number $γ_i(G)$ is the minimum cardinality among all independent dominating sets of $G$. Since determining the domination number for general graphs is NP-complete, we focus on the class of $k$-trees. Favaron established a tight upper bound for $1$-trees, while Campos and Wakabayashi determined a tight upper bound for maximal outerplanar graphs, a subclass of $2$-trees. We generalize these results and establish a tight upper bound for the independent domination number of $k$-trees for all $k\in \mathbb{N}$.

Future lithium-based batteries are expected to use solid electrolytes to achieve higher energy density and fast charge capabilities. The majority of solid electrolytes are thermodynamically unstable against layered oxide cathodes. Here, the stability of LiCoO2 (LCO) cathode with Li10GeP2S12 (LGPS) solid electrolyte is investigated using ab initio molecular dynamics (AIMD) and machine learning molecular dynamics (MLMD). The propensity of ionic interdiffusion, formation of a passivation layer, and corresponding decay in cell performance is addressed using a continuum model. The large-scale MLMD simulations confirm that the LCO|LGPS interface permits interdiffusion of Co and other ionic species, leading to the formation and growth of a resistive interphase and dramatic capacity fade even in the first cycle. We then examine the literature evidence that incorporating a thin layer of LiNb0.5Ta0.5O3 (LNTO) between LCO and LGPS prevents the interdiffusion of ions. Atomistic simulations suggest that the substitution of Li in LNTO with Co is not thermodynamically favorable, which helps to minimize the ionic interdiffusion process. The stable Nb/Ta5+ states form a rigid metal-oxide framework, which consequently also prevents the substitution of Nb/Ta. However, continuum level analysis suggests that due to the higher mechanical stiffness of LNTO, interfacial delamination between the LCO and LNTO is possible, which can minimize the effectiveness of the protective layer. This paper suggests the need for the development of novel interlayers that balance low interdiffusion with low stiffness.

Advances in data collecting technologies in genomics have significantly increased the need for tools designed to study the genetic basis of many diseases. Effective statistical methods should excel in both prediction accuracy and biomarker identification. We introduce a novel approach to high-dimensional binary classification that integrates regularization with ensembling techniques. The method constructs compact ensembles of interpretable models derived by optimizing a global objective function. In medical genomics applications, the proposed approach identifies critical biomarkers overlooked by competing methods. We develop a variable importance ranking system to help researchers prioritize promising genes. The method's asymptotic properties are established, and an efficient computational algorithm is provided. Through extensive simulations across complex scenarios and analysis of cancer genomics datasets, we demonstrate strong predictive performance. Based on the numerical experiments, we offer practical guidelines for determining optimal ensemble size.

Interactions between quantum systems enable quantum gates, the building blocks of quantum information processing. In photonics, direct photon-photon interactions are too weak to be practically useful, so effective interactions are engineered with linear optics and measurement. A central challenge is to realize such interactions non-locally, i.e., between photons that remain spatially separated. We present experimental proposals for several essential non-local multiphoton quantum gates that act on spatially separated photons, in both qubit and high-dimensional qudit systems. All solutions were discovered by the AI-driven discovery system called PyTheus. Rather than using pre-shared entanglement or Bell state measurements, our gates use as a resource quantum indistinguishability by path identity - a technique that exploits coherent superpositions of the photon pair origins. While analyzing these solutions, we uncovered a new mechanism that mimics much of the properties of quantum teleportation, without shared entanglement or Bell state measurements. Technically, our results establish path indistinguishability as a practical resource for distributed quantum information processing; conceptually, they demonstrate how automated discovery systems can contribute new ideas and techniques in physics.

Magnetic and polar skyrmions exhibit topologically protected quasiparticle behavior, including emergent fields, deformation, and the formation of a densely packed skyrmion lattice, beyond conventional domain configurations described by Kittel's law. Analogous to atomic crystals, lattice defects, especially dislocations and their associated strain fields, are crucial for understanding the lattice behavior of skyrmions; however, their features and roles remain insufficiently understood. Here, we show that magnetic skyrmion dislocations develop a core-split structure due to a significant skyrmion elongation up to 180% of their original length, reaching a topological transition from a single skyrmion to two half-skyrmions. Despite such a distinct structure, the long-range strain fields around the dislocation perfectly obey conventional Volterra's elasticity theory, in contrast to polar skyrmion lattices, where skyrmion deformations cause a breakdown of the elasticity theory. Furthermore, an energetic analysis shows that Dzyaloshinskii-Moriya interaction drives the large skyrmion deformation of the dislocation core. Our findings not only clarify the coexistence of topological core-reconstruction and a robust long-range elastic field of dislocations in magnetic skyrmion lattices, but also reveal that magnetic and electric domains, long regarded as dual and analogous, exhibit fundamental differences when extended into the regime of collective topological quasiparticles.

This work presents sparse invariant coordinate selection, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate selection, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes consistency and breakdown point results for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with multiple simulations. The method is illustrated with an example in constructing sparse causal graphs and we also propose a graphical tool for selecting the appropriate sparsity level in SICS.

Fabrication of quantum processors in advanced 300 mm wafer-scale complementary metal-oxide-semiconductor (CMOS) foundries provides a unique scaling pathway towards commercially viable quantum computing with potentially millions of qubits on a single chip. Here, we show precise qubit operation of a silicon two-qubit device made in a 300 mm semiconductor processing line. The key metrics including single- and two-qubit control fidelities exceed 99% and state preparation and measurement fidelity exceeds 99.9%, as evidenced by gate set tomography (GST). We report coherence and lifetimes up to $T_\mathrm{2}^{\mathrm{*}} = 30.4$ $μ$s, $T_\mathrm{2}^{\mathrm{Hahn}} = 803$ $μ$s, and $T_1 = 6.3$ s. Crucially, the dominant operational errors originate from residual nuclear spin carrying isotopes, solvable with further isotopic purification, rather than charge noise arising from the dielectric environment. Our results answer the longstanding question whether the favourable properties including high-fidelity operation and long coherence times can be preserved when transitioning from a tailored academic to an industrial semiconductor fabrication technology.

Superior computational power promised by quantum computers utilises the fundamental quantum mechanical principle of entanglement. However, achieving entanglement and verifying that the generated state does not follow the principle of local causality has proven difficult for spin qubits in gate-defined quantum dots, as it requires simultaneously high concurrence values and readout fidelities to break the classical bound imposed by Bell's inequality. Here we employ heralded initialization and calibration via gate set tomography (GST), to reduce all relevant errors and push the fidelities of the full 2-qubit gate set above 99 %, including state preparation and measurement (SPAM). We demonstrate a 97.17 % Bell state fidelity without correcting for readout errors and violate Bell's inequality with a Bell signal of S = 2.731 close to the theoretical maximum of $2\sqrt{2}$. Our measurements exceed the classical limit even at elevated temperatures of 1.1 K or entanglement lifetimes of 100 $μs$.

In recent years, sliding ferroelectricity has emerged as a topic of significant interest due to its possible application in non-volatile, reconfigurable storage devices. This phenomenon is unique to two-dimensional van der Waals materials, where out-of-plane ferroelectric polarization switching is induced by relative in-plane sliding of adjacent layers. The intrinsic stacking order influences the resulting polarization, creating distinct polarization regions separated by domain walls. These regions and the domain walls can be manipulated using an applied vertical electric field, enabling a switchable system that retains the environmental robustness of van der Waals materials under ambient conditions. This study investigates 3R-MoS$_2$ using various optical measurement techniques at room temperature. The spatially resolved optical measurements reveal apparent signal changes corresponding to different ferroelectric stacking orders and variations in layer count. Our findings demonstrate that fast optical mapping at room temperature is a reliable method for probing ferroelectric potential steps in 3R-stacked MoS$_2$ samples, thereby facilitating the identification of the ferroelectric configuration. This approach does not require a conductive substrate or an electrical contact to the sample, making it more versatile than traditional atomic force probe techniques.

High harmonic generation (HHG) is a crucial technology for compact, high-brightness extreme ultraviolet (XUV) and soft X-ray sources, which are key to advancing both fundamental and applied sciences. The availability of advanced driving lasers, with tunable wavelength, power, and pulse duration, opens new opportunities for optimizing HHG-based sources. While scaling laws for wavelength are well understood, this work focuses on how pulse duration impacts HHG efficiency and introduces a unified framework that links microscopic dynamics to macroscopic performance. We establish a practical scaling law for the single-atom dipole moment under phase-matching conditions, demonstrating a 1/t dependence at 515 nm wavelength. By connecting this microscopic scaling to macroscopic conversion efficiency, we provide clear guidelines for optimizing HHG output across different gases and driving wavelengths. Furthermore, we identify fundamental constraints, including the carrier-envelope-phase (CEP) walk-off, which limits efficiency at longer driver wavelengths and becomes especially significant for very short pulses. All predictions are based on simple, accessible formulas, eliminating the need for complex numerical simulations. Experiments confirm these predictions and highlight when short pulses are advantageous, particularly in scenarios where CEP walk-off and absorption effects are minimized. These findings offer practical principles for designing next-generation HHG sources, capable of Watt-level average power and extended spectral reach, enabling more versatile and powerful HHG-based XUV and soft X-ray sources.

Single nuclear spins in silicon are a promising resource for quantum technologies due to their long coherence times and excellent control fidelities. Qubits and qudits have been encoded on donor nuclei, with successful demonstrations of Bell states and quantum memories on the spin-1/2 $^{31}$P and cat-qubits on the spin-7/2 $^{123}$Sb nuclei. Isoelectronic nuclear spins coupled to gate-defined quantum dots, such as the naturally occurring $^{29}$Si isotope, possess no additional charge and allow for the coupled electron to be shuttled without destroying the nuclear spin coherence. Here, we demonstrate the coupling and readout of a spin-9/2 $^{73}$Ge nuclear spin to a gate-defined quantum dot in SiMOS. The $^{73}$Ge nucleus was implanted by isotope-selective ion-implantation. We observe the hyperfine interaction (HFI) to the coupled quantum dot electron and are able to tune it from 180 kHz to 350 kHz, through the voltages applied to the lateral gate electrodes. This work lays the foundation for future spin control experiments on the spin-9/2 qudit as well as more advanced experiments such as entanglement distribution between distant nuclear spins or repeated weak measurements.

We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable algebras of the Drinfeld center to identify the intrinsically gapless symmetry protected topological (igSPT) phases. In previous work, the relation between igSPT phases and resolving anomalies by embedding an anomalous symmetry inside a larger fusion category was demonstrated. Here we present more examples of this mechanism that involve both group-like and categorical symmetries.

Discrete games are central tools for empirical analysis of strategic interaction, but equilibrium multiplicity and partial identification often make them computationally difficult to estimate. This paper develops tractable methods for estimation and inference in complete-information discrete games. The key idea is to construct an outer set by comparing observed frequencies of action profiles with singleton-class generalized likelihoods: model-implied probabilities that those profiles can arise as equilibria. The resulting conditional moment inequalities avoid computationally expensive equilibrium enumeration, numerical simulation, and grid search. Under standard empirical assumptions used in discrete-game models, including logit payoff shocks, these restrictions have closed-form expressions and are convex in a subvector of structural parameters. I develop the approach for both unordered and ordered action spaces. Monte Carlo experiments and empirical applications show that the methods deliver informative outer sets and can reduce computation time by several orders of magnitude relative to existing approaches.

With advancements in distributed ledger technologies and smart contracts, tokenized voting rights gained prominence within Decentralized Finance (DeFi). Voting rights tokens (aka. governance tokens) are fungible tokens that grant individual holders the right to vote upon the fate of a project. The motivation behind these tokens is to achieve decentral control. Because the initial allocations of these tokens is often un-democratic, the DeFi project Yearn Finance experimented with a fair launch allocation where no tokens are pre-mined and all participants have an equal opportunity to receive them. Regardless, research on voting rights tokens highlights the formation of oligarchies over time. The hypothesis is that the tokens' tradability is the cause of concentration. To examine this proposition, this paper uses an Agent-based Model to simulate and analyze the concentration of voting rights tokens post fair launch under different trading modalities. It serves to examine three distinct token allocation scenarios considered as fair. The results show that regardless of the allocation, concentration persistently occurs. It confirms the hypothesis that the disease is endogenous: the cause of concentration is the tokens tradablility. The findings inform theoretical understandings and practical implications for on-chain governance mediated by tokens.

Using the density functional tight binding method (DFTB) and the GFN1-xTB (Geometries, Frequencies, and Noncovalent interactions Tight Binding) Hamiltonian, we have investigated the structural, electronic and magnetic properties of vacancy defects, hydrogen and oxygen passivated defects, and Fe adsorption in two-dimensional (2D) graphitic carbon nitride (gt-C$_3$N$_4$) 2D material. The ring shape is the most preferred vacancy evolution path, with significant stability of the semicircle fourfold C-N-C-N vacancy. We found that bare gt-C$_3$N$_4$ which is non-magnetic becomes magnetic by 2-, and 5-defects creation, hydrogen/oxygen passivation of the defects, and upon Fe adsorption. Interestingly, Fe atoms interact with the gt-C$_3$N$_4$ sheet and result in a ground ferromagnetic (FM) state. In addition, we investigate the effects of passivating the vacancies by hydrogen in gt-C$_3$N$_4$ on its structural, electrical, and magnetic properties. We found that substituting the 1, 2, and 3 vacancies with hydrogen and passivating the 6-defect with oxygen turns on magnetism in the system. Due to structural distortion, the passivated defects do not have a well-ordered magnetic orientation. However, passivating the remaining defected structures maintains the nonmagnetic state. It is also shown that passivation leads to a semiconductor with a band gap value higher than that of the bare material. We also calculate the electronic and magnetic properties of transition metal (TM) atoms, including V, Cr, Mn, Fe, Co, Ni-adsorbed gt-C$_3$N$_4$ monolayer. All TM atoms show slight lattice distortion, and the adsorbed system almost maintains the original structure type. Moreover, a FM alignment was observed with a total magnetic moments of 2.89 $μ_B$, 2 $μ_B$, and 1 $μ_B$ for V, Fe, and Co atoms, respectively. The Cr, Mn, and Ni atoms induce no magnetism to the non magnetic gt-C$_3$N$_4$ system.

Modern embedded Linux devices, such as routers, IP cameras, and IoT gateways, rely on complex software stacks where numerous daemons interact to provide services. Testing these devices is crucial from a security perspective since vendors often use custom closed- or open-source software without documenting releases and patches. Recent coverage-guided fuzzing solutions primarily test individual processes, ignoring deep dependencies between daemons and their persistent internal state. This article presents STAFF, a firmware fuzzing framework for discovering bugs in Linux-based firmware built around three key ideas: (a) user-driven multi-request recording, which monitors user interactions with emulated firmware to capture request sequences involving application-layer protocols (e.g., HTTP); (b) intra- and inter-process dependency detection, which uses whole-system taint analysis to track how input bytes influence user-space states, including files, sockets, and memory areas; (c) protocol-aware taint-guided fuzzing, which applies mutations to request sequences based on identified dependencies, exploiting multi-staged forkservers to efficiently checkpoint protocol states. When evaluating STAFF on 15 Linux-based firmware targets, it identifies 42 bugs involving multiple network requests and different firmware daemons, significantly outperforming existing state-of-the-art fuzzing solutions in both the number and reproducibility of discovered bugs.

In this study, we consider a spring-block system that approximates a $d$-dimensional linear elastic body, where $d=2$ or $d=3$. We derive a $d\times d$ matrix as the spring constant using the P1 finite element method with a triangular mesh for the linear elasticity equations. We mathematically analyze the symmetry and positive-definiteness of the spring constant. Even if we assume full symmetry of the elasticity tensor, the symmetry of the matrix obtained as the spring constant is not trivial. However, we have succeeded in proving this in a unified manner for both 2D and 3D cases. This is an alternative proof for the 2D case in Notsu-Kimura (2014) and is a new result for the 3D case. We provide a necessary and sufficient condition for the spring constant to be positive-definite in the case of an isotropic elasticity tensor, along with a sufficient condition in terms of mesh regularity and the Poisson ratio. These theoretical results are supported by several numerical experiments. The positive-definiteness of the spring constant derived from the finite element method plays a vital role in fracture simulations of elastic bodies using the spring-block system.

This paper investigates the differential-geometric and topological properties of the Cayley condition in Poncelet porism for triangles, defined as the locus of pairs of non-degenerate conics that admit a Poncelet triangle. While the algebraic condition for this porism, established by Cayley, is classical, the geometric nature of the set of solutions has remained largely unexplored. We demonstrate that this Cayley set is a smooth, connected, 9-dimensional complex manifold. This is proven by showing it is an open subset of a smooth algebraic variety endowed with a trivial fiber bundle structure over the space of non-degenerate conics. To further analyze its structure, we construct the moduli space of transversely intersecting conic pairs under the action of $\mathbb{P}GL_3(\mathbb{C})$ and identify it with an open subset of $\mathbb{CP}^2/S_3$. We compute the fundamental group of a generic orbit. The elliptic j-invariant is then introduced as a holomorphic map on this space of conics, which factors through this moduli space. We analyze the subset of the Cayley set where this map is a submersion - its regular part - which corresponds to excluding points whose j-invariant is one of the critical values $0$ or $1728$. We prove that this regular part is the total space of a fiber bundle over $\mathbb{C} \setminus \{0,1728\}$. This structure allows for the computation of the fundamental group via the long exact sequence of homotopy. Finally, we provide a principal bundle formulation for the Poncelet correspondence itself over orbits of conic pairs.

Reasoning about programs in the presence of mutation and aliasing is notoriously difficult. Rust has popularized lifetime-based ownership tracking in systems programming, but its "shared XOR mutable" model is fundamentally at odds with higher-level functional programming. Reachability types offer an alternative: they enable safe sharing and escape of mutable data by tracking which resources each expression's result can reach. To track internal reachability within complex object graphs, reachability types adopt self-references that let components refer to enclosing resources from inside, just like `this` pointers in OO languages. While natural for declaratively typing escaping data, self-references complicate subtyping and furthermore type inference: variance restricts where self-references may appear, yet useful type conversions must allow them to vary in controlled ways, which in turn imposes constraints on inference. As an undesirable result, prior works require programmers to insert term-level coercions for even just avoidance -- avoiding ill-scoped names in types. With all prior works being declarative, we investigate algorithmic reachability types in this work. We introduce a refined subtyping relation that permits more flexible usages of self-references. We further develop a sound and decidable bidirectional typing algorithm, implemented and verified in Lean. The algorithm automatically avoids ill-scoped names in types, and infers qualifiers via a lightweight unification mechanism. As a step towards practical reachability programming, we show that the system is capable of tracking diverse reachability patterns without explicit coercions in complex Church-encoded datatypes.

Let f be a zero entropy automorphism of a compact Kähler manifold X. We study the polynomial log-volume growth Plov(f) of f in light of the dynamical filtrations introduced in our previous work with T.-C. Dinh. We obtain new upper bounds and lower bounds of Plov(f). As a corollary, we completely determine Plov(f) when dim X = 3, extending a result of Artin--Van den Bergh for surfaces. When X is projective, Plov(f) + 1 coincides with the Gelfand--Kirillov dimensions GKdim(X,f) of the twisted homogeneous coordinate rings associated to (X,f). Reformulating these results for GKdim(X,f), we improve Keeler's bounds of GKdim(X,f) and provide effective upper bounds of GKdim(X,f) which only depend on dim X.

Let $G$ be a simple graph. The $k$-th neighborhood of a vertex subset $S \subseteq V(G)$, denoted $Λ^k(S)$, is the set of vertices that are adjacent to at least $k$ vertices in $S$. The $k$-th binding number $β^k(G)$ is defined as the minimum ratio $|Λ^k(S)|/|S|$ over all subsets $S \subseteq V(G)$ with $|S| \ge k$ and $Λ^k(S) \ne V(G)$. This parameter generalizes the classical binding number introduced by Woodall. Andersen showed that the condition $β^1(G) \ge 1$ does not guarantee the existence of a $1$-factor in $G$, while Barát et al. proved that $β^2(G) \ge 1$ suffices for the existence of a $2$-factor. In this paper, we extend this result to general $k \ge 2$ by showing that any graph $G$ with even $k|V(G)|$ and $β^k(G) \ge 1$ contains a $k$-factor. Moreover, if $G$ is additionally a split graph of even order, then it admits a $(k+1)$-factor. We also prove that any graph $G$ with $β^k(G) \ge 1$ contains at least $k-1$ disjoint perfect or near-perfect matchings. Finally, for any bipartite graph $G$ with bipartition $(X, Y)$, we introduce an analogue of the $k$-th binding number and show that, under the condition $β^k(G, X) \ge 1$, the graph admits $k$ disjoint matchings, each covering $X$.

Let $X$ be a compact Kähler manifold. We study subgroups $G \le \mathrm{Aut}(X)$ of biholomorphic automorphisms of zero entropy when $\mathrm{Aut}^0(X)$ is compact (e.g. when $\mathrm{Aut}^0(X)$ is trivial). We show that the virtual derived length $\ell_{\mathrm{vir}}(G)$ of $G$ satisfies $\ell_{\mathrm{vir}}(G) \le \dim X -κ(X)$, where $κ(X)$ is the Kodaira dimension of $X$. Modulo the main conjecture of our previous work concerning the essential nilpotency class, we obtain the same upper bound $c_{\mathrm{vir}}(G) \le \dim X -κ(X)$ for the virtual nilpotency class $c_{\mathrm{vir}}(G)$, together with a geometric description of the $G$-action on $X$ when the equality holds.

The super-neighborhood of a vertex set $A$ in a graph $G$, denoted by $Λ^2(A)$, is the set of vertices adjacent to at least two vertices in $A$. We say that a bipartite graph $G=(X, Y)$ with $|X| \geq 2$ satisfies the double Hall property (with respect to $X$) if $|Λ^2(A)| \geq |A|$ for any subset $A \subseteq X$ with $|A| \geq 2$. Kostochka et al. first conjectured that if a bipartite graph $G=(X, Y)$ satisfies a slightly weaker version of the double Hall property, then $G$ contains a cycle that covers all vertices of $X$. They verified their conjecture for $|X| \leq 6$. In this paper, we extend their result to $|X| = 7$. Later, Salia conjectured that every bipartite graph satisfying the double Hall property has a cycle covering all vertices of $X$. We show that Salia's conjecture is almost equivalent to a much weaker conjecture requiring vertices in $Y$ to have high degrees. By extending a result of Barát et al., we also show that Salia's conjecture holds for some graphs where the vertices of $Y$ have degree either $2$ or very high. Finally, we establish a lower bound for the maximum degree of graphs satisfying the double Hall property and present deterministic and probabilistic constructions of such graphs that approach this bound.

Let $X$ be a very general hypersurface of degree $d$ in the projective $(n+1)$-space with $n \ge 3$, and $f: X \to Y$ a non-birational surjective morphism to a normal projective variety $Y$. We first prove that $Y$ is a klt Fano variety if ${\rm deg} \, f \ge C$ for some constant $C = C(n, d)$ depending only on $n$ and $d$. Next we prove an optimal upper bound ${\rm deg} \, f \le {\rm deg} \, X$ provided that $Y$ is factorial, ${\rm deg} \, f$ is prime and ${\rm deg} \, f \ge E(n)$ for some constant $E(n)$ (with $E(n) = n(n+1)$ when $Y$ is smooth). As a corollary, we show that $Y\cong {\bf P}^n$ under some conditions on $Y$ and ${\rm deg} \, f$.

We first extend Calderón's transfer principle to weighted spaces, and then we apply our results to obtain some new weighted inequalities in ergodic theory and ergodic $H^1$ spaces.

Scaling quantum computers remains a substantial scientific and technological challenge. Leveraging the full range of intrinsic degrees of freedom in quantum systems offers a promising route towards enhanced algorithmic performance and hardware efficiency. We experimentally study the use of $^{137}$Ba$^+$ ions for quantum information processing, achieving high-fidelity state preparation and readout of up to 25 internal levels, thus forming a 25-dimensional qudit. By probing superpositions of up to 24 states, we investigate how errors scale with qudit dimension $d$ and identify the primary error sources affecting quantum coherence. Additionally, we demonstrate high-dimensional qudit operations by implementing a 3-qubit Bernstein-Vazirani algorithm and a 4-qubit Toffoli gate with a single ion. Our findings suggest that quantum computing architectures based on large-dimensional qudits hold significant promise.

Several key states in various regions of the U.S. have experienced recent sawtimber as well as pulp and paper mill closures, which raises an important policy question: how have and will key macroeconomic and industry specific indicators within the U.S. forest sector likely to change over time? This study provides empirical evidence to support forest-sector policy design by using a vector error correction (VEC) model to forecast economic trends in three major industries - forestry and logging, wood manufacturing, and paper manufacturing - across six of the most forest-dependent states found by the location quotient (LQ) measure: Alabama, Arkansas, Maine, Mississippi, Oregon, and Wisconsin. Overall, the results suggest a general decline in employment and the number of firms in the forestry and logging industry as well as the paper manufacturing industry, while wood manufacturing is projected to see modest employment gains. These results also offer key insights for regional policymakers, industry leaders, and local economic development officials: communities dependent on timber-based manufacturing may be more resilient than other forestry-based industries in the face of economic disruptions. Our findings can help prioritize targeted policy interventions and inform regional economic resilience strategies. We show distinct differences across forest-dependent industries and/or state sectors and geographies, highlighting that policies may have to be specific to each sector and/or geographical area. Finally, our VEC modeling framework is adaptable to other resource-dependent industries that serve as regional economic pillars such as mining, agriculture, and energy production offering a transferable tool for policy analysis in regions with similar economic structures.

We introduce a method to calculate defect-assisted Shockley-Read-Hall (SRH) recombination rates in imperfect semiconductors from first principles. The method accounts for the steady state recombination dynamics under given non-equilibrium conditions (split quasi Fermi levels), by invoking a full solution to the rate equations describing transitions across the band gap via all possible charge states of the defect. Transition rates due to radiative and non-radiative multi-phonon emission processes are calculated from first principles. The method is used to evaluate the effect of selected defects on the photovoltaic device parameters of seven emergent photovoltaic semiconductors. These examples clearly highlight the limitations of commonly employed approximations to the recombination dynamics. Our work advances the description and understanding of defect-induced losses in photovoltaics and provides a basis for developing the important concept of defect tolerant semiconductors and to discover high-performance photovoltaic materials computationally.

The ongoing energy crisis has underscored the urgent need for energy-efficient materials with high energy utilization efficiency, prompting a surge in research into organic compounds due to their environmental compatibility, cost-effective processing, and versatile modifiability. To address the high experimental costs and time-consuming nature of traditional trial-and-error methods in the discovery of highly functional organic compounds, we apply the 3D transformer-based molecular representation learning algorithm to construct a pre-trained model using 60 million semi-empirically optimized structures of small organic molecules, namely, Org-Mol, which is then fine-tuned with public experimental data to obtain prediction models for various physical properties. Despite the pre-training process relying solely on single molecular coordinates, the fine-tuned models achieves high accuracy (with $R^2$ values for the test set exceeding 0.95). These fine-tuned models are applied in a high-throughput screening process to identify novel immersion coolants among millions of automatically constructed ester molecules, resulting in the experimental validation of two promising candidates. This work not only demonstrates the potential of Org-Mol in predicting bulk properties for organic compounds but also paves the way for the rational and efficient development of ideal candidates for energy-saving materials.

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR -- Correlated Atomic Vibration Imaging with sub-Angstrom Resolution -- that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric $Σ$9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of $10.8\pm0.1$, $13.6\pm0.6$, $18.0\pm0.2$, $25.5\pm1.5$ THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm$^3$ volume. This ability to spatially resolve correlated atomic motion makes CAVIAR a unique tool to explore atom dynamics at the finest scale with the potential to be instrumental in the development of phononic devices, in studying phonon-based decoherence in quantum systems, or other emerging phonon-based applications.