In this paper, we study DNA-based molecular communication with microarray-style reception under reversible hybridization, where the bound-state observation exhibits both inter-symbol interference and colored counting noise. To capture these effects in a communication-oriented form, we develop a Markov state-space framework based on a voxelized reaction--diffusion model, in which a block-structured transition matrix describes molecular transport and binding/unbinding dynamics. For the microarray specialization, this representation yields the channel impulse response, the equilibrium gain, and a settling-time-based characterization of the effective channel memory. Building on the resulting symbol-rate observation model for on--off keying, we derive a grouped-binomial counting model and obtain a closed-form expression for the covariance of the counting noise. Based on these statistics, we further develop a differential-threshold detector and a finite-memory decision-feedback equalizer. Numerical results validate the theoretical correlation behavior and show that the relative performance of the proposed receivers depends strongly on the channel-memory regime.

The deterministic realization of quantum light sources operating at telecom wavelengths is essential for long-distance fiber-based quantum communication and distributed quantum computing. In this work, we demonstrate that telecom O-band emission can be achieved from site-controlled InGaAs/GaAs quantum dots (QDs). Our concept utilizes a buried AlAs/Al$_2$O$_3$ stressor layer with the unique feature that induces a well-defined and controllable tensile strain field at the growth surface, enabling both a redshift of QD emission to the $\sim$1.3~μm range and site-selective nucleation at the mesa centers. This concept eliminates not only the need for strain-reducing layers (SRLs), which are known to degrade optical coherence, but also provides spatial control and spectral tunability. The grown telecom QDs show pure single-photon emission with $g^{(2)}(τ) = (5.0 \pm 1.0) \times 10^{-2}$ at 4 K and $(2.8 \pm 0.3) \times 10^{-1}$ at 77~K, demonstrating the quantum nature and thermal stability of the emitters. The emission characteristics of complex excitonic states are analyzed using 8-band $k \cdot p$ and configuration-interaction modeling, which quantitatively reproduces the experimental observations. Finally, we present a theory-supported strategy to further redshift the emission toward the center of the O-band and beyond by employing a multi-buried-stressor approach. This combined framework of experiment and theory establishes the buried stressor concept as a scalable route toward highly coherent, position-controlled O-band quantum emitters compatible with industrial photonic integration.

A user's ownership perception of virtual objects, such as cloud files, is generally uncertain. Is this valid for streaming platforms featuring accounts designed for sharing (DS)? We observe sharing practices within DS accounts of streaming platforms and identify their ownership characteristics and unexpected complications through two mixed-method studies. Casual and Cost-splitting are the two sharing practices identified. The owner is the sole payer for the account in the former, whereas profile holders split the cost in the latter. We distinguish two types of ownership in each practice -- Primary and Dual. In Primary ownership, the account owner has the power to allow others to use the account; in Dual ownership, Primary ownership appears in conjunction with joint ownership, notably displaying asymmetric ownership perceptions among users. Conflicts arise when the sharing agreements collapse. Therefore, we propose design recommendations that bridge ownership differences based on sharing practices of DS accounts.

Family-Vicsek (FV) scaling provides an understanding for the growth and finite-size saturation of fluctuations in classical systems. Here, we extend the FV roughness to transferred segment magnetization after quantum quenches in a dissipative XXZ spin chain with homogeneous gain and loss, starting from a nonequilibrium steady state with finite magnetization. In the non-interacting limit, we derive a closed-form expression for the roughness in the presence of dissipation. It displays two-parameter FV scaling and smoothly interpolates between the clean ballistic behavior and the dissipation dominated scalings. For interacting chains, tensor-network simulations show that the non-dissipative ballistic growth at finite magnetization is robust, whereas the full Lindblad evolution is generically controlled by the dissipative relaxation time and exhibits a dissipation-dominated collapse.

Teleoperated driving (TD) is envisioned as a key application of future sixth generation (6G) networks. In this paradigm, connected vehicles transmit sensor-perception data to a remote (software) driver, which returns driving control commands to enhance traffic efficiency and road safety. This scenario imposes to maintain reliable and low-latency communication between the vehicle and the remote driver. To this aim, a promising solution is Predictive Quality of Service (PQoS), which provides mechanisms to estimate possible Quality of Service (QoS) degradation, and trigger timely network corrective actions accordingly. In particular, Reinforcement Learning (RL) agents can be trained to identify the optimal PQoS configuration. In this paper, we develop and implement two integrated RL agents that jointly determine (i) the optimal compression configuration for TD sensor data to balance the trade-off between transmission efficiency and data quality, and (ii) the optimal scheduling configuration to minimize the end-to-end latency by allocating radio resources according to different priority levels. We prove via full-stack ns-3 simulations that our integrated agents can deliver superior performance than any standalone model that only optimizes either compression or scheduling, especially in constrained or congested networks. While these agents can be deployed using either centralized or decentralized learning, we further propose a new meta-learning agent that dynamically selects the most appropriate strategy between the two based on current network conditions and application requirements.

We study the distribution of envy in random matching markets under the Deferred Acceptance (DA) algorithm. Using tools from applied probability, we compute the expected number of proposing agents whom nobody envies and those who envy nobody. We obtain an exact finite-market expression for the former, based on a connection with the coupon collector problem, and asymptotic bounds for the latter. To put these quantities into perspective, we compare them to their counterparts under Random Serial Dictatorship (RSD): while RSD assigns a constant fraction of agents to their top choice, both DA and RSD leave exactly $H_n$ proposing agents unenvied in expectation. Our results show that these clearly unimprovable proposing agents constitute a vanishing fraction of the market.

We present a high-energy spectral analysis of GRB 250129A, which was triggered by the Swift-BAT. The burst exhibits a complex, multi-peaked temporal structure characterized by two distinct emission episodes, with the main peak occurring approximately 180 seconds after the BAT trigger. The time-integrated spectral analysis in the 15 - 150 keV energy range indicates that a broken power-law (BPL) model provides the best fit, signifying a non thermal origin of the prompt emission. A time resolved spectral analysis, performed using the Bayesian block technique, shows that the intervals around the main emission peak are well described by the BPL model, while the fits for low count intervals remain less constrained. An evident intensity tracking behavior is observed between the flux and the spectral peak energy (Ep). Furthermore, both the Amati relation and hardness - intensity correlation suggest that GRB~250129A occupies an intermediate regime, acting as a bridge between long and ultra long GRBs.

We present a simple method to study the dynamics of planar Kahan-Hirota-Kimura (KHK) maps preserving rational fibrations. Using this approach, we show that integrable KHK maps may exhibit complex dynamics, even when obtained from vector fields with trivial behavior. As an application, we study the KHK map associated with a quadratic planar vector field with an isochronous center. This map preserves the original first integral and admits the vector field as a Lie symmetry. Moreover, for a dense set of values of the integration step, it is globally periodic and exhibits all possible periods except 2. We also provide evidence of non-integrability for KHK maps associated with other quadratic vector fields possessing isochronous centers. To overcome this issue, we introduce the notion of pseudo-KHK maps, as alternative integrable discretizations for vector fields with isochronous centers. These maps are constructed to preserve the first integrals of the original vector field and to ensure that the vector field itself is a Lie symmetry of the map. The construction can be extended to isochronous centers of degree greater than two.

Tangent numbers $T_{2n-1}$, which enumerate alternating permutations of odd length, play a prominent role in the Taylor series expansion of the tangent function $\tan(x)$. In this work, we adopt a combinatorial approach based on the excedance statistic of permutations, which allows us to interpret the coefficients of the tangent series in a structural and enumerative way. Using this framework, we establish a classical identity that relates the alternating sum of excedances to the hyperbolic tangent function. This perspective highlights deep connections with Eulerian polynomials, provides a combinatorial interpretation of tangent numbers, and links these sequences to Genocchi numbers and related arithmetic properties. The approach not only unifies analytic and combinatorial viewpoints but also opens the way to generalizations to other permutation statistics and families of specialized permutations.

We report reproducible magnetization anomalies appearing below room temperature in copper-doped apatite materials belonging to the LK-99 family synthesized via hydrothermal methods. These anomalies are observed consistently across samples prepared under comparable conditions. Although the extracted Mydosh parameter lies within the range often associated with vortex-glass behavior in superconductors, a detailed analysis of DC magnetization, AC susceptibility, field dependence, and magnetic memory effects demonstrates that the observed phenomena are not related to superconductivity. Instead, the data are consistent with glassy magnetic freezing of interacting clusters. Compositional and structural analysis identifies covellite (CuS), an ubiquitous secondary phase in these intrinsically multiphase materials, as the primary origin of the observed behavior. Our results clarify the magnetic origin of LK-99-related anomalies and highlight the importance of phase complexity in interpreting apparent superconducting signatures in this materials family.

The cosmic distance duality relation (CDDR), expressed as $d_L(z) = (1+z)^2 D_A(z)$, is a fundamental relation in modern cosmology. In this work, we apply a method to test the CDDR using simulated strongly lensed gravitational-wave (SLGW) signals from massive binary black holes (MBBH) as observed by proposed space-based detector networks. Our analysis is conducted under the point-mass lens model, considering the strong lensing scenario that produces two images. We generate 90 days of simulated SLGW data for 10 events based on the Population III stellar formation model, with source redshifts in the range $z_s \in [2,6]$ and lens redshifts in $z_L \in [0.2,1]$. The deviation of CDDR is parameterized by $η_1(z) = 1 + η_0 z$ and $η_2(z) = 1 + η_0 z/(1+z)$, and we incorporate the deviation parameter $η_0$ directly into the waveform model. Parameter estimation is performed within a Bayesian statistical framework, combining simulated data from both Taiji and LISA. For a single lensed event, the joint Taiji+LISA analysis improves the measurement precision of $η_0$ by roughly a factor of two compared with Taiji-only observations. By combining 10 simulated events, the population-level constraints on $η_0$, quantified by the half width of the $95\%$ credible interval, reach approximately $2.61\times10^{-4}$ ($1.72\times10^{-4}$) for the $η_1(z)$ parameterization and $1.22\times10^{-3}$ ($6.86\times10^{-4}$) for $η_2(z)$ in the Taiji-only (Taiji+LISA) scenario, respectively. The inferred values of $η_0$ remain consistent with $η_0 = 0$ within the estimated uncertainties, with no statistically significant evidence for deviations from the CDDR at the achieved precision. These results demonstrate the significant advantage of joint space-based observations for high-precision tests of the CDDR.

Progress in particle physic leads to increasing in detector luminosity and a consequent increasing overheating induced by Joule effect. An effective cooling strategy is the exploitation of CO\textsubscript{2} heat latency in phase-change. An additional challenge, relevant to detectors for High Energy Particles, is the consequent geometrical constrain due to the limited space avialable for the cooling system within the detector arrangement, leading to the implementation of cooling system by means of millichannels. In this context, at relative high vapour quality the liquid phase exhibits annular flow, anticipating the dryout. Dryout is a critical condition where the heat transfer coefficient dramatically drops and dangerous temperature levels can be reached, potentially leading to catastrophic consequences. Experimental evidences reveal that its behavior in two-phase annular flows differs from conventional refrigerants and the fundamental inception-mechanism is not yet understood. This study aims at investigating the key new idea whereby dryout inception is triggered by instability of the liquid-vapour interface. A mathematical model for two-phase annular flow is presented and the stability of the interface between the two fluids is studied through the linear theory. The stability analysis reduces to solving a coupled forth-order differential eigenvalue problem that is treated numerically with an in-house code based on the Chebyshev-$τ$ method. Numerical investigations identify a critical value for the vapour quality, named $x_{dry}$, that leads to interface instability. The resulting predictions on $x_{dry}$ are confirmed by experimental data collected from two independent experimental campaigns, validating the hypothesis that dryout inception is governed by interfacial instabilities.

In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.

A dg cyclic operad $BVHgraphs$ of hypergraphs is introduced which comes equipped with an explicit quasi-isomorphism $BV\rightarrow BVHgraphs$ from the { cyclic} operad $BV$ of Batalin-Vilkovisky algebras. A proof that the cohomology of $BVHgraphs$ equals $BV$ occupies most of this paper. We use this model to construct an explicit quasi-isomorphism $Chains(FFM_2) \rightarrow BVHgraphs$ from the chain operad of the cyclic operad $FFM_2$ of the compactified moduli spaces of genus zero curves with marked framed points to the dg cyclic operad $BVHgraphs$ which, combined with the main result mentioned above, gives a new proof of the cyclic formality of $FFM_2$.

Materials identification and structural understanding from powder X-ray diffraction (PXRD) data is a long-standing challenge in materials science, fundamental to discovering and characterizing novel materials. A prerequisite for full structure solution is the accurate determination of the crystal lattice, including lattice parameters and crystallographic symmetries. Traditional methods for this are iterative and typically require expert input, and while existing deep learning approaches have shown promise, a robust, single-shot method for comprehensive lattice determination from experimental data remains a key goal. Here, we introduce AlphaDiffract, a deep learning framework that achieves state-of-the-art performance in predicting the crystal system, space group, and lattice parameters directly from PXRD patterns. AlphaDiffract utilizes a 1D adaptation of the ConvNeXt architecture, a modern convolutional neural network that integrates key design principles from transformers, coupled with dedicated prediction heads for each crystallographic property. The model is trained on the largest-to-date physics-based dataset of over 31 million simulated diffraction patterns, generated by augmenting 312,267 curated structures from the ICSD and Materials Project databases. Crucially, it demonstrates strong generalization to experimental data, achieving 81.7% crystal system accuracy and 66.2% space group accuracy on the RRUFF dataset while additionally predicting all six lattice parameters. By providing a unified model for rapid and accurate lattice determination from PXRD data, AlphaDiffract represents a significant step forward in leveraging deep learning for high-throughput materials discovery.

We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$, we equip $P$ with a certain zero-dimensional Hausdorff topology and use a certain compactification $γP$ to get the base space for a continuous field of Hilbert C*-bimodules over $γP$. As a motivating example, we consider the set $D(X,Y)$ of coarse equivalence classes of metrics on the disjoint union of two metric spaces, $X$ and $Y$. Each such class gives rise to a uniform Roe bimodule, a TRO linking the uniform Roe algebras of $X$ and $Y$. The resulting family of TROs is non-decreasing with respect to the natural partial order on $D(X,Y)$ and thus yields a tautological continuous field of Hilbert C*-bimodules over $γD(X,Y)$.

Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules. Moreover, we completely determine which of them admit a finite-dimensional Nichols algebra.

Dynamic languages such as Python and JavaScript widely use function decorators to extend behavior. In TypeScript, a common way to type such patterns uses Parameters<T> and ReturnType<T>. In practice, this idiom relies on a function-type bound for T that is expressed using the unsafe type any, which weakens static guarantees. At the core is a standard typing principle: application is justified only when the callee is exposed as an arrow type. We present F<:DR, a calculus that adds domain and range projection types, Dom(T) and Range(T), for arbitrary types T. These projections permit typing applications through abstract function types: an argument of type Dom(T) witnesses callability, and the result is typed as Range(T). This design complements, rather than replaces, standard arrow-based application, which remains admissible via subtyping in System F<:. We mechanize F<:DR in Rocq and prove semantic type soundness using logical relations with path selection, which delays projection interpretation until function structure is resolved. The same technique extends to additional projection types, illustrated for primitive pairs, i.e., product types.

Gamma-Ray Burst (GRB) afterglows arise from the interaction of relativistic ejecta with the circumburst medium and are observed across the electromagnetic spectrum. Afterglow polarisation is expected at early and late phases depending on the presence of reverse shocks (RS) and the observer's viewing geometry relative to the jet. Polarimetric observations of GRB afterglows provide a unique diagnostic tool to probe the geometry and structure of magnetic fields in the emitting region, which cannot be inferred from photometric or spectroscopic data alone. We report late-time (~19 hours post-burst) spectropolarimetric observations of GRB 250129A using the Southern African Large Telescope (SALT). The data reveal a hint of linear polarisation, with no evidence for rotation in the polarisation angle across wavelengths. Polarisation is typically expected during the early afterglow (<100 s) when the RS dominates. However, multi-wavelength modelling shows no indication of RS contribution at late times. Modelling incorporating both forward shock (FS) and RS components confirms that the RS fades rapidly after ~100 s. The afterglow emission is best explained by an off-axis viewing geometry of a jet with a Gaussian core and wings evolving in a uniform density environment. GRB 250129A thus provides rare observational evidence linking late-time polarisation to jet geometry and structure.

This proof-of-concept study introduces a novel multimodal framework combining synchronized EEG-fNIRS modalities with neuronal avalanche analysis to identify early network dysfunction in Alzheimer's disease. The approach leverages complementary neural signals to examine motor network dynamics during execution and imagery tasks within an interactive task environment. Preliminary analysis of a small pilot cohort (N=4 subjects, including one with Mild Cognitive Impairment) validated the technical feasibility of the multimodal framework and revealed observable condition-dependent patterns in network organization. Two primary observations emerged: a reduced neural contrast between motor execution and imagery states, and increased trial-to-trial variability in network organization in the MCI participant. These initial results successfully validate the technical pipeline and provide hypothesis-generating observations for future statistically powered studies. The convergence of findings across modalities suggests that multimodal assessment of network flexibility may help detect functional changes in early Alzheimer's continuum, supporting the future development of this BCI-inspired framework into an engaging diagnostic tool.

This study analyzes Graph Neural Networks (GNNs) for distribution system state estimation (DSSE) by employing an interpretable Graph Neural Additive Network (GNAN) and by utilizing an edge-conditioned message-passing mechanism. The architectures are benchmarked against the standard Graph Attention Network (GAT) architecture. Multiple SimBench grids with topology changes and various measurement penetration rates were used to evaluate performance. Empirically, GNAN trails GAT in accuracy but serves as a useful probe for graph learning when accompanied with the proposed edge attention mechanism. Together, they demonstrate that incorporating information from distant nodes could improve learning depending on the grid topology and available data. This study advances the state-of-the-art understanding of learning on graphs for the state estimation task and contributes toward reliable GNN-based DSSE prediction technologies.

Reading constructed a Cambrian lattice $C_Γ$ for each oriented finite type Coxeter diagram $Γ$. We show that the derived category of representations of $C_Γ$ is fractionally Calabi-Yau for any $Γ$, confirming a conjecture of Chapoton. This extends a result of Rognerud for Cambrian lattices of type $A$ with linear orientation, better known as Tamari lattices. If $Γ$ is crystallographic, then $C_Γ$ is given by the lattice of torsion classes of any hereditary algebra $Λ$ of type $Γ$. In this case we introduce and study a class of intervals in $C_Γ$ whose combinatorics matches the combinatorics of $2$-cluster tilting objects in the 2-cluster category of $Λ$. This allows us to compute the Calabi-Yau dimension of $C_Γ$.

Immersive technologies, such as virtual and augmented reality, are transforming digital heritage by enabling users to explore and interact with culturally significant sites. It is now possible to view and augment digital twins, or digitally reconstructed versions of them, and to enable access to previously unreachable locations for a broader audience. Here, we investigate retrieval-augmented generation (RAG)-based avatars as an interface for accessing further information about digital cultural heritage objects while immersed in dedicated virtual environments. We present a requirement design space that spans the application realm, avatar personality, and I/O modalities. We instantiate it with a RAG system coupled to a conversational avatar in a virtual reality (VR) environment, using the Maxentius mausoleum from the 4th century AD as a case study, through which users gain access to curated on-demand information of the digitised heritage object. Our workflow utilises scholarly texts and enriches them with metadata. We evaluate various RAG configurations in terms of answer quality on a small expert-crafted question-answer set, as well as the perceived workload of users of a VR setup using such a RAG avatar. We demonstrate evidence that users perceive the overall workload for interacting with such an avatar as below average and that such avatars help to gain topical engagement. Overall, our work demonstrates how to utilise RAG-driven VR avatars for archaeological purposes and provides evidence that they can offer a pathway for immersive, AI-enhanced digital heritage applications.

The latest Wi-Fi security standard, IEEE 802.11, includes a secure authentication protocol called SAE, whose use is mandatory for WPA3-Personal networks. The protocol is specified at two separate but linked levels: a traditional cryptographic description of the communication logic between network devices, and a state machine description that realises the former in each single device. Current formal verification efforts focus mainly on communication logic. We present detailed formal models of the protocol at both levels, provide precise specifications of its security properties, and analyse machine-checked proofs in ProVerif and ASMETA. The integrated analysis of the above two models is particularly novel, enabling us to identify and address several issues in the current IEEE 802.11 specification more thoroughly than would have been possible otherwise, leading to several official revisions of the standard.

Star lattice, which can be visualized as a honeycomb network with each vertex replaced by a triangle, provides a rare platform for realizing exotic quantum states such as quantum spin liquids and disorder-driven random-singlet (RS) states. Herein, we investigate the ground-state properties of the three-dimensional (3D) stuffed hyper-star lattice Li$_2$Cu$_2$(MoO$_4$)$_3$, which exhibits a crossover from short-range spin correlations to a disorder-driven RS-like state below $T^{*}\sim$15.8 K. Thermodynamic and microscopic measurements capture this crossover through a change in the power-law behavior of various observables, from $\sim T^{0.25}$ for $T > T^{*}$ to $\sim T^{-0.50}$ for $T < T^{*}$. Upon further cooling, a quasi-frozen state emerges near $T_{\rm f} = 0.32$ K, likely associated with weakly coupled spin chains within the hyper-star spin network. Our results underscore the crucial role of orphan spins and weak residual interactions in stabilizing a disorder-driven quantum-disordered state in 3D.

Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by the interplay of mechanical properties, rheological behavior, and system geometry. While fracture mechanics has long addressed structural failure, the relationship among fracture, elasticity, and nonlinear geometry has recently revived as a focal point in condensed matter and biophysics. However, a unified framework that systematically explains how surface geometry prescribes the transition between disparate fracture morphologies remains elusive. Here we show that shell curvature provides a geometric blueprint for fracture, governing the evolution of complex crack networks through induced stress anisotropy. By internally pressurizing thin, bilayer spheroidal shells, we demonstrate that a rich diversity of crack morphologies across lateral, longitudinal, and random orientations depends on the curvature ratio between the pole and the equator. We find that these patterns arise from the nonlinear mechanics of the shell, which can be leveraged to effectively control crack growth. Our results establish a direct link between structural curvature and fractures, providing a predictive framework that integrates nonlinear geometry with the classical Griffith and von Mises criteria. Beyond our model system, we find that the disparate fracture patterns observed in ripening muskmelons and in the icy crust of Europa follow the same geometric principles. We expect that this unified understanding of crack morphogenesis will inform the design principles of novel functional materials that are resilient to fracture and provide insights into the mechanical performance of curved biological and geophysical architectures.

The $k$-center problem is a fundamental clustering variant with applications in learning systems and data summarization. In several real-world scenarios, the dataset to be clustered is not static, but evolves over time, as new data points arrive and old ones become stale. To account for dynamicity, the $k$-center problem has been mainly studied under the sliding window setting, where only the $N$ most recent points are considered non-stale, or the fully dynamic setting, where arbitrary sequences of point arrivals and deletions without prior notice may occur. In this paper, we introduce the dynamic setting with lifetimes, which bridges the two aforementioned classical settings by still allowing arbitrary arrivals and deletions, but making the deletion time of each point known upon its arrival. Under this new setting, we devise a deterministic $(2+\varepsilon)$-approximation algorithm with $\tilde{O}(k/\varepsilon)$ amortized update time and memory usage linear in the number of currently active points. Moreover, we develop a deterministic $(6+\varepsilon)$-approximation algorithm that, under tame update sequences, has $\tilde{O}(k/\varepsilon)$ worst-case update time and heavily sublinear working memory.

Over the past decade, substantial progress has been made in clarifying a central question of the Fermi-Pasta-Ulam-Tsingou problem: whether weakly nonlinear lattice systems thermalize and, if so, through what mechanisms. The current understanding is as follows. (a) Classical lattice systems fall into two universal classes. In the first, the Hamiltonian has extended normal modes. For sufficiently large systems, the thermalization time scales as $T_{\rm eq}\sim g^{-γ}$ with $γ=2$, where $g$ denotes the effective nonlinear strength, i.e., the perturbation strength or degree of non-integrability. Thus, in the thermodynamic limit, these systems inevitably thermalize. Typical examples include common one-, two-, and three-dimensional lattice models. In the second class, all normal modes are localized. Here the relaxation time is essentially independent of system size. Although one may still formally write $T_{\rm eq}\sim g^{-γ}$, the exponent $γ$ diverges as $g\to0$, implying that arbitrarily weak nonlinear perturbations cannot induce thermalization. For sufficiently small $g$, such systems may therefore be viewed, in a theoretical sense, as thermal insulators. (b) In systems of the first class, disorder does not obstruct thermalization. Rather, by breaking translational symmetry and relaxing wave-vector resonance constraints, it increases the number of quasi-resonant processes and can therefore accelerate thermalization. (c) In systems of the second class, when both on-site potentials and disorder are present, all normal modes become localized in sufficiently large systems, suppressing thermalization. The perturbative framework underlying these conclusions will also be presented systematically, with particular emphasis on the thermalization criterion based on resonance-network connectivity, an approach rooted in weak wave turbulence theory.

As AI accelerators gain prominence, their potential for traditional scientific computing workloads remains unclear. This paper explores Tenstorrent's Wormhole architecture, a spatial computing platform designed for neural network acceleration, by implementing three numerical kernels and composing them into a conjugate gradient solver. We present architecture-specific optimizations for sparse numerical algorithms, evaluate their performance against Nvidia GPUs, and expose both challenges and opportunities in porting numerical methods to spatial architectures. Our results demonstrate that AI accelerators merit consideration for workloads traditionally dominated by CPUs and GPUs, and more work should be invested in understanding the capabilities of these architectures and making them accessible to the scientific computing community.

A device and process strategy for achieving reliable indium gallium zinc oxide and indium oxide transistors compatible with a 400oC BEOL thermal budget and without performance degradation is demonstrated by fully exploiting intrinsic oxide material properties. An indium oxide transistor with a novel amorphous In2O3 mixed with SiO2 capping layer exhibits a positive threshold voltage, high extrinsic saturation mobility 33.1 cm2/V.s ,and only a 5mV Vt shift after positive-bias stress at 3 MV/cm for 1000s at room temperature, superior to conventional SiO2 encapsulation.