We study a driven optomechanical cavity with two movable mirrors and an intracavity optical parametric amplifier, focusing on how direct phonon-phonon coupling changes the observed normal-mode spectrum. Although the linearized system supports three hybrid modes, in the absence of direct mechanical coupling one collective mechanical mode contributes only weakly to the optical response, leading to an apparent two-peak structure. We show that finite phonon-phonon coupling mixes this weakly participating mode with the optically visible modes, making a third resonance clearly resolvable. This change appears in the mirror displacement spectrum, the output-field spectrum, and the output quadrature spectra, and becomes more pronounced with increasing coupling strength and drive power. Our results show that direct mechanical coupling provides a useful way to tune spectral visibility and multimode hybridization in two-mirror optomechanical cavity with intracavity parametric amplification.

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.

We present a two-channel extension of the Allen-Dynes framework that unifies phonon-mediated and spin-fluctuation-mediated pairing channels for predicting superconducting critical temperatures. Channel 1 employs the standard Allen-Dynes formula with material-specific electron-phonon coupling; Channel 2 incorporates a spin-fluctuation coupling parameter extracted from inelastic neutron scattering data. Blind predictions for 19 materials spanning conventional superconductors, MgB2, iron pnictides, iron chalcogenides, heavy fermions, cuprates, and hydrides achieve R-squared = 0.96 across five orders of magnitude in Tc (0.4-250 K) without free parameters. We further demonstrate a quantum-metric no-go result: the Peotta-Torma geometric superfluid weight, while essential for flat-band systems, cannot serve as a universal predictor of Tc because it correlates with band-structure topology rather than pairing strength. The framework identifies the spin-fluctuation channel as the dominant contributor to Tc enhancement in unconventional superconductors, providing quantitative design rules for materials with Tc above 100 K.

With the increase in the complexity of the materials used in various sophisticated electronic devices, recycling of E-waste is becoming challenging. In the present study, we have converted thermoelectric (TE) waste into functional HER electrocatalyst by considering circular-economy and low-carbon approach. The as received TE waste was processed through ball milling (TE waste-BM) and melting casting (TE waste-M) routes. Morphological and structural evaluations revealed that the formation of BiSbTe3/ZnTe heterostructure in TE-waste-M promote HE efficiency when compared to the presence of Bi2Te3/BiSbTe3 heterostructure (TE-waste-BM). TE waste-M exhibited lower overpotential (641 mV at 10 mA/sq.cm), smaller Tafel slope (233 mV/dec) and stable operation for 5.5 h with negligible current decay than that of TE waste-BM, attributed to the accelerated charge transfer, fast water dissociation steps and rapid hydrogen adsorption in TE waste-M, originated from the presence of BiSbTe3/ZnTe heterostructure, defect enriched interfaces. Density functional theory calculations supported the experimental findings, revealing that heterostructures strengthens the bonding states near the Fermi level, thereby enhancing the HER activity of BiSbTe3/ZnTe heterostructure. This work simultaneously integrates waste management with green hydrogen production by offering an economically viable, scalable and low-carbon approach for HER catalysts.

An analysis of the latest, most accurate experimental data on neutron decay indicates the need to expand the Standard Model by introducing an admixture of the right vector boson $W_R$ with a mixing angle of $ζ= -0.039\pm0.014$ with the left vector boson $W_L$ and a ratio of the squares of the masses of $W_1$ and $W_2$ equal to $δ= 0.070\pm0.010$. In this regard, the possibility of describing CP-violation effects in neutral meson oscillations within the framework of the left-right weak interaction model with parameters $δ$ and $ζ$ was investigated. It was shown that within this model, CP violation effects in the decays of $K^0$-mesons, $D^0$-mesons, $B^0$-mesons, and $B_s^0$-mesons can be successfully described. The results of calculations within the extended left-right model with parameters $δ$ and $ζ$ are confirmed by experimental results. Thus, the nature of CP violation is related to the presence of a right-handed vector boson admixture.

High-precision determinations of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements are essential probes of physics Beyond the Standard Model (BSM). Current precision tests show a deficit in the first row unitarity relation. At the current level of precision, the only relevant CKM matrix elements that contribute to this test are $|V_{ud}|$ and $|V_{us}|$. Without resorting to nuclear inputs, they can be extracted from the combination of the experimental decay width of kaon and pion leptonic decays, along with the theoretical calculation of their decay constants; combined with the decay width of semileptonic kaon decays, with the computation of the corresponding form factor at zero momentum transfer. We review current efforts by the Fermilab Lattice and MILC collaborations towards a correlated analysis of the lattice inputs needed for this test using Highly Improved Staggered Quarks (HISQ) on the $N_f=2+1+1$ MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit.

This paper presents a novel concept for electrically small antenna arrays incorporating chiral parasitic elements of opposite handedness. This configuration mitigates the detrimental effects of electromagnetic mutual coupling, which in conventional arrays causes a 180 degree phase shift between adjacent antenna currents when the element spacing is less than half a wavelength. The proposed approach is experimentally validated using a seven-element monopole ESAA with compact dimensions, specifically below half-wavelength in cross-section and one-sixth to one-fourth of a wavelength in vertical range. The antenna elements are spaced less than one-sixth wavelength apart, ensuring a highly compact footprint. Measurements show a minus 10 dB return loss, a fractional bandwidth of 5 to 15 per cent, and a realised gain of 5 to 9 dBi, along with full 360 degrees of azimuthal beam steering. The results confirm that employing oppositely handed chiral parasitic elements can significantly enhance performance in densely packed, electrically small antenna arrays.

The governance of frontier AI increasingly relies on controlling access to computational resources, yet the hardware-level mechanisms invoked by policy proposals remain largely unexamined from an engineering perspective. This paper bridges the gap between AI governance and computer engineering by proposing a taxonomy of 20 hardware-level governance mechanisms, organised by function (monitoring, verification, enforcement) and assessed for technical feasibility on a four-point scale from currently deployable to speculative. For each mechanism, we provide a technical description, a feasibility rating, and an identification of adversarial vulnerabilities. We map the taxonomy onto four governance scenarios: domestic regulation, bilateral agreements, multilateral treaty verification, and industry self-regulation. Our analysis reveals a structural mismatch: the mechanisms most needed for treaty verification, including on-chip compute metering, cryptographic proof-of-training, and hardware-embedded enforcement, are also the least mature. We assess principal threats to compute-based governance, including algorithmic efficiency gains, distributed training methods, and sovereignty concerns. We identify a temporal constraint: the window during which semiconductor manufacturing concentration makes hardware-level governance implementable is narrowing, while R&D timelines for critical mechanisms span years. We present an adversary-tiered threat analysis distinguishing commercial, non-state, and nation-state actors, arguing the appropriate security standard is tamper-evident assurance analogous to IAEA verification rather than absolute tamper-proofing. The taxonomy, feasibility classification, and mechanism-to-scenario mapping provide a technical foundation for policymakers and identify the R&D investments required before hardware-level governance can support verifiable international agreements.

The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators for nonlinear systems with control inputs. To this end, we treat the inputs as parameters throughout this paper. We then introduce the Koopman operator for a parameterized dynamical system with a globally exponentially stable equilibrium point and analyze how eigenfunctions of the operator depend on the parameter. As a main result, we obtain a global linearization, which enables one to transform the nonlinear system into a finite-dimensional linear system, and we show that it depends continuously on the parameter. Subsequently, for a control-affine system, we investigate a condition under which the transformation providing a global bilinearization does not depend on the parameter. This provides the condition under which the global bilinearization for the control-affine system is independent of the parameter.

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$. Interestingly, our methods show that all constraints on the pushforward are ``explained'' by multiplication in an algebra. Finally, we show that all possible pushforwards are realized by covers with a nontrivial proper subcover.

This paper investigates the optical and dynamical properties of a static spherically symmetric black hole in the presence of a Kalb--Ramond (KR) field coupled to perfect fluid dark matter (PFDM). We analyze the effects of the Lorentz-violating parameter $α$ and the dark matter parameter $λ$ on photon trajectories and their observational signatures in the strong-gravity regime. Furthermore, we study the quasinormal mode spectrum under scalar, electromagnetic, and gravitational perturbations, examining how the model parameters influence the characteristic oscillation frequencies and damping rates. In particular, the interplay between the effective potential structure and perturbative dynamics is clarified, and it is found that, within the validity of the eikonal approximation, the quasinormal modes of the black hole considered here exhibit good agreement with the properties of null geodesics. Our results show that the model parameters significantly affect both the optical appearance of the black hole and the dynamical features of the ringdown phase, providing potential observational constraints on Lorentz-violating effects and dark matter environments in strong-field regimes.

In the rapidly evolving landscape of software engineering, the demand for robust and secure systems has become increasingly critical. This is especially true for self-adaptive systems due to their complexity and the dynamic environments in which they operate. To address this issue, we designed and developed the SAFT-GT toolchain that tackles the multifaceted challenges associated with ensuring both safety and security. This paper provides a comprehensive description of the toolchain's architecture and functionalities, including the Attack-Fault Trees generation and model combination approaches. We emphasize the toolchain's ability to integrate seamlessly with existing systems, allowing for enhanced safety and security analyses without requiring extensive modifications and domain knowledge. Our proposed approach can address evolving security threats, including both known vulnerabilities and emerging attack vectors that could compromise the system. As a use case for the toolchain, we integrate it into the feedback loop of self-adaptive systems. Finally, to validate the practical applicability of the toolchain, we conducted an extensive user study involving domain experts, whose insights and feedback underscore the toolchain's relevance and usability in real-world scenarios. Our findings demonstrate the toolchain's effectiveness in real-world applications while highlighting areas for future improvements. The toolchain and associated resources are available in an open-source repository to promote reproducibility and encourage further research in this field.

Large language models (LLMs) are bringing richer dialogue and social behavior into games, but they also expose a control problem that existing game interfaces do not directly address: how should LLM characters participate in live multiplayer interaction while remaining executable in the shared game world, socially coherent with other active characters, and steerable by players when needed? We frame this problem as bounded autonomy, a control architecture for live multiplayer games that organizes LLM character control around three interfaces: agent-agent interaction, agent-world action execution, and player-agent steering. We instantiate bounded autonomy with probabilistic reply-chain decay, an embedding-based action grounding pipeline with fallback, and whisper, a lightweight soft-steering technique that lets players influence a character's next move without fully overriding autonomy. We deploy this architecture in a live multiplayer social game and study its behavior through analyses of interaction stability, grounding quality, whisper intervention success, and formative interviews. Our results show how bounded autonomy makes LLM character interaction workable in practice, frames controllability as a distinct runtime control problem for LLM characters in live multiplayer games, and provides a concrete exemplar for future games built around this interaction paradigm.

In this paper, a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided downlink non-orthogonal multiple access (NOMA) Terahertz (THz) wireless system is proposed for indoor and outdoor transmissions. We consider a near-field communication scenario where an access-point (AP) is deployed near a STAR-RIS panel. For links from the STAR-RIS to users, $α-μ$ distribution is adopted for the indoor small-scale fading channels, whereas the outdoor channels are based on Gaussian mixture or mixture of gamma, which follows the recent practical measurement reports. To facilitate performance analysis, we derive exact expressions of a probability density function (PDF) and a cumulative distribution function (CDF) of a weighted sum of $α-μ$ variates. Approximate PDF and CDF expressions of a weighted sum of Gaussian mixture variates are derived as well. Based on these results, closed-form expressions of the outage probability and the ergodic capacity, together with their asymptotic formulas at high signal-to-noise ratio (SNR), are obtained. Moreover, we analyze the capacity of the THz system at the low SNR regime. Impacts of hardware impairments and STAR-RIS protocols (i.e., energy splitting and mode-switching) on the system performance are evaluated. All developed analytical results are validated and demonstrated via numerical simulations.

The widespread adoption of generative artificial intelligence (GenAI) tools in higher education has fundamentally altered the conditions under which academic work is produced, challenging long-standing assumptions about authorship, responsibility, and learning. While much of the existing literature has focused on technical, ethical, or pedagogical implications of GenAI, comparatively little attention has been paid to the legal and normative aspects of authorship in AI-aided academic work. In this work, we examine how the use of GenAI intersects with the concept of authorship as understood within European regulatory and institutional frameworks. Drawing primarily on European copyright law, notably the requirement of human intellectual creation, the paper argues that authorship functions as a qualitative threshold rather than a binary attribute. Authorship may remain attributable to the student where GenAI operates as cognitive support under human intellectual control. By contrast, attribution becomes legally and normatively disputable once AI output displaces creative autonomy. The analysis places this doctrinal framework alongside broader regulatory principles arising from the AI Act, data protection law, and emerging suprainstitutional governance practices in higher education. We propose a qualitative threshold framework designed to assist in authorship-sensitive assessment of GenAI-aided academic work. This framework provides criteria for distinguishing legitimate AI-assisted academic production from practices that undermine authorship, responsibility, and academic integrity.

Theories of the measured homodyne current generated by a stochastic Schrödinger equation (SSE) can be tested in a simulation of the Einstein-Podolsky-Rosen (EPR) correlations for a two-mode squeezed state. We carry out such a simulation, and determine the correct stochastic term for the measured current in the broad-band limit. Stratonovich rather than Ito stochastic noise agrees with experiment. We show that this is relevant to measurement noise and errors in quantum technologies. By analyzing the SSE trajectories as measurement settings are changed, we propose a modern version of Schrodinger's gedanken experiment, where one measures position and momenta simultaneously, ``one by direct, the other by indirect measurement''.

We show that the gauge-invariant ideal parametrisation results of the author and Kakariadis are in agreement with those of Bilich in the case of a proper product system over $\mathbb{Z}_+^d$. This is accomplished in two ways: first via the use of Nica-covariant representations and Gauge-Invariant Uniqueness Theorems (the indirect route), and second via the definitions of the parametrising objects alone (the direct route). We then apply our findings to simplify the main parametrisation result of the author and Kakariadis in the proper case, thereby fully describing the gauge-invariant ideal structure of each equivariant quotient of the Toeplitz-Nica-Pimsner algebra. We close by providing applications in the contexts of C*-dynamical systems and row-finite higher-rank graphs.

Private information retrieval (PIR) allows private database queries but is hindered by intense server-side computation and memory traffic. Modern lattice-based PIR protocols typically involve three phases: ExpandQuery (expanding a query into encrypted indices), RowSel (encrypted row selection), and ColTor (recursive "column tournament" for final selection). ExpandQuery and ColTor primarily perform number-theoretic transforms (NTTs), whereas RowSel reduces to large-scale independent matrix-matrix multiplications (GEMMs). GPUs are theoretically ideal for these tasks, provided multi-client batching is used to achieve high throughput. However, batching fundamentally reshapes performance bottlenecks; while it amortizes database access costs, it expands working sets beyond the L2 cache capacity, causing divergent memory behaviors and excessive DRAM traffic. We present GPIR, a GPU-accelerated PIR system that rethinks kernel design, data layout, and execution scheduling. We introduce a stage-aware hybrid execution model that dynamically switches between operation-level kernels, which execute each primitive operation separately, and stage-level kernels, which fuse all operations within a protocol stage into a single kernel to maximize on-chip data reuse. For RowSel, we identify a performance gap caused by a structural mismatch between NTT-driven data layouts and tiled GEMM access patterns, which is exacerbated by multi-client batching. We resolve this through a transposed-layout GEMM design and fine-grained pipelining. Finally, we extend GPIR to multi-GPU systems, scaling both query throughput and database capacity with negligible communication overhead. GPIR achieves up to 305.7x higher throughput than PIRonGPU, the state-of-the-art GPU implementation.

As modern Coarse Grain Reconfigurable Arrays (CGRAs) grow in size, efficient utilization of the available fabric by a single application becomes increasingly difficult. Existing CGRA mappers either fail to utilize the available fabric or rely on rigid static code transformations with limited adaptability. Multi-tenant CGRAs have emerged as a promising solution to increase hardware utilization, but current attempts fail to address key challenges such as fabric fragmentation and live migration. To address this gap, we present Mestra, an end-to-end system for CGRA multi-tenancy that supports dynamic scheduling and resource allocation in a shared environment. Mestra addresses fabric fragmentation caused by kernels completing out of order by supporting both stateless and stateful live kernel migration as a de-fragmentation mechanism. We assess our solution on an Alveo-U280 data-center-grade FPGA card, reporting area, frequency, and power. Performance is evaluated using routines from the PolyBench benchmark suite and kernels derived from common machine learning operators. Results show that spatial sharing of the available fabric across multiple users improves workload makespan by up to 70.48%, while live kernel migration reduces tail latency on fragmented layouts by up to 29.60%. The custom tightly coupled controller and read-back paths required for virtualization and stateful migration introduce a LUT cost of 0.13% per region. Our evaluation reveals that multi-tenancy is important for efficient CGRA utilization, and live kernel migration can further improve performance by recovering fragmented space with minimal hardware cost.

The phenomenon of interaction-free measurement (IFM) enables the probabilistic detection of an absorbing object with reduced photon absorption. We report the experimental implementation of a simultaneous IFM of multiple objects using a single quantum probe on the cloud-based Ascella photonic processor of company Quandela. We demonstrate sequential IFM of up to 5 objects using a single photon, significantly extending the original IFM scheme for a single object. The experimental error-mitigated results confirm the theoretical predictions for this sequential IFM setup, and demonstrate a practical approach to scaling IFM to more complex quantum interrogation tasks.

Empathy has been discussed as a relevant human capability in software engineering, particularly in activities that require understanding users, stakeholders, and the societal implications of technological systems. This relevance becomes more pronounced in the context of artificial intelligence, where software increasingly participates in decisions that affect diverse individuals and communities. However, limited guidance exists on how empathy can be integrated into technical software engineering education in ways that connect with the development of AI-enabled systems. This study investigates teaching practices that educators use to incorporate empathy into software engineering courses. Using qualitative analysis of educator-reported practices, we identified five categories through which empathy is operationalized within technical coursework: societal framing of AI systems, fairness and accessibility considerations in design and evaluation, representation of diverse users, stakeholder role awareness and responsibility, and structured reflection and feedback during development processes. The findings indicate that empathy can be embedded within core development activities rather than taught as a separate topic, enabling students to reason about bias, accessibility, accountability, and the societal consequences of AI technologies. These results contribute a structured view of how empathy-oriented practices can be incorporated into software engineering education to support the preparation of students who will develop AI-enabled systems.

We give a direct proof that the proalgebraic graded Grothendieck-Teichmüller group $\mathsf{GRT}_{\mathbb{K}}$ is isomorphic to the group of automorphisms of the prounipotent cyclic operad of parenthesized ribbon chord diagrams based on Furusho's $5$-cycle reformulation of the pentagon equation. As an application, we describe a $\mathsf{GRT}_{\mathbb{K}}$-action on the category of framed chord diagrams with self-dual objects, which is closely related to the target category of the Kontsevich integral for framed tangles.

While supersymmetric models provide a solution to the big hierarchy problem, natural SUSY is also allowed by the little hierarchy problem. In supersymmetric models which include the Peccei-Quinn (PQ) solution to the strong CP problem, one expects the presence of an axion-axino-saxion supermultiplet with a micro-eV-scale axion and a saxion with mass of order the soft breaking scale. The axino mass is much more model-dependent, and may occur in the range of keV-TeV: over 9 orders of magnitude. This leads to the possibility of the axino as lightest SUSY particle (LSP) and the presence of mixed axion plus axino dark matter. The case of natural SUSY with higgsino-like WIMPs as LSP seems (nearly) excluded by multi-ton noble liquid WIMP detector limits, even in the case where the LSP has a depleted abundance compared to axions. We examine the case where the axino is LSP leading to mixed axion-axino dark matter in a natural SUSY context. We map out regions of PQ scale f_a vs. axino mass m_{\ta} parameter space where such a scenario remains viable in both the SUSY DFSZ and KSVZ axion models. For axino mass ~100 keV, we find solutions in accord with the measured dark matter abundance with mainly warm axino dark matter for f_a~ 10^{11} GeV and also solutions with mainly axion cold DM and a tiny axino contribution for higher f_a~ 3\times 10^{12} GeV.

In this paper, we investigate high-altitude platform station (HAPS) wireless networks for simultaneous non-orthogonal unicast and multicast transmissions. Specifically, stacked intelligent metasurface (SIM)-based wave-domain beamforming is proposed to enable efficient HAPS-to-ground communications. Also, the system performance is investigated from an energy-efficiency (EE) perspective, which is a crucial for HAPS operations. For performance analysis, we derive approximate closed-form expressions for the outage probability over Rician fading channels. For EE optimization, we jointly optimize the transmit power and the SIM phase-shifts for the maximal EE. Two methods are proposed to solve this non-convex optimization problem. The first method develops an efficient alternating optimization (AO) framework based on golden-section search and projected gradient ascent (PGA) for transmit power and phase-shift optimization, respectively. The second method uses unsupervised deep neural network (DNN) that does not require labeling. Performance comparison between the two methods, as well as with other benchmarks schemes are examined. Additionally, the impacts of the number of SIM elements per layers, the number of SIM layers, the maximum transmit power on the EE performance are evaluated. Simulation results are provided to demonstrate the performance of the proposed systems.

Homomorphic encryption (HE) enables computation over encrypted data but incurs a substantial overhead. For sparse-matrix vector multiplication, the widely used Halevi and Shoup (2014) scheme has a cost linear in the number of occupied cyclic diagonals, which may be many due to the irregular nonzero pattern of the matrix. In this work, we study how to permute the rows and columns of a sparse matrix so that its nonzeros are packed into as few cyclic diagonals as possible. We formalise this as the two-dimensional diagonal packing problem (2DPP), introduce the two-dimensional circular bandsize metric, and give an integer programming formulation that yields optimal solutions for small instances. For large matrices, we propose practical ordering heuristics that combine graph-based initial orderings - based on bandwidth reduction, anti-bandwidth maximisation, and spectral analysis - and an iterative-improvement-based optimization phase employing 2OPT and 3OPT swaps. We also introduce a dense row/column elimination strategy and an HE-aware cost model that quantifies the benefits of isolating dense structures. Experiments on 175 sparse matrices from the SuiteSparse collection show that our ordering-optimisation variants can reduce the diagonal count by $5.5\times$ on average ($45.6\times$ for one instance). In addition, the dense row/column elimination approach can be useful for cases where the proposed permutation techniques are not sufficient; for instance, in one case, the additional elimination helped to reduce the encrypted multiplication cost by $23.7\times$ whereas without elimination, the improvement was only $1.9\times$.

It is shown that a duplication of the hypercharge, which is identical for the normal sector but different for the dark sector, may manifestly address neutrino mass and dark matter.

Twin boundaries play a central role in the functional behavior of martensitic materials, yet the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Further, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis, and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries.

In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and distance of order $q^4$, and locality $r =q-1$. In addition, the cases $q = 4$ and $q=8$ are studied.

We establish a Trudinger-Moser type inequality with a Tintarev-type constraint in fractional-dimensional spaces and prove the existence of maximizers in the critical regime. Our results provide a refinement of those in (Calc. Var. 52 (2015), 125-163) in the setting of fractional-dimensional spaces, as well as of those in (Ann. Global Anal. Geom. 54 (2018), 237-256) for classical Sobolev spaces.

In this paper, we study the Koshliakov zeta function $η_p(s)$, whose theory appears to be more involved than that of its counterpart $ζ_p(s)$, owing to the fact that its defining series is not of Dirichlet type. We derive formulas for $η_p(s)$ at both even and odd values of $s$. In the limiting case $p\to\infty$, our results yield the celebrated formulas of Euler and Ramanujan for the Riemann zeta function. Moreover, our results lead to several consequences concerning closed-form expressions for Lambert series and their arithmetic properties, recovering results due to Berndt, Cauchy, Ramanujan, and others. We also propose $p$-analogues of the transformation formula for the classical Eisenstein series. Moreover, we introduce two families of $p$-analogues of Ramanujan polynomials and establish functional equations satisfied by them.