Multi-winner approval voting selects a size-$k$ committee that aggregates voters' approval preferences over a set of alternatives. A central question is coalitional stability: No coalition should be able to pick a committee -- of size at most its proportional share -- under which every coalition member has strictly more approved alternatives. This notion, introduced by Aziz et al. (2017) as core-stable committees, is naturally interpreted as a core notion with non-transferable utility. We introduce multi-winner voting games, a cooperative-game framework that unifies prior work and supports a systematic study of two utility-transfer models across different voting rules. Players are voters. Each coalition has a proportional seat cap and may only propose admissible committees up to that size. Fixing a multi-winner rule, each admissible committee induces a utility vector for the members of the coalition. In the transferable utility (TU) model, a coalition may redistribute the total utility of an admissible committee among its members. In the non-transferable utility (NTU) model, a coalition may only use utility vectors that are realized directly by some admissible committee. The core consists of utility vectors feasible for the grand coalition that are not blocked by any coalition. A coalition is blocking if it can propose an admissible committee that makes all its members strictly better off, directly in NTU and after redistribution in TU. When instantiated with the standard PAV/approval utility, the NTU-core is equivalent to the core-stable committee concept studied in prior work. To our knowledge, the TU-core for multi-winner voting has not been previously studied. We analyze core existence and computation for four prominent rules: Approval Voting (AV), Satisfaction Approval Voting (SAV), Chamberlin--Courant (CC), Proportional Approval Voting (PAV).

Negative Selection Algorithms (NSAs), inspired by the self/non-self discrimination mechanism of the human immune system, have been widely employed in anomaly detection. However, their effectiveness is often constrained by the efficiency of detector generation. This paper presents the Quantum Genetic Negative Selection Algorithm (QGNSA), a novel approach that integrates a Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA algorithm, replacing its classical evolutionary optimization process. The proposed method exploits quantum superposition and probabilistic amplitude adjustment to enhance search space exploration and convergence efficiency in the detector generation process. Empirical evaluations using the Metaverse Financial Transactions Dataset demonstrate that QGNSA achieves superior anomaly detection accuracy compared to its classical counterpart while maintaining robustness under varying hyperparameter configurations. The experimental results highlight the potential advantages of quantum computing in artificial immune systems, particularly in high-dimensional anomaly detection tasks. Future research will focus on further optimizing quantum circuit design, deploying the algorithm on real quantum hardware, and exploring hybrid quantum-classical approaches for improved computational efficiency.

Recent advances in coding agents have shown remarkable progress in software issue resolution. In practice, real-world issues are typically bug fixes or feature requests in which human developers naturally incorporate refactoring as part of the resolution process, resulting in tangled refactoring. Since LLMs are trained on large-scale open-source repositories, coding agents may inherit such behaviors. In this paper, we conduct an empirical study on Multi-SWE-bench, analyzing 3,691 valid patches generated by three agent frameworks with 12 LLMs. We find that coding agents introduce tangled refactorings less frequently (21.43% vs. 36.72%) and with lower intensity (0.66 vs. 1.75) than human developers, although they exhibit a broader diversity of refactoring types. Logistic regression analysis further shows that tangled refactorings are strongly associated with reduced compilability, while exhibiting no significant association with functional correctness. Based on these findings, we propose a refactoring-aware refinement approach that assesses the necessity and safety of tangled refactorings and selectively removes or repairs problematic operations. Our approach improves compilability from 19.34% to 38.33%, and additionally resolves 2.79% previously unresolved issues. Overall, this work presents the first step towards understanding tangled refactoring practices in agentic issue resolution and opens up avenues for future work.

Processing sequential inputs is a fundamental brain function, underlying tasks such as sensory perception, language, and motor control. A challenge in sequence processing is to represent not only the order of events, but also their precise timing. While existing computational models can learn sequential structure, many lack biologically plausible mechanisms to encode element-specific timing and to flexibly control the speed of sequence replay. The spiking Temporal Memory (sTM) model, a biologically inspired network model, provides a framework for key aspects of sequence processing. In the sTM model, each sequence element is represented by a small set of neurons firing synchronously, where the set of active neurons encodes the element's identity in its sequential context. In its original version, however, the sTM model learns the order but not the timing of sequence elements. Further, it remains an open question in neuroscience how the speed of sequence replay can be flexibly modulated. We propose a mechanism where the duration of sequence elements is represented by a sequential activation of element specific neuronal populations, enabling the model to encode sequences across a wide range of timescales. This provides a biologically plausible basis for learning and replaying complex temporal patterns. Additionally, we show that oscillatory background inputs can serve as a clock signal and provide a robust and flexible mechanism for controlling the speed of sequence replay. Our findings suggest that elapsed time is encoded by unique and sparse spatiotemporal patterns of neural activity, and that the speed of sequence replay during wakefulness and sleep is correlated to the characteristics of global oscillatory activity observed in EEG or LFP recordings.

The engineering of superlattices in two-dimensional van der Waals materials has enabled the realization of rich phase diagrams hosting topological and strongly correlated phases. While incommensurability is widespread in three-dimensional systems, the role of moiré potentials in bulk materials remains largely unexplored. Here, using scanning tunneling microscopy, we demonstrate that a bulk transition-metal dichalcogenide polytype, 4Hb-TaS$_2$, hosts an emergent incommensurate potential between its alternating 1T and 1H layers. Interplay with a concomitant incommensurate charge-density wave suppresses the long-range order of this potential, leading to intricate coupling with electronic correlations in the doped 1T surface layer. Combining density functional theory with dynamical mean-field theory, we show that the lattice mismatch locally modulates the interlayer distance, thereby tuning both hybridization and charge transfer between the correlated 1T and metallic 1H layers. This redistribution of charge drives the system towards a doped Mott regime, in which the remaining local moments become self-screened, giving rise to a zero-bias resonance. We further find that bulk superconductivity competes with both the underlying landscape and the associated charge transfer. Our results establish incommensurate potentials as a previously overlooked ingredient in hybrid transition-metal dichalcogenides, highlighting their central role in the interplay between electronic correlations, charge-density-wave order, and unconventional superconductivity.

Inspired by previous extensive numerical studies of a cell fluid model with Curie-Weiss interactions, we concentrate on some analytically tractable special cases in its description. The key ingredient of the model is a competition between global attraction and local repulsion interactions between particles with coupling constants $J_1$ and $J_2$, respectively. We provide analytical results in several limiting cases, including the ideal-gas limit $J_1=J_2=0$ and the strong-repulsion limit $J_2\gg J_1$. For $J_2\gg J_1$, a detailed analytical study is presented. We derive explicit expressions for the critical point parameters, the equation of state, and the binodal and spinodal curves in closed form. The equation of state is found to be in full agreement with that of the van der Waals lattice gas, and the order parameter satisfies the standard Curie-Weiss equation. In a neighborhood of the critical point, a Landau expansion is shown to have the same form and symmetry as that of the classical lattice gas within the mean-field approximation. Moreover, based on the explicit knowledge of a few leading terms in the asymptotic expansion of the deformed exponential function governing the physics of the cell model, we extend its validity range to include the marginal case of thermodynamic stability, $J_1=J_2$. In particular, this extension makes a consideration of the ideal-gas limit $J_1=J_2=0$ formally legitimate. For the generic marginal case $J_1=J_2\ne0$ systematically avoided in previous works, we present numerical data and phase diagrams that augment their findings for $J_2>J_1$.

We introduce algebroid desingularizable Poisson manifolds, a class of Poisson manifolds induced by symplectic Lie algebroids with almost-injective anchors, generalizing structures including log-symplectic, $b^m$-symplectic, $E$-symplectic manifolds, and hypersurface algebroids. We show that the dual of real, finite-dimensional, non-abelian, reductive Lie algebras never admit such algebroids. We finish by giving two infinite families of $2$-step nilpotent Lie algebras, one of which is desingularizable, and one of which is not.

In non-centrosymmetric materials, light can be rectified into two types of DC photocurrents, known as injection and shift currents, through the bulk photovoltaic effect. Recent theory has uncovered their deep relation with the two-state quantum geometry of resonant transitions: In non-magnetic crystals, where these currents have been routinely observed, the injection current responds to circular light and probes the Berry curvature, while the shift current responds to linear light and probes the geometric connection. Magnetic crystals have been predicted to show a new set of hitherto unobserved magnetically switchable photocurrents, with the roles of linear and circular light interchanged: A linear injection current, which probes the quantum metric, and a circular shift current, which probes the geometric torsion. In this work, we demonstrate the existence of such currents for the first time, demonstrating the switching of the current by flipping the Néel vector in a van der Waals antiferromagnet. Furthermore, their specific frequency and temperature dependence confirm the assignment of circular shift and linear injection currents. Our work demonstrates a new way to control photocurrents in magnets that are directly tied to geometry and have promising applications in antiferromagnetic spintronics and light harvesting.

Using Jacobian Elliptic functions, we introduce a novel parametrization of a hyperbolic pencil of coaxal circles which reveals a remarkable group structure on the pencil. The geometric properties of the group elements lead to a new proof of of the general Poncelet theorems, which in turn leads to a proof of the so called closure theorem. In particular we prove: if $T$ and $% D $ are members of the pencil, then an interscribed $n$-gon to $T$ and $D$ exists, if and only if $D$, the inside circle, is an element of order $n$ in the group.

We study the problem of computing the isolated regular solutions of a system \((f_1,\ldots,f_n)\) of \(n\) polynomial equations in \(n\) variables \((X_1, \dots, X_n)\) over a field of characteristic zero \(k\). We focus on systems with a \emph{composable structure}, where each polynomial \(f_i\) can be expressed as a composition \( f_i = h_i(g_1,\dots,g_n)\). Exploiting this structure allows us to reduce the original system to one in the \(g_j\) variables, thereby significantly improving the efficiency of symbolic solution algorithms. We present a probabilistic algorithm that computes all isolated regular solutions, with arithmetic complexity being polynomial in the input size and in the number of solutions. A first important application is when \(f_1, \dots, f_n\) belong to the subring \(k[g_1, \dots, g_n]\), where \(g_1, \dots, g_n\) are algebraically independent polynomials in \(k[X_1, \dots, X_n]\). Another important application is to systems of invariant polynomials under finite reflection groups, since by the Chevalley-Shephard-Todd theorem their invariant rings are polynomial algebras. Typical examples include the symmetric groups \(S_n\), the hyperoctahedral groups \(B_n\), the dihedral groups \(I_2(m)\), and the exceptional finite reflection groups \(E_6, E_7, E_8, F_4, H_3, H_4\).

In this paper, we consider the restricted $p$-Schatten class Grassmannian $\mathrm {Gr}_{{\rm res}, p}(\mathcal{H})$ consisting of infinite-dimensional and infinite codimensional subspaces $W$ of a polarized complex separable Hilbert space $\mathcal{H} = \mathcal{H}_+\oplus \mathcal{H}_-$ such that the orthogonal projection from $W$ onto $\mathcal{H}_+$ is Fredholm and the orthogonal projection from $W$ onto $\mathcal{H}_-$ is in the Schatten ideal $L_p$, $p\geq 1$. The aim of this paper is to show that, for $1\leq p\leq 2$, the restricted $p$-Schatten class Grassmannian $\mathrm {Gr}_{{\rm res}, p}(\mathcal{H})$ is an affine (co-)adjoint orbit of an infinite-dimensional restricted unitary group $\operatorname{U}_{{\rm res}, p}(\mathcal{H})$, and that it admits natural weak symplectic structures. These results follow from the fact that the Lie algebra of the restricted $p$-Schatten class unitary group $\operatorname{U}_{{\rm res}, p}(\mathcal{H})$ admits a non-trivial $2$-cocycle.

Massive galaxies experience complex evolutionary processes, including mergers and gas accretion, which can disrupt the chemical equilibrium between their stellar and gaseous components. Using the IllustrisTNG (TNG100) simulation at $z=0$, we investigated the prevalence and physical properties of such chemically decoupled systems within the massive star-forming galaxy population. We identify a substantial subpopulation ($\sim 31.5\%$ of the sample) that exhibits systematic stellar-gas decoupling, characterised by a metal-rich stellar component coexisting with a diluted gas reservoir. These non-equilibrium galaxies are closely linked to recent merger activity and partial quenching, and display systematically suppressed star-formation rates and reduced gas fractions, consistent with a transitional evolutionary phase. We then examined the implications of this phase for galaxy-scale habitability prescriptions by applying a terrestrial planet abundance proxy that combines stellar mass, gas-phase metallicity, and the rate of sterilising events. Despite their diluted gas reservoirs, non-equilibrium galaxies dominate the high end of the inferred present-day habitability proxy distribution, exceeding equilibrium systems by more than an order of magnitude. We interpret this as a habitability trade-off: the same gas dilution and quenching processes that reduce the efficiency of future terrestrial planet formation simultaneously create a transient phase of suppressed radiation hazards for existing planets. The Andromeda galaxy (M31) shows qualitative similarities to this chemically decoupled population, suggesting that galaxies exiting their peak star-forming phase represent a distinct and highly relevant demographic for galaxy-scale habitability. Galactic habitability is therefore intrinsically time-dependent.

Fluid reconfigurable intelligent surfaces (FRIS) extend conventional reconfigurable intelligent surfaces (RIS) by adding spatial reconfigurability through switchable apertures, pattern-reconfigurable units, fluidic conductive materials, or movable surface elements. This article studies how FRIS can support index modulation (IM), where information bits select a surface configuration and the receiver detects the index from the induced receiver-side response. A key challenge is that many feasible FRIS layouts do not necessarily lead to many reliable spatial indices. After propagation, mutual coupling, hardware distortion, and receiver observation, different layouts may produce similar receiver-side responses and cause index-detection errors. To address this issue, we present a response-aware design view, in which FRIS spatial codebooks are selected according to response-domain separability rather than layout diversity alone. We also discuss actuation granularity as a practical design knob that balances spatial diversity, pilot overhead, coupling robustness, and hardware feasibility. The resulting workflow helps select compact, trainable, and controllable spatial-index codebooks from dense FRIS layouts, providing design guidance for future programmable wireless environments.

IR microspectroscopy of single biological cells is challenged by strong light scattering, which produces baseline effects and peak distortions in the IR spectra and hinders the direct extraction of chemical information. Current methods for scattering correction typically rely on Mie theory and are accurate only under the assumption that the cell can be approximated by a sphere. Here, we present a framework for the scattering correction of IR absorbance spectra that is based on 3D ellipsoid models and provides efficient scattering correction for both suspended (spherical) and adhered (flattened) cells. Our approach combines deep learning approaches with computational IR microspectroscopy based on the finite-difference time-domain (FDTD) method. The FDTD method generates a synthetic library of realistic training spectra, while the deep learning model enables fast spectral inversion. We demonstrate scattering correction in silico using numerical cell phantoms of cervical cancer cells (HeLa) and show that the true absorption spectra can be inferred from IR absorbance spectra. We further show that the 3D cell dimensions can be recovered from the IR absorbance spectra, highlighting that the inherent light scattering could be exploited to realize the full analytical potential of IR spectroscopy. We anticipate that deep learning-based scattering corrections can be readily extended to increasingly complex sample geometries owing to the flexibility of the FDTD method to model arbitrary geometries.

Supermassive black holes power Active Galactic Nuclei (AGN), injecting energy that regulates accretion and shapes host galaxies. We investigate the morphology, excitation, and kinematics of molecular hydrogen (H2) in the inner circumnuclear disk of Centaurus A, the nearest radio galaxy. We present JWST/MIRI MRS integral-field spectroscopy of the central 170x100 pc2 at 0.3"-0.7" (5-12 pc) resolution, focusing on pure rotational H2 lines. The spectra show strong nuclear continuum and bright H2 emission from S(1) to S(8), including the first S(8) detection in Centaurus A. Optically thin nuclear lines enable maps of temperature, column density, and ortho-to-para ratio from spaxel-level excitation-diagram fitting. Warm H2 shows a complex morphology, dominating the central region where CO emission is weak or undetected. Low-excitation H2 lines trace an inhomogeneous ring with a 20-pc-radius cavity aligned with the jet's near side, suggesting that the jet affects the morphology of the molecular disk. Higher-excitation lines form filamentary structures around the AGN. Kinematics are rotational with an S-shaped distortion, indicating non-circular motions or a warped disk. A coherent, low-dispersion (70 km/s) streamer spirals inward. A power-law temperature distribution yields a warm (100-2000 K) H2 mass of (5.6+/-1.4)e5 Msun and a dynamical mass of 5e8 Msun within 100 pc. Shock excitation is supported by enhanced H2/continuum and H2/PAH ratios, elevated [Ne III]/[Ne II], and sub-equilibrium ortho-to-para ratios (1.6-2.4). Turbulent dissipation can balance H2 cooling and likely dominates heating beyond 30 pc. In the inner 100 pc of Centaurus A, AGN feeding and feedback are linked: shocks excite H2, regulate the gas temperature, and prevent cooling below 100 K, explaining the weak CO emission and lack of a massive outflow. These shocks may drive angular momentum loss and help fuel the nucleus.

Let X be a smooth projective variety over a field k. For k separably closed, we prove that the subgroup of unramified classes in the Milnor K-group $K^M_i(k(X))$ of the function field of X is contained in the subgroup of n-divisible elements of $K^M_i(k(X))$ for any integer n invertible in k. This generalizes to a statement for unramified motivic cohomology of arbitrary bidegree. We further show that whenever k is finite or separably closed and l is a prime invertible in k, then all but the last step in the Bloch--Ogus filtration of the motivic cohomology of X are l-divisible up to torsion. Generalizations of this last result to arbitrary quasi-projective k-schemes are also proven.

In Opportunistic Networks (OppNets), the dissemination of information can only rely on transient pairwise radio contacts between mobile devices (peers). Designing distributed applications that can run in such conditions is a challenge, but replicated data types, and in particular Conflict-free Replicated Data Types (CRDTs), can help meet this challenge. A CRDT is inherently replicated data type whose replicas can be updated locally, yet eventually converge thanks to an anti-entropy algorithm that allows all replicas to synchronize in the background. Whether the replicas of a CRDT can actually converge in an OppNet, and how fast they can converge, depend on the occurrence of radio contacts between mobile devices. In this paper we investigate the idea of using mobile relays as a means to boost the convergence of stated-based CRDT replicas in an OppNet. New protocols are presented that allow the synchronization of replicas and relays, and new metrics are defined to observe and characterize the convergence of replicas. Simulation results show that using relays can significantly improve this convergence, and even make it possible in scenarios where the replicas alone would be unable to converge.

Dynamic line rating (DLR) is a methodology that requires timely monitoring data to determine the real-time ampacity of power lines. However, DLR monitoring devices (MD) are vulnerable to connectivity disruptions, leading to missing or delayed data. Although unmanned aerial vehicles (UAV) can enable resilient data collection from MD, their limited onboard energy challenges timely monitoring over extended transmission corridors with flight hazards. This paper proposes a cooperative UAV-based data collection framework with integrated sensing and communication (ISAC) to support timely DLR updates. In this framework, ISAC is employed to maintain the sensing and communication quality required for safe and cooperative UAV data collection. Accordingly, a joint energy minimization problem is formulated over UAV trajectories and collection scheduling under ISAC constraints. To solve it, a hybrid algorithm combining deep reinforcement learning (DRL) and semidefinite relaxation (SDR) is proposed, where DRL optimizes the trajectory and collection scheduling, while SDR is used to handle the non-convex ISAC constraints. Simulation results show that the proposed scheme reduces energy consumption by up to 34.6% compared with offline benchmarks and by about 2.2% compared with the separated sensing-and-communication baseline, while satisfying the minute-level timescale requirement of DLR.

The Lyman-$α$ forest refers to the series of absorption features observed in the spectra of distant quasars that are produced by neutral hydrogen in the intergalactic medium. Observed over a wide range of redshifts with both ground- and space-based facilities, the Lyman-$α$ forest provides a powerful probe of numerous physical processes, including the thermal state of intergalactic gas, the timing and topology of cosmic reionization, the expansion history of the Universe, the growth of cosmic structure, massive neutrinos, and the nature of dark matter. This chapter reviews the transformative impact of machine-learning techniques on Lyman-$α$ forest analyses, particularly in overcoming the computational and methodological limitations of traditional approaches. We discuss a broad range of machine-learning applications, including the automated characterization of individual absorption systems, improved reconstruction of the intrinsic quasar continuum, accelerated emulation of hydrodynamical simulations, and the development of simulation-based analyses, field-level inference methods, and three-dimensional reconstruction techniques for the underlying matter density field. As current and upcoming surveys continue to increase both the volume and precision of Lyman-$α$ forest observations, ML-driven pipelines are becoming an essential component of next-generation astrophysical and cosmological analyses.

We study the construction and convergence of semi-explicit and iterative decoupling schemes for an elliptic-parabolic problem using higher-order Runge-Kutta methods. For the semi-explicit schemes, which are constructed using a nearby delay system with $k$ time delays, we establish the convergence of $k$th-order Runge-Kutta methods under a weak coupling condition. We develop the convergence analysis by adapting the Fourier stability and perturbation techniques of [Lubich, Ostermann, Math. Comp., 64(210):601--627, 1995]. The key tool is the generating function framework, in which the Runge-Kutta discretization is encoded through an operator-valued function. Stability estimates are then obtained via Parseval's identity on the unit circle. We further present convergence results for iterative (fixed-stress and undrained-split) higher-order Runge-Kutta schemes. Here, a spectral decomposition of the Schur complement operator is central. Finally, we provide numerical examples to verify the proven convergence results.

With the rise of AI-assisted materials screening, extraordinary properties are now frequently predicted in experimentally uncharted material systems, highlighting the need to develop new synthesis methods for unconventional materials beyond the classic bulk powder form. Here, we establish the first thin-film growth route for any metal sulfonitride compound by realizing Zr2SN2 films with a rare and compelling combination of optical and electrical properties. Zr2SN2 is transparent across most of the visible range while exhibiting a very high average refractive index of 2.95 in the visible, exceeding expectations based on conventional refractive index-bandgap scaling. Importantly, the same Zr2SN2 film shows degenerate n-type conductivity with carrier density above 10^20 cm-3 and intragrain mobility above 8 cm2V-1s-1, approaching those of established transparent conductive oxides. Zr2SN2 thus demonstrates that strong light-matter interaction, optical transparency and electrical conductivity can be reconciled within a single material platform, revealing a new class of high-refractive-index transparent conductors.

We prove density results for neural-network classes on compact sets \(K\subset X\), where \(X\) is a topological vector space whose continuous dual \(X^*\) separates points. Let \(Ψ:\mathbb R\to\mathbb R\) be a continuous squashing function. We show that the class \[ Σ_X(Ψ) = \left\{ \sum_{j=1}^{N}ω_jΨ(f_j(x)+b_j): N\in\mathbb N,\ ω_j,b_j\in\mathbb R,\ f_j\in X^* \right\} \] is dense in \(C(K)\) with respect to the uniform norm. As a consequence, if \(μ\) is a Radon probability measure supported on \(K\), then \(Σ_X(Ψ)\) is dense in \(L^p(K,μ)\) for every \(1\le p<\infty\).

We introduce a mathematical and cryptographic framework for exact recovery of noisy hidden paths in high dimensional discrete path spaces. The work is inspired by the path integral viewpoint, where global quantities arise from contributions over many possible trajectories. Instead of approximating a global path sum, we study the inverse problem of recovering one exact hidden trajectory from incomplete, noisy, projected, and aggregated observables. The hidden object is a planted discrete path whose transitions may include macro steps, microscopic perturbations, and discrete noise. Public information is represented by large observable vectors rather than short hash digests, since excessive compression would bound the effective recovery problem by the digest size. We formalize several recovery notions, including planted exact recovery, arbitrary witness recovery, canonical recovery, quotient recovery, and recovery of derived encodings. The main distinction is that approximate reconstruction and exact recovery are fundamentally different tasks. A method may reveal coarse geometry or dominant regions without recovering the precise microscopic sequence defining the hidden path. We also discuss attack surfaces relevant to future cryptographic use, including linearization, lattice style recovery, dynamic programming, meet in the middle attacks, SAT and SMT formulations, approximation followed by rounding, witness collisions, and generic quantum search. This work does not claim a complete post quantum cryptosystem. It provides a formal framework for studying exact hidden path recovery as a possible foundation for future cryptographic constructions

Chapter $7$ of Langlands' monograph "On the functional equations satisfied by Eisenstein series" employs a sophisticated residue scheme to construct a portion of the discrete automorphic spectrum. We show, by examples, applications, and heuristics, that this construction is a straightforward regularization of cuspidal Eisenstein series at distinguished points, and that the regularization must track BOTH the zeros and the poles of these Eisenstein series. Unlike the one-variable case, the zero set and pole set of a several-complex-variable meromorphic function can intersect at a point. The distinguished points supporting the discrete spectrum are typically of this kind. The zeros of cuspidal Eisenstein series - largely invisible in the rank-one case - begin to play a starring role in higher rank situations, on equal footing with the poles. We redo Langlands' famous $G_{2}$ calculation and show that once zeros are tracked, the calculation reduces to elementary algebra. Drawing on rank-two examples, we introduce a program to re-think Langlands' construction from first principles, giving zeros and poles of cuspidal Eisenstein series equal standing from the very beginning. The program has the advantage of making the underlying phenomenon transparent, though carrying it out in full generality will require substantial further work.

We provide a new proof of Ishii's conjecture for any dihedral reflection group $G\subset GL_2(\mathbb{C})$ from the viewpoint of Bridgeland stability conditions. Our strategy is to reduce the problem, via the derived McKay correspondence, to a geometric construction of Bridgeland stability conditions on the root stack of the maximal resolution along the strict transform of the discriminant divisor.

Silicon's bandgap inherently restricts its photodetection to wavelengths below 1100 nm, necessitating the integration of costly III-V semiconductors for short-wave infrared applications. Hyperdoping silicon beyond the solid solubility limit offers a promising "silicon-native" alternative, yet achieving practical short-wave infrared applications at room temperature remains a formidable challenge. Here, we demonstrate a high-detectivity hyperdoped silicon photodetector enabling room-temperature computational short-wave infrared imaging beyond Si bandgap wavelength at λ = 1550 nm. By integrating an ultrafast laser heating process step to reduce the dark current while keeping high responsivity, we achieve a specific detectivity D^* exceeding 10^9 Jones for 1550 nm at room temperature working in a forward-biased, photoconductive mode. The improved detectivity, coupled with a 59.4 dB linear dynamic range and kHz-scale bandwidth, allows us to demonstrate a single-pixel imaging system that reconstructs 1550 nm scenes at 65x63 pixels without cryogenic cooling. Our devices simultaneously support visible-light imaging, offering a path toward monolithically integrated, multispectral Si-native optical sensors. These results establish ultrafast-laser hyperdoped silicon as a viable platform for low-cost, room-temperature, short-wave infrared photonics, bridging the gap between advanced materials science and practical computational imaging system.

We study the arithmetic and geometric iterated monodromy groups associated to the postcritically finite (PCF) quadratic rational function $f(x)=\frac{2}{(x-1)^2}$ defined over a number field $k$, whose critical points are both strictly pre-periodic. We give explicit recursive descriptions of the topological generators of the geometric iterated monodromy group of $f$ and show that the arithmetic iterated monodromy group has Hausdorff dimension zero. We describe an explicit criterion to determine the values $a\in k$ for which the associated arboreal Galois group achieves its maximum possible size. In particular, we show that maximality of the arboreal Galois group can already be verified at level four, which is computationally accessible. Finally, we determine the intersection of the constant field of the arithmetic iterated monodromy group with $k(μ_{2^{\infty}})$, providing the first full study of a PCF quadratic map with non-abelian constant field.

We propose a hybrid inflation model where a pseudo-Nambu-Goldstone boson inflaton couples to $N$ waterfall scalar fields respecting a $Z_N$ symmetry. We identify the phases for the inflation and the consequent waterfall transition, concretely, in $Z_2$, $Z_3$ and $Z_4$ cases. From the Coleman-Weinberg potential for the inflaton, we show that the quadratically divergent corrections coming from the waterfall sector are cancelled due to the $Z_N$ symmetry, while the logarithmically divergent corrections are absent only for $N>2$, ensuring the radiative stability of the inflaton potential. We show the parameter space for a successful inflation with the loop-corrected inflaton potential in each model and compare the results between different discrete symmetries. We further analyze the vacuum structure of the models and the reheating process due to the $Z_N$-invariant Higgs-portal couplings for the waterfall fields. We find that the reheating temperature can be smaller than the mass of the waterfall field condensate such that the $Z_N$ symmetry is not restored after reheating and there is no domain wall problem in the models. We also comment on the possibility of multi-component dark matter from the $Z_N$ partners of the waterfall field condensate.

Automated Guided Vehicles (AGV) in factory automation are increasingly capable of moving autonomously in close proximity to human workers. While their physical safety is regulated by standards and directives, perceived safety and workers comfort in close-proximity interactions are being actively investigated in studies. There are three limitations in the prior art research to that end. Firstly, AGVs with larger payloads are understudied. Secondly, the test participants are usually students and not working professionals. Thirdly, while conducting in-person experiments with heavy machinery can be dangerous, the transfer of safety perception results from simulated experiments remains open. In this paper, we investigate industrial workers perceived safety in shared spaces with large AGVs in a real-world encounter and in virtual reality. We vary the passing distance and the shape of the collision avoidance maneuver, and evaluate perceived threat level using a handheld pressure-sensitive trigger interface and a post-experiment questionnaire. Additionally, we ask participants to set their own collision avoidance parameters based on their experience with the demonstrated trajectory profiles. In a within-subject study, we found that, while the threat levels are perceived overall slightly higher in VR, the passing distance of 1.5 to 2 meters is preferred among the demonstrated profiles, as well as in the self-defined trajectories.

We investigate the robustness of topological phases in a Kitaev ladder composed of two coupled superconducting chains under the perturbing influence of a finite charge current. By introducing an effective Hamiltonian depending on the quasiparticle momentum induced by the current, we show that the two-mode topological phase, present in the isolated ladder, is fragile against a finite current flux. To characterize this behavior, we combine bulk topological invariants with real-space diagnostics, including the edge-edge quantum conditional mutual information Iee, which provides an entanglement-based signature of topological order. Our results provide an effective framework to describe how current injection and measurement processes can affect topological protection in superconducting nanostructures.