Papers

Large language models are usually interpreted through concepts that humans already possess: truthfulness, refusal, deception, personality, harmfulness, and related categories. This paper asks whether models may also represent and use distinctions for which no adequate human concept exists. We call such internal structures xeno-representations, and their study xeno-interpretability. We distinguish the human-interpretable semantic space from the xeno-semantic space: the region of model-native representations for which no adequate human conceptual counterpart is available. We show that the space of possible internal distinctions in an LLM is substantially larger than the space available through finite human descriptions. We then separate experimental identification from semantic interpretation: an internal representation may be reproducibly located, geometrically characterized, causally manipulated, and linked to downstream behaviour even when its semantic content cannot be adequately expressed in human terms. On this basis, we sketch an empirical programme to identify xeno-representations. We finally examine the implications for AI safety and multi-agent systems, where model-native representations may propagate and stabilize across interacting agents while remaining only partially visible through human-readable communication. Xeno-interpretability therefore shifts the aim of interpretability from finding human concepts inside models toward discovering and characterizing the representational structures that are native to the models themselves and might affect their behaviour in unpredictable ways.

Free-flying robots rely on multiple thrusters to maneuver in space. If one or more of these thrusters fail, the robot may lose control authority and risk mission failure. At the same time, their free-flying nature implies that, even in the absence of actuation, they continue along (locally) straight-line trajectories. In this work we present a probabilistic, proactive, motion planning framework that explicitly accounts for actuator failures in space. We model actuator failure modes as a Markov chain and propagate the probability of successfully reaching the goal along the planning horizon. Precomputed reachable sets evaluate the robot's capabilities of reaching waypoints under potential failures and an RRT$^*$-based planner concatenates these waypoints. The resulting algorithm maximizes the overall target-reaching probability, providing maximally resilient motion plans utilizing free-flying properties. We validate our approach experimentally on a physical free-flyer platform with injected actuator failures.

Recent advances in the field of quantum computing hardware motivate the search for applications which demonstrate so-called quantum advantage. One promising use case that has been identified is the simulation of quantum many-body systems. The computational resources required for performing such a simulation on a classical computer generally grow exponentially with the size of the system being modeled, which is ultimately due to the exponential growth of the Hilbert space in which the dynamics of such a system take place. While digital quantum computers natively evolve quantum states directly in such a Hilbert space, thus naively avoiding this problem, the result of such a computation is typically not obtained as a deterministic output. Rather, it requires projective measurements which are fundamentally affected by shot noise. Any desired expectation values must therefore be reconstructed from repeated measurements, making the number of those measurements a relevant computational resource, and thus an important consideration for any potential claims of quantum advantage. In this work, we study how this resource scales with system size (a scaling which itself depends on the desired accuracy of the final result), using the simulation of nuclear magnetic resonance (NMR) spectra as a test case. We study this scaling for both real-world molecules, as well as a class of model NMR Hamiltonians which allow for efficient large-scale simulations with one-dimensional, two-dimensional, and all-to-all interactions. We find that the required resources increase only weakly with molecular size, far below the exponential growth of the underlying Hilbert space. This result suggests that shot noise should not pose a fundamental barrier to achieving quantum advantage in the simulation of NMR systems, and perhaps for many-body systems more broadly.

I consider a neoclassical growth model with a constant absolute risk aversion (CARA) utility function and derive a global closed form approximation that is arbitrarily precise as the discount rate $\rho$ is close to the population growth rate $n$. I use it to show that the consumption function is strictly concave and that countries can have two different paths converging to the steady-state: front-loading and back-loading.

Agricultural soils are a major untapped carbon sink. Carbon farming is emerging as a promising practice for tapping this potential. Smallholder farmers, who dominate agriculture across South Asia and sub-Saharan Africa, are key to scaling climate mitigation via carbon farming. It is ironic that real-world carbon programs largely fail to reach them. We study this important gap through the lens of contract design. An aggregator offers a single pooled contract to a heterogeneous population of smallholder farmers who have private adoption costs (adverse selection) and exert unobserved effort (moral hazard), with agronomic outcomes evolving over multiple seasons. We formulate this evolving contracting problem as a POMDP and use reinforcement learning to learn a dynamic profit-maximising contract. We analyse the performance of the aggregator under various conditions. We find that a profit-maximising aggregator does not merely inherit the exclusion of smallholders, it amplifies it. On large farms the aggregator realises 87.7% of achievable adoption, against only 8.2% on smallholdings. Per-hectare Measurement, Reporting and Verification (MRV) costs fall as farm size rises, and the aggregator's pooling contract compounds this gradient rather than offsetting it. A counterfactual that makes MRV costs purely area-proportional eliminates this disparity. Our results and simulation can guide contract and policy design that opens carbon income to smallholders while enabling agricultural soils to contribute to climate mitigation at scale.

We classify the automorphism groups of smooth cubic threefolds and fourfolds. We also show that there are $156$ (respectively, $40$) connected families of smooth cubic fourfolds (respectively, threefolds) with specified automorphism group action. For each family, the group action and defining equations are also given. The classification combines both representation theory (based on GAP) and lattice theory (based on SageMath).

Let $q=3^m$, let $K=\mathbb F_{q^2}$, and let \[\mathcal T=\{x\in K^*:\operatorname{N}_{K/\mathbb F_q}(x)=1\}.\] For both cyclic and constacyclic Gashkov-Sidel'nikov codes, we show that the set of signed parity-check column labels is precisely $\mathcal T$. Consequently, the decoding problem separates into two stages: determining the minimum error weight associated with a syndrome $S$ and constructing an error vector attaining this minimum. We identify the former quantity with the minimum additive length of $S$ with respect to $\mathcal T$ and determine it exactly by the norm and the quadratic character of $\mathbb F_q$. We also determine the complete coset-weight distribution and recover the known covering radius $3$. For the constructive part, we use quadratic-character sums and Weil bounds to construct a coset leader for every syndrome of coset weight three. The resulting procedures give complete maximum-likelihood decoders.

We introduce a kernel–wreath construction for finite skew braces. Let $C$ be a finite skew brace, write $(C,+)=A$ and $(C,\circ)=R$, and let $\chi:R\twoheadrightarrow T$ be an epimorphism onto a non-trivial finite abelian group. We show that a natural index-$|T|$ kernel in the permutational wreath product $R\wr T$ acts regularly on $A^T$, and hence defines a new skew brace $\KT_T(C,\chi)$ with additive group $A^{|T|}$. The construction preserves every finite abelian quotient of the multiplicative group, as well as solvability, and contains the seed brace $C$ as a diagonal subbrace. It can therefore be iterated indefinitely. More precisely, if $Q$ is a non-trivial finite abelian quotient of $R$ and $p\in\pi(Q)$, then one obtains an infinite tower \[ C=C_0\hookrightarrow C_1\hookrightarrow C_2\hookrightarrow\cdots \] with $(C_m,+)\cong A^{p^m}$ for every $m\geq0$. Our main permanence result shows that if $C$ is simple and is not a trivial skew brace, then $\KT_T(C,\chi)$ is again simple. Consequently, a single simple seed whose multiplicative group has a non-trivial finite abelian quotient gives rise to infinite families of finite simple skew braces. In particular, starting from suitable solvable regular subgroups of the holomorph of a finite non-abelian simple group $S$, we obtain infinite families of simple skew braces with additive groups $S^{p^m}$ and solvable multiplicative groups. Further applications are given to the simple skew braces of order $12$ and to Byott's family.

We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization $\varepsilon$. In particular, we quantify the sparsity of the support of the regularized optimizer. For smooth marginal densities in $\mathbb{R}^d$, this support lies within a distance of order $\varepsilon^{1/(d+2)}$ from the Brenier graph, and every section of the support is sandwiched between balls with radii of that order. The geometry of the support is closely linked to the dual potentials. We show that the potentials satisfy uniform two-sided Hessian bounds and converge uniformly at rate $\varepsilon^{2/(d+2)}$, while their gradients converge at rate $\varepsilon^{1/(d+2)}$. The rates are sharp, and we further identify the regularity threshold where convergence breaks down.

We propose sparse identification of port-Hamiltonian systems (SIPHy), enabling structure-preserving symbolic regression from noisy trajectory observations. The method applies to port-Hamiltonian systems, which provide a general framework for describing dynamical systems in terms of energy exchange, dissipation and control. Our algorithm can jointly identify the Hamiltonian as well as the dissipation and input matrices. Furthermore, we introduce Hamiltonian flow splines to better approximate derivatives of trajectory data corrupted by noise or with missing time points, a major challenge of system identification for differential equations. This method assembles flows of piecewise polynomial Hamiltonians to produce a smooth, differentiable trajectory necessary for sparse regression. Combining flow splines with SIPHy yields interpretable, physically grounded models from noisy and incomplete trajectory data. Because the Hamiltonian, dissipation, and input matrices are identified as separate components, the resulting models can be simulated under control inputs and dissipation regimes never observed during training, thus improving the robustness and generalization capabilities of model discovery methods.

Semantic parsing (SP)-based knowledge base question answering aims to answer natural language questions by generating executable logical forms (LFs) over knowledge bases (KBs). When applying Large Language Models (LLMs) to this task, a key challenge over large, heterogeneous KBs is selecting question-related schema elements (i.e., relations and classes) and composing them into complex LFs. Recent LLM-based methods often make early discrete commitments to schema elements during intermediate reasoning, allowing incorrect intermediate schema decisions to propagate and finally result in incorrect LFs. To overcome this limitation, we propose SALR, a schema-anchored latent reasoning method for LF construction. It performs multi-step reasoning by generating continuous thoughts in the model's hidden states, thereby delaying the explicit commitment to LF decisions. To ground this latent reasoning process in the corresponding KB schema, SALR aligns continuous thoughts with a codebook of KB schema elements through an alignment objective supervised by schema traces deterministically derived from gold LFs. It then incorporates the aligned schema codes into inputs for subsequent reasoning steps. This schema-mediated feedback guides LF generation without requiring the model to emit an explicit textual reasoning trajectory. Experiments on GrailQA and WebQSP show that SALR achieves consistent overall gains over strong baselines. Notably, on compositional questions from GrailQA, SALR outperforms TIARA, a strong SP-based baseline, by 2.86 F1 points. Further analyses show that schema-mediated feedback affects LF generation and that schema information is recoverable from the latent states.

Self-similar solutions to the porous medium equation with dominating spatially inhomogeneous absorption $$ \partial_tu=\Delta u^m-|x|^{\sigma}u^p, \quad (x,t)\in\real^N\times(0,\infty), \quad N\geq1, $$ with exponents $1<p<m$ and $\sigma>0$, are classified. Looking for solutions in the form $$ u(x,t)=t^{-\alpha}f(|x|t^{\beta}), \quad \alpha=\frac{\sigma+2}{\sigma(m-1)+2(p-1)}, \quad \beta=\frac{m-p}{\sigma(m-1)+2(p-1)}, $$ it is shown that all their profiles satisfy the behavior at infinity given by $$ \lim\limits_{\xi\to\infty}\xi^{\sigma/(p-1)}f(\xi)=\left(\frac{1}{p-1}\right)^{1/(p-1)}, $$ but the solutions strongly differ with respect to their behavior near the origin: there exist a unique solution with $f(0)>0$, $f'(0)=0$, another unique solution such that $f$ presents a dead-core; that is, $f\equiv0$ for $\xi\in[0,\xi_0]$ for some $\xi_0>0$, and, finally, there exists $K^*\in(0,\infty)$ such that, for any $K\in(0,K^*)$, there is at least a solution such that $$ \lim\limits_{\xi\to0}\xi^{-(\sigma+2)/(m-p)}f(\xi)=K. $$ The large time behavior of general solutions, making strong use of these three types of self-similar solutions, will be addressed in a companion work.

Robots operating in cluttered environments must often manipulate objects whose locations are only partially observable. A central challenge is deciding whether to acquire another observation or to first manipulate objects that may occlude the target. Conventional task and motion planning (TAMP) approaches typically make this decision using symbolic action costs or expensive geometric planning, neither of which adequately captures how likely an observation is to reveal an occluded target. We introduce Imagine-TAMP, an interleaved planning and execution framework that uses semantic and geometric imagination to compare alternative task-level strategies under partial observability before committing to expensive motion planning. A vision-language model shapes a particle belief over target locations using commonsense relationships between the target and visible objects, while a generative scene model estimates plausible geometry in unobserved regions. Given a target hypothesis and imagined scene, Imagine-TAMP generates multiple symbolic plan skeletons and assigns non-unit costs that approximate both manipulation effort and target visibility from sensing actions, distinguishing a short but poorly informative observation strategy from a longer strategy that first manipulates an occluder to better expose the target. The selected skeleton is then refined into a feasible continuous plan and executed, with new observations updating the belief and triggering replanning when necessary. Experiments show that imagination-guided evaluation improves observation-versus-manipulation decisions: in viewpoint-constrained shelf scenes, non-unit geometric evaluation increases success from 46.0% to 84.0%, while semantic belief shaping further reduces manipulation and replanning. On a real robot, the complete system reduces planning time by 32% relative to a geometry-only ablation.

This work studies adaptive sparse-grid discontinuous Galerkin (DG) discretizations for the Bhatnagar–Gross–Krook (BGK) model, a kinetic equation posed in four- and six-dimensional phase-space. Standard DG methods are rendered impractical for the BGK model by the curse of dimensionality, motivating compressed representations that adapt to the solution in time. Using the adaptive sparse-grid DG method, we quantify accuracy and compression by comparing the adaptive degrees of freedom to full-grid DG methods and by assessing the resulting kinetic and fluid quantities in both fluid and rarefied regimes. Test cases include a relaxation problem, a multidimensional Sod shock tube, and shear/expansion flows used in prior low-rank BGK studies. To build an efficient Maxwellian evaluation without violating conservation, a central obstacle for structure-perserving BGK simulations, we introduce a hybrid interpolation strategy that exploits velocity separability to recover the correct discrete collision invariants and prove conservation of the resulting discrete collision operator on adaptive sparse grids. Our results show that the adaptive sparse-grid strategy can recover accurate and physically relevant solutions with sharp gradients, and the method reduces the active degrees of freedom by factors ranging from several-fold to several orders of magnitude, with the largest reductions occurring in the six-dimensional examples. All computations are performed with the open-source ASGarD adaptive sparse-grid DG library.

We derive a novel diffuse-like BRDF based on microfacet theory. Its main novelty lies in the fact that it admits an elementary expression for both evaluation and importance sampling, while accounting exactly for all scattering orders under the Smith shadowing assumption. As such, it is the first to settle the question of whether such a construction was possible. In practice, the BRDF produces Lambertian reflectance at normal incidence and progressively concentrates reflected light around the mirror direction as incidence approaches grazing. We showcase this effect by comparing rendering results against Lambertian and state-of-the-art stochastic microfacet BRDFs.

This paper develops inference for a Gaussian-nested hypergeometric family of distribution functions. The family \[ G_c(z) = \frac12 + z\,\frac{\Gamma(c-1/2)}{2\sqrt2\,\Gamma(c)}\,{}_1F_1\!\left(\frac12;c;-\frac{z^2}{2}\right),\quad c\ge\frac32, \] contains the standard normal distribution at the boundary $c=3/2$. Away from the boundary, the density has algebraic tail behaviour $g_c(z)\sim(c-3/2)|z|^{-3}$, so the parameter $c$ indexes a directed heavy-tailed deformation of the Gaussian law. The distribution also admits an equivalent beta-precision normal scale-mixture representation, in which the Gaussian boundary corresponds to degenerate unit precision. I establish the admissibility of the hypergeometric family, derive minimum-distance estimators, and obtain both regular interior asymptotics and nonstandard boundary asymptotics under the normal null. The standardised fit-improvement statistic converges to the mixture distribution $\tfrac12\delta_0+\tfrac12\chi_1^2$. I extend the theory to plug-in location-scale procedures, including a robust median/IQR version. Simulations document accurate null size and directed power against heavy-tailed alternatives. An application to daily S&P 500 returns, both unconditionally and after GARCH(1,1) filtering, illustrates the empirical implications for tail fitting and risk quantiles, and documents that GARCH filtering substantially reduces but does not eliminate the symmetric heavy-tailed departure detected by the test.

In this work, we study the unquenched effects on the low-lying $\Omega_b(1P)$ states with a coupled-channel equations. We reveal how the unquenched effects affect the $\Omega_b(1P)$ spectroscopy and component mixing. The numerical results indicate that the $J^P=1/2^-$ $\Omega_b(1P)$ state dominated by the $j_\ell=0$ configuration exhibits significant coupled-channel effects due to its $S$-wave coupling to the $\Xi_b\bar{K}$ channel, where $j_\ell$ denotes the total angular momentum of the light flavor degrees-of-freedom. In this scenario, the mass of this state may be shifted close to or below the $\Xi_b\bar{K}$ threshold, making the radiative and isospin-breaking channels kinematically allowed decay processes. The present analysis provides a coupled-channel perspective on the low-lying $\Omega_b(1P)$ spectrum and offers guidance for future experimental studies of excited bottom baryons.

We investigate energy fluctuations of solvated DNA in three conformations: G-quadruplex, Hairpin, and Duplex. Our comprehensive molecular dynamics (MD) simulations demonstrate that the time-series of interaction energies for DNA self, DNA-water and DNA-ion show 1/f noise with a universal decay exponent $\beta \simeq 0.90$. We show that DNA topology and structural rigidity modulate its dynamic coupling with the surrounding hydration shell and mobile counter-ions. This coupling critically shapes the 1/f noise profile: DNA self energies in flexible structures (G-quadruplex, Hairpin) display pronounced low-frequency modes absent in the rigid Duplex. These findings reveal how the interplay between DNA topology and environmental coupling governs different stochastic behavior in biologically relevant forms of DNA.

We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős–Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.

Offline policy evaluation (OPE) is crucial in high-stakes reinforcement learning applications, where new policies must be assessed reliably before deployment. In such settings, point estimates alone are insufficient; principled uncertainty quantification, such as confidence intervals and variance estimates, is essential for safe and risk-aware decision-making. A comprehensive way to unify these tasks is to estimate the sampling distribution of the evaluation error. Existing approaches, however, often suffer from limited robustness, scalability, or finite-sample validity. In this paper, we propose a model-based bootstrap framework for uncertainty quantification of OPE in finite-horizon, time-inhomogeneous Markov decision processes (MDPs). Unlike classical bootstrap methods that rely on resampling complete episodes, the proposed method regenerates trajectories from an estimated MDP and can therefore accommodate a much broader range of offline data formats, including complete trajectories, transition-level observations, and trajectory fragments. This flexibility further improves finite-sample statistical efficiency. We establish bootstrap distributional consistency, asymptotically valid confidence intervals, and consistent variance estimation for the target policy value. Extensive simulations show that the proposed method accurately captures the sampling distribution of the OPE estimator, yielding tighter confidence intervals and more accurate variance estimates in most settings.

Vision-Language Navigation in Continuous Environments (VLN-CE) requires an embodied agent to execute long-horizon instructions in unknown environments. Existing zero-shot VLN-CE systems typically maintain spatial states through geometric localization or coordinate-based representations. Recent geometry-constrained navigation removes depth and globally consistent coordinates, but maintaining persistent spatial awareness for place confirmation, progress verification, and recovery remains challenging. We present Navi-Agent, a zero-shot VLN-CE agent that constructs a coordinate-free spatial state from visual observations and executed motion histories. Navi-Agent organizes this state as a navigation topology, where nodes represent visual places and edges represent motion transitions. This representation enables observation-based approximate self-localization, task progress verification, and visual revisitation-based recovery. Navi-Agent performs closed-loop navigation by decomposing instructions into sub-goals, executing local visual navigation, and verifying visited places through the constructed spatial state. Experiments on zero-shot VLN-CE benchmark and real-world robot platforms show that Navi-Agent achieves state-of-the-art performance among geometry-constrained methods while remaining competitive with approaches relying on geometric localization.

Strain engineering is a powerful route for controlling the exciton dynamics in van der Waals (vdW) heterostructures (HSs). The interlayer energy transfer (ET) process is another key factor in controlling the photocarrier relaxation pathways in vdW HSs. In this work, we combine these two processes to achieve an 8-fold enhancement to the relative photoluminescence (PL) quantum yield (QY) in a HS formed from monolayers of ReS2 and MoSe2, separated by a thin hBN interlayer, placed onto an hBN bubble. We achieve this enhancement by applying only 0.1% biaxial tensile strain, which results in efficient exciton funneling and an increased transition dipole moment. Our experimental data are supported by first-principles density-functional theory and coherent transfer-matrix method calculations, ruling out optical interference as the dominant origin of the enhancement. This work provides an innovative route for enhancing the PL QY of vdW materials via interplay between the tensile strain and the ET process.

Iris presentation attack detection (PAD) is security-critical when a subsystem that appears reliable during development encounters presentation attack instruments (PAIs) or acquisition conditions absent from validation data. We benchmark three compact scratch-trained computer-vision models, each with at most approximately 0.26 million trainable parameters, on the Notre Dame subset of LivDet-Iris 2017 under PAI-driven domain shift and environmental degradation. All models are trained without external pretraining or data augmentation and evaluated over five seeds. A validation-selected threshold is transferred unchanged to the known-attack, unknown-attack, corrupted, and pooled test partitions. From known to unknown attack presentations, Attack Presentation Classification Error Rate (APCER) increases by 17.11-30.47 percentage points and Detection Equal Error Rate (D-EER) increases by 7.38-12.73 percentage points. At the validation-selected threshold, ZACH-ViT obtains the lowest unknown-attack APCER (47.69 +/- 4.84%) and D-EER (38.87 +/- 0.93%), while Compact-TransMIL obtains the lowest Bona Fide Presentation Classification Error Rate (BPCER). ZACH-ViT also gives the lowest unknown-attack BPCER at an APCER limit of 10% (81.29 +/- 1.95%). The high absolute errors show that the comparative advantage of the best compact model does not constitute deployment readiness under unknown PAIs.

Let $\mathbb N$ denote the set of nonnegative integers. For an integer $k>1$ and a set $A\subseteq\mathbb N$, let $R_{1,k}(A,n)$ denote the number of solutions of $n=a_1+ka_2$ with $a_1,a_2\in A$. For integers $k>1$ and $t\ge1$, Yang and Chen defined $f_k(t)$ to be the number of sets $A\subseteq\mathbb N$ for which \[ R_{1,k}(A,n)=R_{1,k}(\mathbb N\setminus A,n) \] for all integers $n\ge t$, and asked whether $f_k(t)$ and $f_l(t)$ are eventually equal for any integers $k,l>1$. We prove that \[ f_k(t)\asymp_k \frac{2^t}{t^{k/2}}, \] which gives a negative answer to their problem.

Backbone resonance assignment is a prerequisite for most biomolecular NMR applications, yet conventional multidimensional strategies frequently fail for intrinsically disordered proteins (IDPs) and regions (IDRs) because of severe spectral overlap, rapid amide proton exchange with water, and missing sequential correlations. In many biological applications, however, complete protein assignment is unnecessary, as only a limited sequence segment surrounding a functional site is required. Here we introduce segmental backbone assignment, an assignment strategy implemented by FOcused SpectroscopY (FOSY), which concentrates experimental effort on relatively short regions while retaining the high-dimensional sequential connectivity needed for unambiguous assignments. We present a self-consistent suite of selective two-dimensional FOSY experiments that enables bidirectional assignment walks along the protein sequence through complementary forward and backward transfer schemes. The methodology employs frequency-selective polarisation transfer to replace high-dimensional experiments with sensitive and readily interpretable 2D spectra while preserving the information content of multidimensional correlation experiments. The approach is demonstrated by completing the assignment of G302-K311 segment, which is missing in the published assignment of the 441-residue human Tau protein. The approach complements conventional multidimensional or residue type-selective assignment strategies by providing an efficient means of traversing assignment interruptions and rapidly characterising functionally important segments in intrinsically disordered proteins.

Hollow-core fibres (HCFs) are a promising means of increasing the throughput of coherent transmission systems. In addition to their advantages in terms of low latency, nonlinearity and attenuation, HCFs can potentially improve the energy efficiency of coherent transmission systems by reducing the number of repeaters and enabling more efficient modulation formats than SMF links. However, the relationship between the link parameters (e.g. launch power, amplifier efficiency and transceiver noise) and the energy efficiency has not been explored. In this work, we investigate energy-efficient operating regimes in HCF transmission systems. We show that the optimum energy per bit in SMF systems is ultimately throughput-limited - maximising throughput will minimise energy per bit. In contrast, the transceiver-limited throughput of HCF leads to two separate launch power optima - minimum-energy-per-bit and maximum-throughput. We derive a closed-form equation for the minimum-energy-per-bit launch power for HCF links in terms of the link parameters, including the amplifier efficiency, transceiver power consumption and link gain. We use our model to explore the impact of span length and fibre attenuation in both operating regimes, showing how energy per bit considerations significantly impact the optimum span length. Optimising for energy efficiency can lead to 50% reduction in link energy per bit for only a 3% throughput penalty at 3000 km, whilst also reducing the required amplifier launch power from >33 dBm to <23 dBm. This work highlights the importance of including physical layer energy considerations in HCF link design.

We investigate the scalar quasinormal mode (QNM) spectrum of Schwarzschild-AdS black holes with a partially reflective surface placed near the event horizon. The corresponding QNM problem is solved numerically using Chebyshev spectral collocation. The resulting spectra exhibit a characteristic cavity structure at sufficiently large real part, where the modes form approximately equally spaced sequences whose spacing and damping are controlled mainly by the cavity length and the surface reflectivity. For large AdS radius, an additional weakly damped quasibound-state branch appears due to trapping between the centrifugal barrier and the AdS potential wall. We show that these spectral features can be understood within a finite radial cavity picture. A WKB analysis provides a quantitative asymptotic description of the spectra which have high real parts. We find that changes in the near-horizon boundary condition can lead to substantial changes in the QNM spectrum, indicating the strong sensitivity of Schwarzschild–AdS QNMs to the effect of horizon correction.

We measured state selective scattering angle distributions in non-dissociative-state single electron capture in $\lbrace 5, 7.5, 10\rbrace$ keV/u, $\left[\mathrm{H^+ + H_2}\right]$ and $\left[\mathrm{H_2^+ + H_2}\right]$ collisions, using Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS). In our measurements, range of the scattering angle was small where diffraction effect is expected to take place, and, the ground state electron capture - symmetrical resonant channel for the $\mathrm{H_2^+}$ projectile and near resonant channel for the $\mathrm{H^+}$ projectile - was fully resolved from other channels. We analyzed the data considering $\mathrm{H_2^+}$ and $\mathrm{H_2}$ possess two independent-identical scattering centers and exhibit multi center interference effect. By comparing these equal-velocity collisions, we investigated the atomic nature of the individual scattering centers. We observed Fraunhofer diffraction from a circular aperture like patterns with equal fringe widths, for both the projectiles, in ground state channel. We applied a simple toy model to reconstruct the circular apertures.

We prove that the Bézout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavitch. We give two separate proofs of the conjecture. Along the way, we also prove characterizations of simplices in terms of longest chords or relative inradii.

The increasing structural complexity of BEOL interconnect stacks in advanced integrated circuits demands a structure-aware thermal conductivity (ąppa}) modeling framework. However, generalizable models derived from layer-resolved thermal measurements that quantitatively capture the dependence of ąppa} on interconnect structures remain lacking, limiting predictive thermal analysis. Here, we establish an experimentally derived, structure-aware ąppa} modeling framework enabled by time-domain thermoreflectance measurements with ~100 nm depth resolution. Statistical analysis of a compiled dataset comprising over 40 experimentally measured layer-resolved ąppa} values across diverse BEOL layers reveals a generalizable empirical structure-to-ąppa} relationship, enabling predictive modeling based on interconnect structure. An intra-layer three-dimensional ąppa} distribution model based on effective medium theory and realistic layouts further resolves spatial ąppa} variations within practical interconnect layers. Together, these models establish an experimentally derived, structure-aware ąppa} modeling framework for predictive and generalizable thermal analysis of advanced interconnect stacks and 3D ICs.