Papers

We prove that the local Dirichlet-to-Neumann map of $\Delta_g+q$ determines a compact connected real-analytic Riemannian manifold of dimension at least three and a real-analytic real-valued potential, up to a diffeomorphism fixing the observed boundary and the conformal gauge of the equation. The result is new even when \(q\) is constant, i.e. for the fixed-frequency (Helmholtz) equation \(\Delta_g u+\lambda u=0\). The measurements are restricted to an arbitrary nonempty open boundary set $\Gamma$. The proof develops conformal Poisson embeddings method and uses coordinates given by quotients of solutions.

The proximal Galerkin algorithm is a structure-preserving solver for variational inequalities that results in discretization-independent nonlinear iteration counts. However, in large three-dimensional simulations, the arising Newton saddle point systems cannot be feasibly solved by direct methods. To leverage an iterative linear solver, we propose a robust and scalable block preconditioner. Instead of using the usual dual Schur complement that acts on the latent variable, we design a preconditioner for the primal Schur complement. This leads to a block preconditioner that requires two approximate inverses of the latent block and only one of the primal Schur complement. The latent block represents an algebraic equation which, after a small perturbation, can be cheaply inverted. We then introduce two choices of approximations for the primal Schur complement: a PDE-operator-based and an algebraic approach. Either approximation can be efficiently inverted by geometric multigrid. We investigate the effectiveness of these strategies when proximal Galerkin is applied to obstacle, Signorini, and strain-constrained elasticity problems and also compare with a monolithic multigrid approach. Choices of standard relaxation methods, in the block preconditioner route, lead to robust iteration counts with respect to the mesh size and discretization degree. Moreover, in the context of the Signorini, specialized relaxation and prolongation also result in effective solvers for nearly-incompressible elastic materials. The linear solves are parameter-robust in 2D, with only mild growth in 3D. This allows for the solution of a three-dimensional contact problem, with a Poisson's ratio of 0.499, discretized with over ten million degrees of freedom.

Recent results [arXiv:2602.04378, arXiv:2602.22608] have established worst-case objective-error lower bounds of order $1/T^2$ after $T$ linear minimization oracle (LMO) calls, matching the upper bound [arXiv:1406.1305] in its dependence on $T$ and thereby resolving a long-standing open question. Upon close inspection, however, both lower bounds are somewhat brittle. The first [arXiv:2602.04378] applies only to the standard Frank–Wolfe algorithm, and, as we show, its prescribed slow exact-line-search trajectories can amplify sufficiently small initialization errors exponentially, corresponding to roughly one additional bit of initialization accuracy per iteration. The second [arXiv:2602.22608] obtains lower bounds for any deterministic LMO-based first-order method via a resisting oracle that adversarially adapts to the queries of the algorithm. In both cases it is conceivable that randomization may circumvent these lower bounds; in particular, neither establishes a lower bound for unrestricted randomized first-order LMO methods. We close this gap by proving an $\Omega(L\operatorname{diam}(S)^2/T^2)$ distributional lower bound for randomized first-order linear minimization oracle methods over strongly convex sets. While our construction reuses the family of [arXiv:2602.22608], our proof characterizes the conditional distribution of the hidden permutation after adaptive queries and bounds the expected decrease of a combinatorial statistic controlling optimizer variance. We further show that the same error threshold holds with probability at least $3/4$ and yields a stopping-time tail bound.

Practical fault-tolerant quantum computing requires qubit-efficient quantum error correction (QEC). Clifford deformations (CDs) modify the stabilizers of a QEC code to lower its logical error rate at no additional resource cost. However, the number of possible CDs grows exponentially with the number of qubits, making exhaustive search infeasible beyond small codes. In this work, we further show that under circuit level noise the optimal CD depends strongly on both the noise model and decoder. To make systematic CD optimization possible, we introduce Evolution-Based Best-arm Identification (EBBI), a shot-efficient search algorithm that treats the circuit, noise model and decoder as a black box. We benchmark EBBI's performance on the rotated surface code, under two strongly $Z$-biased circuit-level noise models with the PyMatching decoder. At distance 3, EBBI finds the optimal CD using up to $\sim 1100\times$ fewer shots than random search. At distance 5, when run at the target error rate, the median EBBI run converges to the CDs we believe to be optimal, while random search never converges. Under a $Z$-biased SI1000-like noise model, EBBI discovers a new CD, the B-XZZX code, which we generalized to larger distances. It differs from XZZX on only a fraction $\mathcal{O}(d^{-1})$ of the qubits at code distance $d$, yet its relative advantage grows from $\approx 5\%$ at $d = 3$ to $\approx 12\%$ at $d = 11$. We thus show that the B-XZZX pattern found by EBBI can be systematically scaled to larger code distances. Our work represents a first step towards scalable CD optimization for general QEC codes.

Uncertainty quantification for electric vehicle (EV) charging demand is essential to turn the increasing pressure of EV adoption on power systems into a source of flexibility. We study a large-scale dataset of public charging stations in Scotland, where demand exhibits a hierarchical structure, organized across multiple aggregation levels, from individual charging points to regional and national scales. The charging infrastructure is continuously evolving, with new stations deployed and existing ones occasionally removed, which calls for forecasting and uncertainty quantification methods tailored to this evolving structure. To address these challenges, we combine hierarchical forecasting with recent advances in conformal prediction with missing data. The conformal procedures considered produce valid prediction intervals at every node of the hierarchy and the algorithm CP-MNR-Nested successfully accounts for the time-varying hierarchical structure of the data.

The properties of NGC 7009 knots are investigated by employing UV-to-near-infrared data from the X-Shooter spectrograph. These structures belong to the category of low-ionization structures (LISs), which are characterized by enhanced emission from low-ionization species and whose origin remains enigmatic. Our main goal is to conduct the first dedicated spectroscopic study of LISs using X-Shooter, that covers a wide spectral range from the UV to the near-IR, simultaneously. As a pilot study, we focus on NGC 7009 to investigate its ionized, atomic, and molecular gas, aiming to better characterize the physical properties of its LISs and explore their largely unexplored molecular content. The spectrum was processed through the ESO Reflex pipeline, and the physical properties of LISs were derived with the latest version of PyNeb. More than 250 emission lines were detected in the spectra of NGC 7009 LISs, including rare, forbidden transitions from low- ionization species such as Fe+ and Ni+, as well as two transitions from P+, identified here for the first time in LISs. The detection of multiple shock tracers, together with the shock excitation of [Fe II] and [O I], as revealed by emission-line diagnostics, supports the presence of shocks at LISs. The richness of the spectrum allowed us to derive electron temperatures and densities at the LISs using both collisionally excited and optical recombination lines. In the near-IR spectrum of the LISs, nine ro-vibrational H2 emission lines were detected, seven of which were reported here for the first time. These lines were used to construct the H2 excitation diagram, providing new insights into the physical conditions of the nebular gas. The excitation of molecular hydrogen is most likely dominated by collisional processes through shocks.

We study scale-separated AdS$_3$ models with full moduli stabilization in massive IIA supergravity on G2 orientifolds. In addition to constructing new examples, we investigate the properties of these models once the singularities of the G2 toroidal orbifold are resolved. The blow-up moduli are shown to be stabilized using fluxes in a parametric regime that preserves scale separation and control under the supergravity approximation. We further show that the apparent orientifold intersections in the singular orbifold description do not exist on such resolved spaces. Finally, we analyze the brane dual picture of such models using flux backtracking. We highlight several interesting features from such analysis such as a finite interval solution of the resulting flow equations in some of the models and the desirable low-energy decoupling of brane modes.

We'll call a map from basic to clopen sets of binary sequences an encoding if it preserves uniform Lebesgue measure and the disjointedness relation. For some notion of randomness $R$ we can ask if there is a computable encoding $E$ such that for every non-Martin-Löf-random (non-MLR) sequence $\alpha$, the sequences in $E(\alpha)$ are non-$R$. Thus we can use $E$ and randomness test for $R$ to construct a randomness test for MLR. We show that there is no such $E$ for partial computable randomness (PCR), but there is one for Kolmogorov-Loveland randomness. Indeed, there is a total computable $E$ and a pair of total computable non-monotonic betting strategies such that on every sequence in $E(\alpha)$ at least one of the strategies wins whenever $\alpha$ is non-MLR.

We show that a two-dimensional classical array of conventional superconducting islands coupled by altermagnetic Josephson junctions supports an independent charge-4e phase. Tuning the altermagnetic splitting suppresses the leading single-pair tunneling harmonic while retaining strong double-pair coupling, producing a finite charge-4e region between staggered and uniform charge-2e states. Using the complete temperature-dependent microscopic Josephson spectrum, we find short-range ordinary pair correlations alongside algebraic coherence of pairs of Cooper pairs. Berezinskii–Kosterlitz–Thouless scaling and a half-flux response further identify the charge-4e phase. Our results establish altermagnetism as a microscopic means to select between ordinary and composite superconducting coherence.

Detectors of machine-generated text score almost perfectly on scientific-literature benchmarks, implying we can reliably distinguish with these detectors human and machine-generated documents. We looked at ten scientific-document subsets from six popular resources, and on several of them that apparent ease is a side effect of how the documents were put together. A logistic regression using 27 superficial features reached 0.833-0.997 macro-F1, and on the three arXiv subsets it outperformed every detector we evaluate with F1-scores 0.951-0.997. The strongest cue to the detector is the PDF extraction artifact: human texts retain their original line breaks, whereas generated texts are extracted as a single block of prose. This cue, together with three other formatting features, tell the classes apart at 0.996 AUC. To distinguish benchmarks that contain such a signal from detectors that rely on one, we introduce format counterfactuals: just re-wrapping a machine-written abstract without changing a single word reverses 20-27% of a public detector's correct decisions. Normalizing formatting before training reduces the generalization gap from 0.32 to 0.22. On format-clean benchmarks, it also raises out-of-domain macro-F1 from 0.33 to 0.65 for detectors trained on artifact-containing subsets.

Transport networks are key to living and engineered systems. How can transport networks adapt efficiently using only local rules, without a global objective or specific boundary conditions? Inspired by observations in biological transport networks, we adapt networks by subsequently pruning edges by relative resistance, thus removing edges whose resistance is higher than the resistance for routing flow through the rest of the network. We find that adaptation by such a local, boundary-condition-free measure of redundancy, set by topology alone, yields sparse, loop-rich, low-dissipation networks.

We study the de Rham cohomology and Deligne splitting for a class of Eisenstein-Kronecker forms by introducing a modular weight grading. As an application, we compute a particular cohomology class that gives rise to generating series of Gromov-Witten invariants of elliptic curves.

Chromatic villainy measures the largest number of vertices that must change color to repair a rearrangement of an optimal coloring while preserving every color multiplicity. Weak villainy allows different multiplicities in the repair. On the odd cycle $C_{2r+1}$, we determine the largest repair distance from arbitrary color assignments with a prescribed color-count vector (profile) $\mathbf m$ to proper colorings with any realizable target profile $\mathbf p$: it equals $2r+1-\sum_X\min\{p_X,\lceil m_X/2\rceil\}$. In particular, every feasible profile $(a,b,c)$ has ordinary and weak repair radius $\lfloor a/2\rfloor+\lfloor b/2\rfloor+\lfloor c/2\rfloor$, and $B(C_{2r+1})=r$ for $r\ge2$, answering a question of Clark et al. For arbitrary complete multipartite graphs, we give an arithmetic formula for ordinary villainy with at most $k^2$ candidates and an exact finite formula for weak villainy, where $k$ is the number of parts. Both values are fixed-parameter tractable in $k$ for binary-encoded part sizes. We also determine the maximum of each parameter among all $n$-vertex $k$-chromatic graphs. For $k\ge3$, the ordinary maximum is $\min\{n,4(n-k)\}$, except when $n=4(n-k)-1$ or $(n,k)\in\{(5,3),(7,3)\}$, when it is $n-1$. For $k\ge2$, the weak maximum is $n-\max\{\lceil n/k\rceil,2k-n\}-\varepsilon$, where $\varepsilon\in\{0,1\}$ is determined explicitly by $n$ and $k$. Both extrema are attained by complete multipartite graphs, and a weak extremizer needs at most three distinct part sizes.

We study correlation-based entanglement evaluation in rank-2 mixed states of two- and multi-qubit systems. The relevant two-dimensional subspace is treated as a logical qubit embedded in the physical Hilbert space, and factorizable realizations of its logical Pauli operators are classified. For two qubits, this yields nontrivial canonical encodings related by local Clifford transformations. The relation between logical and physical Bloch vectors admits a geometric interpretation as a transversely deformed Bloch sphere, leading to closed-form expressions for two-qubit concurrence and generalized concurrence across $N$-qubit bipartitions. The entanglement scaling factor is obtained directly from complementary-subsystem correlations, without prior calibration of state-preparation parameters. Noisy simulations using the IBM Quantum FakeKingston backend model, with readout-error mitigation and zero-noise extrapolation, confirm the analytical results up to $N=10$ qubits. The protocol therefore enables entanglement estimation from only a small number of measurement settings for this class of rank-2 logical states.

Pre-trained robot policies, such as Vision-Language-Action (VLA) models, provide a strong foundation for generalist robotic manipulation, but adapting them to new tasks with only a few demonstrations remains challenging. Directly fine-tuning a pre-trained policy often achieves strong in-distribution performance, yet it can distort the representations learned during pre-training and weaken the model's generalization ability under out-of-distribution shifts. We propose Retrieval-Anchored Representation Alignment (RARA), a two-stage adaptation method, to address this issue. First, RARA retrieves representation features from pretraining with similar task intent and motion, and aligns the policy's representations of the target demonstrations with the pre-trained representations of the retrieved demonstrations. Second, RARA fine-tunes the policy on the target demonstrations while limiting how much its representations of the retrieved demonstrations change during fine-tuning. By reducing the representation mismatch before action learning and preserving pre-trained knowledge during adaptation, RARA limits unnecessary representation drift during fine-tuning. Experiments with Diffusion Policy and GR00T on 13 tasks in RoboTwin, RoboCasa, and on a real robot show that RARA improves the average success of fine-tuning by 9.5 points in-distribution and 13.6 points out-of-distribution, and outperforms all compared baselines. Project page: https://shua-kang.github.io/RARA_robot/

We study the long-time behaviour of multi-dimensional first-order symmetrizable quasilinear hyperbolic systems with nonlinear feedback boundary conditions. Assuming strict interior and boundary Lyapunov inequalities for the linearized system and non-characteristic boundaries, we prove global existence for small initial data and exponential H^s decay, with s>d/2+1 an integer. We consider both bounded smooth domains and flat periodic cylinders, and illustrate the results with physical examples and numerical simulations.

This paper presents a path-following guidance framework for a turn-rate-constrained unmanned aerial vehicle (UAVs). The proposed guidance strategy uses commanded course angle as a tanh-hyperbolic shaping function of the lateral deviation from the desired path. Stability characteristics illustrating asymptotic convergence to the desired path are established using Lyapunov analysis. Analytical expressions for the turn-rate and corresponding maximum turn-rate bound are derived, enabling direct gain selection for a turn-rate-limited vehicle. Numerical simulations are performed for straight-line following scenarios under both ideal and non-ideal initial heading conditions. Furthermore, a comparative study against representative arctan-, arcsine-, and arccos-based vector-field guidance laws is conducted using analytically feasible gains selected from their respective turn-rate bounds. Comparative numerical results demonstrate the proposed formulation achieves reliable boundary convergence while maintaining smooth steering behavior and a compact analytical gain-design framework.

We present a new four-fermion model with a strongly non-polynomial coupling. To eliminate these non-polynomialities, we introduce two auxiliary vector fields and show that the dynamical Lorentz symmetry breaking is possible in our theory, as revealed by the effective potential generated for these vector fields. We explicitly calculate the low-energy effective action for these fields, which is given by the sum of three Maxwell terms (one for each field and a mixed one) plus a potential term displaying nontrivial minima.

Feature selection is a central problem in high-dimensional financial regression, where large numbers of engineered variables and strong correlations among predictors reduce model stability and interpretability. $L_1$ regularization (Lasso) is widely used for sparse regression, but its shrinkage can be restrictive when informative signals are spread across correlated variables. Exact sparse regression avoids this shrinkage but requires solving a combinatorial optimization problem that is computationally difficult and is typically fit to minimize in-sample rather than out-of-sample error. This paper presents a feature selection framework based on Monte Carlo Tree Search with Generalized Nested Rollout Policy Adaptation (GNRPA). Feature selection is formulated as a sequential decision process, and candidate subsets are scored by their out-of-sample validation performance rather than training error. The method also supports a lexicographic objective accounting for subset size and multicollinearity. We study this approach on a contemporaneous explanatory regression task: explaining the weekly return of the NASDAQ-100 index from 1,072 engineered features spanning market, macroeconomic, and factor data. This isolates the value of subset selection under multicollinearity from the separate problem of predictive forecasting. On this task, the proposed method identifies sparse feature subsets with higher out-of-sample explanatory power than an optimized Lasso baseline, reaching an out-of-sample $R^2$ of 0.6961 versus 0.6313 for Lasso. These results suggest that Monte Carlo Tree Search is a practical alternative to convex regularization for sparse explanatory feature selection in financial regression, with potential value for factor attribution and risk decomposition where transparency matters as much as out-of-sample fit.

Materials scientists increasingly combine information from several public databases, each with its own interface, schema, units and calculation conventions. MatQuery is a prototype and experimental infrastructure for studying how a natural-language request can be turned into queries over such databases and how the returned values can be interpreted. This report describes what has been built and the preliminary results obtained so far. The prototype holds frozen, self-verifying local copies of six public materials databases (about 10,000 records each), a catalog of declared fields derived from them, a database-independent query representation with an adapter for each database, and an eight-step pipeline in which a language model proposes and deterministic program steps check, execute and assemble. A benchmark generator produces questions whose reference queries are verified by execution on the frozen copies and whose wording is checked by back-translation and review. An evaluation harness runs direct prompting, CHESS and Alpha-SQL on the same frozen basis. Preliminary experiments on an 800-question development set show that direct generation with three demonstrations reaches 82.4% strict execution accuracy (56.5% without demonstrations), that a low-cost scorer selects the exact set of databases for 85.0% of complete requests with well-calibrated probabilities, and that band gaps differ by more than 0.5 eV in 31.6% of composition-matched cross-database clusters. Two pilots show the limits of the current approach: a probe-then-ask policy gave answers rated valid by both reviewers in only 11 of 50 sessions, and only 115 of 300 sampled record pairs could be compared by structure. The complete pipeline is in smoke testing and has not yet been evaluated at scale.

Humanoid tennis requires reactive whole-body coordination under rapidly changing ball dynamics, yet collecting task-specific motion-capture demonstrations that cover diverse approach states, contact locations, and timing conditions is costly. Inspired by how humans acquire new skills by combining reusable motor experience with task-specific demonstrations, we present ATHLETE, a framework for learning reactive humanoid tennis from generic locomotion data and ordinary tennis videos. ATHLETE combines LAFAN1 locomotion with video-derived striking motions and uses Trajectory-Guided Motion Matching (TGMM) to construct diverse task-conditioned whole-body references. These references are transformed into a reactive policy through physics-based teacher–student learning with online DAgger distillation, followed by PPO fine-tuning for the tennis task. The resulting policy responds directly to robot and ball observations without requiring reference-motion inputs at deployment. On a real humanoid robot, ATHLETE achieves forehand and backhand hit rates of $90.00\%$ and $86.67\%$, respectively, and enables multi-shot rallies with human players. These results demonstrate that ATHLETE can learn dynamic humanoid tennis skills from reusable locomotion data and video demonstrations. Result videos and code can be found at https://anonymous.4open.science/w/ATHLETE2027/.

We study simultaneous competitive and regret guarantees for TCP acknowledgment. Each acknowledgment serves all pending packets, and the objective is to minimize the total acknowledgment and waiting costs. It is well known that no deterministic online algorithm achieves a competitive ratio better than $2$. Given $k$ randomized online experts and $0<\varepsilon<1$, we construct a randomized online algorithm whose realized total cost is always at most $(2+\varepsilon)$ times the offline optimal cost $\mathrm{OPT}$ and whose expected regret against the expert with the smallest realized cost is $O(\sqrt{\mathrm{OPT}\log(k+1)}+\log(1/\varepsilon))$. The algorithm requires no advance knowledge of the number of packets or $\mathrm{OPT}$. Our algorithm controls switching costs between experts and uses the gap between the permitted competitive bound and its current cost to determine when to learn. We also prove lower bounds showing that, for $k\ge 2$, this regret bound is asymptotically optimal in $\mathrm{OPT}$, $k$, and $\varepsilon$, and that $\varepsilon>0$ is necessary for sublinear regret.

Reasoning models can benefit from test-time scaling, but continued reasoning may become ineffective or harmful, a phenomenon termed overthinking. Evaluations against full thinking compare accuracy and token usage but lack references for overthinking severity and strategies' theoretical mitigation potential. To characterize overthinking at the model-task level, we first introduce Step-wise Truncation Probing (STP), repeatedly generating answers from multiple retained prefixes along each fixed sampled reasoning trajectory. Using each trajectory's earliest measured position attaining maximum empirical accuracy as a reference, we define Overthinking Ratio and Accuracy Degradation as the fraction of thinking tokens generated afterward and the accuracy decrease from this reference to full thinking, respectively. Secondly, we then formulate dynamic routing, fixed budgets, and dynamic early exit within a unified framework to quantify the theoretical mitigation potential of different termination strategies. Based on this unified framework, we use the complete STP measurements to construct a token-accuracy Pareto frontier for each strategy under a common normalized thinking-token budget. We further develop OTBench, a reusable benchmark built from the STP process, which produced 70.5B reasoning tokens and the corresponding probing measurements across six models and four benchmark groups.

We study concurrent stochastic games in which a team of agents plays against an adversarial environment. If the agents could access a shared source of randomness, then these games reduce to two-player games. Despite being common in the literature on coalition games, this assumption does not accurately model real-world systems. In this paper, we consider the setting where the agents only have access to individual sources of randomness, and must satisfy a given reachability or safety objective. The limit-sure problem asks whether the team can ensure that the objective is satisfied with probability at least $1-\lambda$ for every $\lambda>0$. For reachability objectives, we show that this problem is $\mathsf{NP}$-complete. For safety objectives, we show that limit-sure winning coincides with almost-sure winning, which is known to lie in $\mathsf{P}$. As a corollary of these results, we conclude that model checking of the qualitative fragment of the logic Individually Randomised ATL – introduced in the recent work of Brice et al. – is $\mathsf{P}^{\mathsf{NP}}$-complete.

We present Rationally Linearized Multilayer Perceptrons(RaLiMPs), a new approach to efficiently linearizing MLPs using low-degree rational approximations of standard activation functions. Inspired by polynomial-based MLP linearization, we show that rational approximations can provide accurate representations at substantially lower degree. RaLiMPs exploit these approximations to construct kernel representations with narrow bottlenecks, enabling efficient composition across MLP layers. We provide theoretical guarantees for the resulting approximation and evaluate RaLiMPs across applications ranging from implicit 3D models to large language models. Our experiments demonstrate favorable accuracy–efficiency tradeoffs, with RaLiMPs achieving competitive or improved accuracy while substantially reducing inference cost.

Targeted vaccination often prioritizes individuals who contribute most to transmission. However, this rationale may change under leaky protection, whereby vaccination reduces susceptibility at each exposure rather than fully preventing infection. Here, we use a survey-derived individual-level exposure framework for 2,279 residents to simulate infection dynamics across ranges of transmission intensity and vaccine efficacy. We compare two vaccination strategies: the high-exposure strategy (prioritizing highly exposed individuals) and the oldest-first strategy (prioritizing older individuals). As transmission intensity changes, we identify three patterns in the relative advantages of these two strategies. At low transmission, the high-exposure strategy outperforms the oldest-first strategy in reducing both epidemic peak size and final infection proportion. At intermediate transmission, it lowers epidemic peak size but increases final infection proportion, revealing a trade-off between these metrics. At high transmission, differences between the strategies narrow, and the oldest-first strategy has a slight advantage for both metrics. Overall, our findings highlight the importance of considering vaccine failure mode when evaluating vaccination policies under different transmission dynamics.

The $SU(2)$ Skyrme model admits exact solutions when coupled to General Relativity in four spacetime dimensions. Here, we demonstrate that relevant gravitational configurations, such as black holes, wormholes, and cosmologies, are robust under the extension to $SU(N)$ with an arbitrary number of flavors. We show that key physical features, such as the thermodynamic properties, the baryon number of the configurations, and the geometry, are crucially determined by the number of flavors as well as the coupling constants of the theory. In particular: first, we prove that an increase in the matter content favors the local thermal stability of spherically symmetric black holes. Second, for cosmological solutions, we demonstrate analytically that as the hadronic matter content increases, the scale factor grows more slowly due to enhanced gravitational attraction, while the expansion rate (measured by the Hubble parameter) increases as a consequence of the higher energy density. Third, we find that the throat of traversable wormhole solutions can be enlarged by increasing the number of flavors, since the energy density required to keep the throat open does not grow indefinitely but rather saturates at a finite value.

We place the Appell shift theorem for asymptotic expansions inside a Borel–Laplace framework and apply it to two classical functions of analytic number theory: the Hurwitz zeta function \(\zeta(m,q)\) and the Lerch transcendent \(\Phi(z,m,a)\). The resulting shifted expansions have coefficients given by Appell polynomials evaluated at the shift, with remainders controlled uniformly on compact sets. The generating sequences are identified explicitly in terms of the Taylor coefficients of the Borel kernels. In a second direction, we extend the Appell–Mellin framework of Navas, Ruiz and Varona to Dirichlet \(L\)-functions. For a primitive non-principal character \(\chi\) modulo \(q\), we construct an explicit Appell–Mellin generating function \(A_\chi(t)\) whose associated Appell sequence satisfies \(R_n^\chi(x) = L(-n,\chi,x)\), and we prove the functional equation \(A_\chi(t) = \chi(-1)A_\chi(-t)\). We further establish five structural properties of the polynomials \(R_n^\chi\): identification with generalized Bernoulli polynomials, a difference equation, an explicit formula, a Fourier expansion, and the trivial zeros of \(L(s,\chi)\). To the best of our knowledge, these results do not appear in the literature.

This paper investigates the physical characteristics of the liquid Trimethyl-Bismuth (TMBi) relevant for charge readout in potential TMBi filled detectors for Positron-Emission-Tomography (PET) instruments. The high photo-efficiency and the possibility of fast timing by detection of Cherenkov light created in the liquid are both favorable for use of TMBi in a PET system. However, to obtain a high position and energy resolution also a readout of the charge signal created due to the absorption of a 511 keV photon is required. For this purpose the liquid has to be clean of electro-negative and ionic impurities. A distillation technique was developed within this study as one of the possible methods to remove such impurities and a measurement on the efficiency of this cleaning method is provided. The relevant quantities for an efficient charge readout are the free ion yield and the electron mobility of the liquid. We report on a new measurement of the zero-field free ion yield in TMBi and, using that result, produce an estimate of the electron mobility. The rather low zero-field free ion yield and its much lower expected electron mobility compared to tetramethyl-n compounds like TMSi question the use of the trimethyl molecule TMBi for a PET detector liquid. But we are also giving arguments that the tetramethyl molecule TMPb could be an interesting alternative.

Repository-level issue-resolution benchmarks such as SWE-bench evaluate submitted patches primarily based on whether they pass the correctness tests, leaving the runtime performance of different test-passing patches largely unexplored. Evaluating patch performance is essential but challenging since designing performance workloads for each benchmark instance is costly. However, these benchmarks already provide a natural candidate: the built-in FAIL\_TO\_PASS (F2P) tests, which exercise the behavior affected by the issue fix. We therefore investigate whether the provided F2P tests can be repurposed to evaluate patch performance. Overall, we choose four frontier models, Claude Opus~5, GPT~5.6, DeepSeek V4 Pro, and Qwen~3.8 Max, paired with SWE-agent to resolve the pre-filtered measurable corpus from verified splits of SWE-bench and SWE-bench-Live, yielding 262 cases with at least two different correct solutions, including the developer ground-truth patch. We then measure each solution's runtime performance in instruction count and wall-clock time on the native F2P test, and use Welch ANOVA instead of the RSD proposed in prior work as a more robust statistical discrimination criterion. We find that this methodology exhibits notable discrimination capability in runtime performance and identifies performance differences among patches in almost half of the instances. Our empirical study shows that the runtime performance of generated patches is independent of the issue resolution rate of LLMs, with nearly reversed model rankings. The case study also shows that the performance analysis reveals architectural regression in some patches that the correctness evaluation overlooked. These findings suggest that resolution rate does not adequately characterize LLMs' capability for repository-level issue resolution, motivating future evaluations to consider patch performance alongside it.