Mutual information (MI) quantifies statistical dependence between variables and is widely used across scientific disciplines, yet accurate estimation from finite data remains notoriously difficult. Common approaches fail in high-dimensional, undersampled regimes ($N \lesssim K$) typical of modern experiments, and no accepted tests exist to detect when neural network-based estimators fail, making them effectively unusable as scientific instruments. We show that neural MI estimators can be made reliable when the statistical dependencies admit a low-dimensional latent representation. Sample complexity is then governed by the latent dimensionality $K_Z \ll K$ rather than the ambient dimension -- a regime shift we confirm empirically and ground theoretically via random matrix theory. Building on this insight, we develop a practical protocol that provides neural estimators with explicit statistical consistency checks, bias correction, and confidence intervals. We additionally introduce a new class of probabilistic critics (the VSIB family) that substantially reduce bias and variance at higher MI values where standard estimators break down. We validate the protocol on synthetic benchmarks ($K=500$, $N$ as low as $256$), on the standard 40-dataset benchmark suite of Czyz et al. (2023), on noisy MNIST ($K=784$), and on CIFAR-10/100 ($K=3072$) with a ResNet-20 backbone. Our protocol consistently matches or exceeds existing methods while being the only approach to report confidence intervals and flag unreliable estimates, achieving reliable MI detection well below the ambient pixel dimension on real images.

The existence of small-time asymptotics for the heat kernel of the Kohn Laplacian on a general CR manifold has remained an open problem. In this paper, we resolve the problem in the non-degenerate case. More precisely, let $X$ be a compact oriented CR manifold of dimension $2n+1$, $n \ge 1$, with a nondegenerate Levi form of constant signature $(n_-, n_+)$. Suppose that condition $Y(q)$ holds at each point of $X$, we establish the small-time asymptotics of the heat kernel of Kohn Laplacian. Suppose that condition $Y(q)$ fails, we establish the small-time asymptotics of the kernel of the difference of the heat operator and Szegő projector. As an application we define the analytic torsion on compact oriented nondegenerate CR manifolds and study its dependence on changes of the metrics. Let $L^k$ be the $k$-th power of a CR complex line bundle $L$ over $X$. We establish the asymptotics, as $k \to \infty$, of the analytic torsion with values in $L^k$, under a variant of spectral gap condition. Furthermore, when $X$ admits a transversal CR $S^1$-action, we establish the small-time asymptotics of the $S^1$-equivariant heat kernel of the Kohn Laplacian with values in $L^k$. As an application we define the $S^1$-equivariant Quillen metric with values in $L^k$ and study its dependence on changes of the metrics. Finally, we establish the asymptotics, as $k \to \infty$, of the $S^1$-equivariant analytic torsion with values in $L^k$.

We use logistic regression to estimate the value of the pieces in standard chess and several chess variants, namely Chess 960, Atomic chess, Antichess, and Horde chess. We perform our regressions on several years of data from Lichess, the free and open-source internet chess server. We use the published player ratings to control for the confounding effect of differential player skill. We adjust for the attenuation bias in regressions due to the noise in observed ratings. We find that major piece values, relative to the value of a pawn, are fairly consistent with historical valuation systems. However we find slightly higher value to bishops than knights. We find that piece values are smaller, in absolute value, in Atomic and Antichess than standard chess. We also present approximate values of the pieces to equalize odds when players of varying skill face off. We briefly consider self-play experiments using the Stockfish engine, which give a contrasting view of piece value.

We propose an efficient reconstruction algorithm named the frozen Gaussian grid-point correction (FGGC) for computing the Schrödinger equation in the semi-classical regime using the frozen Gaussian approximation (FGA). The FGA has demonstrated its superior efficiency in dealing with semi-classical problems and high-frequency wave propagations. However, reconstructing the wave function from a large number of Gaussian wave-packets is typically computationally intensive. This difficulty arises because these wave-packets propagate along the FGA trajectories to non-grid positions, making the application of the fast Fourier transform infeasible. In this work, we introduce the concept of ``on-grid correction'' and derive the formulas for the least squares approximation of Gaussian wave-packets, and also provide a detailed process of the FGGC algorithm. Furthermore, we rigorously prove that the error introduced by the least squares approximation on each Gaussian wave-packet is independent of the semi-classical parameter $\varepsilon$. Numerical experiments show that the FGGC algorithm can significantly improve reconstruction efficiency while introducing only negligible error, making it a powerful tool for solving the semi-classical Schrödinger equation, especially in applications requiring both accuracy and efficiency.

Stochastic unraveling schemes are powerful computational tools for simulating Lindblad equations, offering significant reductions in memory requirements. However, this advantage is accompanied by increased stochastic uncertainty, and the question of optimal unraveling remains open. In this work, we investigate unraveling schemes driven by Brownian motion or Poisson processes and present a comprehensive parametric characterization of these approaches. For the case of a single Lindblad operator and one noise term, this parametric family provides a complete description for unraveling scheme with pathwise norm-preservation. We further analytically derive dynamically optimal quantum state diffusion (DO-QSD) and dynamically optimal quantum jump process (DO-QJP) that minimize the growth rate of the variance of an observable locally in time. Compared to jump process ansatz, DO-QSD offers two notable advantages: firstly, the variance for DO-QSD can be rigorously shown not to exceed that of any jump-process ansatz locally in time; secondly, it has very simple expressions. Numerical results demonstrate that the proposed DO-QSD scheme may achieve substantial reductions in the variance of observables and the resulting simulation error.

Inspired by Terao's freeness conjecture, we examine Ziegler pairs, which are pairs of hyperplane arrangements that share the same underlying matroid but have different modules of logarithmic derivations. In this paper, we present a general construction that yields the first known families of Ziegler pairs in arbitrary dimension and size, starting from examples in the complex projective plane.

Network interference occurs when the treatment status of one unit affects the potential outcomes of other units, giving rise to spillover effects that are difficult to test for. We propose treating the network as a random variable rather than a fixed quantity to address this challenge. This overcomes a key challenge of non-imputability of potential outcomes under the null and avoids the computational intractability of existing conditional randomization tests. Our quasi-randomization test builds the null distribution of no spillover effects using random graph null models, is exactly valid in finite samples under mild assumptions on the network-generating process, and offers substantially improved power over existing methods, particularly in cluster-randomized trials. We validate our approach via simulation and illustrate it by testing for interference in a weather insurance adoption experiment in rural China.

K2-18b, a sub-Neptune orbiting in the habitable zone of an M dwarf, has attracted significant interest following observations with the Hubble Space Telescope (HST) and, more recently, with the James Webb Space Telescope (JWST), which reveal detectable atmospheric features across the near- and mid-infrared. Using free-chemistry Bayesian retrievals, we investigate whether hydrocarbon hazes can explain the apparent mismatch of spectral feature amplitudes between the JWST NIRISS/NIRSpec and MIRI LRS datasets. We additionally assess the impact of stellar parameter uncertainties on the derived bulk properties of the planet and explore how planetary mass uncertainties affect atmospheric retrievals. We find that hazy scenarios can reproduce the combined JWST spectrum and provide a consistent explanation for the reduced NIRISS/NIRSpec feature amplitudes relative to the stronger MIRI features. Across all retrievals, the atmosphere remains consistent with an H$_2$-dominated sub-Neptune, with CH$_4$ and CO$_2$ as the dominant absorbers. Our hazy models retrieve systematically lower molecular abundances compared to haze-free models, reflecting the degeneracy between haze opacity and mean molecular weight. In addition, we identify strong degeneracies between planetary mass, temperature, and mean molecular weight. The retrieved planetary mass is particularly poorly constrained, with $2σ$ uncertainties reaching up to $\sim71\%$. We demonstrate that different mass assumptions can significantly bias the inferred atmospheric properties, with higher masses favouring warmer and lower mean molecular weight atmospheres. Breaking these degeneracies will require improved stellar characterisation to obtain more precise mass measurements. More laboratory-focused studies and future JWST observations are essential for interpreting these temperate sub-Neptune atmospheres.

We propose an approach to Carrollian geometry using principal $\mathbb{R}^\times$-bundles ($\mathbb{R}^\times := \matthbb{R} \setminus \{0\}$) equipped with a degenerate metric whose kernel is the module of vertical vector fields. The constructions allow for non-trivial bundles, and a large class of Carrollian manifolds can be analysed in this formalism. A key result in this is that once a principal connection has been selected, there is a canonical non-degenerate metric that can be leveraged to circumvent the difficulties associated with a degenerate metric. Within this framework, we examine the Levi-Civita connection and null geodesics.

AI's transformative impact on work, education, and everyday life makes it as much a political artifact as a technological one. Current AI models are opaque, centralized, and overly generic. The algorithmic automation they provide threatens human agency and democratic values in both workplaces and daily life. To confront such challenges, we turn to Scandinavian Participatory Design (PD), which was devised in the 1970s to face a similar threat from mechanical automation. In the PD tradition, technology is seen not just as an artifact, but as a locus of democracy. Drawing from this tradition, we propose Participatory AI as a PD approach to human-centered AI that applies five PD principles to four design challenges for algorithmic automation. We use concrete case studies to illustrate how to treat AI models less as proprietary products and more as shared socio-technical systems that enhance rather than diminish human agency, human dignity, and human values.

We present a theoretical study of the magnetic field generated by a toroidal current loop situated in the equatorial plane of a non-rotating Schwarzschild black hole, based on the dynamics of charged particles. Using the exact general relativistic solution for the magnetic field, we analyze particle motion both analytically and numerically, identifying regions of stable and unstable orbits. In particular, we classify charged particle dynamics into attractive and repulsive Lorentz force configurations and show that in the attractive case, charged particles can accumulate near the current loop, forming collective currents that oppose the original current loop magnetic field. We demonstrate that charged particle accumulation can lead to the formation of toroidal structures analogous to radiation belts in the BH magnetosphere. We compare the curved spacetime solution to flat spacetime analogs and highlight general relativistic effects such as the existence of the innermost stable circular orbit for charged particles, which sets a lower bound for radiation belt formation. The divergence of the vector potential at the loop location in the idealized infinitesimal loop model is addressed, and we argue that a physically realistic model must consider a finite-width current distribution to avoid unphysical divergences in the effective potential.

This article considers the problem of testing conditional independence between two random vectors \(bm X\) and \(\bm Y\) given a confounding random vector \(\bm Z\). An exchangeable-pairs framework is introduced through which the conditional independence testing problem is reformulated as a two-sample testing problem. The framework is motivated by ideas from the model-X literature and is based on a fundamental exchangeability property that holds under the null hypothesis of conditional independence. An energy-distance/maximum mean discrepancy type measure is employed on the resulting exchangeable pairs to quantify departures from conditional independence. A consistent estimator of the proposed discrepancy measure is constructed and its theoretical properties are established under general assumptions. A conditional independence test is then developed using this estimator as a test statistic and is calibrated through a suitable resampling procedure. It is shown that the proposed test is consistent against fixed alternatives, possesses nontrivial asymptotic power against local contiguous alternatives, attains the minimax separation rate for detecting alternatives characterized by the proposed discrepancy measure, and remains consistent when the data dimension diverges with the sample size. The effect of estimating the conditional distribution used to generate the exchangeable pairs is also investigated, and condition under which validity and power properties are preserved is established. Extensive simulation studies demonstrate that the proposed procedure performs competitively with some state-of-the-art methods.

Robertson and Seymour proved that for every finite tree $H$, there exists $k$ such that every finite graph $G$ with no $H$ minor has path-width at most $k$; and conversely, for every integer $k$, there is a finite tree $H$ such that every finite graph $G$ with an $H$ minor has path-width more than $k$. If we (twice) replace ``path-width'' by ``line-width'', the same is true for infinite graphs $G$. We prove a ``coarse graph theory'' analogue, as follows. For every finite tree $H$ and every $c$, there exist $k,L,C$ such that every graph that does not contain $H$ as a $c$-fat minor admits an $(L,C)$-quasi-isonetry to a graph with line-width at most $k$; and conversely, for all $k,L,C$ there exist $c$ and a finite tree $H$ such that every graph that contains $H$ as a $c$-fat minor admits no $(L,C)$-quasi-isometry to a graph with line-width at most $k$.

We study single-shot distinguishability of locally implementable multipartite unitaries under Local Operations and Classical Communication (LOCC) and global operations. As unitary discrimination depends on both the choice of probing states and the measurements on the evolved states, we classify LOCC and global distinguishability into two categories: adaptive strategies, where probing states are chosen based on measurement outcomes from other subsystems, and restricted strategies, where probing states remain fixed. Our findings uncover three surprising features in the bipartite setting and establish new structural limits for unitary discrimination: (i) Certain pairs of unitaries are globally distinguishable with restricted strategies but indistinguishable under LOCC, even with adaptive strategies. (ii) There exist sets of four unitaries that are distinguishable via LOCC, yet remain globally indistinguishable with restricted strategies. (iii) Some sets of unitaries are globally indistinguishable under adaptive strategies, when probed with separable states, but become distinguishable via LOCC.

Most blockchains cannot hide the binary code of programs (i.e., smart contracts) running on them. To conceal proprietary business logic and to potentially deter attacks, many smart contracts are closed-source and in many cases exhibit code obfuscation, either intentionally introduced to hide internal logic or unintentionally produced by optimizations. However, we demonstrate that such obfuscation can obscure critical vulnerabilities rather than enhance security, a phenomenon known as insecurity through obscurity. To systematically analyze these risks on a large scale, we present SKANF, a novel EVM bytecode analysis tool tailored for closed-source and obfuscated contracts. SKANF combines control-flow deobfuscation, symbolic execution based on historical transactions to identify and exploit asset management vulnerabilities. Our evaluation on real-world Maximal Extractable Value (MEV) bots reveals that SKANF detects vulnerabilities in 1,030 contracts and successfully generates exploits for 394 of them, with potential losses of \$10.6M. Additionally, we uncover 104 real-world MEV bot attacks that collectively resulted in \$2.76M in losses.

The transition to a modern and efficient future grid relies on the seamless coordination of distributed energy resources and applications such as Demand Response (DR). While this transformation enables greater flexibility, it increases grid complexity and decentralization, requiring the effective coordination of millions of hardware assets and software agents. Realizing this vision demands advances in interoperability to ensure these heterogeneous systems can communicate without prohibitive customization costs. Semantic interoperability aims to address this by leveraging ontologies to guarantee the unambiguous interpretation of exchanged data. However, current ontologies in the commercial building and DR domains face two critical limitations. First, existing ontologies are often developed without a formal framework that reflects real-world DR requirements. Second, proposals for integrating general and DR-specific ontologies remain mostly conceptual, lacking formalization or empirical validation. In this paper, we begin to address these gaps by applying a formal ontology evaluation/development approach to define the information requirements (IRs) necessary for semantic interoperability, focusing on incentive-based DR programs for commercial buildings in the United States as a starting point. We identify the IRs associated with each stage of the incentive-based DR. Using these IRs, we evaluate how well existing ontologies, specifically Brick, DELTA, EFOnt, and CIM support the operational needs of DR participation. Our findings reveal substantial gaps between current ontologies and practical DR requirements and we propose a roadmap of necessary extensions and integrations for these ontologies. This work ultimately aims to enhance the interoperability of today's and future smart grid, thereby facilitating scalable integration of DR systems into the grid's complex operational framework.

A long-standing conjecture of Caro (Discrete Math, 1994), confirmed by Ferber and Krivelevich (Adv Math, 2022), states that every $n$-vertex graph $G$ without isolated vertices contains an induced subgraph of order linear in $n$ in which every vertex has odd degree. We generalize this result to graphs $G$ whose vertices are labeled by $\ell: V(G)\to \{0,1\}$. We require, in an induced subgraph, all $0$-labeled vertices to have even degree and all $1$-labeled vertices to have odd degree. Let $h_{\ell}(G)$ denote the maximum order of such a subgraph. Let $f_{oe}(G)=\min_{\ell} h_{\ell}(G)$ be the worst-labeling parameter. We establish a pointwise lower bound for $h_{\ell}(G)$ that immediately yields a linear lower bound in $|V(G)|$ for $f_{oe}(G)$, where $G$ has no isolated vertices. For an $n$-vertex connected graph, we obtain a sharp lower bound for $f_{oe}(G)$: $f_{oe}(G)\ge \lceil (n-1)/χ_{mm}{(G)} \rceil ,$ where $χ_{mm}{(G)}$ is the maximum chromatic number of a minor of $G.$ Using proved cases of Hadwiger's Conjecture, we show that for $t\in \{3,4,5,6\}$, if an $n$-vertex connected graph $G$ is $K_t$-minor-free, then $f_{oe}(G)\ge \lceil (n-1)/(t-1)\rceil$ and this bound is sharp for each $t\in \{3,4,5,6\}$. Finally, we conjecture that $f_{oe}(G)\ge f_o(G)/2$ for all graphs $G$ and confirm the conjecture for all trees and complete multipartite graphs.

This paper studies the relation between agreement and strongly linearizable implementations of various objects. This leads to new results about implementations of concurrent objects from various primitives including window registers, interfering primitives and stacks. We identify that lock-free, respectively, wait-free, strongly linearizable implementations of several concurrent objects entail a form of agreement that does not require full consensus but cannot be implemented in a strongly-linearizable manner with combinations of non-universal primitives. In both cases, lock-free and wait-free, this form of agreement requires a distinguished process to referee a competition that involves all other processes. Our results show that consistent refereeing of such competitions (i.e., once resolved, the outcome cannot be revised in any extension of the execution) requires high coordination power. More specifically, two contest objects are defined and used to help characterize coordination constraints imposed by strong linearizability in lock-free and wait-free implementations, respectively. Both objects are strictly weaker than consensus, in the sense that they have a wait-free linearizable (in fact, decisively linearizable) implementation from reads and writes. The contest objects capture strong linearizability in two complementary ways. First, they admit strongly linearizable implementations from several high-level objects such as queues, snapshots, and counters, so impossibility results for the contest objects immediately carry over to these objects. Second, they admit powerful impossibility results for strong linearizability that involve window registers, interfering primitives and stacks, which are non-universal.

In this paper we investigate a oscillator network based reservoir computer with a large number of oscillators and a low dimensional read-out. The read-out is a function on the average phases with respect to each oscillator population. Hence, this read-out provides a robust measurement of the oscillator states. We consider a low number of populations which leads to a low-dimensional read-out. Here, the task is time-series prediction. The input time-series is introduced via a forcing term. After a training phase the input is learned. Importantly, the training weights are introduced in the forcing term meaning that the oscillator network is left untouched. Hence, we can apply classical methods for oscillator networks. Here, we consider the continuum limit for Kuramoto oscillators by using the Ott-Antonsen Ansatz. Consequently, a mean field reservoir computer arises. The success and failure of the reservoir computer is then studied by bifurcations in the coupling and forcing parameter space. We will also show that the average phase read-out can naturally arise when considering the read-out on the phase states. Finally, we give numerical evidence that at least 4 oscillator populations are necessary to learn chaotic target dynamics.

With its third data release (DR3), Gaia begins unveiling dormant candidate compact object (CO) binaries with luminous companions (LC) as predicted by several past theoretical studies. To date, 3 black hole (BH), 21 neutron star (NS), and 3200 white dwarf (WD) candidates have been identified with LCs in detached orbits using astrometry. We adopt an observationally motivated sampling scheme for the star formation history of the Milky Way, and initial zero-age main-sequence binary properties, incorporate all relevant binary interaction processes during evolution to obtain a realistic present-day intrinsic population of CO--LC binaries. We apply Gaia's selection criteria to identify the \colc\ binaries detectable using the observational cuts applicable for DR3 as well as its end-of-mission (EOM). We find that under the DR3 selection cuts, our detectable population includes no BH--LCs, approximately 10-40 NS--LCs, and around ~4300 WD--LCs. Our predicted NS--LC population is in good agreement with the current DR3 census, both in its predicted yield and in the orbital and stellar properties, and we recover a close analogue of the Gaia NS1 candidate together with its detailed formation pathway. For WD--LCs, we find that a moderate natal kick of 5-15 km/s imparted at WD formation is required to match the observed orbital properties of WD-LC candidates in DR3. We further show that Gaia BH3-like binaries can form through standard isolated binary evolution without invoking any additional modelling assumptions, whereas reproducing Gaia BH1 and BH2 remains challenging within this framework. Looking ahead to the EOM, we predict detection of ~30-300 BH--LCs, ~1500-5000 NS-LCs, and ~10^5-10^6 WD-LC binaries, primarily due to the significantly longer observational baseline.

We study discrete time-crystalline (DTC) phases in one-dimensional spin-1/2 chains with power-law-graded Ising interactions under periodic Floquet driving. By generalizing Stark localization to power-law-graded Ising interaction profiles, we identify robust period-doubled dynamics across a wide range of interaction exponents, stabilized by the interplay between coherent driving and spatially varying coupling. Within the DTC phase, the energy stored in the system, interpreted as a quantum battery, increases superlinearly with system size, although no scaling advantage persists in normalized power. Beyond energy storage, we demonstrate that the DTC phase supports enhanced quantum sensing. The quantum Fisher information associated with estimating timing deviations in the drive scales superextensively with system size, surpassing the Heisenberg limit. The degree of quantum advantage can be tuned by varying the interaction exponent, though DTC behavior remains robust throughout. Our results position power-law-graded Ising interacting Floquet systems as robust platforms for storing quantum energy and achieving metrological enhancement.

We give an equivalent condition for the validity of the Hasse norm principle for finite separable extensions of prime squared degree of global fields. Our theorem recovers the result of Drakokhrust--Platonov, which claims that the Hasse norm principle holds for adequate extensions of prime squared degree.

TensorKit$.$jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries through the ``TensorMap'' type. We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries, illustrating its practical applications through select case studies.

Parametric instability of Alfvén wave packets with monochromatic carrier wave in low-$β$ plasma is studied using one-dimensional magnetohydrodynamic simulations. The results show spatial growth of incoming perturbations as they propagate through the mother wave. For sufficiently short packets, the perturbations emerge downstream of the packet as small-amplitude reverse Alfvén waves and forward slow magnetosonic waves. For larger packets the perturbations reach non-linear amplitude while still inside the mother wave. In this case, a downstream section of the mother wave collapses but the remaining upstream section stays largely intact and enters the phase of very slow evolution. The length scale separating the linear and non-linear regimes, as well as determining the size of the surviving section in the non-linear regime, is set by the Alfvén crossing time of the packet, the growth rate of the parametric instability for the unmodulated carrier wave, and the amplitude of incoming perturbations. The results are discussed in connection with the physics of solar wind.

Doubly robust estimators for estimating the population mean (or prevalence) of an outcome have been proposed for integrating outcome and covariate data from a nonprobability sample with covariate data from a probability survey. These estimators combine inverse probability weighting estimation with mass imputation. However, the question of how to combine these doubly robust estimators with a Horvitz-Thompson or Hajek estimator that uses only outcome data from the probability survey has received only limited attention. In this paper, we first review previously proposed doubly robust estimators that use outcome data from only the nonprobability sample. We extend these estimators to enable estimation of domain (subpopulation) means (or prevalences), possibly using data from individuals outside the domain to improve estimation when the domain is small. We then consider how to combine this doubly robust estimator with a Horvitz-Thompson or Hajek estimator that uses only the probability survey data. We describe efficient combined estimators, and provide formulae for their repeated-sampling variances and for estimators of these variances. We also investigate the asymptotic relative efficiencies of the combined estimators compared to their two component estimators, and carry out a simulation study to assess their relative efficiencies in finite samples. These relative efficiencies depend on the ratio of the variances of the two component estimators and on how predictive the covariates are of the outcome.

Background: Lithium is of broad interest in nuclear astrophysics, fusion energy research, and nuclear technology. From a theoretical perspective, the nucleus $^7$Li presents a remarkable challenge, as its bound and resonant states can exhibit contributions from both the $^4$He + $^3$H cluster configuration and configurations involving a neutron or proton coupled to a $^6$Li or $^6$He core, respectively. Purpose: We aim to achieve a unified ab initio description of bound-state and continuum properties of $^7$Li by explicitly including simultaneously the coupled mass/charge partitions $^4$He + $^3$H, $^6$Li + $n$, and $^6$He + $p$. Specifically, we investigate the effect of inter-partition coupling on the spectrum of $^7$Li and calculate cross sections for the $^6$Li($n,p)^6$He, $^6$He($p,n)^6$Li, and $^6$He($p,t)^4$He reactions. Method: We employ the no-core shell model with continuum for the first time in a calculation that couples three mass/charge partitions of the aggregate nucleus $^7$Li, using a chiral nucleon-nucleon interaction as input. Results: The calculated spectrum reproduces all the experimentally observed states of $^7$Li in the correct order and predicts additional resonances. The calculation also reproduces the overall energy dependence of the $^6$Li$(n,p)^6$He cross section. Improved agreement with measured cross sections is obtained after phenomenological adjustment of resonance energies. Conclusions: The present results show that coupling the relevant mass/charge partitions is important for a consistent description of the $^7$Li spectrum and reaction cross sections, and offers a useful framework for interpreting existing data and guiding future measurements.

Characteristic function-based goodness-of-fit tests are suggested for multivariate distributions. The test statistics, which are straightforward to compute, are defined as two-sample criteria measuring discrepancy of empirical characteristic functions between multivariate ranks of the original observations and the ranks obtained from an artificial sample generated from the reference distribution under test. Multivariate ranks are constructed using the theory of the optimal measure transport, thus rendering the tests of a simple null hypothesis distribution-free, while bootstrap approximations are still necessary for testing composite null hypotheses. Asymptotic theory is developed and a simulation study, concentrating on comparisons with previously proposed tests of multivariate normality, demonstrates that the method performs well in finite samples. The broad applicability of the proposed methods is illustrated through an application to a real dataset.

We study optimal contracting when workers face career concerns. Labor markets infer ability from performance, but effort affects how informative performance is. This feedback can generate strategic uncertainty: bonuses inducing effort under optimistic beliefs about effort may fail under pessimistic beliefs. We characterize this force through a criterion tied to skill-effort complementarity and solve for the least-cost policy implementing effort in every equilibrium. Under strategic uncertainty, the employer uses dispersed bonuses. High bonuses rule out pessimistic beliefs, raising the reputational stakes and letting lower bonuses motivate effort. Pay dispersion among observationally identical workers grows with career concerns and skill-wage assortativeness.

Axion dark matter induces electromagnetic radiation in conductors through nearly perpetual oscillations of electrons, driven by axion-electron interactions through the so-called chiral magnetic effect. It therefore provides a complementary probe of the axion-electron coupling $g_{ae}$ beyond the conventional axion-photon coupling $g_{a γ}$ in cavities. We show that existing axion cavity experiments can constrain the coupling to $g_{ae}\lesssim 10^{-5}$ over the scanned axion mass ranges, $1\,μ\, {\rm eV}\lesssim m_a\lesssim 20\,μ\,{\rm eV}$. Although we find that the radiation due to $g_{ae}$ at the copper cavity surface of electric conductivity $σ$ is suppressed by $m_a^2/σ^2\sim 10^{-20}$, compared to the radiation inside the cavity by the axion-photon conversion due to $g_{aγ}$, a sensitivity of about $10^{-9}$ could be achieved for $g_{ae}$ over a wider range of $m_a$, including values higher than those previously probed, if copper walls are replaced with carbon-based conductors.

Global control provides a promising route to implementing multi-qubit gates without individual qubit addressing. This is especially appealing for permutation-invariant (PI) gates, whose symmetry is often broken when they are compiled into individually addressed one- and two-qubit gates. Important examples include SWAP, $\sqrt{i\text{SWAP}}$, and the n-qubit controlled-Z gate, which is equivalent, up to two single-qubit Hadamard gates, to the multi-qubit Toffoli gate. Motivated by this global-control perspective, we show that all PI unitaries on an arbitrary number of qubits can be realized using the Tavis-Cummings (TC) interaction, the multi-qubit version of the Jaynes-Cummings interaction, together with global uniform z and x fields. Here, the $n$ qubits are identically coupled to a single bosonic mode (oscillator), which is initialized in and returned to its vacuum state. A corollary is that all PI states, including GHZ and Dicke states, can be prepared using the same global control. For the case n=2 qubits, which is particularly important in quantum computing, we also find explicit pulse sequences for implementing all PI qubit unitaries that conserve angular momentum in the z direction, using only the TC interaction and global z fields. This includes controlled-Z, SWAP, and $\sqrt{i\text{SWAP}}$.