Metalenses have emerged as a powerful platform for compact wavefront engineering; however, their performance stability under refractive index fluctuations induced by environmental perturbations, such as temperature shifts, remains a critical concern. Here, we demonstrate the intrinsic refractive index robustness of dielectric metalenses and elucidate its physical origin. By parametrically sweeping the refractive index, we observe that the metalens maintains a stable focal profile with negligible deviations in best-focus position and spot size over a broad range of variations. We identify that this robustness arises from the structural invariance of the zone boundaries: despite index-induced local phase deformations, the spatial locations of the 2π phase-reset boundaries remain stationary, thereby maintaining the effective wavefront gradient. Furthermore, we reveal that this robustness enables a "quasi-scale-invariant" focusing behavior, where the focusing performance follows a predictable linear trend under uniform geometric scaling even in the presence of material dispersion. Our findings suggest that metalenses can maintain stable focusing behavior against refractive index variations that may arise from unavoidable environmental perturbations in practical optical systems.

Recently, the ACS team applied an Ubercal framework to assess the photometric repeatability of stars observed across the WFC detector using 15 years of post-SM4 calibration data in the globular cluster 47 Tuc (Ryan et al., 2024). A surprising finding was an apparent 0.05 mag global difference in sensitivity between the WFC1 and WFC2 chips, which had not been seen in prior tests of sensitivity variations around the field-of-view. Given the many degenerate variables within the Ubercal framework such as CTE losses, time-dependent sensitivity, and flat-field corrections, we obtained new calibration data to perform a straightforward test of the reported $\sim$5$\%$ flux offset between detectors. We observed three white dwarf standards with three filters at four positions on the detector (each on a different amplifier), but with the same number of x and y pixel transfers to mitigate differential CTE-related effects. For the F606W and F814W filters, the agreements are good to 0.4$\%$ on average, and always 1$\%$ or better in individual cases. The consistency of these two filters over all three stars and the four dither positions provides very strong evidence against the large global sensitivity offset between WFC1 and WFC2 as seen in the Ubercal work. Larger variations seen in the bluer F435W filter are likely a result of a sensitivity of the flat field in that filter to underlying spectral type, warranting a future solution.

Assembling genomes from short-read sequencing data remains difficult in repetitive regions, where reference bias and combinatorial complexity limit existing methods. Pangenome-guided sequence assembly (PGSA) mitigates reference bias by reconstructing an individual genome as a walk through a population-level graph. The associated problem, identifying a walk whose node visits match read-derived copy numbers, is NP-hard and already challenges classical solvers at a moderate scale. We develop near-term quantum optimisation approaches for this computational bottleneck. We consider two problem encodings: an established quadratic unconstrained binary optimisation and a new higher-order binary optimisation (HUBO) formulation. The latter reduces the number of variables from $O(N^2)$ to $O(N\log N)$ and places moderate-sized instances within the qubit budget of current devices. We solve both using the Iterative-QAOA framework, which combines a fixed linear-ramp QAOA schedule with iterative warm-start bias updates, avoiding the overhead of full variational parameter optimisation. A custom circuit compilation strategy reduces hardware gate overhead by up to 67\% compared with standard tools. In noiseless simulations of QUBO problems, Iterative-QAOA reliably identifies optimal assemblies from as few as $10^{-17}\%$ of all candidate solutions, and \textit{IBM} quantum hardware closely reproduces relevant results with sufficient sampling via CVaR-style post-selection. For HUBO, the variable reduction comes at the cost of deeper compiled circuits and greater noise sensitivity: an expected qubit--depth trade-off. Our findings establish pangenome assembly as a concrete, biologically motivated problem class at the scale where quantum optimisation may first provide practical value.

A central challenge in mechanism design is to identify mechanisms whose performance is robust under uncertainty about the environment. The maxmin optimality criterion is commonly used for this purpose, but it often yields a large and economically uninformative set of mechanisms. This paper proposes a lexicographic approach to refining the maxmin criterion and characterizes the efficiency of optimal mechanisms. In canonical screening and auction environments, the strongest refinement $\unicode{x2013}$ proper robustness $\unicode{x2013}$ selects ex post efficient mechanisms. By contrast, in a public good provision environment, it identifies the precise form of optimal inefficiencies, which become severe in large economies.

Wearable augmented reality (AR) represents the next interface to all things computing, extending what smartphones and laptops can do. This involves providing access to digital information during activities like walking or jogging. In this work we argue that the impact of physical movement on AR interaction is not direct, but mediated by UI placement - the spatial relationship between the user and the interface. Current research often treats interaction techniques in isolation, overlooking how their performance is fundamentally linked to where the UI is placed. This position paper highlights the need to reconceptualize UI placement beyond traditional anchoring views, explore novel interaction techniques designed for specific UI placements during locomotion, and rigorously evaluate UI placement as an independent variable in experimental studies. By centering the analysis on the relative movement between user and interface, we can unlock more effective on-the-go AR interaction.

In the light of the growing connectivity and sensitivity of industrial data, cyberattacks and data breaches are becoming more common in the Industrial Internet of Things (IIoT). To cope with such threats, this study presents an anomaly detection system based on a novel Federated Learning (FL) framework. This system detects anomalies such as cyberattacks and protects industrial data privacy by processing data locally and training anomaly detection models on industrial agents without sharing raw data. The proposed FL framework incorporates two key components to enhance both privacy and efficiency. The first component is Homomorphic Encryption (HE), which is integrated into the framework to further protect sensitive data transmissions such as model parameters. HE enhances privacy in FL by preventing adversaries from inferring private industrial data through attacks, such as model inversion attacks. The second component is an innovative dynamic agent selection scheme, wherein a selection threshold is calculated based on agent delays and data size. The purpose of this new scheme is to mitigate the straggler effect and the communication bottleneck that occur in traditional FL architectures, such as synchronous and asynchronous architectures. It ensures that agents are not unfairly selected by the different delays resulting from heterogeneous data in IIoT environments, while simultaneously improving model performance and convergence speed. The proposed framework exhibits superior performance over baseline approaches in terms of accuracy, precision, F1-scores, communication costs, convergence speeds, and fairness rate.

A first-of-its-kind experiment was conducted in the DIII-D tokamak under WEST similarity constraints on plasma shape and core parameters. This work presents a detailed transport study comparing a reference regime dominated by intrinsic carbon radiation and a high-radiation regime resulting from controlled tungsten (W) injection using the Laser Blow-Off system, with a core tungsten concentration $n_{\mathrm{W}}/n_e \sim 3\times 10^{-4}$ and a radiated-power fraction $f_\mathrm{rad}>0.5$. The W-induced radiative cooling lowered the electron temperature, thereby decreasing $T_e/T_i$ and stabilizing trapped-electron-mode (TEM) turbulence. This transition in turbulence regime reduced momentum and ion thermal diffusivities, yielding ion temperature peaking and a factor-of-two increase in toroidal rotation. At the outer plasma region, enhanced $E\timesB$ shear and increased collisionality further suppressed ion-scale turbulence, causing a sharp drop in ion heat flux. Consequently, impurity transport, predominantly turbulent in the low-radiation regime, acquired a strong neoclassical inward W convection during radiative cooling, bootstrapping the cooling cycle. Despite $f_\mathrm{rad}>0.5$, radiative collapse was not observed, likely owing to collisional ion-to-electron energy exchange acting as an electron-energy reservoir, together with $1/1$ MHD activity modulating the radiated power through core impurity neoclassical $T_i$-screening. These results support preparation for a tungsten wall change in DIII-D by elucidating tungsten-induced turbulence stabilization. They also provide key insights for interpreting plasma performance in WEST and are relevant to future reactors expected to operate with radiating tungsten-walled plasmas.

The value of proof-of-work cryptocurrencies critically depends on miners having incentives to follow the protocol. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is well known not to constitute an equilibrium: Eyal and Sirer (2018) construct a profitable deviation called ``selfish mining'' which relies on strategically delaying disclosure of newly mined blocks rather than publishing them immediately. We propose inertial mining, a novel mining protocol. When miners follow inertial mining, they produce the outcome intended by Nakamoto, i.e., a single longest chain. But unlike the Bitcoin mining protocol, inertial mining constitutes an equilibrium (assuming no miner controls more than half of the mining power). Indeed, neither selfish mining nor any other deviation is profitable. Furthermore, inertial mining only changes miners' behavior in the event of off-path forks, and can be implemented in Bitcoin without any changes to its consensus mechanism or blockchain architecture.

This paper investigates the leader-following consensus problem for a class of multi-agent systems subject to adversarial attack-like external inputs. To address this, we formulate the robust leader-following control problem as a global coalitional min-max zero-sum game using differential game theory. Specifically, the agents' control inputs form a coalition to minimize a global cost function, while the attacks form an opposing coalition to maximize it. Notably, when these external adversarial attacks manifest as disturbances, the designed game-theoretic control policy systematically yields a robust $H_\infty$ control law. Addressing this problem inherently requires solving a high-dimensional generalized algebraic Riccati equation (GARE), which poses significant challenges for distributed computation and controller implementation. To overcome these challenges, we propose a two-fold approach. First, a decentralized computational strategy is devised to decompose the high-dimensional GARE into multiple uniform, lower-dimensional GAREs. Second, a dynamic average consensus-based decoupling algorithm is developed to resolve the inherent coupling structure of the robust control law, thereby facilitating its distributed implementation. Finally, numerical simulations on the formation control of multi-vehicle systems with feedback-linearized dynamics are conducted to validate the effectiveness of the proposed algorithms.

We study the relation between emergent 1-form symmetries and soft photon theorems in QED. We show that in the relevant massive and massless kinematic regimes, described respectively by HQET and SCET, the soft sector admits electric and magnetic 1-form symmetries. We then show that these symmetries give rise to an infinite-dimensional Abelian algebra of ordinary conserved charges, with a central extension. In Minkowski spacetime, suitable choices of hypersurfaces reduce these charges to the familiar asymptotic symmetry charges and imply the leading electric and magnetic soft photon theorems. We further show that the central term in this algebra fixes a contact term appearing in scattering amplitudes involving two soft photons with mixed electric-magnetic polarizations. Finally, we extend the same construction to inclusive observables and apply it to QED photon detectors.

We develop a comprehensive framework for constructing quantum error correcting codes (QECCs) from Abelian lattice gauge theories (LGTs) using quantum reference frames (QRFs) as a unifying formalism. We consider LGTs with arbitrary compact Abelian gauge groups supported on lattices in arbitrary numbers of spatial dimensions, and we work with both pure gauge theories and theories with couplings to bosonic and fermionic matter. The codes that we construct fall into two classes: First, Gauss law codes identify the code subspace with the full gauge-invariant sector of the theory. In models with matter coupled to gauge fields, these codes inherit a natural subsystem structure in which gauge-invariant Wilson loops and dressed matter excitations factorize the code space. Second, vacuum codes restrict the code subspace to the matter vacuum sector within the gauge-invariant subspace, yielding codes where errors correspond to gauge-invariant charge excitations rather than to violations of the Gauss law. Despite their distinct setup, we show that when the gauge group is finite, vacuum codes are unitarily equivalent to pure gauge theory Gauss law codes, and that when the group is continuous, this is only true upon a charge coarse-graining of the vacuum code. In all cases, QRFs provide a systematic apparatus for fully characterizing the codes' algebraic structures and correctable error sets. For clarity, we illustrate our general results in $\mathbb{Z}_2$-gauge theory, as well as in scalar and fermionic QED. These findings offer fundamental insights into the parallelism between quantum error correction and gauge theory and point toward practical advantages for simulating LGTs on noisy quantum devices.

Gyrokinetic simulations are essential for understanding and controlling turbulence in fusion plasmas, yet they are oftentimes implemented in legacy codebases, in many cases CPU-bound. These are both hard to maintain and especially incompatible with optimization and ML workflows. gyaradax is a minimal JAX/CUDA solver for local flux-tube gyrokinetics. We base our implementation on GKW (Peeters et al., 2009), but with added native GPU acceleration and automatic differentiation. We validate gyaradax against analytical cases and empirical benchmarks, achieving formal agreement and statistical parity with GKW alongside a substantial speedup. We deliberately and extensively utilized agentic workflows in this project. A key contribution is showing that coding agents, guided by human expertise, structured prompting, and measurable progress through unit testing enabled extremely fast translation of complex Fortran code, and further optimizations. Gyaradax facilitates research at the intersection of ML and plasma physics. We showcase this through practical examples in inverse problems and sensitivity analysis.

It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules associated to a finite Coxeter group are related by the relative full twist. Several cases of this conjecture are known including for symmetric groups, crystallographic Coxeter groups, and dihedral groups. We prove this conjecture in complete generality using the theory of Abe-Bott-Samelson bimodules and the Achar-Riche-Vay mixed derived category.

The nonlinear Hall effect (NHE) is a recently discovered member of the Hall effect family in which the Hall voltage shows a nonlinear behavior when a transverse electric field is applied. While the NHE does not require broken time-reversal symmetry, such as that induced by a magnetic field, it requires broken inversion symmetry, which limits the range of suitable systems and potential applications. Here, we demonstrate an ultrafast NHE in centrosymmetric black phosphorus through dynamical symmetry breaking using femtosecond light pulses. We provide a detailed microscopic picture of excited carrier dynamics and induced fields using momentum-resolved photoemission spectroscopy combined with \textit{ab-initio} calculations. The ultrafast NHE is observed exclusively for the light polarization aligned with the armchair high-symmetry direction and persists over 300 fs, which opens new possibilities for selective and ultrafast light-to-current conversions.

Too light primordial black holes evaporate and are therefore strongly constrained by various bounds, e.g. Cosmic Microwave Background distortion. However, if they are formed strongly clustered, the corresponding haloes may collapse in heavier black holes which may form the entirety of the dark matter of the universe. The indirect signal of such scenario is the production of a flat stochastic background of gravitational waves which is detectable by the Einstein Telescope.

We report predictions for the transverse momentum ($p_T$) spectra of $π^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$ in various collision centrality from Au + Au collisions at beam energies ($E_{lab}$) of 6.7, 8, 11, and 25 A~GeV using a parton-hadron string dynamics (PHSD) transport model. We studied the dependence of particle yields ($dN/dy$), mean transverse momenta ($\langle p_T \rangle$), and particle ratios on collision energy and centrality to understand the underlying mechanisms of particle production. A comparison of the PHSD model results with available experimental measurements provides a qualitative description of these observables. Our results highlight the importance of baryon stopping, strangeness production, pair production, and baryon-antibaryon annihilation in the high baryon density region. These findings also provide theoretical insights relevant to the ongoing beam energy scan program at RHIC and the future heavy-ion programs at FAIR and NICA.

In this work, we study a discrete Schrödinger bridge problem with partial marginal observations. A main difficulty compared to the classical Schrödinger bridge formulation is that our problem is not strictly convex and standard Sinkhorn-type methods cannot be directly applied. To address this issue, we propose a scalable computational method based on an entropic proximal scheme. Furthermore, we develop a framework for this problem that includes duality results, characterization of the optimal solutions, and an observability condition that determines when the optimal solution is unique. We validate the method on the problem of estimating contamination in a water distribution network, where the partial marginals correspond to measured pollutant concentrations at the sensor locations. The experiments were conducted on a laboratory-scale water distribution network.

While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce the first general rigorous Gibbs sampling framework for bosonic many-body systems, showing that physically relevant bosonic models admit gapped dissipative generators, enabling efficient preparation of thermal states. Although our results hold for broad classes of models, we illustrate them using Bose-Hubbard Hamiltonians, both within and beyond the mean-field regime. In both cases, we show that the associated dissipative generators maintain a positive spectral gap, thereby implying exponential convergence to the thermal state. Our argument in the multi-mode case is based on a finite-rank reduction of the dissipative dynamics, which allows us to control the generator via compact perturbations and deduce the discreteness of the spectrum and the stability of the gap. We apply our results to provide efficient preparation of the corresponding Gibbs state on qubit hardware, and by that a quantum algorithm to compute thermal properties of the associated model. This provides the first mathematically controlled route to Gibbs sampling in infinite-dimensional systems, with implications for quantum simulation, thermalization, and many-body complexity, where quantum advantages may arise.

With the advancement of the Materials Genome Initiative, high-throughput computation has become central to accelerating materials discovery. However, conventional first-principles workflows are cumbersome and error-prone. Existing high-throughput tools, while efficient at batch job submission, lack intelligence: they cannot automatically plan tasks based on scientific objectives or dynamically adapt workflows according to intermediate results. To address these limitations, this paper proposes and implements HTC-Claw, an intelligent high-throughput computational platform built upon the OpenClaw framework. The key innovations of HTC-Claw are: 1) An agent-based framework for automatic decomposition of high-level research goals into parallelizable task sets; 2) A closed-loop execution engine that integrates real-time analysis and reporting; 3) Adaptive decision-making and workflow iteration capabilities based on intermediate results; and 4) A decoupled, modular architecture that separates the scheduling system from functional modules, enhancing extensibility and robustness. Case studies demonstrate that HTC-Claw enables an intelligent, end-to-end workflow from user intent to final reporting in materials exploration

Due to rising electricity demand, accurate short-term load forecasting is increasingly important for grid stability and efficient energy management, particularly in resource-constrained edge settings. We present a hardware-efficient Quantum Reservoir Computing (QRC) framework based on a fixed, untrained quantum circuit with Chebyshev feature encoding, brickwork entanglement, and single- and two-qubit Pauli measurements, avoiding quantum backpropagation entirely. Using the Tetouan City Power Consumption dataset, we examine the effect of post-training fixed-point quantization on the classical readout layer, with the reservoir architecture selected through a genetic search over 18 candidate configurations. Under finite-shot evaluation, 8-bit and 6-bit quantization maintain forecasting accuracy within 1% of the FP32 baseline while reducing readout memory by 75% and 81%, respectively. These results suggest that quantized readout can improve the hardware efficiency and deployment practicality of QRC for memory-constrained energy forecasting.

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.

We propose a cooperative sensing framework for mmWave ISAC networks in which a target is sensed by its nearest BS while opportunistically exploiting bistatic echoes from neighboring BSs. Cooperation requires no dedicated resources or exchange of sensing results, and is realized via non-coherent echo-power combining. Using stochastic geometry, we characterize sensing/communication coverage and rates and, for the first time, the cooperative sensing meta-distribution to quantify reliability across targets. Results show substantial sensing gains with limited communication loss and improved high-reliability tail, increasing the fraction of targets meeting stringent reliability guarantees crucial for safety-critical applications.

This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and continuous price movements. To overcome these limitations, we use Monte Carlo simulation alongside the GARCH model, Heston stochastic volatility model, and Merton jump-diffusion model. The Black-Scholes-Monte Carlo method simulates diverse stock price paths using geometric Brownian motion. The GARCH model forecasts time-varying volatility from historical data. The Heston model incorporates stochastic volatility to capture volatility clustering and skew. The Merton jump-diffusion model adds sudden price jumps via a Poisson process. Results show the Heston model consistently produces estimates closer to market prices, while the Merton model performs well for volatile assets with sudden price movements. The GARCH model provides improved volatility forecasts for future option price prediction. All experiments used live market data from November 2024.

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we obtain Wasserstein discretization bounds for Euler-type samplers in dimension $d$: with $N$ discretization steps, the error achieves the optimal rate $\sqrt{d}/N$ up to logarithmic factors. Moreover, the constants do not deteriorate exponentially with the spatial extent of $p^\star$. We also show that the one-sided Lipschitz control yields a globally Lipschitz transport map from the standard Gaussian to $p^\star$, which implies Poincaré and log-Sobolev inequalities for a broad class of probability measures.

In this paper we investigate the long range gravitational effect of curvature-scalar field non-minimal coupling, in the form of $ξR ϕ^2$, in the perturbative quantum gravity framework. Such coupling is most naturally motivated from the renormalisation of a scalar field theory with a quartic self interaction in a curved spacetime background. This coupling results in two scalar-$n$ graviton vertices which contain no explicit momenta of the scalar, qualitatively different from the usual, e.g. $κh^{μν}T_{μν}$-type minimal matter-graviton vertices. Assuming the dimensionless coupling parameter $ξ$ to be small, we compute the 2-2 scattering Feynman amplitudes between such scalars up to ${\cal O}(G^2 ξ)$. From the non-relativistic limit of these amplitudes, we compute the corresponding long range gravitational potential. There exists no tree level contribution $({\cal O}(ξG))$ here, and hence the one loop ${\cal O}(G^2 ξ)$ result is leading. Recently, the effect of a cosmological constant in such non-minimal interaction and the subsequent gravitational potential was computed. In this work we take the cosmological constant to be vanishing. The resulting potential is found to have $r^{-4}$ leading behaviour. We further extend these results for scalar-massive spin-1 and massive spin-1/2 scattering. Spin and polarisation dependence of the two body potential have been explicitly demonstrated. We discuss some possible physical implications of these results.

We consider event-triggered linear-quadratic Gaussian (LQG) control when sensor updates are transmitted over an i.i.d. packet-erasure channel. Although the optimal controller in a standard LQG setup is available in closed form, choosing when to transmit remains computationally and analytically difficult because packet drops randomize packet delivery and couple scheduling decisions with the estimation-error dynamics, making direct dynamic-programming solutions impractical. By certainty equivalence, the co-design problem becomes choosing a binary send/skip sequence that balances control performance and communication cost. We derive a closed-form expansion of the error covariance as precomputable Gramian terms scaled by a survival factor that depends only on the number of transmission attempts on each interval. This converts the problem into an unconstrained binary program that we linearize exactly via running attempt counters and a one-hot encoding, yielding a compact MILP well suited to receding-horizon implementation. On the linearized Boeing-747 benchmark, a model predictive control (MPC) scheduler lowers cost while attempting far fewer transmissions than a one-shot baseline across channel success rates.

We present a spectroscopic follow-up program targeting closely-separated dual quasar candidates selected from imaging of SDSS quasars with the Subaru Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Using two-dimensional image decomposition, our selection identifies PSF-like companions within 0.6-4 arcsec separation (< 30 kpc) around the SDSS quasar. We newly confirm six broad-line dual quasars and eleven offset quasars (quasar-galaxy pairs), spanning 1.5 < z < 3.3 for the duals and predominantly z < 0.6 for the offset systems. No obvious lensed quasars were discovered from this program. We obtained 99 spectra of these candidates from NTT/EFOSC2, Gemini/GMOS-N, Keck/NIRES, and Subaru/FOCAS. From the spectra, we measure the emission-line properties of these dual black holes (BH). At z > 1.5, the confirmed duals exhibit high black hole mass ($M_{\rm BH}$ $=10^{8.5}$-$10^{10} M_{\odot}$) with high bolometric luminosities ($L_{bol}$ $=10^{45.5}$-$10^{47.5}$ erg s$^{-1}$), yet accrete at moderate Eddington ratios ($λ_{\rm Edd}=$0.01-0.4). From the spectroscopically-confirmed samples, we estimate the dual fraction of SDSS quasars with separations of 0.6-4 arcsec to be 0.2%-1.2% at z<0.8, 0.08%-0.24% at 0.8<z<1.5, and 0.06% at 1.5<z<3.3. These values are broadly consistent with other recent optical studies, but lower than theoretical expectations of a rising dual fraction at cosmic noon. However, we note that these fractions, especially at high $z$, still need a more accurate assessment of selection and observation effects.

In this article we study the moduli space of conically singular instantons (or Hermitian Yang--Mills connections) with prescribed tangent connections over a 6-manifold equipped with an $\mathrm{SU}(3)$-structure. That is, we develop a Fredholm deformation theory for such $\mathrm{SU}(3)$-instantons in which we fix the tangent connection but allow the underlying principal bundle (and, in particular, the singular set) to vary. This leads to the existence of a Kuranishi structure for this moduli space. Moreover, we investigate the cokernel of the instanton deformation operator and give under certain assumptions a formula for its dimension. Ultimately, we apply our results to conically singular instantons with structure group $\mathbb{P}\mathrm{U}(n)$ and give a formula for the virtual dimension of their moduli space in terms of sheaf cohomology of certain vector bundles over $\mathbb{P}^2$.

A relative entropy code for a source $X \sim P_X$ is a stochastic code that encodes random samples from a prescribed $P_{Y \mid X}$ using as few bits as possible. A generalisation of entropy coding, it is a standard result that the minimum number of bits required to achieve this is at least the mutual information $I[X\,\Vert\,Y]$. However, a particularly fascinating feature of relative entropy coding compared to entropy coding is that, in general, this lower bound is only achievable to within an additional logarithmic factor. As such, an important research direction is to identify channels where we can reduce this gap. Sriramu and Wagner achieved such success by exhibiting a relative entropy code for so-called singular channels with sub-logarithmic asymptotic redundancy. However, their code is quite involved and, sadly, cannot be implemented in practice. In this paper, we construct the bits-back rejection sampler (BBRS), a relative entropy code that combines ideas from bits-back coding and (greedy) rejection sampling. Our analysis of BBRS reveals that the algorithm achieves the same asymptotic efficiency as Sriramu and Wagner's sampler, but with much simpler analysis and better constants. Moreover, BBRS can be implemented using standard relative entropy coding methods.

QCD at finite isospin density is considered for a large number of colors $N_c$. A linear sigma model is used to model the meson content of the theory at low density. At isospin chemical potential $μ_I << Λ_{QCD}$, this matter forms a Bose condensate. For $μ_I >> \sqrt{N_c} Λ_{QCD}$, unlike QCD remains confined, but the degrees of freedom of the system are mesons and Cooper pairs bound on size scales small compared to the QCD size scale determined by the superfluid gap. For most purposes this matter may be analyzed using weak coupling methods. For $ Λ_{QCD} \le μ_I \le \sqrt{Nc} Λ_{QCD}$, we argue that meson matter is quarkyonic, with quarks bound into mesons on a size scale of order $Λ_{QCD}$ corresponding to a filled Fermi sea of quarks, with possible Bose condensation at the Fermi surface and/or Cooper pairs with finite width of the surface of order $Λ_{QCD}$.