Papers

Non-local quantum computation (NLQC) asks two parties to apply a joint operation to their quantum inputs using an entangled resource state and one round of simultaneous quantum communication. NLQC has applications across quantum information, including attacks on quantum position verification, communication complexity, and quantum gravity. Every bipartite unitary has an approximate NLQC protocol with finite entanglement, and exact protocols are known for several structured families. However, it has remained open whether every fixed unitary admits an exact protocol with finite-dimensional resources. We show that, even for two qubits, Haar-almost every unitary does not admit such a protocol, even when the resource state and local operations are tailored to the target. The proof first shows that smooth deformations of an exact protocol can only change its target by local unitaries. For a fixed architecture, semialgebraic geometry limits the exact protocols to finitely many connected families, so each architecture reaches only finitely many local-unitary orbits. Taking the union over all architectures, the exactly implementable unitaries form countably many local-unitary orbits. We also show that some natural targets do not admit a protocol: the controlled phase $\mathrm{diag}(1,1,1,e^{i\theta})$ has no exact protocol with finite-dimensional resources whenever $e^{i\theta}$ is transcendental, for instance for $\theta = 1$. Our results also apply to localizable quantum measurements, whose outcome is obtained from local measurements on inputs and a shared entangled resource state without communication. A rank-one projective measurement in a Haar-random basis is almost surely not localizable with a finite-dimensional resource state and finitely many local outcomes.

We define the unitary design strength of a finite unitary ensemble to be the maximal integer $t$ for which its $t$-th statistical moment is identical to that of the unitary group. In the presence of physical symmetry, not all operators of an ensemble are symmetry-compatible. This motivates us to define the symmetric design strength of a finite unitary ensemble to be the maximal integer $t$ for which the $t$-th moments of its symmetry-compatible sub-ensemble match those of the group of symmetry-compatible unitaries. We show that in sufficiently high dimension and for a broad family of symmetries, which includes the global on-site $\mathrm{U}(1)$ and $\mathrm{SU}(d)$ symmetries, there exist finite unitary ensembles of arbitrarily high design strength whose symmetric design strength is strictly higher. Ensembles with this property may be more versatile under symmetry constraints for protocols that rely on unitary randomization than they are without symmetry. Our results extend the previous work [Mitsuhashi and Yoshioka, PRX Quantum 4.4 (Nov. 2023)] showing that the symmetric design strength of the Clifford group is strictly upper bounded by its unitary design strength for symmetries that do not trivialize the symmetry-compatible unitaries. Due to the special significance of unitary designs with a group structure, we also derive a variety of bounds on the unitary and symmetric design strengths of finite unitary ensembles whose operators form a group. In particular, we provide a simple proof that an arbitrary ensemble of operators forming a finite group must have a symmetric design strength of at most two under the global on-site $\mathrm{U}(1)$ and $\mathrm{SU}(d)$ symmetries. Along the way, we show that there exist uniformly weighted groups of arbitrarily high symmetric design strength in arbitrary dimension and analyze their structure.

Bosonic quantum systems are among the leading architectures for quantum information processing, offering continuous-variable degrees of freedom with strong error-correction capabilities. However, standard bosonic quantum computation models such as the Lloyd-Braunstein [Lloyd and Braunstein, 1999] and hybrid oscillator-qubit models [Brenner, Dias, and Koenig, 2025; Liu et al., 2026] permit dramatic energy growth, leading to unphysical computational power and the breakdown of fundamental algorithmic tools such as universal and efficient compilation [Brenner et al., 2026; Rudolph et al., 2025]. To address this, we introduce a new model of bosonic quantum computation, Bosonic Energy-Preserving Quantum Computation (BEQC), in which energy is treated as a computational resource. Namely, energy is supplied solely through input coherent states, and all gates are generated by energy-preserving Hamiltonians. Thus, by construction, dramatic energy growth is impossible, making the model physically grounded. We next show that BEQC is a computationally robust and universal model in many respects, including: (1. Computational power) BEQC efficiently simulates all polynomial-energy computations in existing models, and exactly recovers BQP in the polynomial energy setting. It further admits several complexity-theoretic upper bounds when varying the energy, precision, and space parameters of the model. (2. Universal gate sets and state synthesis) BEQC has natural universal gate sets based on linear optics and Kerr interactions. In particular, we obtain a Solovay-Kitaev theorem which circumvents previous no-go results. We give various applications, including (a) a protocol for engineering GKP states with rigorous preparation guarantees, (b) Fock state preparation to exponential precision, and (c) native Fock space simulation of any qubit-based unitary.

Electric ride-pooling must jointly manage passenger service, routes, batteries, and finite chargers; a locally useful relocation can reduce later service. We introduce a discrete-event ride-pooling simulator with ordered passenger stops, pickup and ride-time constraints, battery reserves, charger travel, and finite first-come, first-served (FCFS) charging queues. On top of a common dispatcher, we add a learned repair layer that moves uncollected passengers between vehicles, uses a supervised score to estimate later effects, and uses a two-stage proximal-policy-optimization (PPO) policy to focus computation on promising moves. Every executed move must satisfy route, battery, and time constraints and provide an immediate route-cost improvement. For larger instances, we limit the number of candidate moves and apply several non-conflicting repairs at once. On 12 held-out Manhattan episodes with 100 requests, 30 EVs, and one plug per station, supervised repair reduces operational cost by 6.57% versus no repair (12/12 wins) and serves 74.92 rather than 72.75 requests. Two-stage PPO stays within 1.43% of supervised repair with 95.4% fewer exact trials, while our experiments scale to 8,000 requests and 2,400 EVs with cost reductions across all three larger development settings. Queue-aware charging reduces waiting by 41.0%; under a declared 1.5-kW queue-idle load, operational electricity per served request falls 1.73%.

In this work, we present a first-principles analysis of the scale evolution of the two-point energy-energy correlator (EEC) for quark and gluon jets propagating through QCD matter. The EEC is a jet substructure observable that encodes the angular distribution of energy flow within jets and has proven valuable for precision tests of QCD in elementary collisions. Extending this framework to reactions with nuclei, we derive a factorized description of the in-medium EEC using Soft Collinear Effective Theory with Glauber gluon interactions, allowing systematic inclusion of medium-induced interactions. Working in the opacity expansion, we compute the medium-modified quark and gluon jet functions at one loop and perform leading-logarithmic resummation of large-scale logarithms. We find an experimentally accessible kinematic regime where medium effects manifest directly through medium-induced corrections to the anomalous dimensions, providing a transparent probe of in-medium dynamics. We test the theoretical framework by comparing our analytic predictions with EEC measurements in p-Pb collisions and discuss its implications for small collision systems (O-O) and the EIC.

Stabilizer operations describe a fragment of quantum theory that is known to be efficiently classically simulable, thanks to the Gottesman-Knill theorem. For this reason, nonstabilizer resources such as magic states are necessary for universal quantum computation. Interestingly, the operational and axiomatic approaches to the resource theory of magic differ: the set of free operations in the former, namely, stabilizer operations (SO), is strictly smaller than that in the latter, namely, completely stabilizer preserving operations (CSPO). A simple example showing the separation is given by a three-qubit stabilizer product basis whose states cannot be perfectly discriminated using SO, but which do admit perfect discrimination using CSPO. Such an ensemble of states is said to exhibit nonstabilizerness without magic (NSWM). Here we obtain a principled understanding of this phenomenon, proving necessary and sufficient conditions for its existence. We first derive a simple criterion to decide whether, given a stabilizer basis, its states can be perfectly discriminated using stabilizer operations alone. We then consider the case where the stabilizer basis contains only product states and use its link with process functions—classical models of paradox-free causal loops—to prove the following: the states in a stabilizer product basis require nonstabilizerness for perfect discrimination if and only if the corresponding process function violates a causal inequality. This provides a new operational meaning to causal inequality violations as witnesses of nonstabilizerness, a form of computational nonclassicality.

When a camera revisits a previously observed region, a video world model should reproduce what was there before. This requires both remembering past observations and retrieving the right one for the current viewpoint. Key-value caches preserve visual detail but grow with video length; recurrent memory is compact but compresses history into a fixed-size state, so individual past observations are no longer directly accessible. We introduce LOCI, a hybrid spatial-memory architecture that keeps both representations. In half of the transformer blocks, main attention keeps a key-value cache of past observations; in the other half, it is restricted to the current chunk and complemented by a recurrent linear-attention memory whose reads and writes are conditioned on projective camera geometry, so viewpoint enters both memory addressing and stored content. Recurrent readouts flow into subsequent cache-backed blocks and supply their queries with accumulated scene context. On the public MIND memory benchmark and on held-out recorded trajectories, LOCI reproduces revisited content more faithfully than representative world models and a same-recipe full-softmax model; with full history, it lowers peak memory at equal length by about 30% relative to full softmax. With a bounded bank of retained observations, it streams long videos at constant memory and remains more faithful than full softmax under the same budget.

Training LLM agents with reinforcement learning (RL) is bottlenecked by environments, which must provide verifiable rewards, support long-horizon interaction, and scale cheaply. Existing approaches rely on costly human-curated data or on LLM-generated environments that risk hallucinations and benchmark contamination. We show that LLMs can instead be trained into capable search agents using synthetic environments generated entirely by rules, whose generation requires no LLM and has zero marginal cost. We build PhantomEnvironments, multi-turn RL environments from fictional worlds, where agents must search a corpus of templated articles to answer multi-hop questions. Despite sharing no facts with the real world, these strikingly simple environments yield agents that transfer to real-world multi-hop search benchmarks, often outperforming real-world training data on newer benchmarks. Trained agents generalize to unseen fictional universes, and Qwen models learn to scale their search budget roughly linearly with question difficulty, suggesting emergent search scaling from environment interaction alone. Ablating environment complexity reveals that hop count drives transfer more than constraints or comparisons: even the simplest rule-generated environments are a surprisingly effective, free resource for training generalizable LLM agents.

Understanding the complexity of low-energy quantum states is a central problem in quantum complexity theory and many-body physics. Here we prove the no low-energy trivial magic (NLTM) conjecture, constructing a family of local Hamiltonians for which every state within a positive energy density window requires circuit depth $\Omega(\log n)$ to prepare from arbitrary stabilizer state that may themselves be highly entangled. Notably, our result is intrinsic in the sense that the same Hamiltonian family and energy density threshold apply to arbitrary qudit stabilizer inputs with any bounded local dimensions. Our construction builds on non-Abelian gauged sheaf codes obtained using the cup product structure on good quantum locally testable codes. We establish constant operator soundness for the associated Hamiltonians, enabling their protected logical structure to constrain all states at sufficiently low energy density. By excluding shallow stabilizer-based classical witnesses, Our result substantially strengthens NLTS and advances our understanding of low-energy complexity relevant to quantum PCP.

World Action Models (WAMs) couple visual dynamics prediction with action generation, yet they do not explicitly support the reuse of action experience across manipulation tasks. Furthermore, existing WAMs struggle to capture underlying cross-task semantic relationships that could guide target action prediction, as redundant background elements interfere with the extraction of key visual information. To address these challenges, we develop a novel Action Experience Dictionary (AED) that encodes historical physical action trajectories into shared action embeddings to support skill reuse and model cross-task relationships. Specifically, we first aggregate historical actions to align with visual observations and retrieve action embeddings from the AED using a pretrained action tokenizer. Subsequently, we visually condition the pooled embeddings through cross-attention and prepend them to noisy action tokens, providing interaction context and action intent for prediction. To model action-related motion and reduce reliance on irrelevant background cues, we introduce a motion-aware transition loss that supervises visual feature change prediction over random temporal intervals. Experiments on simulation benchmarks and in real-world cross-embodiment settings verify the effectiveness of our AED. The project code is available at https://github.com/JiahuaDong/AED .

Purifications are often used as a convenient mathematical representation of quantum states and channels when constructing protocols for quantum information processing tasks. Although powerful, this perspective can suggest that the purifying degrees of freedom and its correlations with an environment are just a useful change of representation. Here we show how they can instead be exploited as an operational resource in sequential quantum channel discrimination, even when the environmental reference frame is unknown or averaged. In contrast to state discrimination and parallel channel discrimination, for which bare and averaged-purification access are equivalent, sequential access to purified resources exhibits a strict advantage in probability of success. We prove this strict separation via two main results. In the first, we construct a pair of families of qubit-qubit channels with a strict separation in the two-query case, and in the second, we show an example of a pair of qubit-qubit channels whose purifications are perfectly distinguishable with three queries while no finite number of bare (non-purified) queries suffices for perfect discrimination. These separations imply an advantage of sequential over parallel strategies for channel discrimination and establish the impossibility of converting bare channel queries into averaged-purification queries via transformations that allow arbitrary interventions between queries, strengthening previous results.

The volume estimation problem is a classic task in computational geometry. The development of randomized algorithms for this problem spurred the development of many influential algorithmic techniques related to Markov Chain Monte Carlo and simulated annealing, and the problem connects to several important geometrical results, like the KLS conjecture. In this work, we quantize the state-of-the-art $\widetilde{O}(d^{3.5}+d^3/\varepsilon^2)$-query randomized algorithm developed by Cousins and Vempala, and obtain a $\widetilde{O}(d^{3.5} + d^{1.75}/\varepsilon)$-query quantum algorithm, improving over the $\widetilde{O}(d^{3.5} + d^{2.25}/\varepsilon)$ state-of-the-art bound. Our key technical contribution is a framework for amortizing the cost of a quantum walk. The framework is based on the recent transducer toolkit introduced by Belovs, Jeffery and Yolcu. It is this amortized quantum walk framework that allows us to exploit the amortized analysis of the ball walk by Cousins and Vempala, thus overcoming the key barrier that previously barred its quantum implementation.

Betti numbers are central to topological data analysis but fail to capture torsion in integral homology. Torsion can distinguish topological structures with identical Betti numbers, and examples from classical topological data analysis show that it can affect the topology inferred from data. Related torsion-sensitive quantities are also known to have practical applications in graph-based machine learning, including biomedical applications. We investigate how quantum spectral methods can access this additional information. Log pseudodeterminants, obtained by summing the logarithms of the nonzero boundary-Laplacian eigenvalues, summarize spectral information about a simplicial complex. Under explicit topological assumptions, an alternating combination of these quantities gives the size of a higher critical group, the higher-dimensional analogue of a graph sandpile group. With stronger certification, a related construction recovers the size of the torsion subgroup in homology itself. This is, to our knowledge, the first provably correct quantum estimator of integral-homology torsion order. We give a new quantum algorithm for estimating these quantities, with explicit dependence on how the input is queried, the required accuracy, and the spectral gaps. Exact spectra for balanced multipartite clique complexes provide favorable gaps, and a related construction gives an explicit torsion-bearing benchmark. With compact query access, the algorithm need not construct the exponentially large boundary matrices explicitly. For a restricted torsion-bearing family, a tailored amplitude-estimation routine uses quadratically fewer queries than any randomized classical algorithm given comparable access when estimating the log pseudodeterminant. Estimating the full, unnormalized quantity to fixed additive error still costs in proportion to the candidate-space dimension $D$.

Distillable entanglement—the maximum rate of Bell states extractable from the given noisy entangled states via local operations and classical communication (LOCC)—has been a central quantity to characterize the operational value of entangled states. However, this operational meaning had been known to be valid only under a crucial assumption: both parties know the description of the input state and can choose the protocol tailored to it, which does not necessarily reflect the natural operational setting. Here, we show that the distillable entanglement is the fundamental operational quantity even without this assumption. We present a universal LOCC protocol—whose description does not depend on the input state and thus works universally for any input—that achieves the distillable entanglement of an arbitrary unknown input state. Our result therefore lifts the distillable entanglement to a robust notion of an operationally meaningful quantity and clarifies that input-state knowledge is not necessary to achieve the optimal rate of entanglement distillation. Our protocol is based on state merging for compound states, together with the uniform convergence property of the finite-block quantity toward distillable entanglement.

Open quantum systems can rapidly lose most microscopic information, leaving only a few degrees of freedom to govern their long-time dynamics. Classical Markov state models (MSMs) describe such metastable dynamics as transitions among a few representative phases and are widely used to reduce complex-system dynamics in condensed matter and chemical physics. In quantum systems, however, phase labels alone are insufficient when coherence persists between metastable states. Even when the slow modes are known, their spectral projection need not produce valid quantum states. We construct quantum Markov state models (QMSMs) that describe the surviving information and its evolution on a small physical state space containing classical sectors and quantum matrix blocks. We quantify metastability by assuming that the evolution channel $\mathcal C$ changes little when applied a second time, with sufficiently small defect $\eta=\|\mathcal C^2-\mathcal C\|_\diamond$, and that the number of slow degrees of freedom is bounded independently of the full system size. Under these assumptions, we construct compression and reconstruction channels whose composition recovers every reduced state exactly, while the reverse composition gives an exactly idempotent channel approximating $\mathcal C$, answering Kitaev's exact-rounding question [Kit25]. Our constructions give an optimal diamond-norm bound of $\mathcal{O}(\eta^{1/3})$ on all input states, as well as an improved bound of $\mathcal{O}(\eta^{1/2})$ on metastable states prepared by $\mathcal C$, with constants depending only on the slow dimension. The reduced transition channel can be iterated to predict the microscopic dynamics with controlled error. We illustrate the QMSM through a weakly driven dissipative spin chain supporting either a metastable logical qubit or long-lived classical phases.

Hirose formulated a duality conjecture for a $q$-discretization of iterated integrals on the four-punctured projective line, incorporating word-dependent $q$-shifts of the parameters. In this paper, we prove this conjecture using a symmetric terminating ${}_{4}\phi_{3}$ connector.

This study compared classifiers that differentiate between urbanized and non-urbanized areas based on unmanned aerial vehicle (UAV)-acquired RGB imagery. The tested solutions in-cluded numerous vegetation indices (VIs) thresholding and neural networks (NNs). The analysis was conducted for two study areas for which surveys were carried out using different UAVs and cameras. The ground sampling distances for the study areas were 10 mm and 15 mm, respectively. Reference classification was performed manually, obtaining approximately 24 million classified pix-els for the first area and approximately 3.8 million for the second. This research study included an analysis of the impact of the season on the threshold values for the tested VIs and the impact of image patch size provided as inputs for the NNs on classification accuracy. The results of the con-ducted research study indicate a higher classification accuracy using NNs (about 96%) compared with the best of the tested VIs, i.e., Excess Blue (about 87%). Due to the highly imbalanced nature of the used datasets (non-urbanized areas constitute approximately 87% of the total datasets), the Mat-thews correlation coefficient was also used to assess the correctness of the classification. The analysis based on statistical measures was supplemented with a qualitative assessment of the classification results, which allowed the identification of the most important sources of differences in classification between VIs thresholding and NNs.

We develop a submodular framework for the von Neumann entropy of discrete quantum convolutions, providing a noncommutative counterpart to the direct side of entropic additive combinatorics. We first introduce globally weighted quantum convolutions, which form compatible families indexed by admissible subsets of a fixed collection of inputs. Our main theorem reveals a polymatroidal geometry underlying their entropy growth: relative to any fixed admissible input block, the entropy gains admit a normalized, monotone, submodular extension to all subsets of the remaining inputs. The theorem yields convolutional strong subadditivity, quantum Ruzsa triangle inequality, and quantum entropic Plünnecke–Ruzsa inequalities for arbitrary input states. For repeated inputs, it gives sharp comparisons of entropy growth across admissible scales; in particular, the quantum doubling constant controls all higher admissible convolution entropies with optimal exponents. Together, these results bring submodular methods from additive combinatorics into the quantum setting and provide a systematic route to broad families of convolutional entropy inequalities.

Let \(N_t\) denote the least number of nodes in a positive cubature formula of degree \(t\) on \(S^2\). We prove that a formula of degree \(2m+1\) cannot have exactly \((m+1)(m+2)+1\) nodes for any \(m\ge2\). Excluding equality in the Fisher bound then gives \[ N_{2m+1}\ge (m+1)(m+2)+2 \] for \(m\ge3\), and known constructions yield the exact values \(N_7=22\) and \(N_9=32\). For general odd degrees, positive circle measures on Lobatto latitudes give an upper bound with quadratic coefficient \(13/8\), parity-dependent linear terms, and an \(O(m^{2/3})\) remainder. We determine the sharp constant \(49\sqrt[3]{3}/72\) for the scalar remainder in this construction. Lower bounds are obtained from continuous weighted LP–Turán inequalities and radial caps whose Helmholtz companions are nonnegative measures. We prove that the cap functional admits a maximizer at each fixed admissible support radius and derive explicit finite-degree lower bounds by a positivity-preserving transfer to the sphere.

Materials design is an inverse problem: finding the couplings of a microscopic Hamiltonian whose ground state exhibits a desired property. For strongly correlated quantum systems, this remains largely out of reach, as each candidate Hamiltonian requires its own costly simulation. Here we show that Foundation Neural-Network Quantum States, single wave functions that encode the ground states of an entire family of Hamiltonians, make this search efficient. Because the Hamiltonian couplings enter as neural-network inputs, any ground-state property can be optimized by gradient descent directly in coupling space. We use this approach to search for nonmagnetic phases in two-dimensional spin models in coupling spaces of increasing dimensionality. Specifically, we focus on quantum spin liquids, exotic phases of matter in which quantum fluctuations prevent magnetic order at zero temperature. In the largest search space considered, spanned by eight superexchange couplings and containing many paradigmatic frustrated spin systems, the optimization converges to the $J_1$-$J_2$-$\delta$ Heisenberg model when starting from a magnetic phase. We show that the ground state at the optimum set of couplings has neither magnetic nor valence-bond order in the thermodynamic limit, leading to a new quantum spin-liquid candidate. The approach is completely general and can be extended to other models and physical properties to optimize, demonstrating that Neural-Network Quantum States are tools not only for simulating quantum matter but also for designing it.

Extending single Unmanned Aerial Vehicles (UAVs) exploration methods to multi-UAV teams can improve coverage speed and robustness, but introduces challenges such as consistent mapping, safe navigation, and deployment strategy. In this work, we present a centralized multi-UAV exploration framework that enables the use of existing single-UAV sampling-based planners in a multi-UAV setting. The proposed architecture allows multiple UAVs to collaboratively explore unknown environments using a shared global Truncated Signed Distance Field (TSDF) map and centralized planning. Building on the voxblox library, we adapt its mapping pipeline to support real-time fusion of depth measurements from multiple UAVs into a common TSDF representation. In addition, inter-UAV collision avoidance and robot self-filtering mechanisms are integrated into the system to ensure safe navigation and prevent reconstruction of other UAVs as static obstacles. The framework is evaluated in simulation using four sampling-based exploration planners - RH-NBVP, KRH-NBVP, AEP, and KAEP - whose core sampling logic is preserved, with only system-level adaptations for multi-UAV operation. Experiments are conducted across multiple environments and under two deployment configurations: Joint Start (JS), where UAVs are initialized in close proximity, and Separated Start (SS), where UAVs are initialized in distinct locations. Results show that SS deployments consistently achieve faster exploration and improved coverage across all planners, highlighting the importance of the deployment strategy in multi-UAV exploration performance.

Quadratic Chabauty computations for $X_0(N)^*$ are complicated by local height contributions at primes of bad reduction. For squarefree $N$, we explain a strategy for constructing a global $p$-adic height for which all the contributions at the primes of bad reduction vanish. As our first main result, we show that such a $p$-adic height exists for all squarefree levels $N>714$. In order to do this, we first give an explicit description of the minimal regular model of $X_0(N)^*$ at primes of bad reduction, and show this model is semi-stable. Each component of this model gives rise to a linear condition which ensures that the contribution at that component vanishes. Using embeddings of quadratic orders into quaternion algebras, we obtain an upper bound for the number of these conditions; when the genus of $X_0(N)^*$ is greater than one more than this bound, there is enough freedom to choose a suitable correspondence, simplifying quadratic Chabauty computations. As an application, we determine the rational points on several curves $X_0(N)^*$ for which this was not done before.

In physics-based simulations, the evaluation of nonlinear constraint forces represents a primary source of computational complexity. Within the framework of projective dynamics, the solver alternates between estimating these forces and updating vertex positions for the subsequent frame. This work investigates the potential of snapshot-based subspace methods to accelerate the computation of constraint terms while maintaining the fidelity of nonlinear dynamics. We focus specifically on the Discrete Empirical Interpolation Method (DEIM), examining whether it can identify a reduced set of constrained mesh elements that enable accurate interpolation and approximation of forces across the full system. Our experiments demonstrate that DEIM is neither intuitive nor consistently effective for constraint projection reduction. In particular, its performance degrades when constraints involve multiple vertices. To validate these observations, we present comparisons between full-order and reduced-order simulations on both surface meshes embedded in three dimensions and volumetric meshes. Furthermore, we report reconstruction errors for various classes of constraints, providing quantitative evidence of the method limitations in this context.

We compute one-loop unpolarized quark and gluon quasi- and pseudo-distributions in $\overline{\mathrm{MS}}$ and match them to light-cone PDFs. Decomposing the gluon correlator into six covariant form factors, we derive the $6\times6$ renormalization mixing matrix: its eigenvectors classify multiplicatively renormalizable combinations, and any lattice operator choice projects onto our results without a further loop calculation. Evaluating all Fourier transforms in $d$ dimensions, we resolve the structure of the exterior $|x|>1$ in quasi-distributions. The correlator carries a short-distance logarithm with a branch cut at $\nu=0$. By the Paley-Wiener theorem, the analytic part transforms into $|x|\le1$, so the exterior is generated solely by this branch cut. At leading power, the exterior carries no independent non-perturbative physics: it is fixed by the light-cone PDF through the renormalization group. In the gluon channel, the matching kernel of Balitsky, Morris and Radyushkin differs from our $\overline{\mathrm{MS}}$ result by a finite polynomial, identical across index choices. We trace this to contracting an internal loop index over two instead of $d-2$ transverse directions, omitting an evanescent operator on the collinear pole. Using our basis, we show that the independent kernel of Yao, Ji and Zhang agrees with ours, separated from Balitsky et al. by the same polynomial. While the ratio scheme protects the momentum fraction $\langle x\rangle_g$, this kernel difference suppresses the extracted normalized second and third gluon moments by $11\%$ and $13\%$ at $\alpha_s=0.3$, so the true $\overline{\mathrm{MS}}$ gluon is systematically harder than reported.

When recalling the orientation of recent stimuli, observers are systematically biased away from the cardinal axes. The prevailing explanation is that this ”anti-cardinal bias” arises because cardinal orientations are encoded with greater neural resources and therefore less noise, consistent with efficient coding of environmentally common features. Under this account, the bias should occur independently for each stimulus; any serial attraction towards previously seen orientations should be independent of absolute orientation. By contrast, we find that serial effects in orientation recall are unexpectedly strong and reflect a hitherto unrecognised hierarchical interaction, consistent with recurrent connectivity across hierarchies of sensory processing in the brain. We found that serial dependence in visual orientation recall is dominated not by attraction to the previous orientation itself, but to a compound feature representing both a tilt and its mirror reflection about the cardinal axes. Consistent with greater spatial abstraction at higher levels, the influence of this compound feature persisted across the visual midline, whereas orientation-specific effects weakened between hemifields. We developed a quantitative model based on the optimal combination of a noisy representation of the current stimulus with a hierarchical memory trace incorporating these compound features. Remarkably, although the coding fidelity was uniform across angles, this model accurately reproduced not only the serial dependence, but also the anti-cardinal bias. Our results suggest that memory traces are not isolated to single features, but reflect compound reactivation of hierarchical representations. Furthermore, they reveal that inference across hierarchical representations can generate systematic perceptual distortions previously ascribed to coding constraints.

Quantum measurements and channels determine how information is extracted, encoded, and transmitted in quantum protocols. Optimizing their performance often requires numerical methods that remain practical as Hilbert space dimensions increase. The Reimpell-Werner iteration offers a practical approach to these tasks through repeated matrix updates that respect the constraints. Here, we generalize this iteration to linear objectives with arbitrary Hermitian cost matrices. We prove that the iterates converge to a global optimum whenever the initialization satisfies suitable support overlap conditions. For each fixed problem, choice of iteration parameters, and admissible initialization, $\mathcal{O}(1/\varepsilon)$ iterations suffice asymptotically to bring the objective value within $\varepsilon$ of the optimum. These results provide a rigorous foundation for the iteration and broaden the class of optimization problems to which its convergence guarantees apply.

Brain age gap is a promising machine learning (ML)-driven bio\-marker of accelerated biological aging and is derived from neuroimaging data. Recent works on coVariance neural networks (VNN) for brain age gap prediction have provided an explainable and anatomically verifiable framework for brain age gap prediction. Notably, VNN outcomes are derived by filtering inputs along covariance eigenvectors, providing a mechanism for explaining their decisions in terms of latent (orthogonal) vectors. In this paper, we investigate the longitudinal brain age gap effects in a Mild Cognitive Impairment (MCI) cohort using a VNN-driven brain age gap prediction framework. Specifically, using Integrated Gradients (IG) as the attribution mechanism, our results demonstrate that the eigenspectrum of the anatomical covariance matrix explains the different longitudinal effects observed in brain age gap in amyloid positive vs amyloid negative subcohorts more prominently than individual brain regions ($83.2\%$ with the leading eigenvector versus a maximal value of $7.7\%$ for any brain region). Therefore, the covariance-based latent explanation identifies a key coordinated input pattern that carries most of the observed longitudinal effect in brain age gap.

Supporting Uncrewed Aerial Vehicles (UAVs) with mobile charging stations enables persistent UAV autonomy in infrastructure-sparse environments. In this setting, trajectory optimization for UAVs is challenging because it couples task scheduling with when and where to recharge, as well as terrain-access constraints on where charging is available. We propose a smooth nonlinear trajectory optimization model for UAV with mobile charging support. Compared with existing results, the proposed model allows nonlinear charging dynamics mode via a unified battery dynamics model with disjunctive constraints on the time allocated to each mode. Furthermore, it provides smooth approximations of the disjunctive constraints with bounded approximation errors. By avoiding integer variables, these approximations enable efficient solution using smooth nonlinear optimization algorithms. We evaluate the proposed model on UAV missions with multiple spatially distributed tasks, nonlinear constant-current–constant-voltage charging dynamics, and terrain-access constraints on mobile charging support. Compared with mixed-integer nonlinear programs, the proposed model provides high-quality approximate solutions while reducing the computation time by orders of magnitude.

We show that compact locally symmetric manifolds $M$ with universal cover the symmetric space $X$ for $SL(n,\mathbb{R})$ form a topological higher $d$-expander family for $d\leq n/8$. We prove the same statement for $SL(n,\mathbb{R})$ replaced by a split simple non-compact real Lie group $G$ and for $d$ linear in the rank of $G$. We accomplish this by showing that minimal submanifolds of low codimension in such $M$ must have volume comparable to the volume of $M$. Our proof is based on a new monotonicity formula for minimal submanifolds of $X$, together with bounds on the decay of matrix coefficients for unitary representations of higher rank Lie groups. We also give the first locally symmetric example of power-law systolic freedom. This paper partially supersedes \cite{fl24}.

With the STAR's Beam Energy Scan II, a rich amount of data exists to search for the QCD critical point. However, a central challenge is that the critical point cannot be directly extracted from data but rather is probed dynamically in an expanding, cooling system that may be far-from-equilibrium. In this talk, we show the latest results from equations of state with a movable critical point generated by the MUSES collaboration, run in the 3+1D relativistic viscous hydrodynamics code CCAKE. We discuss numerical improvements to CCAKE that include “glass” initial conditions and adaptive smoothed particle hydrodynamics, allowing us to rapidly and accurately obtain numerical solutions to the hydrodynamic equations of motion. We can quantify the interplay between beam energy, location of the critical point, and rapidity range.