Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization etc. Although quantum computing offers paths forward, including variational techniques, embedding strategies, and quantum linear solvers, the discussion remains scattered. Without shared terms or structure, evaluating progress in hybrid quantum-classical DFT efforts becomes challenging. To bring order, we introduce a three-axis scheme based on where the method connects into DFT, whether the quantum part boosts precision or cuts time, alongside intended device type: current noisy machines or future error-corrected ones. Sorting known approaches in this way shows why embedding frameworks fit modern tools better, while faster linear algebra waits for more advanced systems.

In this work we study the integrability of a family of nonlinear oscillators. Dynamical systems from this family appear in different applications from mechanics to chemistry. We propose an approach for finding first integrals and integrating factors, which is based on the construction and classification of transcendental invariant curves whose cofactors are polynomial or rational in one of the variables. We demonstrate that this approach can be efficiently used for finding non-Liouvillian and non-Puiseux integrable dynamical systems. Its application involves finding solutions only of linear algebraic and linear ordinary differential equations. This allows one to study singularities, including essential ones, of the invariant curves in the complex plane. We illustrate this approach by proving non-Liouvillian integrability of two dynamical systems from the Painlevé--Gambier classification and non-Puiseux integrability of an oscillator from the considered family. Furthermore, we construct equivalence classes of the first two dynamical systems with respect to nonlocal transformations. We show that among these equivalence classes there are interesting examples of integrable dynamical systems.

The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional extensions forbid the existence of a unique, symmetric, and gapped ground state at fractional fillings in quantum many-body systems with a conserved particle number (or spin angular momentum) and the conventional translation symmetry of Euclidean lattices. In this work, we propose a generalization of the LSM theorem to quantum many-body systems on hyperbolic lattices, i.e., regular tessellations of two-dimensional negatively curved space. By leveraging concepts from hyperbolic band theory in a many-body setting, we adapt Oshikawa's flux-threading argument to periodic hyperbolic lattices with a non-Euclidean (Fuchsian) translation symmetry and compute a lower-bound to the ground-state degeneracy as a function of filling and lattice geometry. We explore the consequences of LSM constraints for gapped phases of hyperbolic quantum matter and suggest frustrated spin models on hyperbolic analogs of the square and triangular lattices as promising platforms for realizing symmetric spin liquids in hyperbolic space.

We study the rate of convergence to the steady state in the True Moving Bed model of linear chromatography, as a function of the six parameters that appear in the model. The model is a system of eight linear partial differential equations of hyperbolic type, coupled through the equations themselves and also through boundary conditions. We prove that the rate of convergence is given by a dominant eigenvalue, whose existence we prove by means of the Krein-Rutman Theorem, and by comparison arguments. We show how to construct a (not at all simple) characteristic function, whose roots are the eigenvalues. We also study the asymptotic profile of the solutions for large times, although this part is not purely analytical, but a combination of analytical and numerical techniques. Beyond the theoretical results, these models also offer explicit quantitative information: we apply all our results to a Case Study, namely the separation of omeprazole enantiomers. Finally, we consider a simpler limit case, where all the calculations become explicit.

The gamma-ray emitting binary stellar system LS I +61 303 was observed with the Imaging X-ray Polarimetry Explorer (IXPE) on two successive orbits over orbital phases of 0.74 to 1.05. Polarization is detected at a significance of 4.2$σ$ with an average polarization degree of $13.1\% \pm 3.0\%$ in the 2-8~keV band after background subtraction. This is the second detection of polarization of the X-ray synchrotron emission from a gamma-ray binary and, again, suggests that the magnetic field in the particle acceleration region has a significant ordered component. The orbital motion on the sky of LS I +61 303 is not well determined, which leads to ambiguity in interpretation of the X-ray electric vector polarization angle (EVPA) measurement. Use of orbital elements determined via radial velocity measurements combined with radio imaging of variable nebular emission, suggests an offset between the X-ray EVPA and the compact object-massive star axis on the order of ~30$^{\circ}$. Such an offset could be produced by Coriolis forces due to binary motion. Use of two different sets orbital elements determined via optical polarimetry suggest either no offset or a perpendicular orientation, but require an unexpectedly high inclination. Use of orbital elements derived from modeling of the keV/TeV light curves suggest good alignment between the X-ray EVPA and the compact object-massive star axis. Such alignment was found for the gamma-ray binary PSR B1259-63. If the same physical situation holds for LS I +61 303, that would favor the orbital elements derived from the keV/TeV light curves.

We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in rows and in columns, then it admits such a decomposition. We apply this result to study optimization of quadratic forms over the standard simplex. As a corollary, we obtain that a natural relaxation of this problem is tight when the objective function is separable, resolving an open question of Dey and Kocuk.

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function. Its unitary evolution obeys a Schrödinger equation. Statistical observables are represented by operators which do not commute with the ones associated to classical observables. Examples are functions of the quantum energy or the quantum angular momentum. They are important conserved quantities. We construct a complex functional integral for the quantum system which describes the probabilistic classical transport equation. The characteristic features of quantum mechanics, as the superposition of wave functions, interference, the importance of phases, non-commuting operators or a unitary time evolution, are realized by probabilistic classical transport equations.

A systematic study of chiral effects is presented using an Effective Field Theory framework. By integrating out a massive Dirac fermion at finite temperature in presence of vector and axial background fields, the currents and their anomalies are computed from the path-integral. Chiral effects previously considered separately naturally arise in a unified computation, including new mass corrections. The link between each anomalous transport effect and the anomalies is clearly established, beyond the identification of their coefficients. In particular, we can appreciate how these effects are sourced by the anomalous nature of the theory even in configurations where the anomaly itself vanishes. The consistent and covariant anomalies are both encapsulated in master formulae for the currents which result from a careful treatment of the regularisation. It is finally found that, at finite temperature, the physical currents cannot be inferred simply from the Chern-Simons terms whose divergence reproduce the chiral anomalies.

This paper introduces a quasi-Bayesian approach for local projection instrumental-variables (LP-IV) estimation. It builds a moment-based quasi-posterior using the generalized method of moments (GMM) objective and applies a roughness-penalty prior to smooth impulse responses over different horizons. The approach maintains the key first-order features of traditional LP-IV methods, while enhancing stability in finite samples and allowing for joint inference through simultaneous bands. Simulations indicate that this regularization decreases root mean squared error compared to standard GMM, especially at medium and longer horizons. An application to Danish electricity markets highlights the method's practical usefulness.

Website Fingerprinting (WFP) has traditionally focused on inferring which website a user visits from encrypted traffic metadata such as packet sizes and timing. In this paper, we identify and quantify a new privacy risk in modern web settings: an adversary can infer a user's persona using only packet-length and inter-arrival-time sequences. To study this risk at scale, we build an LLM-driven multi-agent browsing framework that enforces controllable persona constraints while a computer-use agent interacts with real websites and collects corresponding encrypted traffic traces. We formalize persona fingerprinting under both closed-set and open-world settings and further evaluate whether persona information is already embedded in representations learned by existing WFP models and can be amplified at low cost. Across 10 modern websites and 15 personas (plus an open-world class), persona inference achieves about 84% accuracy on mixed-site traffic; moreover, a lightweight multi-task objective can boost persona accuracy to around 80% while retaining strong site classification performance (about 93% baseline). Our results show that, on modern websites, encrypted traffic metadata can leak not only which site a user visits, but also how they browse and who is browsing.

Energy system models are increasingly dependent on representative climate input. Yet, a fundamental mismatch persists between the hundreds of simulated years often used in climate science and the handful of years that computationally demanding power system models can process. Current practice, including ENTSO-E's European Resource Adequacy Assessment, relies on climate year selections that have not been validated against explicit representativeness criteria. This risks biased investment decisions and blind spots for plausible weather conditions. This study proposes simulated annealing as an optimisation method for selecting representative subsets of complete climate years from large climate ensembles. Representativeness is quantified using the seasonal sliced Wasserstein distance, a metric from optimal transport theory that captures representativeness on marginal distributions, inter-variable correlations, and seasonal structure simultaneously. We evaluate simulated annealing against the alternative methods random search, filtered random search, and K-Medoids clustering across three test cases spanning the Netherlands and Europe, using 180 climate years from the Pan-European Climate Database as a reference. Simulated annealing consistently produces the most representative subsets and outperforms all compared methods. Simulated annealing achieves an effective sample size four to five times the actual subset size. The resulting subsets are roughly 2.5--3.5 times more representative than current ENTSO-E practice. The method is application-agnostic and its output can serve as a validated climate data input to any subsequent (energy) impact study.

Vector search (VS) is now available in most database engines. However, while vector search is a common feature in AI/ML/LLMs where the dominant computing platforms are GPUs, existing database engines operate on CPUs even when implementing vector search. This raises the question of whether integrating vector processing on GPUs as part of the engine would be a better design. In this paper, we explore this question in detail. First, we extend the TPC-H benchmark with vector data (from text and images) and propose a number of representative SQL+VS queries. Second, we develop a modular execution engine that can run SQL+VS queries across CPU and GPU. Third, we perform extensive experiments on a number of deployments: running the SQL+VS queries across CPU and/or GPU, with data residing in CPU or GPU memory, with existing indices and novel, optimized versions, as well as across different GPUs and interconnects (PCIe, NVLink). The results provide actionable and counter-intuitive insights on how to run such queries over CPUs and GPUs. For instance, the relational components benefit much more from running on the GPU than the vector search part. In addition, when the vector search involves moving data and indexes, using the GPU is not the best option, even with fast interconnects. Thus, we develop an alternative organization of vector index and embeddings that reduces the size of the index, making GPU-based vector search more competitive. With these improvements, the final result is that both the relational and vector search components are faster on the GPU, particularly on fast interconnects, in contrast with the architecture used in existing engines.

Here we present a massive longitudinal dataset of public Telegram content, comprising over 5.9 billion messages dating from 2015 to 2025, collected from 712 thousand channels and groups, enriched with metadata on forwards, reactions, and polls. The dataset spans multiple languages including Russian and Farsi, representing countries where Telegram shows mainstream adoption, as well as Western languages where Telegram is used in specific sub-communities. The dataset has several advantages. First, when restricted by language, it provides a versatile example of an algorithm-free platform, contrary to many other social media platforms that are strongly influenced by opaque content-curation algorithms. Second, it enables comparative studies across different languages, communities, and user bases under identical platform affordances. The dataset thus offers a foundation for studying engagement patterns, network evolution, and community formation in the absence of algorithmic curation.

A simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided near-field integrated sensing, communication, and power transfer (ISCPT) framework is proposed. We formulate a robust harvested power maximization problem under imperfect cascaded channel state information (CSI), with constraints on required user rate, eavesdropper tolerable rate, and minimum sensing beampattern gain. To address this non-convex problem, we adopt alternating optimization (AO). First, we approximate the semi-infinite inequality constraints using the S-procedure and obtain rank-one active beamforming via sequential rank-one constraint relaxation (SROCR); then we update the passive STAR-RIS coefficients with a penalty-based scheme refined by successive convex approximation (SCA). Simulations in the near field demonstrate notable gains in harvested power while meeting secrecy and beampattern targets, outperforming conventional baselines.

We consider a quantum system described by a quantum channel $Φ$ that is applied at every time step and study the time evolution of its information capacities. When $Φ$ is a GNS-symmetric channel (this includes Pauli channels, for example), we give explicit exponential convergence bounds for the classical and quantum capacities. These bounds are in terms of entropic properties of $Φ$. We further illustrate how these results help quantify the performance of active versus passive error-correction setups.

This work extends the generalized nearest neighbor decoding (GNND), originally developed as a receiver architecture for memoryless channels, to a vectorized GNND (Vec-GNND) suitable for in-block memory (IBM) channels. Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture. Furthermore, we formulate a GMI-based joint design viewpoint for Gaussian codebook covariance and decoding metrics. Since the metric optimization admits a closed-form solution for each fixed covariance, the joint design is reduced to an input-covariance optimization problem; for the diagonal covariance family, we derive first-order self-consistent optimality conditions. Numerical evaluations on block noncoherent additive white Gaussian noise channels and phase noise channels demonstrate consistent performance gains over conventional scaling-based baselines, highlighting the substantial advantages and potential relevance of the proposed Vec-GNND in realistic communication scenarios.

We investigate the viability of one-zero neutrino mass textures within the framework of resonant Type-II leptogenesis. Considering a two-triplet scalar realization of the Type-II seesaw mechanism, we analyze the compatibility between neutrino texture structures, CP asymmetry generation, and the observed baryon asymmetry of the Universe. We perform extensive numerical scans over the neutrino parameter space and classify the phenomenologically viable one-zero textures under both hierarchical and resonant leptogenesis scenarios. We show that several one-zero textures remain compatible with neutrino oscillation data while simultaneously generating sizable CP asymmetries through resonant enhancement. We further investigate the thermal evolution of the generated asymmetry using Boltzmann equations and demonstrate the freeze-out behavior of the baryon asymmetry. Extending the analysis to a flavor-resolved framework, we study the separate evolution of electron, muon, and tau asymmetries and show that flavor-dependent washout effects play a crucial role in determining the final baryon asymmetry. Our analysis establishes a direct connection between neutrino flavor textures, resonant thermal leptogenesis, and flavor-dependent baryogenesis dynamics.

Stacking (i.e. averaging) the value of a given astrophysical field around sources allows us to detect new cosmological signatures, such as the kinematic Sunyaev-Zel'dovich, and gain insight on the astrophysical properties of galaxies and their environment. Further information may be gained by orienting these stacks along preferred axes defined by a local directed field, such as the transverse galaxy velocities, galaxy shapes, or the local tidal forces. Examples of this are searches for the moving lens effect, the detection of dipole signatures, or the study of cosmic filaments. Here we show that all directional stacking signals may be reconstructed, without loss of information, in terms of the cross-power spectrum between the quantity of interest and the $E$ and $B$ modes of the spin field used to define the preferred axes weighted by the local galaxy density. The power spectrum approach has several practical advantages, in terms of speed, finite-resolution effects, data visualisation, and combination with other cosmological probes. We also argue that, in some cases, such as stacking using velocities or tidal forces reconstructed from the density field, the recovered signal may be dominated by information that is already present in the cross-spectrum between the target field and the galaxy overdensity itself.

We propose a method for generating collective spin cat states in a cavity-coupled atomic ensemble by exploiting strong light-matter entanglement and anti-squeezing associated with the superradiant phase transition. We numerically and analytically demonstrate that the cat states can be heralded by photon-number measurement on the ground state of the Dicke model. The near-critical regime enhances both the cat-state size and the probability of obtaining larger photon-number outcomes, and outcomes with larger photon numbers yield even larger cat states. We also show that a thermodynamic-limit analysis clarifies the generation mechanism and connects it to a natural light-matter analogue of generalized photon subtraction for optical cat-state generation. These results suggest that exploiting criticality in strongly coupled light-matter systems could open new directions for matter-based many-body quantum technologies.

We study the classical problem of community recovery in stochastic block models with a fixed number of communities, with a twist: We seek algorithms that are stable with respect to node-wise changes in the graph structure, formally defined as a differential privacy constraint. The algorithms we develop are based on spectral clustering, where we introduce privacy to the community recovery pipeline in the form of directly privatizing the adjacency matrix; private PCA; private convex optimization; private low-rank matrix estimation; and private approximate subspace estimation. Straightforward applications of existing private algorithms lead to a rapid increase in the privacy parameter $ε$ in order to ensure consistent estimation under node differential privacy, in contrast with the simpler setting of edge privacy. To alleviate these issues, we develop novel algorithms based on (1) sampling from an exponential mechanism with a Lipschitz extension and (2) a general framework for constructing smooth projections from the space of undirected graphs to the space of bounded-degree graphs, which can then be combined with various edge-private algorithms. Importantly, the methods we develop are all computable in polynomial-time as a function of the number of nodes in the graph. We also develop novel lower bounds on the growth rate of $ε$ required in order to achieve consistent community estimation under node privacy. On a technical note, our paper highlights the complications that arise when analyzing private algorithms under the non-standard scaling $ε\rightarrow \infty$ and proposes some solutions. We also provide a novel application of the HGR maximal correlation from information theory in the context of accuracy amplification in PAC learning, which may be of independent interest.

We propose Intra-Gauge Rotated Vector Sum (IG-RVS), a DSP-based fading mitigation method for coherent $φ$-OTDR. IG-RVS exploits spatial diversity within the gauge length by phase-aligning and coherently summing neighboring bins, thereby suppressing Rayleigh fading while preserving spatial resolution.

We report the discovery of a correlated energy-dependent time lag and degree of polarization for Swift J1727.8-1613 during its 2023 outburst. The energy-dependent time lag is measured around the type-C quasi-periodic oscillations (QPO) observed by IXPE on 2023-09-07, while the degree of polarization is obtained from energy-resolved polarimetric measurements. The Spearman correlation coefficient was found to be 0.8, with a null hypothesis probability of 4.2\%. Furthermore, the correlation value drops as the quality factor, or Q value, of the observed QPO frequencies decreases. The spectral properties of Swift J1727.8-1613 are analyzed using simultaneous Insight/HXMT data. Thereafter, we present model-independent theoretical arguments to show that processes other than inverse Comptonization also contributes to both the observed polarization and time lags. This correlation may therefore point to additional mechanisms contributing to the connection between the spectral, temporal, and polarimetric properties of black hole binaries in their hard state.

Crossed Andreev reflection (CAR) is a nonlocal quantum transport phenomenon that arises at the interface between a superconductor and two spatially separated metals. In this process, an electron incident from one metal combines with another electron originating from the other metal to form a Cooper pair in the superconductor. As a consequence, a hole is emitted into the second metal, establishing a nonlocal electron-hole conversion process. In contrast to local Andreev reflection -- where electron-to-hole conversion occurs within the same region -- CAR intrinsically links two spatially separated carriers, giving rise to nonlocal correlations and quantum entanglement. In bipolar magnetic semiconductors (BMSs), the conduction and valence bands possess opposite spin polarizations. We propose to achieve tunable control of CAR by independently adjusting the chemical potentials of the two regions. By engineering the alignment of spin-polarized bands in the two BMS leads, CAR can be selectively enhanced or suppressed. This tunability enables precise manipulation of nonlocal transport, and correlated electron dynamics, offering promising prospects for spintronic and superconducting device applications.

Control science is a core representative of the third industrial revolution and is so important to modern civilization. Control systems are the main subject of control science and may involve many aspects of consideration, such as hardware consideration, software consideration, operation consideration, maintenance consideration, economy consideration, society consideration. However, besides all such aspects of consideration, one aspect that is most essential to the control system is methodology consideration in mathematical sense, knowledge on which is what we refer to as control theory. Besides its importance from the mathematical perspective, control theory is even more charming as it is deeply rooted in practical applications. Charms of control theory consist in both know-why and know-how and it is the fusion of control theory and practical applications that highlights such charms. Control theory for practical applications, especially when somewhat with so-called "advanced" flavour, involves several fundamental aspects. This article introduces the State Estimation aspect of Advanced Control Theory for Practical Applications [1,2].

In this paper, we make a case that endogenous tokens such as cryptoassets are not money. First, we define and classify tokens found on public, permissionless ledgers, contrasting them with privately issued stablecoins and proposed CBDC designs. We then discuss the work of Kahn et al in Money is Privacy on cash versus simplified credit, and we extend their analysis to the situation found on most public, permissionless ledgers. Many public, permissionless ledgers utilize an account-based abstraction for balances, resulting in a default state that maps onto the most harmful models of agent interaction enumerated in Money is Privacy. The conclusion is threefold: that most blockchain economies lack a cash-like primitive; that stablecoins do not intrinsically fulfil this role; and that the reliance of a network on an endogenous token for security exposes holders even of a privacy-preserving asset to the same risk, if that asset relies on the same global ledger state as the endogenous token.

We first show how the cohomology of some Bernstein-Gelfand-Gelfand (BGG) sequences that are important for the numerical analysis of partial differential equations, can be obtained through the construction of a long exact sequence connecting cohomology groups. Then we explain the extension of this result to the non-injective/surjective case through the systematic use of short exact sequences of complexes and their associated long exact sequences of cohomology groups. Finally an interpretation in terms of spectral sequences is given.

Designing safe and sustainable chemicals is critical to combat chemical pollution in our environment. Machine learning (ML) methods have been developed to aid with de novo molecule design. However, data on the environmental impacts of chemical compounds are sparse, resulting in low-fidelity ML oracles and unreliable candidate proposals. Furthermore, generative ML models rely on numerical scoring functions that cannot fully capture the nuanced chemical intuition of expert scientists required for real-world molecular design. We present GEMS-an interactive visual analytics tool that enables domain experts to directly collaborate with a genetic algorithm for molecule design. Users can integrate their expert knowledge to guide the evolutionary process by modifying the scoring function and molecule population without programming knowledge or ML developer support. A usage scenario demonstrates the system's application in designing sustainable antioxidant alternatives. In an interview session with domain scientists, we collected feedback on the usefulness of GEMS.

The standard small-time functional central limit theorem of semimartingales has been established in (Gerhold, S., Kleinert, M., Porkert, P., and Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications. Stochastics, 87), proving that the scaling limit law of a large class of stochastic processes in increasingly small time scales is that of a Brownian motion with a possibly nontrivial variance-covariance matrix. In this paper we focus on the time-homogeneous diffusion processes described by Itô SDEs. Instead of the simple time scaling $1/n$ of (Gerhold, S., Kleinert, M., Porkert, P., and Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications. Stochastics, 87) we consider the scaled processes stopped at the first exit times from the balls of decreasing radius $n^{-1/2}$ without scaling time itself. To the best of our knowledge, this particular scaling has not been investigated in the literature. We prove that this is a nontrivial example of a sequence of processes which converges in the sense of finite-dimensional distributions over a dense subset of $[0,\infty)$, but it does not converge weakly in the sense of laws of càdlàg processes. We also characterise the limit law of the scaled processes evaluated at their respective first exit times.

In this paper, the Bak--Tang--Wiesenfeld model for various substrate topologies and a variety of neighborhoods is reconsidered. With computer simulation, we study the distribution of avalanche sizes. Using the Z-score we confirm that independently of the substrate topology and the range of neighborhood, the exponent that governs the power law of the probability distribution of the size of avalanches is the same and approximately equal 1.208(39). However, this requires a smartly chosen number of deposited grains in relation to the linear size of the system.

We experimentally demonstrate a universal, parameter-independent test for asymmetric source discrimination. The test allows us to discriminate faint sources well beyond the diffraction limit by exploiting spatial mode demultiplexing (SPADE) and single-photon detectors. Our test yields a rate of false negatives well below what can be achieved by diffraction-limited direct imaging. Our tabletop experimental setup is inspired by the problem of exoplanet detection, where one aims at detecting the presence of a faint source in the proximity of a brighter one. We present a complete theory, modelling arbitrary modal crosstalk, and collect data across a range of values for the source separations and intensity ratios. We show that SPADE retains an advantage over direct imaging in the relevant regime of small separations and low intensity ratios. Remarkably, we identify an experimentally accessible crosstalk threshold $C_{\mathrm{th}}\simeq 0.1$ below which the exponential rate of false negatives stays well below that of direct imaging. For example, for crosstalk of $10^{-2}$, SPADE needs up to one order of magnitude fewer photons than direct imaging to achieve the same error rate. These results demonstrate that SPADE offers an effective methodology for subdiffraction asymmetric hypothesis testing, under realistic imperfections and crosstalk, paving the way to photon-starved imaging tasks.