Decarbonising energy systems reduces emissions and fossil fuel dependency, but expanding renewables increases demands for critical raw materials. Most energy system models, however, neglect material demands, putting the material feasibility of energy scenarios at question. We combine a systematic review of 59 highly decarbonised European energy system modelling studies with a quantitative ex-post assessment of material demands for 5 key technologies and 19 materials. We find that material demands exceed Europe's population-based shares of current global reserves for seven materials (Ga, In, Ir, Te; less pronounced for Ag, Se, V), in particular if multiple sectors of the energy system are considered. Competing non-energy demand further amplifies the scarcity, while technological innovation can either alleviate or intensify it. We conclude that energy efficiency, recycling, expanding reserves and technological innovation may only partly address the identified shortages and call for energy sufficiency measures to achieve sustainability in the energy-material nexus.

Large Language Models (LLMs) offer unprecedented potential for enhancing recommendation systems through their world knowledge and reasoning capabilities. However, existing approaches often rely on structured IDs or offline processing, limiting semantic richness, real-time adaptability, and user-facing interpretability. In this paper, we introduce a novel framework that enables real-time generation of LLM-based user interest personas for a large-scale commercial video recommendation platform. Our method generates natural-language user interest personas that address the exploitation-exploration trade-off by combining the summarization of existing interests with novel topics, directly during serving. To overcome the computational challenges of online LLM inference at a billion-user scale, we design a cost-efficient architecture leveraging knowledge distillation, asynchronous inference, and input optimization via semantically clustered video representations. Extensive offline evaluations, user studies, and live A/B tests demonstrate significant improvements in viewer value. This work bridges the gap between high-level semantic understanding and industrial-scale recommendation, paving the way for more dynamic, explainable, and satisfying personalized experiences.

Brouwer's Laplacian conjecture states that the sum of the largest $k$ eigenvalues of a graph's Laplacian is less than or equal to the number of edges plus $\binom{k+1}{2}$. We give a proof of this conjecture. Our proof relies on the Grone--Merris--Bai theorem for \emph{split} graphs. We also show the converse, thereby establishing an equivalence between Brouwer's conjecture and the Grone--Merris--Bai theorem.

We get bounds on the Hausdorff dimension of the set where the Minkowski question mark function has infinite derivative.

We show that for any $A\subseteq \mathbb{F}_q^n$ lacking non-trivial solutions to a translation-invariant linear equation of genus one, meaning that no nonempty proper subset of the coefficients sums to $0$, there is a set $B\subseteq \mathbb{F}_q^m$ in some higher dimension which also lacks non-trivial solutions, such that \[|B|^{1/m}>|A|^{1/n}.\] In particular, this implies that no fixed cap set in $\mathbb{F}_3^n$ gives an asymptotically optimal lower bound by direct products alone.

In this paper, we develop a continuity method for the Dirichlet problem of Hessian equations on Riemannian manifolds. Such equations, introduced by Caffarelli, Nirenberg and Spruck, are defined in terms of the eigenvalues of the Hessian and a given pair $(f,Γ)$, where $f$ is a symmetric function defined in a symmetric cone $Γ\subset\mathbb{R}^n$, and $Γ$ specifies the set of admissible eigenvalues for the solution. Our method combines techniques from Morse theory with a characterization of the pair $(f,Γ)$. More precisely, in the type 2 case, we first construct admissible functions using Morse theory, and then solve the Dirichlet problem without any additional assumptions on the boundary or the subsolution. Building on this characterization of the pair, we can approximate the type 1 equation by a family of type 2 equations.

In this paper a general framework for convex integration is developed, in order to construct weak solutions to the Cauchy problem, by building on ideas from [C. De Lellis and L. Székelyhidi, Arch. Ration. Mech. Anal., 195 (2010)] and [S. Markfelder, Nonlinearity, 37 (2024)]. This framework may be applied to a large family of partial differential equations in order to construct weak solutions in $L^\infty ((0,T) \times Ω)$ (for a bounded domain $Ω)$ which are weakly continuous in time with respect to the weak topology of $L^r (Ω)$ for some $r \in (1,\infty)$. This allows us to construct solutions which obey an energy inequality. In the second part of the paper we apply the framework to several inviscid models appearing in the field of geophysical fluid mechanics in order to show existence of weak solutions for all initial data, and to prove that there exist initial data for which there are infinitely many solutions which satisfy an energy inequality. We first consider the incompressible and the barotropic compressible Euler equations to recover the corresponding results from the literature. In addition, the framework allows us to prove a new result for the incompressible Euler equations, namely the global existence for the Cauchy problem in $L^\infty$. Moreover, we use the framework in the context of the hydrostatic Euler equations (also known as the incompressible inviscid primitive equations), which leads to the first convex integration approach which is able to construct admissible solutions with the natural energy for this system. A crucial ingredient in the proof of this result is the computation of a large subset of the convex hull. Finally, we apply the framework to the compressible inviscid primitive equations and to the inviscid quasi-geostrophic equations to obtain the first results on existence of wild data for these two geophysical models.

We study the roughening of an interface with nonlinear elasticity driven by temporally correlated noise, which breaks statistical tilt symmetry. Using scaling arguments and a self-consistent Hartree approximation, we derive the crossover diagram and the steady-state structure factor. We identify three scaling regimes associated with the Larkin, anharmonic Larkin, and Edwards--Wilkinson universality classes, and obtain the crossover lengths separating them. Numerical simulations of large systems confirm the analytical predictions over the full parameter range. Our results provide a unified description of finite-size and crossover effects in a minimal nonlinear-elastic Ornstein--Uhlenbeck active interface.

We construct a simple, separable, unital, nuclear C$^*$-algebra without uniform property $Γ$. The construction is based on a new topological obstruction arising from the Thom-Porteous theory of degeneracy loci. Constructions of pathological nuclear C$^*$-algebras over the past 30 years have used Chern class calculations introduced by Villadsen to obstruct the existence of large trivial subbundles. Here, by contrast, we use determinantal Schur classes to force every bundle map between certain equal-rank vector bundles to vanish somewhere on the base space. A quadratic Schubert calculus computation shows that this obstruction can persist across an inductive system and ultimately obstructs the comparison of projections by traces in the uniform tracial completion. The relevant Thom-Porteous classes live in degree proportional to the square of the forced rank loss, which in turn forces dimension growth of the same order in the constituent homogeneous C$^*$-algebras of our example. This identifies a new geometric threshold in the structure theory of nuclear C$^*$-algebras, linking the presence or absence of uniform property $Γ$ to quadratic dimension growth.

We consider the strategic facility location problem in $\ell_q(\mathbb R^d)$ spaces where the social cost is defined by an arbitrary $p$-norm of the individual costs. While the optimal approximation ratios for deterministic strategyproof mechanisms are well established in the $d = 1$ setting, the guarantees for multi-dimensional spaces under an arbitrary $p$-norm are less understood. In this work, we analyze the well-studied, strategyproof coordinate-wise median (CM) mechanism and provide approximation guarantees for these generalized social costs. For $d = 2$, we establish tight approximation ratios for all $p, q \geq 1$. In particular, we show that the CM mechanism is a $2^{1 - 1/ \max(p, q)}$-approximation, resolving a conjecture of Goel and Hann-Caruthers (Social Choice and Welfare, 2023). Furthermore, for $d\geq 3$, we give upper bounds on the approximation ratio of the CM mechanism for arbitrary $p$-norm social costs, generalizing the recent result of Gravin and Jia (STOC, 2025) for the utilitarian social cost. Remarkably, we show that this approximation ratio never exceeds 3, regardless of the dimension.

We develop new inference procedures for a linear IV model that are robust to identification strength and heteroskedasticity of unknown form, and nonparametric with respect to the first-stage equation. Our first test is tailored for inference on parameters of endogenous explanatory variables. Our new statistic modifies that of Antoine and Lavergne (2003) to directly account for heteroskedasticity of unknown form. As a result, it is asymptotically pivotal, so that inference is greatly facilitated in practice. We also develop (i) an identification-robust subvector inference procedure that does not rely on the knowledge of identification strength for the remaining parameters, and (ii) a pure specification test. In both cases, the tests are conservative but powerful. We show that our procedures are computationally friendly and competitive with existing ones in simulations and an application.

This paper develops a new toolbox for estimation and inference in panel data threshold regression models with interactive fixed effects and a fixed number of time periods, T. The toolbox is designed to be simple, accurate and computationally efficient. It is based on a simple least squares style estimator of the model parameters, and includes a number of inferential procedures for testing hypotheses regarding not only the threshold but also other parameters. The new toolbox is applied to study the impact of inflation on economic growth.

We present almost sure polynomial bounds for Hölder norms of solutions of the 1d periodic fractional Benjamin-Bona-Mahony (BBM) equation. Namely, we apply quantitative quasi-invariance of certain Gaussian measures with energy cutoff using the strategy from Tzvetkov (2015) and the globalization argument from Bourgain (1994) in order to extend, almost surely, the $L^2$-based deterministic control to the $L^{\infty}$-based setting.

Given a finite group $G$, we prove that there exist signs $\varepsilon\in\{\pm1\}^G$ such that $$\left\| \sum_{g\in G} \varepsilon_gρ(g) \right\|\leq C\, \sqrt{|G|},$$ where $ρ$ is the left regular representation of $G$, and $C$ is a universal constant. This special case of the Matrix Spencer conjecture was posed in [BKMZ24], where it was established for simple groups.

Single-wall carbon nanotubes (SWCNTs) are narrow ribbons of graphene with atomically precise edges and a single quantum transport channel, at experimentally-relevant dopings. This makes them ideal systems to harness quantum transport straintronics (QTS), i.e. using mechanical strain to control accurately quantum transport. We present QTS data from three single-wall carbon nanotube quantum dot (SWCNT-QD) transistors over a broad range of in-situ tunable and reversible uniaxial strain ($Δ\varepsilon_\text{mech}\approx$ 0 to 3 %). We first present the nanofabrication of the suspended SWCNT transistors whose channel lengths are $\approx$ 30 nm. The channels are strained by moving gold clamps holding firmly the nanotubes. We present detailed charge transport data, $dI/dV_{\text{B}} - V_{\text{B}} - V_{\text{G}}$ and $dI/dV_{\text{B}} - V_{\text{B}} - Δ\varepsilon_\text{mech}$, showing a large mechanical-gating effect of the SWCNT-QDs. The precise reversibility of the data, and their agreement with QTS theory, confirms that the tubes are strained elastically. We demonstrate that the mechanical control of the QD doping is not due to capacitive-gating effects, but to quantitatively predictable bandstructure changes including a strain-tunable bandgap. This precise mechanical control of the doping and bandgap of SWCNT-QDs could find applications in qubits, condensed matter physics, and homojunction molecular transistors.

A large body of work studies the problem of learning an approximation to an implicit matrix $A\in \mathbb{R}^{m\times n}$ that is only accessible implicitly via matrix-vector product queries (matvec queries) of the form ${x} \rightarrow {A}{x}$ or ${x} \rightarrow {A}^T{x}$. Of particular interest are methods that learn a near-optimal approximation with a fixed sparsity pattern. For example, we might want to learn a near-optimal diagonal, banded, or arrow-head approximation to an implicit matrix $A$. Naturally, the number of matvec queries required to solve this problem depends on the sparsity pattern, which can be encoded as a binary matrix ${S}\in \{0,1\}^{m\times n}$. The query complexity of previous algorithms scales with quantities like the total number of ones in ${S}$, its maximum column/row sparsity, or the chromatic number of a its "conflict graph". These quantities are incomparable: for a given ${S}$, parameterizing by one might yield lower query complexity than another. In this work, we unify and tighten these prior results by providing a nearly sharp characterization of the matvec query complexity of sparse matrix approximation. Generalizing a definition from graph algorithms, let the degeneracy, ${degen}({S})$, denote the smallest number $k$ so that, if we iteratively delete all rows and columns of ${S}$ with $\leq k$ ones, we are left with an empty matrix. We show that a near-optimal approximation to $A$ with sparsity pattern $S$ can be learned with $\tilde{O}({degen}({S}))$ matrix-vector product queries, and $Ω({degen}({S}))$ queries are necessary, for any sparsity pattern ${S}$. Moreover, unlike prior work based on graph coloring, all of our methods run in polynomial time.

Let $M \subset \{0,\pm1\}^n$ be a set such that $(m,m)=4$ for every $m\in M$, and $(m_1,m_2)\in\{-4,-3,-2,-1,0,3\}$ for any two distinct vectors $m_1,m_2\in M$. We determine the maximum possible cardinality of such a set $M$ for all sufficiently large $n$.

Moving horizon estimation (MHE) provides high precision state estimation for nonlinear systems, but it is often limited by the substantial computational demands of solving a nonlinear optimization problem at every sampling step. To address this issue, we develop an efficient MHE scheme based on linear parameter-varying (LPV) formulation, where the scheduling parameters are given by the estimated states of the system and used to construct inexact Jacobians. Due to the LPV representation, the Jacobian can be pre-specified offline in a structured form and then updated in the quadratic programming (QP) subproblem, which reduces computational cost commonly used in standard nonlinear programming (NLP) systems. We illustrate the performance by numerical simulations.

This paper develops a decoupled low-order conforming finite element method for a fourth-order elliptic singular perturbation problem in three dimensions. By means of a generalized Helmholtz decomposition, the problem is reduced to two second-order elliptic problems and a system of generalized singularly perturbed Stokes-type equations subject to a curl-free constraint. The former are discretized by standard linear finite elements. For the latter, we employ the MINI element and show that, after adding an $L^2$ term involving a Lagrange multiplier, the resulting discretization becomes robust with respect to the perturbation parameter. We further establish an error estimate of order $h^{1/2}$ uniform with respect to the perturbation parameter. Numerical experiments are included to support the theory.

We use effective field theory to factorize production matrix elements that appear in the NRQCD framework for quarkonium cross sections. By applying a Hubbard-Stratonovich transformation and appropriate field redefinitions, we show that the soft and ultrasoft sectors of NRQCD can be decoupled from the heavy quark and antiquark fields in a hybrid vNRQCD/pNRQCD Lagrangian at leading order in the velocity power-counting. This enables us to re-factorize quarkonium production matrix elements in terms of matrix elements of color-singlet composite fields, which we can write as the wave-function at the origin, and state independent vacuum correlators of chromo-electric and chromo-magnetic gluon fields. This approach verifies powerful relationships between the LDMEs of different S-wave quarkonia originally derived using pNRQCD. Additionally, it allows us to derive new relationships for the production matrix elements used in the transverse momentum dependent factorization (TMD) framework, known as TMD soft transition functions, providing a much stronger set of constraints on these nonperturbative operators. This work significantly advances our understanding of quarkonium production, particularly in the TMD framework.

Quantifying the likelihood of extreme events underpins risk assessment, yet classical Extreme Value Theory relies on asymptotic assumptions that fail in the data-sparse, non-stationary regimes practitioners increasingly face. We introduce the Data-Driven Extreme Value Distribution (DDEVD), a non-parametric estimator that aggregates all observations metastatistically and reconstructs the base distribution with a kernel, removing parametric tail assumptions. We derive its optimal bandwidth and prove a stability law $m < C\,n^{1+γ/2}$ relating reliable extrapolation to the extreme value index $γ$. In sub-hourly Alpine precipitation, DDEVD recovers stable 100-year return levels from single decades (calibration ratio $0.96$), departing from the full-record reference by over $50\,\%$ in fewer than one window in fifty -- versus one in five for a GEV fit. In metallurgical micrographs, it matches a generalised extreme-value fit on the safety-relevant grain-size tail, where the standard log-normal over-predicts by $58\,\%$ at $1\,\mathrm{cm}^{2}$.

Randomness amplification, the task of extracting uniform private bits from biased seeds that may be partly known by a malicious third party, is of central importance in cryptography. The highest security in this task is provided by a class of quantum protocols known as device-independent, which however are challenging to integrate into scalable devices. Semi-device-independent (SDI) protocols are a promising alternative that guarantees security under few natural assumptions, such as bounds on the amount of energy used by the devices. Here, we provide the first demonstration of SDI randomness amplification on an integrated silicon photonic chip, achieving a throughput rate of 20 Mbps suitable for practical applications. This rate is achieved through a novel technique for SDI entropy certification, which delivers strictly tighter von Neumann entropy bounds compared to existing methods and remains valid even if the preparation and measurement devices share quantum correlations. Overall, the methods developed in this work enable the integration of SDI technology into portable telecom devices, opening up a new generation of quantum cryptographic hardware.

Motivated by earlier approaches, we develop a worldsheet framework for computing correlation functions in the single trace $T \overline{T}$-deformed tensionless AdS$_3$/CFT$_2$ duality. By describing the deformed bulk theory as a Berkovits-Vafa $\mathcal{N}=4$ topological string, we obtain a consistent definition of physical states and correlation functions, yielding a tractable setup for testing aspects of holography beyond AdS/CFT. We construct deformed physical vertex operators and compute their tree-level two-point functions exactly. We discuss the relation of our results to previous proposals for $T \overline{T}$-deformed two-point functions obtained from alternative worldsheet approaches, JT gravity, and perturbative field theory computations.

We develop a stochastic framework for the stationary spherical Jeans equation, motivated by the field-dependent nature of the gravitational coupling in scalar--tensor theories. We model unresolved spatial fluctuations of the scalar sector as an effective stochastic contribution to the gravitational coupling, $\Geff(r,ω)=\Gbar(r)+Γ_G(r)ξ(r,ω)$. This approach induces a linear Itô stochastic differential equation for the radial velocity dispersion $y(r)=σ_r^2(r)$, defining a nonautonomous radial random flow rather than a time-evolution problem. We derive the associated Fokker--Planck equation and obtain integral expressions for the mean, variance, and covariance of the radial velocity dispersion. Because the noise is additive, the deterministic Jeans solution is recovered as the mean profile, while the stochastic sector produces a probability band around it. We specialize the construction to Navarro--Frenk--White, Hernquist, and Einasto halo models and propagate the radial covariance to the projected line-of-sight velocity dispersion. This provides a semi-analytical framework for assessing how effective gravitational fluctuations can affect halo kinematic observables in the stationary Jeans regime.

Fiber optical cavities offer small mode volumes and correspondingly strong light-matter interactions in an open Fabry-Perot geometry. However, existing fabrication techniques do not reliably produce substrates with surface profiles amenable to high mode matching between the cavity mode and fiber core, thereby limiting the achievable collection efficiency. Here we present a technique to fabricate fiber mirror substrates while using $\textit{in situ}$ reflectometry to constrain the achievable mode matching prior to coating. By measuring the back-reflection from freshly cleaved fiber tips, we pre-select 138 fibers compatible with 96.5-99.5% mode matching, and after a single CO$_2$ laser ablation pulse, these fibers remained compatible with 95.3-99.2\%. This simple technique provides rapid feedback during each stage of substrate fabrication, greatly enhancing the yield of viable fiber mirror substrates prior to (expensive) coating runs.

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms that generate revenues through resource usage. We focus on a challenging setting where: (i) infrastructure deployment requires substantial upfront investment, which the InP must recover via payments by firms that depend on their uncertain future revenues; (ii) firms' resource usage is jointly influenced by exogenous factors, infrastructure pricing, operational costs, and resource congestion; and (iii) firms exhibit heterogeneous risk aversion. This setting is typical in emerging technologies, e.g., Mobile Edge Computing (MEC). We formalize this setting as a novel Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader and jointly optimizes capacity dimensioning and access pricing, while firms act as followers that share the infrastructure and commit upfront to future resource usage under uncertain revenues. Followers' heterogeneous risk aversion is modeled through Conditional Value-at-Risk (CVaR). We prove the existence of a Stackelberg equilibrium (SE), in which the followers' decisions constitute a generalized Nash equilibrium, and develop a polynomial-time algorithm that computes an approximate SE with a bounded optimality gap. We also derive a lower bound on the followers' Probability of Profit (PoP). Monte Carlo simulations for a MEC case study show that higher followers' risk aversion reduces infrastructure capacity, pricing, and leader profit, while increasing followers' PoP.

There is a conundrum regarding the binding of $α$ particles in nuclei. On one hand, auxiliary-field Monte Carlo simulations of Hamiltonians on discrete spatial lattices proposed that attractive two-nucleon potentials, alone or together with attractive three-nucleon potentials, yield accurate nuclear binding. On the other hand, such Hamiltonians typically overbind all but the lightest nuclei in continuum-space approaches. We address this puzzle by performing Hartree-Fock computations of the light nuclei $^4$He, $^8$Be, $^{12}$C, and $^{16}$O, and of nuclear and neutron matter using established lattice Hamiltonians. These variational upper bounds for the ground-state energies show that the Hamiltonians with only two-nucleon potentials do not yield accurate binding, in contrast to the results from auxiliary-field Monte Carlo simulations. The case is different for Hamiltonians with three-nucleon potentials although it is the dense packing on the lattice -- and not repulsive potentials -- that yield a constant binding energy per nucleon.

The problem of pricing mobility services has attracted significant attention. In most studies, uncertain demand is modeled as an exogenous random variable with known distribution. This assumption overlooks the likely effect of prices on user adoption decisions. To address this dependency, we formulate the pricing problem as a stochastic program with decision-dependent demand uncertainty. Specifically, we make the non-standard assumption that the probability distribution of demand depends on pricing decisions. We show that the problem can be written as a mixed-integer linear program whose size is exponential in the input parameters. To find exact numerical solutions we specialize the L-shaped method for stochastic programs with decision-dependent uncertainty. In particular, we devise efficient separation routines by proving closed-form primal and dual solutions to the involved subproblems. In addition, we develop problem-specific valid inequalities and cut-sharing mechanisms which significantly improve convergence. We show that the method outperforms by far a commercial solver used to solve the monolithic formulation. Furthermore, in a case study based on a real-world carsharing system, we show that incorporating decision-dependent uncertainty improves expected profits by 8.39% compared to a benchmark that considers deterministic price-elastic demand, and by 8.53% compared to a benchmark that considers exogenous random demand, on average. In addition, we evaluate the performance of preventive pricing and relocation decisions under two vehicle allocation policies. The results suggest that a controlled allocation of vehicles to customers can improve service rates while only marginally affecting profits.

Air pollution regulatory limits are typically defined in terms of exceedances of concentration thresholds which are naturally related to conditional quantiles of the pollutant distribution and are therefore of direct relevance for assessing severe pollution events. At the same time, it is important to determine not only whether a covariate affects air pollution but also whether this effect is linear, nonlinear, or both. We address these issues by developing a Bayesian effect selection approach for additive quantile regression. While commonly used mixed model representations (MMRs) of penalized splines allow for flexible nonlinear effects, they do not provide a meaningful separation of linear and nonlinear effect components. We therefore employ a Demmler-Reinsch basis expansion, which yields an orthogonal decomposition of each additive effect into linear and nonlinear parts and show theoretically that both effect components can be estimated consistently. To facilitate data-driven model building, we propose Bayesian effect selection with separate spike and slab priors on the scalar importance parameters associated with the linear and nonlinear components and implement an efficient Gibbs sampler. Through simulation studies, we demonstrate robustness to the misspecification induced by the employed asymmetric Laplace working likelihood and show superior performance relative to the MMR. In a detailed analysis of air pollution data in Madrid, Spain we highlight the added value of flexibly modeling extreme nitrogen dioxide (NO$_2$) concentrations and reveal that threshold-relevant pollution levels are driven differently by climatological variables and traffic-related spatial structure. These findings underline the need for advanced statistical models that support short-term decision-making and help local authorities mitigate, or potentially prevent, exceedances of NO$_2$ concentration limits.

Port-Hamiltonian systems provide a structured framework for modeling physical systems by explicitly capturing their energy storage, dissipation, and exchange. However, deriving such models often requires detailed physical insight and precise knowledge of system parameters, which may not be available in practice. In this paper, we propose a kernel-based framework for the identification of port-Hamiltonian systems from input-state-output data. In contrast to conventional parametric approaches, the maps defining the port-Hamiltonian system are represented in suitably chosen reproducing kernel Hilbert spaces. This leads to an infinite-dimensional optimization problem over the corresponding function spaces. Our main result establishes a representer theorem that reduces this problem to a tractable finite-dimensional one. Since the reduced problem is non-convex, we further provide an algorithm for its solution and prove its convergence.