While the interplay of correlations and geometric frustration in doped Mott insulators provides a fertile ground for exotic quantum phases, the nature of the metallic state emerging upon particle doping remains poorly understood. In this work, we investigate the triangular-lattice Hubbard model with particle doping and provide compelling evidence for an intrinsic, interaction-driven quantum state, which we term the Nagaoka supermetal. This state is characterized by a sublinear temperature dependence in the DC resistivity, along with singular behaviors in the charge compressibility and zero-frequency spectral weight. To understand the origin of these singular properties, we derive an effective low-energy model and demonstrate that a higher-order Van Hove singularity emerges from the reconstructed dispersion. This singularity gives rise to a power-law divergence in the density of states, capturing the anomalous properties observed in the supermetallic regime. Our findings offer a new perspective on non-Fermi liquid states in geometrically frustrated systems and are directly accessible in current ultracold atom experiments.

Aggregating building heating, ventilation, and air-conditioning (HVAC) fleets provides substantial real-time flexibility to power system operations. However, real-time aggregation of multi-zone HVAC fleets faces two key challenges: (i) strong coupling across zones and time makes flexibility characterization high-dimensional and computationally demanding, and (ii) the sequential revelation of temperature states and exogenous conditions requires that decisions made at each period preserve feasibility over the remaining horizon using only currently realized information. To address these challenges, this paper proposes a reachable-set decomposition framework comprising an offline decomposition stage and a real-time policy. In the offline stage, backward reachable sets are formulated to encode remaining-horizon feasibility into per-period state constraints, so that any state within the current reachable set is guaranteed to sustain feasible operation over the entire remaining horizon. A tailored inner approximation is then developed for tractable calculation in multi-zone-coupled HVAC settings. In the real-time stage, aggregate flexibility is computed efficiently via building-level parallel linear programs followed by closed-form Minkowski summation of power intervals, and any regulation signal within the reported flexibility interval admits a recursively feasible disaggregation. Case studies demonstrate the effectiveness of the proposed framework in aggregate flexibility characterization, disaggregation feasibility, and scalable computation.

We solve an open problem in entanglement theory posed by Yu et al., {\it Nature Communications 12, 1012 (2021)}. The problem is to show, via an entanglement witness, that the $14$-qubit state $Φ_{\text{E8}}$ is entangled. Inspired by a method from quantum codes, we combine symmetric extension with moment matrices to prove that $Φ_{\text{E8}}$ is entangled. The proof has the form of a rational infeasibility certificate for a semidefinite program, yielding an explicit entanglement witness. Our approach unifies and extends several earlier methods that involve the Lovász theta number of the Pauli anti-commutativity graph, promising scalability and flexibility in further applications.

Rare-earth gain media form the foundation of modern optical communications, emerging quantum hardware, and ultrafast optics. While chip-scale integration can enable fiber-like, and potentially beyond-fiber, functionality with unprecedented scalability, development in the visible and near-infrared remains in its early stages. Here, we demonstrate ytterbium-based optical gain integrated into an aluminum oxide photonic platform, achieving both single-mode lasing and optical amplification in the near-infrared regime. This platform delivers optical amplification with output powers exceeding 0.5 W, an optical-to-optical conversion efficiency above 70%, and a noise figure of 3.3 dB, approaching the quantum limit for phase-insensitive amplification. Furthermore, we achieve femtosecond pulse amplification to a record peak power of 14 kW, enabling supercontinuum generation with visible dispersive waves extending from 780 to 476 nm in conjunction with nonlinear photonic devices. This platform is compatible with heterogeneous integration into standard photonic circuits, laying the foundation for scalable visible-near-infrared photonic systems, including coherent laser arrays, mode-locked lasers, optical clocks, and microwave oscillators.

We demonstrate finite-time blow-up in a simple, realistic shell model of the 3D Navier-Stokes equations, equipped with "smooth" (i.e., rapidly decaying in frequency) initial data and forcing. Previously studied models either exhibit a turbulent cascade that regularizes the three-dimensional viscous dynamics, or rely on highly artificial interactions not transparently realized in the true Euler nonlinearity. We also treat the inviscid, unforced case and obtain singularity formation just above the energy level. We conclude with a discussion of the prospects for embedding the behavior of the dyadic model into the full Euler and Navier-Stokes equations.

We study Hecke operators on moduli spaces of ramified $G$-bundles using the combinatorial language of Hecke graphs. We introduce a general notion of $\mathcal H$-ramification in the spirit of parahoric ramification, which depends on a choice of a divisor and subgroups of $G$ at every point of the divisor. Building on our previous work, we prove that, under mild regularity conditions, the action of a Hecke operator in the deep cusp of $\mathrm{Bun}_G$ in a highly complex ramification mimics an action in a much simpler ramification. This reduces the study to a smaller number of cases which, in particular, involve divisors supported at no more than two points. We demonstrate our methods by computing various examples for $G=\mathrm{PGL}_2$ and computing the dimensions of spaces of Hecke eigenforms for generic eigenvalues.

This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of hostility between countries. For the autonomous case, the asymptotic stability is studied in a comprehensive way, and the Hopf bifurcations occurring as the delay crosses some critical values are described. For the non-autonomous model, conditions ensuring the global asymptotic stability for both the linear approximation and the nonlinear system are established. The framework of special solutions for delay differential equations is also applied.

We study Walker manifolds, that is, pseudo-Riemannian manifolds $(M^n,g)$ admitting a null parallel distribution $\D$ of rank $r\leq\frac{n}{2}$. We show that $\D$ always integrates to a $G$-Lie foliation $\F_\D$, where $G$ is the simply connected Lie group with Lie algebra equal to the structure algebra $\g_\D$ of $\D$. The transverse holonomy group of $(M,g)$ coincides with the image of the holonomy morphism $h:π_1(M)\to G$. We prove that $\mathrm{Ric}(X,\cdot)=0$ for all $X\inΓ(\D)$, and show that in dimension~$3$ the model group is always $\R$, while in dimension~$4$ with rank~$2$ the structure algebra is always abelian. A local classification distinguishes the abelian, nilpotent, and solvable cases, and a rigidity theorem shows that a minimal nilpotent Walker foliation of dimension~$4$ cannot be deformed into a non-nilpotent solvable one.

A search is performed for the electroweak pair production of charginos and associated production of a chargino and neutralino, each of which decays through an $R$-parity-violating coupling into a lepton and a $W$, $Z$, or Higgs boson. This search targets the Higgs boson decay channel of the charginos and neutralinos, using events with three or more $b$-tagged jets and one or two electrons or muons. The analyzed data corresponds to an integrated luminosity of 140 fb$^{-1}$ and 56 fb$^{-1}$ of proton-proton collision data produced by the Large Hadron Collider at center-of-mass energies of $\sqrt{s}=13$ TeV and $\sqrt{s}=13.6$ TeV respectively, collected by the ATLAS experiment between 2015 and 2023. The data are found to be consistent with predictions from the Standard Model. The results are interpreted as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model. Limits are also set on the production of charginos and neutralinos for a Minimal Supersymmetric Standard Model with an additional $B-L$ gauge symmetry that is spontaneously broken. Charginos and neutralinos with masses between 150 GeV and 1100 GeV are excluded at 95% confidence level for a scenario in which they decay via Higgs bosons, assuming equal decay branching fractions to each lepton flavor. Additional limits are derived for flavor-specific decay scenarios.

Bistable tape spring booms are used on spacecraft for their ability to self-deploy using stored strain energy. However, their uncontrolled deployment can induce mechanical shocks that are variable as a function of material properties and temperature, and may damage sensitive satellite components and disrupt attitude control. Because traditional Finite Element Analysis (FEA) struggles to accurately capture this highly nonlinear behavior, we solve the inverse problem to estimate these loads from dynamic response measurements. Previous data-driven approaches using Vector Fitting required time-consuming retesting for every specific load level due to the boom's load-dependent dynamic behavior. To overcome this limitation, we introduce a parametric data-driven framework where a parametric transfer-function model of a composite tape spring boom is developed using force and velocity measurements. The parametric Adaptive Antoulas-Anderson algorithm (p-AAA) is used to construct a single parametric (multivariate) transfer function capable of capturing the nonlinear response of the boom to load amplitude. To evaluate the proposed framework, the boom is excited at its base at 15 distinct load levels using a single-axis reference input signal. Results demonstrate that the single parametric model outperformed the best discrete non-parametric case, reducing the total relative force estimation error for the reference signal by nearly 38\%. For experimental validation, the boom is subjected to sinusoidal, triangular and square signals. The cross validation results further supported this generalized performance. Collectively, these results show that the proposed parametric model accurately reconstructs input forces from velocity measurements alone, offering a solution for onboard diagnostics in future space missions.

Emergency response vehicles (ERVs), such as fire trucks, operate to save lives and mitigate property damage. Emergency vehicle preemption (EVP) is typically implemented to provide the right-of-way to ERVs by giving green signals as they approach signalized intersections along their routes. EVP operations are usually optimized to minimize ERV delay. This study seeks to reduce delay experienced by other vehicles in the network while keeping ERV travel time near its optimum. A machine learning-based EVP strategy, termed MLEVP, is developed to determine EVP trigger times at multiple downstream intersections using real-time sensor data, including vehicle detections, signal indications, and ERV location. MLEVP proactively clears downstream traffic queues to reduce ERV response time while limiting delay on conflicting traffic movements. In the case study, MLEVP is developed using a calibrated microscopic simulation of a signalized corridor testbed in PTV Vissim. The EVP problem is formulated as a regression problem and solved using machine learning models trained on data generated from the simulation. Results demonstrate that the proposed algorithm can produce near-optimal ERV travel times while minimizing impacts on conflicting traffic.

Given a canonically oriented Brieskorn sphere $Y=Σ(a_1,...,a_n)$, we confirm some statements conjectured by Gompf. More specifically, we obstruct the existence of rational homology ball symplectic fillings for any contact structure on $-Y$ if $n=3$, and when there is no half convex Giroux torsion for $n>3$. Furthermore, we show that the same result holds for the Milnor fillable structure on $Y$ with the possible exception of $Σ(3,4,5),$ $Σ(2,5,7)$ and $Σ(2,3,6k+1)$ for $k\geq1$. Along the way, we determine every canonically oriented Brieskorn sphere with vanishing correction term carrying at most two fillable structures, up to isotopy.

We consider the ``metric-affine-like'' generalization of the Yang-Mills theory (mal-YM) which we first proposed earlier. In this model, the connection is no longer assumed to be compatible with the Hermitian form in the fibers. As a consequence, along with the usual YM potential $\boldsymbol{A}_a$ and the field strength tensor $\boldsymbol{F}_{ab}$, it contains non-trivially interacting fields $\boldsymbol{B}_a$, $\boldsymbol{h}$, and $\boldsymbol{G}_{ab}$, $\boldsymbol{N}_a$, forming a non-Abelian generalization of Stückelberg theory. Due to the spontaneous symmetry breaking $GL(n,\mathbb{C}) \to U(n)$, these new fields can be made massive and the limit $M\to\infty$ restores the standard YM theory. We perform a detailed analysis of this theory on the classical level. We discuss in detail geometric motivation for the model, field transformations, gauge symmetry and its spontaneous breaking, action, equations of motion, Noether identities, gauge fixing, and other issues.

We generalize the framework of tilt-stability to singular schemes and formulate the generalized Bogomolov-Gieseker inequality conjecture of Bayer-Macrì-Toda for singular threefolds. We also develop relative versions of these constructions, generalizing corresponding results in [BLM+21]. Along the way, we establish Bogomolov-Gieseker-type inequalities for semistable sheaves on any projective scheme. By extending previous techniques, we verify the conjecture for all Fano threefolds with canonical Gorenstein $\mathbb{Q}$-factorial singularities and a series of singular Calabi-Yau threefolds. Furthermore, we construct stability conditions on the relative Kuznetsov components associated with families of singular Fano threefolds, thereby proving a singular analogue of a conjecture of Kuznetsov-Shinder.

Despite extensive research on chirality-driven spin selectivity, most studies have focused on static magnetic properties, while the influence of chirality on the dynamic magnetic response remains largely unexplored. Here, we investigate how chiral molecular interfaces affect magnetization dynamics in thin Co/Ni multilayers with perpendicular magnetic anisotropy using broadband ferromagnetic resonance spectroscopy. A comparison between bare (reference) films and molecule-functionalized (hybrid) samples reveals no measurable changes in either the resonance field or the linewidth that could be attributed to the presence of the chiral environment. Motivated by our findings we develop a macrospin description that distinguishes equilibrium modifications of the magnetic free-energy landscape (MIPAC-type effects) from non-equilibrium, CISS-induced spin torques. Our analysis shows that equilibrium modifications primarily shift the resonance condition via changes to the free energy landscape and thereby the effective field, whereas damping-like non-equilibrium torques provide a distinct channel for varying the effective damping rate. This approach establishes clear criteria for disentangling chiral-interface-induced energy modifications from torque-driven dynamical effects in ferromagnetic resonance experiments.

We consider non-Fuchsian monodromy preserving deformations on a Riemann sphere. The associated isomonodromic deformation parameters on this surface comprise the positions of the singularities, together with the Birkhoff (spectral) invariants owing to the presence of irregular singularities. Our first main result is the derivation of the Loewner evolution of these isomonodromic deformation parameters. Using this result, we construct martingale observables for Schramm-Loewner evolution (SLE(4)) processes in the presence of double poles. Geometrically, the expressions contain the pre-Schwarzian and Schwarzian of the Loewner evolution, arising from conformal covariance of the observable. Furthermore, we characterize these SLE(4) observables uniquely in terms of confluent BPZ equations of a CFT with central charge c=1.

Our input is a directed graph $G = (V,E)$ on $n$ vertices and $m$ edges with a designated root vertex $r$ and a function $cost: E \rightarrow \mathbb{R}_{\geq 0}$. The problem is to maintain a min-cost arborescence in $G$ in the presence of edge faults (a single fault at a time). Edge faults are transient and once the faulty edge is repaired, the original min-cost arborescence $\mathcal{T}$ is restored. Whenever an edge fault happens, we need to update $\mathcal{T}$ to a min-cost arborescence in $G-f$, where $f$ is the faulty edge. Since computing a min-cost arborescence in $G - f$ takes $O(m + n\log n)$ time, we seek to construct a sparse subgraph $H$ in a preprocessing step such that in the event of any edge $f$ failing, it suffices to compute a min-cost arborescence in $H - f$ in order to find a low-cost arborescence in $G - f$. In the unweighted setting, this is the fault-tolerant subgraph problem for single-source {\em reachability}. Baswana, Choudhary, and Roditty (SICOMP, 2018) showed a $k$-fault tolerant reachability subgraph of size $O(2^kn)$, where $k$ is the number of edge faults. We show a simple polynomial-time algorithm to construct a subgraph $H$ of size $O(n^{3/2})$ such that, for any $f \in E$, a min-cost arborescence in $H-f$ is a 2-approximation of a min-cost arborescence in $G-f$. Thus whenever an edge fault happens, we can find a 2-approximate min-cost arborescence in $G-f$ in $O(n^{3/2})$ time. Our second problem is in the matroid setting. The input is a matroid $M = (E, {\cal I})$ with a function $cost: E \rightarrow \mathbb{R}$. The problem is to compute a sparse $S \subseteq E$ (called a $k$-fault tolerant preserver) such that for any $F \subseteq E$ with $|F| \le k$, the matroid $M|(S\setminus F)$ contains a min-cost basis of $M|(E\setminus F)$. We show a tight bound of $k.rank(E)$ on the size of a $k$-fault tolerant preserver.

The event PS16dtm, which occured in the center of the Narrow Line Seyfert 1 (NLS1) galaxy SDSS J015804.75-005221.8 (z = 0.080440), is one of the few candidates for a tidal disruption event in an already-acretting active galactic nucleus (AGN). We aim to shed light on the character of the tidal disruption event in this source since it exhibits unusual peculiarities, such as the double-peak optical/UV light curve and a low blackbody temperature with a lack of X-ray emission. We perform spectral analysis of the source before and during the event. We model the time evolution of the luminosity profile using a numerical code that describes the viscous evolution of the flow. From the combined spectral and timing studies, we interpret the event as the disruption of a $\sim 0.3 M_{\odot}$ main-sequence star, or gradual partial disruption of the low-mass giant star. The star is likely on a circular orbit, embedded in the accretion disc. The discussion of the evolution of the star rather suggests that the orbit is counter-rotating. We observe the system at a sufficiently large viewing angle that the actual disruption process is not directly observed. The disrupted star and inner disc are shielded from the observer by a gaseous envelope. Further observations of the system returning to the previous NLS1 state, particularly in the X-ray band, are needed to confirm the proposed scenario and to put constraints on the return to a regular NLS1 state.

We investigate the structure and emission properties of a thin accretion disk around a rotating charged black hole described by an effective higher-curvature-inspired spacetime, constructed as a phenomenological deformation of the Kerr Newman geometry. In this framework, the deformation is introduced through a modification of the metric function $Δ$ by an effective Gauss-Bonnet-like parameter $α$, such that the spacetime reduces to the standard Kerr Newman solution in the limit $α\to 0$. Adopting a kinematical approach, we use test-particle motion to derive the specific energy, specific angular momentum, and angular velocity of circular orbits, and analyze the effects of the parameters $α$ and charge $Q$ on the innermost stable circular orbit (ISCO), radiative efficiency, radiation flux, temperature, and differential luminosity of the disk. We find that increasing $α$ shifts the ISCO inward and enhances the disk's radiation flux and temperature, while the presence of charge suppresses these quantities due to electrostatic effects. Our results demonstrate that effective higher curvature deformations of rotating black hole spacetimes can lead to observable deviations from the Kerr case, highlighting accretion disks as sensitive probes of strong-gravity effects without relying on a specific underlying gravitational theory.

Variational quantum algorithms (VQAs) are a central paradigm for noisy intermediate-scale (NISQ) quantum computing, yet their reliance on predesigned and pretrained variational quantum circuits (VQCs) introduces critical security vulnerabilities, particularly backdoor attacks. These attacks embed hidden malicious behaviors that remain dormant under normal conditions but are activated by specific triggers, leading to adversarial outcomes such as incorrect predictions or manipulated objective values. This paper presents a survey of backdoor attacks in VQCs, covering data-poisoning, compiler-level, and quantum-native mechanisms. We formalize key terminology and threat models, and review existing attack strategies along with their empirical characteristics. We also analyze current detection and defense approaches, highlighting their limitations, especially against quantum-specific threats. By synthesizing recent advances, this survey outlines the evolving security landscape of VQCs and identifies key challenges and future directions for developing robust, quantum-aware defenses in hybrid quantum-classical systems.

The three-dimensional symmetric Mahler inequality states that, for every origin-symmetric convex body \(K=-K\subset \mathbb{R}^3\), \[ \VP(K)= |K|\,|K^\circ|\geq \frac{32}{3}. \] It was recently proved by Iriyeh--Shibata \cite{IS2020}, and a shorter proof was later given by Fradelizi--Hubard--Meyer--Roldán-Pensado--Zvavitch \cite{FHMRZ}. Both proofs combine ingenious equipartition arguments of algebraic-topological origin with delicate geometric estimates inspired by Meyer's argument for unconditional bodies. In this paper, we give a new proof of this inequality using a purely geometric approach, based on what we call symmetric admissible shadow systems. This is a natural extension of the new techniques developed in our proof of the three-dimensional non-symmetric Mahler conjecture \cite{CLXX-Mahler}.

We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological $θ$-term, in the dyon condensation phase, is described by a massive two-form field $B_{μν}$ that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling. This corresponds to a quantum consistent "free string" in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the $B_{μν}$ field, instead of living in a higher-dimensional space. It correspondingly contains a massive world-sheet resonance, in addition to the Nambu-Goto phonons, that improves fitting with data. We compute the confining potential and show that it reproduces a generalized Arvis potential $V(L) = aL \sqrt{1 - c/L^2}$ with running parameters $a(L), c(L)$. We compute the mass difference ratios for the heaviest quarkonium and find 2.5 percent agreement with experiment already at the infrared fixed point. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value $α_0 = 1/12$. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.

In this paper, we consider weighted Dirichlet spaces $\cD_ω$, where $ω$ is a positive superharmonic weight on the unit disc $\DD$. These spaces include the standard weighted Dirichlet spaces $\cD_α$ and appear in the description of their invariant subspaces. Our goal is to study the spaces $\cD_ω$. We show that an explicit description of invariant subspaces reduces to the description of those generated by a bounded outer function, and then to the problem of describing cyclic functions, known as the Brown--Shields conjecture. We develop tools, analogous to those used in the harmonic case, that are needed to treat this problem for superharmonically weighted Dirichlet spaces $\cD_ω$. In particular, we obtain a formula for the Dirichlet integral of outer functions of Carleson--Richter--Sundberg type, estimates for the norm of the reproducing kernel of $\cD_ω$, and several properties on the capacity associated with $\cD_ω$. Using these tools, we provide a description of invariant subspaces when the measure $Δω$ is finite measure or if the $\supp(Δω)\cap \TT$ is countable, where $\TT$ denotes the unit circle. Finally, we prove that a smooth outer function $f \in \cD_α$ such that $\cZ (f) $ is "regular" is cyclic in $\cD_α$ if and only if $c_{α}(\cZ(f))= 0$.

The stationary Kuramoto mean field game models a population of phase oscillators that form synchronized Nash equilibria above a critical interaction strength. We prove that the synchronized branch is a unique smooth family of Nash equilibria emerging from the uniform state at the bifurcation: at each supercritical interaction strength the synchronized equilibrium is unique up to rotation of the torus, and converges smoothly to the uniform distribution as the interaction parameter decreases to the critical threshold. Both follow from our main technical result: the scalar self-consistency map is strictly concave, settling a conjecture of Carmona, Cormier, and Soner. The proof decomposes the second derivative of the self-consistency map into two sign-indefinite moments of the equilibrium--a cubic moment and a gradient moment--and controls their signs through sharp shape estimates for the value function, a pointwise geometric-mean monotonicity that determines the sign of the cubic moment via a cosine-skewness inequality, and a reflection argument combined with a correlation inequality for the gradient moment.

Planet-encircling dust storms fundamentally reshape Martian weather and the near-surface electrostatic environment. We investigate the generation and evolution of electric fields during global dust storms using bimodal dust size distributions from the NASA Ames Mars Global Climate Model, coupled with a triboelectric charging and electrostatic diagnostic scheme that links collisional charging to the local dynamical state of the atmosphere. Focusing on the dust-lifting and buildup phase and its subsequent evolution, we quantify the electric-field energy density and discharge characteristics, including onset thresholds, event frequency, and spatial clustering. The simulations reveal broad storm-active belts of enhanced electrification, with the most frequent threshold exceedances occurring in southern low-to-mid latitudes and secondary activity in northern low-to-mid latitudes. Modeled near-surface electric fields reach $10^{2}$--$10^{3}\ \mathrm{V\,m^{-1}}$ comparable to values inferred for smaller-scale dust phenomena. The results indicate that electric-field generation is controlled by the interplay between dust loading, turbulence-driven collisional activity, and conductivity-dependent charge relaxation, with diurnal conductivity variations strongly suppressing daytime electric-field buildup and most events remaining in the weak glow or Townsend discharge regime. While the model captures the large-scale distribution of electrically favorable conditions, the predicted spatial extent of activity likely represents an upper bound, as small-scale turbulent structures are not fully resolved. These results provide a quantitative framework to identify regions where electrostatic discharges are most likely during GDSs and to inform instrument design, power-system protection, and operations planning for future robotic and human missions.

The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural reductions are specified by introducing atomic blocks and global rendezvous points in the parameterized program's thread template. We study the problem of deciding whether a given natural reduction is sound wrt. a given (semi-)commutativity relation. In the case that there is no synchronization between threads, we present a sound and complete polynomial-time algorithm. In the case where synchronization is considered, we provide a general lower bound for the problem (parametric in the synchronization mechanism), and show that the problem is coNP-hard already for a simple mechanism like locking.

Creativity is fundamentally human. As AI takes on more of the generative work that once required human imagination, despite documented limitations in creative ability, a critical question emerges: How does GenAI affect users' creativity? Through a within-subject study followed by retrospective interviews with (N=20) programmers, we investigated the impact of LLMs on participants' process of creative thinking in programming and the creativity of generated solutions. Across two conditions (LLM-assisted vs. unassisted), participants using LLMs had significantly shorter idea-generation periods (p=0.0004), leading to fewer creative moments (p=0.002). Qualitative analysis of participants' interactions and interviews revealed four different human-LLM collaboration modes supporting various problem-solving strategies. However, a comparative analysis of the generated solutions shows that while LLMs can help generate more correct and functional code, their solutions contain roughly the same number of ideas as participant-generated ones. Based on our findings, we discuss design implications and considerations for effectively using LLMs to support user creativity.

Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control terms arising in a bilinear control system are affiliated with a von Neumann algebra of finite type acting on the same Hilbert space. When the control terms satisfy basic norm bound conditions, we prove existence of time-optimal controls. In the more general setting where all operators may be unbounded, we show how the dynamical Lie algebra for the system is still well-defined and may be used to check approximate controllability of the system in question. We discuss how this approach can be applied to classical dynamical systems through the Koopman operator formalism, and investigate potential candidates for the von Neumann algebra which may guide the choice of controls. We illustrate how an affiliation relation naturally arises in both classical and quantum control systems with a few examples.

A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,δ)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $δ$. Previous works introduced this concept and study when and how well one can distinguish between such a pair of symmetric distributions by observing $t$ bits. We use a simple hypergeometric smoothing approach and Hahn polynomials to obtain new upper bounds that apply across a wider range of parameters and improve previously available bounds in several regimes. In particular, prior works left open the basic question of whether there exist constants $0<c_1<c_2<1$ and a pair of $(c_1n,0)$-wise indistinguishable distributions such that the $c_2n$-wise marginals have statistical distance $Ω(1)$. One application of our new bounds is to rule this out for all $c_1,c_2$ and to show that the $c_2n$-wise marginals must in fact be exponentially close. Another application in this setting is to show that the $c_2n$-wise marginals must be super-polynomially close even if the $c_1n$-wise marginals are allowed to have statistical distance $δ$ for any $δ\leq\exp\left({-ω(\sqrt{n\log{n}})}\right)$. Our bounds also yield new results in other regimes, for example when $k$ is sublinear or when $t/n$ tends to 1.

Alt $ν$-Tamari lattices constitute a remarkable family of lattices associated with lattice paths that broadly generalize the Dyck and Tamari lattices. To systematically study the structural properties of this family, we introduce a combinatorial model that realizes the canonical join complex of alt $ν$-Tamari lattices. Serving as a universal tool, this model allows us to prove vertex decomposability, establish an explicit shelling order, and reveal the underlying homology of the canonical join complex of alt $ν$-Tamari lattices.