Hirota-Satsuma gains sharp local well-posedness off-diagonal
Existence holds for unequal regularities when dispersion coefficients meet a ratio condition.
· “Sharp local well-posedness for the Hirota-Satsuma system”
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Ten-lobed domain breaks Pompeiu and Schiffer conjectures
Certified interval arithmetic proves a noncircular real-analytic domain with a boundary-constant Neumann eigenfunction.
· “A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures”
Strong duality holds for weakly communicating average-reward CMDPs
Geometric structure of occupation measures yields primal-dual algorithm with O(T^{2/3}) regret and constraint violation bounds.
· “Learning Weakly Communicating Average-Reward CMDPs: Strong Duality and Improved Regret”
L_alpha matrices track eigenvalues across graph operations
The one-parameter family recovers adjacency, degree, and Laplacian spectra as special cases when graphs are combined by union or join.
· “Eigenvalues of boldsymbol{L_α}-matrices under graph operations”
φ-DeepONet modifies the DeepONet architecture to handle discontinuities by using multiple…
φ-DeepONet learns mappings with discontinuities in inputs and outputs by combining multiple branch networks with a nonlinear interface…
Schubert positivity has a positive rule under two conjectures
If GRH and a derandomization assumption hold, every positive Schubert coefficient gets a poly-time verifiable certificate.
Second copy never unlocks Werner-state distillation
A sharp projection estimate proves the 2-copy threshold matches the 1-copy threshold in every dimension.
Noisy quantum sampler plus repair yields polynomial-time guarantee
Guarantee holds when the ideal circuit gives optimal strings inverse-polynomial weight; noise costs one extra power of n.
· “Polynomial Time Quantum Approximation Schemes for Constrained Optimisation”
Knowledge-guided search finds biological ODEs that data-fitting misses
MEDA shows literature-derived constraints, not trajectory fit, are the load-bearing part of recovering mechanistic models.
Clause substitution creates local blind spot in K-SAT
Indistinguishable SAT/UNSAT pairs force wide clauses in Resolution and push proof size toward 2^N.
· “Self-Referential K-SAT and the Finite Analogue of G\"odel's Incompleteness Theorem”
The minimum free energy randomized design achieves covariate balance while retaining…
Minimum free energy randomization controls imbalance and prevents unobserved factors from dominating error in effect estimates
· “Minimum free energy randomized design to improve covariate balance”
Link failures cap LEO capacity scalability at O(1/n)
Under a Markov model of ISL states, scalability rises to an optimum then falls toward zero as satellite count grows.
· “Capacity Scalability of LEO Constellations With Dynamic Link Failures”
Factored trees let agentic teams reuse past solution paths across problems
GRAFT-ATHENA embeds decision sequences as metric fingerprints so new physics tasks draw on accumulated experience and invent new solvers.
Extreme value theory enables extrapolation beyond training data
Review shows how tail models support regression, classification, dimension reduction and anomaly detection in rare-event settings.
· “Extrapolation in Statistical Learning with Extreme Value Theory”
The paper proves existence of a C^r diffeomorphism on a closed manifold of dimension >2…
It stays strongly pluripotent only on the majority subset, creating a robust obstruction inside the affine family.
· “A robust obstruction to full strong pluripotency for wild blender-horseshoes”
Nodal DG scheme meets all three MHD numerical requirements
HLL flux with entropy-stable speeds plus locally divergence-free projection achieve positivity, entropy stability and divergence control in
· “A positivity preserving and entropy stable nodal discontinuous Galerkin scheme for ideal MHD”
Tensor method scales exact MDP optimization linearly for infrastructure
Kronecker-factored transitions cut complexity from exponential to linear while keeping global dynamic programming solutions intact.
Control duality reduces all EnKF variants to hyperparameter choices
A single framework classifies stochastic and deterministic ensemble Kalman filters and supplies a route to new designs.
· “A Unified Control Theory Derivation of Discrete-Time Linear Ensemble Kalman Filters”
Logs of Schrödinger and discrete Laplacians via extensions
Boundary recovery is more involved than for fractional powers, yet works under reverse Hölder potentials.
· “Extension theorems for logarithmic Schr\"odinger and discrete Laplacian operators”
Explicit optimal Hardy weight found for fractional Laplacian
The weight is null-critical and fixes the sharp constant for n^{-2σ}.
· “An optimal fractional Hardy inequality on the discrete half-line”
Coupled factorizations solved directly by one SVD
When matrices or a matrix and tensor share a common factor their joint decomposition reduces to a single singular value decomposition, with
Infinite family of non-circular domains disproves Schiffer conjecture
A bifurcation branch on a real-symmetry relaxation reaches integer symmetries, refuting Schiffer and Pompeiu together.
Scaled KŁ property proves Bregman iterates converge
It proves Shannon-entropy Bregman iterates converge to critical points on nonconvex problems.
· “On the Iterate Convergence of Bregman Projected Gradient Method”
k-trace definability finds universal k-NIP theories inside NIP bases
Hilbert space, Urysohn space and generic hypergraphs appear as the canonical objects k-trace definable in real closed fields or vector space
One qubit turns sensors into exponential learners
Coupling one control qubit to a sensor learns a kth Fourier feature in O(k) shots; Gaussian sensors need exponentially many.
· “Exponential quantum advantage for learning signals with a single qubit”
One sharp matrix bound controls Schwarz-Pick at n points
For self-maps of the disk the factor is n; for degree-d Blaschke products it drops to min(n,d).
Category dilatation theory is now fully machine-checked
A proof assistant verifies the universal property, the key operations, and two corrections to the earlier printed theory.
Finite entropy systems cut subset entropy to any level
New proof answers an open question; infinite-measure entropy creates a zero-or-infinity gap
· “Hereditary Lowerability of Topological Dynamical Systems”
Smoothing the polar factor turns Muon updates into convergent flows
An epsilon-smoothed polar map yields O(1/T), O(1/t), and exponential rates, plus a local advantage criterion.
Julia-C++ solver pair hits predicted order for self-gravitating gas
Euler-Poisson test passes convergence, Jeans-instability, and Sedov blast-wave checks.
· “Multi-Solver Coupling for Parallel Adaptive Multi-Physics Simulations with Trixi.jl and deal.II”
Measure-driven nonlocal equation on Heisenberg group has a weak solution
Existence is obtained by weak convergence inside a new function space the authors call the Walker space.
Blowup thresholds stay positive for every non-bipartite H
Dense maximal H-free graphs become exact bounded blowups; the spectrum is richer than chromatic thresholds
One weight realizes every symmetric Hales-Jewett coloring
The match reduces the symmetric lower-bound problem to one-dimensional Gallai coloring and supplies HJ(3,3) at least 22.
· “One-Weight Colorings, the Symmetric Class, and Lower Bounds for Hales--Jewett Numbers”
3-manifold fibering decision problem is in NP
A certificate verifiable in polynomial time exists whenever a triangulated manifold fibers over the circle.
One-period bubble truncation yields Lane-Emden ground states at every mass
The gradient tail drop in the periodic direction restores compactness without lower-order perturbations
· “On Dancer-type solutions for the Lane--Emden equation via semivirial-vanishing geometry”
Acc-Sinkhorn accelerates entropy OT to O(1/k²) rate
Bilevel view turns column scaling into accelerated mirror descent, improving unregularized approximation complexity to O(n²/ε).
· “Accelerating Sinkhorn for Entropy-Regularized Optimal Transport”
Uniform distribution maximizes independent-set sampling probability
When a matroid's automorphisms act transitively, the chance of drawing K distinct independent elements peaks at equal probabilities and is a
· “Maximum Probability of Independence in Transitive Matroids”
RL quadrotor controller enables forest under-canopy inspections
End-to-end policy tracks view poses as higher planners ensure safe paths between user-specified regions.
· “Aerial Inspection Behaviors via RL-based Quadrotor Control for Under-canopy Forest Environments”
Steering speeds random walks to near-linear cover
Bounded-degree graphs let a small steering probability visit every vertex in n to the 1 plus little-o of 1 steps with high probability.
Global solutions exist for power-rate fragmentation-coagulation in any dimension
Power rates give classical global solutions without data-size limits once fragmentation dominates diffusion and coagulation.
Learning adaptive bases from data lifts spectral PDE operators
Data-dependent Parseval frames capture localized multiscale features more effectively than fixed global bases while retaining FFT speed.
· “Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs”
Runge-Kutta Langevin method hits O(d^{3/2}h^{3/2}) rate without log-concavity
Two-gradient scheme matches prior convergence guarantees for targets that are merely log-smooth rather than strongly convex.
Environment carries data by distinguishable physical states sensed via RF
Multi-snapshot sensing produces a reliability field that turns state distinction into a geometric codebook problem with an optimal finite-
· “Embodied Communication: Sensing-Induced Reliability Fields and Capacity Bounds”
Rod flow tracks Adam at edge of stability better than stable flows
Joint phase-space model with smooth second moment follows discrete steps for eight optimizers where prior approximations break down.
RL learns to pick cuts that speed Benders decomposition
Policy gradient training yields faster solves than standard or supervised methods on electric vehicle problems and generalizes to new sizes.
· “Learning to Cut: Reinforcement Learning for Benders Decomposition”
Second-order bilevel method reaches Õ(ε^{-1.5}) iterations
FSBA locates approximate second-order stationary points of the hyper-objective faster than first-order baselines under nonconvex-strongly-cx
· “Second-Order Bilevel Optimization with Accelerated Convergence Rates”
New edge-based μ-representation yields distance for orchard networks
It uniquely identifies binary semidirected networks and enables polynomial-time comparisons of evolutionary histories with reticulations.
· “A μ-distance for semidirected orchard phylogenetic networks”
Optimized designs lift heat exchanger performance by 22 percent
Calibrated low-fidelity Darcy model lets topology search find turbulent two-fluid exchangers with better heat transfer and controlled drag
F4-concatenated codes produce optimal binary LRCs
Outer linear codes over four elements yield binary locally repairable codes that meet the Griesmer-like bound and an improved Johnson-like 2
· “Constructions of locally repairable codes via concatenated codes”
Worst-case inventory cost occurs at a multi-point demand distribution
Moment-based ambiguity set plus robust chance constraint yields a deterministic reformulation solvable by nested branch-and-price for cyclic
· “The Distributionally Robust Cyclic Inventory Routing Problem”
Sobolev deficit equals distance to affine extremals
Near-optimal functions sit, up to linear maps, at a squared distance controlled from both sides by the energy gap.
· “Sharp Stability for the Affine Fractional Sobolev Inequality”
Geodesic flows gain integer periods via metric dictionary
Every continuous reparameterization is matched to a group metric; word metrics yield flows with all orbits of integer length.
· “A geometric correspondence for reparameterizations of geodesic flows”
Uniform representation yields simultaneous confidence regions for time series
New high-dimensional theory for dependent observations turns pointwise sieve estimators into simultaneous inference tools.
· “Simultaneous Inference for Nonlinear Time Series, a Sieve M-regression Approach”
Niho functions are locally-APN exactly when Walsh spectrum has four values
The equivalence also fixes the four nonzero weights of the related cyclic codes and determines their differential and boomerang spectra.
· “Walsh Spectrum and Boomerang Properties of Locally-APN Niho Functions”
Uniform generators speed Pearson IV sampling for all shapes
New methods generate random numbers from this distribution at constant speed regardless of shape parameters and support Bayesian models.
· “The Pearson IV distribution: Random variate generation and applications”
LLM search fixes exact Zarankiewicz numbers for three cases
New lower bounds for 41 more parameters sit within one edge of known upper limits in several instances.
· “New Bounds for Zarankiewicz Numbers via Reinforced LLM Evolutionary Search”
Symmetric reset sites remove rate dependence from ruin probability
Under spectral duality the coupling constant equals the classical midpoint value for any bias, any number of sites, and every resetting rate
KAT inequalities fix circle patterns on quasi-simplicial surfaces
The possible curvatures for triangulations with loops and multiple edges are exactly those meeting the inequalities on every subset of the-l
· “Circle Pattern Theorem for Quasi-simplicial Triangulated Surfaces”
Concave partition removes spurious TEE in stabilizer codes
For translation-invariant prime-qudit codes the Levin-Wen formula now gives exact topological entropy without boundary overestimation.
· “Resolving spurious topological entanglement entropy in stabilizer codes”
Power subgroups form cap sets in fields of order 2 to even powers
The (2^n-1)th powers subgroup is always a cap set, with explicit maximal examples from SET and EvenQuads.
Refined homomorphisms induce sl2 symmetry in triplet W-algebras
The maps extend the known derivation property to general parameters and determine the automorphism group of the related superalgebra.
· “Derivations on the triplet W-algebras with mathfrak{sl}₂-symmetry”
Nilpotency of transposed Poisson algebras equals nilpotency of left multiplications
An Engel-type theorem and Frattini results give concrete criteria for radicals, maximal subalgebras, and decompositions.
· “Nilpotency and Frattini theory for transposed Poisson algebras”
Global weak solutions exist for chemotaxis fluid model of vessel formation
Existence holds on the 3D torus for pressure exponents above 4/3 and finite-energy data, grounding long-time descriptions of early blood-v.
Neural replacement inside multilevel solver accelerates RTE by 10x
MgNet keeps recursive skeleton factorization but trains neural networks to replace its coefficient-specific operators, gaining speed and the
· “A Filtered MgNet Solver For Radiative Transfer Equations”
DRO plus generative AI solves green capacity planning efficiently
Real-world tests show stronger economics, maintained feasibility, and faster consistent solutions than standard methods under demand and net
Stochastic dominance testing now works under continuous monitoring
A running product of threshold bets keeps type I error capped at every stop while growing exponentially under alternatives.
· “Betting on Bets: Anytime-Valid Tests for Stochastic Dominance”
New fluxes preserve positivity in DGSEM on curvilinear AMR meshes
Entropy-stable and mortar-based interface treatments extend high-order accuracy and admissibility to adaptive grids with nonconforming 2:1 h
Dual UAV networks eliminate C2 outages in emergency deliveries
Hovering base stations and moving delivery drones coordinate to maintain reliable links and lower hardware costs after disasters.
Nitsche method gives optimal errors for Stokes-Poisson-Boltzmann with slip
Proves well-posedness, optimal convergence, and reliable residual-based error estimators for the coupled system.
· “Nitsche method for the Stokes-Poisson-Boltzmann equation with Navier slip boundary condition”
Close sets to flat cones are bi-Hölder equivalent
Quantitative closeness at every scale and point forces local equivalence to a cone over a simplicial complex.
· “A generalization of Reifenberg's theorem in R^N for flat cones”
Mild solutions proven for fractional Navier-Stokes with Hermite noise
Fixed-point arguments in weighted spaces give unique Hölder-regular solutions in 2D when parameters ensure the stochastic convolution is in
· “Fractional Navier-Stokes Equations with Caputo Derivative Driven by Hermite Noise”
Biased-DMT converges linearly under biased gradients
Decentralized momentum tracking decouples network topology from data heterogeneity and reaches the physical error floor with absolute bias.
· “Improved Convergence for Decentralized Stochastic Optimization with Biased Gradients”
Gradient-free method solves aggregative optimization without derivatives
ARGFree combines randomized finite differences and tracking variables to converge in expectation, with a momentum variant that smooths high-
Regression models Poisson counts in multi-way tensor data
PToTR constrains the coefficient tensor to a low-rank form so that estimated rates remain positive for tensor responses and tensor inputs.
· “Poisson-response Tensor-on-Tensor Regression and Applications”
Agents trade safety margins to protect priority neighbors
Collaborative barrier functions let agents in coupled systems assist higher-priority peers while keeping the whole group safe through local,
· “Collaborative Altruistic Safety in Coupled Multi-Agent Systems”
Neural training recovers Willmore minimizers for genus 0 and 1
A PINN-style loss on neural embeddings yields the round sphere and Clifford torus while searching for genus-2 candidates.
Gradient-flow schemes stay accurate without time-step limits
A zero-valued auxiliary variable restores energy laws and second-order H^{2} error bounds for free
· “A Regularized Auxiliary Variable (RAV) Approach for Gradient Flows”
Sketch-based GPU solver handles 5000-asset portfolios in seconds
Nesterov-accelerated projection with subspace embeddings preserves accuracy while cutting full-model runtime from over a minute to under 3 s
Frobenius quotient maps three-weight line bundles to monomorphism grids
Explicit construction sends the category of vector bundles on weighted projective lines with three weights to a category of monomorphism gr
· “Frobenius quotients, inflation categories and weighted projective lines”
Weak-form networks recover physical laws from noisy measurements
WGFINNs preserve exact thermodynamic constraints and deliver more accurate predictions than strong-form alternatives at all noise levels.
· “WGFINNs: Weak formulation-based GENERIC formalism informed neural networks”
