Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.
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Shiryaev.Limit Theorems for Stochastic Processes
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New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
A no-go theorem excludes Gamma in [0,d] for typical non-topological non-relativistic spherically symmetric solitons, with the same exclusion for barotropic fluid compact objects, ruling out natural soliton explanations for observed dark matter halo cores with Gamma ~1.7.
A clustering system C is the hardwired clustering system of a rooted level-k network if and only if μ(B) ≤ k for every non-trivial block B in the Hasse diagram H[C].
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
A categorical framework characterizes robustness in program analysis as functors and gives recipes for lifting sound robust analyses from restricted models to general programs.
A Monte Carlo estimator converts stateless optimal DPOR into an unbiased poly-time estimator for the number of Mazurkiewicz traces by sampling paths in the exploration tree and using stochastic enumeration to control variance.
A Lean library called Palamedes uses synthesis rules from generator semantics and catamorphism-anamorphism rewriting to automatically produce correct constrained random generators.
Derives sharp condition for positive subcritical annulus-crossing intensity in general continuum percolation by linking crossings to long-edge occurrence, with multiscale argument showing decay rates.
Extends logical relations to recursive session types for PSNI, proves soundness/completeness via biorthogonality with observation-index stratification, and gives an IFC refinement type system with secrecy polymorphism.
Drift analysis on a mixed-integer benchmark shows (1+1)-LB-ES risks premature convergence with large numbers of integer variables while (1+1)-LUB-ES achieves linear convergence after integers are fixed under suitable bounds.
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
Mixed-precision SSA with stochastic rounding preserves ensemble statistics across five biological models while cutting memory use by 2-4x and delivering up to 1.5x CPU speedup.
PCA is used to orthogonalize correlated auxiliary variables for constructing a more efficient estimator of the finite population mean under simple random sampling, with derived bias and MSE showing improved performance in simulations.
Quantum f-divergence equals classical f-divergence of Nussbaum-Szkoła distributions for normal states on semifinite von Neumann algebras.
A fixed-point neural operator framework models stochastic Fredholm integral equations as stochastic deep neural networks and applies them to financial equations including Black-Scholes, contagion dynamics, and Merton jump diffusion, with results reported to agree well.
Families of abelian varieties over curves in char p with small l-adic local systems have non-nef Hodge bundles and are non-liftable to W_2(k).
eFLINT is a normative specification language combining declarative and procedural elements to support automated compliance reasoning before, during, and after software execution.
Presents a hierarchy of private delegated quantum computation protocols separating state privacy, transcript ambiguity, and output privacy under stated leakage and collusion assumptions.
The authors propose Decentralized Consensus Technology (DCT) as an umbrella term for systems with decentralization, trustlessness and eventual consensus, positioning blockchain as one implementation of decentralized ledger technology.
citing papers explorer
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Optimal embedding dimension in the Nash--Tognoli theorem
Every smooth compact submanifold of R^n is isotopically approximable by real loci of nonsingular real algebraic subsets of C^n, settling a version of Nash's conjecture with uniformity for codim >=2.
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Invariants of real affine varieties based on their complexifications
New invariants extracted from the topology of complexifications of real algebraic sets classify algebraic vector bundles over sphere products and obstruct weak algebraic approximation, disproving Kucharz-Kurdyka conjecture.
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A No-Go Theorem for the Mass-Radius Relation of Solitons
A no-go theorem excludes Gamma in [0,d] for typical non-topological non-relativistic spherically symmetric solitons, with the same exclusion for barotropic fluid compact objects, ruling out natural soliton explanations for observed dark matter halo cores with Gamma ~1.7.
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A Characterization of Level-k Realizability for Clustering Systems
A clustering system C is the hardwired clustering system of a rooted level-k network if and only if μ(B) ≤ k for every non-trivial block B in the Hasse diagram H[C].
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Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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A Categorical Basis for Robust Program Analysis
A categorical framework characterizes robustness in program analysis as functors and gives recipes for lifting sound robust analyses from restricted models to general programs.
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State Space Estimation for DPOR-based Model Checkers(Extended Version)
A Monte Carlo estimator converts stateless optimal DPOR into an unbiased poly-time estimator for the number of Mazurkiewicz traces by sampling paths in the exploration tree and using stochastic enumeration to control variance.
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The Search for Constrained Random Generators
A Lean library called Palamedes uses synthesis rules from generator semantics and catamorphism-anamorphism rewriting to automatically produce correct constrained random generators.
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Subcritical annulus crossing in spatial random graphs
Derives sharp condition for positive subcritical annulus-crossing intensity in general continuum percolation by linking crossings to long-edge occurrence, with multiscale argument showing decay rates.
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Logical Relations for Session-Typed Concurrency
Extends logical relations to recursive session types for PSNI, proves soundness/completeness via biorthogonality with observation-index stratification, and gives an IFC refinement type system with secrecy polymorphism.
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Convergence Analysis of Evolution Strategies for Mixed-Integer Optimization
Drift analysis on a mixed-integer benchmark shows (1+1)-LB-ES risks premature convergence with large numbers of integer variables while (1+1)-LUB-ES achieves linear convergence after integers are fixed under suitable bounds.
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From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
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Reduced-Precision Stochastic Simulation for Mathematical Biology
Mixed-precision SSA with stochastic rounding preserves ensemble statistics across five biological models while cutting memory use by 2-4x and delivering up to 1.5x CPU speedup.
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Principal Component Based Estimation of Finite Population Mean under Multicollinearity
PCA is used to orthogonalize correlated auxiliary variables for constructing a more efficient estimator of the finite population mean under simple random sampling, with derived bias and MSE showing improved performance in simulations.
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Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions in Semifinite von Neumann Algebras
Quantum f-divergence equals classical f-divergence of Nussbaum-Szkoła distributions for normal states on semifinite von Neumann algebras.
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Explainable Artificial Intelligence for Financial Integral Equations: A Fixed-Point Neural Operator Approach
A fixed-point neural operator framework models stochastic Fredholm integral equations as stochastic deep neural networks and applies them to financial equations including Black-Scholes, contagion dynamics, and Merton jump diffusion, with results reported to agree well.
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Non-liftability of Families of Abelian Varieties with Small $l$-adic Local System
Families of abelian varieties over curves in char p with small l-adic local systems have non-nef Hodge bundles and are non-liftable to W_2(k).
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Reflections on the design, applications and implementations of the normative specification language eFLINT
eFLINT is a normative specification language combining declarative and procedural elements to support automated compliance reasoning before, during, and after software execution.
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Private Delegated Quantum Computing for User-Level and Industry-Level Settings
Presents a hierarchy of private delegated quantum computation protocols separating state privacy, transcript ambiguity, and output privacy under stated leakage and collusion assumptions.
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Properties of Decentralized Consensus Technology -- Why not every Blockchain is a Blockchain
The authors propose Decentralized Consensus Technology (DCT) as an umbrella term for systems with decentralization, trustlessness and eventual consensus, positioning blockchain as one implementation of decentralized ledger technology.