We find the complete set of fundamental invariants for systems of ordinary differential equations of order under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “fundamental system”
Study shows algebraic dimension of certain twistor spaces is limited to 1 or 0.
problem Limiting the algebraic dimension of twistor spaces over n#CP^2.
method Analyzing the fundamental system as a pencil and proving constraints on algebraic dimension.
result Twistor spaces over n#CP^2 with algebraic dimension 2 have either empty or single fundamental system.
Reconstructs fundamental groups from liquid local systems.
problem Reconstructing fundamental groups from category of liquid local systems.
method Theory of liquid vector spaces and liquid quasicoherent sheaves.
result Reconstructs topological fundamental group and twisted fundamental groupoids.
We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-spa…
We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree associated to any given oriented Riemannian manifold of dimension . The framework is that of the tangent sphere bundle of . We generalise to a R…
The abstract proves optimal regularity for Pfaffian systems and applies it to surface theory.
problem Optimal regularity for Pfaffian systems and surface theory.
method Proving non-trivial solutions in for Pfaffian systems with antisymmetric coefficients and showing the fundamental theorem of surface theory holds for specific forms.
result The fundamental theorem of surface theory holds for prescribed forms in and , satisfying a compatibility condition.
Fundamental weight systems identified as quantum states.
problem Identifying which weight systems are quantum states.
method Analyzing the Cayley distance kernel on the symmetric group and its positivity.
result All fundamental gl(n)-weight systems are quantum states.
This part 2 discusses virtual fundamental chain and cycle technique for K-systems.
problem Foundation of virtual fundamental chain and cycle technique for K-systems.
method Consider a system of spaces with Kuranishi structures and their simultaneous perturbations.
result Discuss the virtual fundamental chain and cycle technique for K-systems.
Carnot groups can be polarized if they have specific coordinate systems.
problem Understanding when Carnot groups can be polarized.
method Proving Carnot groups with certain coordinate systems are polarizable.
result Carnot groups with suitable horizontal polar coordinates are polarizable.
Study shows finiteness of magnetic hypersurfaces on closed manifolds.
problem Understanding the finiteness of magnetic hypersurfaces on closed manifolds.
method Introduced a dynamical version of the second fundamental form to generalize a previous result.
result Real-analytic negatively -curved magnetic systems on closed real-analytic manifolds have only finitely many closed totally -magnetic hypersurfaces.
The paper uses information theory to find limits of feedback control systems.
problem Fundamental performance limitations of feedback control systems.
method Utilizes information theory to derive bounds on control error.
result Bounds are characterized by the conditional entropy of the disturbance.
Proves conjecture on deformation invariance of big fundamental groups.
problem Stability of big fundamental groups under small deformations.
method Deformation regularity of equivariant pluriharmonic maps and techniques from Shafarevich conjectures.
result Deformation openness of big fundamental groups for varieties with big complex local systems.
Estimates interaction laws from agent trajectories without assuming their form.
problem Inferring interaction laws from observational data in complex systems.
method Non-parametric statistical learning approach from trajectory data.
result Effectiveness demonstrated in various disciplines, including physics, opinion dynamics, and biology.
Research develops a DSS for stock selection and asset allocation using fundamental data.
problem Complex financial markets and limited use of fundamental data analysis.
method Data gathering, cleaning, and modeling of fundamental data; integration with macroeconomic conditions.
result Enhanced predictive model for mid- to long-term stock returns.
Study minimizes market inefficiency in systemic economies.
problem Minimizing deviations of market prices from fundamental values.
method Characterized market inefficiency and developed a matrix of holdings to minimize it.
result Portfolio holdings should deviate more from diversification if banks have similar systemic significance.
New cohomology theory shows compact Lie group actions are Morita invariant.
problem Establishing Morita invariance for cohomology of compact Lie group actions.
method Using bibundles to transfer coefficient systems between Morita equivalent groupoids.
result Twisted Bredon-Illman cohomology is Morita invariant for compact Lie group actions.
We present two results about the relationship between fundamental groups of quasiprojective manifolds and linear systems on a projectivization. We prove the existence of a plane curve with non-abelian fundamental group of the complement which does not admit a mapping onto an orbifold with non-abelian fundamental group.…
All DeFi markets are essentially CFMMs with increasing invariants.
problem Ensuring DeFi markets are free of arbitrage opportunities.
method Formalizing DeFi markets as CFMMs and proving the existence of increasing invariants.
result A DeFi market is arbitrage-free if and only if it has an increasing invariant.
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg sub-Laplacian. The resulting dynamical system is known to contain a fundamental inte…
Proves properties of complex algebraic varieties and local systems.
problem Properties of complex algebraic varieties and local systems.
method Analytic Zariski open subsets and algebraic maps.
result Trivializing covering spaces of complex algebraic varieties.
We make an analogy of Culler-Morgan-Shalen theory. Our main goal is to show that there exists a non-empty system of essential 2-suborbifolds respecting a given splitting of the orbifold fundamental group.
Study deformation spaces of irregular isomonodromy systems on Riemann surfaces.
problem Understanding the topology of irregular isomonodromy systems.
method Define and study moduli spaces of deformations of irregular classes on Riemann surfaces.
result Generalize G-braid groups to study fundamental groups of deformation spaces.
New adaptive scheme improves crowdsourcing accuracy with fixed budget.
problem Maximizing accuracy with limited crowdsourced responses.
method Generalized probabilistic model for adaptive task assignment.
result Adaptive scheme matches fundamental accuracy-budget trade-off.
The aim of this paper is to give an explicit formula in order to compute the Maslov index of the fundamental solution of a linear autonomous Hamiltonian system, in terms of the Conley-Zehnder index and the time one flow.
We compute the characteristic Cartan connection associated with a system of third order ODEs. Our connection is different from Tanaka normal one, but still is uniquely associated with the system of third order ODEs. This allows us to find all fundamental invariants of a system of third order ODEs and, in particular, de…
A new double quasi-Poisson bracket on surface groups.
problem Constructing a new mathematical structure on surface groups.
method Proposing and proving a double quasi-Poisson bracket on group algebras.
result The double quasi-Poisson bracket is a noncommutative generalization of the Goldman bracket.
With negative growth in real production in many countries and debt levels which become an increasing burden on developed societies, the calls for a change in economic policy and even the monetary system become louder and increasingly impatient. We research the consequences of a system of credit and debt, that still all…
A novel algorithm estimates frequency in power systems with harmonics using multistage Kalman filtering.
problem Accurate frequency estimation in three-phase power systems with harmonic contamination.
method Two-stage Kalman filtering approach, first stage using quaternion extended Kalman filter, second stage for dynamic frequency estimation.
result Validated through simulations on synthetic and real-world data.
AIBC uses AI and blockchain for efficient resource sharing.
problem Efficient resource sharing in large-scale decentralized systems.
method Two-consensus scheme with DABFT and DPoEV.
result Predictive deep learning for optimal BFT algorithm selection.
We address a fundamental problem that is systematically encountered when modeling complex systems: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information that can be accessed and, as a consequence, the possibility of correctly estimati…
This work develops a learning theory for inferring interaction kernels in complex agent systems.
problem Modeling complex interactions in systems of particles or agents.
method Nonparametric regression and approximation theory.
result Strong consistency and optimal convergence rates for estimators of interaction kernels.
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…
We develop a version of the fundamental theorem of asset pricing for discrete-time markets with proportional transaction costs and model uncertainty. A robust notion of no-arbitrage of the second kind is defined and shown to be equivalent to the existence of a collection of strictly consistent price systems.
Hierarchical AI multi-agent framework optimizes equity portfolios in China's A-share market.
problem Optimizing equity portfolios in China's A-share market using AI and multi-agent systems.
method A hierarchical multi-agent design integrating macro, firm-level, and reinforcement learning approaches.
result Consistently outperforms benchmarks and state-of-the-art systems on risk-adjusted returns and drawdown control.
We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete character…
We compute the small time asymptotic of the fundamental solution of Hörmander's type hypoelliptic operators with drift, at a stationary point, , of the drift field. We show that the order of the asymptotic depends on the controllability of an associated control problem and of its approximating system. If the contr…
The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n-manifold (n > 6). This paper may be viewed as a generalization of Siebenmann's famo…
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
GeoHNN models physics laws for stable, accurate predictions.
problem Violations of physical principles in machine learning models.
method Explicitly encodes geometric priors in inertia and phase space.
result Significantly outperforms existing models in long-term stability and accuracy.
The Geometry of Myller Configurations. Applications to Theory of Surfaces and Nonholonomic Manifoldsmath.DG
The book contents: the notion of Myller configurations, Darboux frame, fundamental formulae and fundamental theorem of existence. The complete system of invariants allows to introduce the notions of Myller parallelism and concurrence as well as a famous Klein's formula. By way it is obtained an important generalization…
In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable syst…
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…
Paper discusses isometric immersion of surfaces with slowly decaying negative Gauss curvature.
problem Isometric immersion of complete surfaces with slowly decaying negative Gauss curvature.
method Gauss-Codazzi system, novel observations on decay properties of Riemann invariants, weighted Riemann invariants, comparison principle.
result Surface has a global smooth isometric immersion in three-dimensional Euclidean space if Gauss curvature decays slowly at infinity.
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated. Using a backward-forward scheme, we show that when the market consists of a…
Maliciously crafted modular learning components can cause ML systems to malfunction.
problem Security threats posed by modular learning components in machine learning systems.
method Demonstrated logic-bomb attacks on two healthcare ML systems.
result Maliciously modified MLCs can cause 100% success rate misdiagnosis of skin cancer.
The paper proves fundamental theorems for timelike surfaces in Minkowski 4-space.
problem Analyzing timelike surfaces without minimal points in Minkowski space.
method Introducing a pseudo-orthonormal frame field and deriving derivative formulas, proving a Bonnet-type theorem.
result Timelike surfaces are uniquely determined by six functions satisfying natural conditions.
Decision-Making Frameworks for Network Resilience -- Managing and Mitigating Systemic (Cyber) Riskq-fin.RM
Framework for managing cyber risks in networks.
problem Managing systemic cyber risks in digital networks.
method Three components: acceptable configurations, risk mitigation interventions, and cost function.
result Effective decision-making for network resilience.
Enhances financial analysis with multi-agent collaboration.
problem Limited use of AI-agent collaboration in financial research.
method Proposes a multi-agent system for financial investment research.
result Multi-agent system outperforms single-agent models.