The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American…
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48 results for “rational parameters”
Minimal rational curves on compactified symmetric spaces are orbit-closures of 1-parameter subgroups.
problem When are minimal rational curves on equivariant compactifications of symmetric spaces orbit-closures of 1-parameter subgroups?
method Combining algebraic geometry of minimal rational curves with differential geometry of symmetric spaces, showing Gauss-nondegeneracy of VMRT.
result The Gauss-nondegeneracy of VMRT implies that minimal rational curves on equivariant compactifications of symmetric spaces are orbit-closures of 1-parameter subgroups.
New framework recovers reward and rationality parameters from game behavior.
problem Statistical ambiguity in identifying reward and rationality parameters in competitive games.
method Blind Inverse Game Theory (Blind-IGT) using entropy-regularized Quantal Response Equilibrium and Normalized Least Squares (NLS) estimator.
result Optimal convergence rate of for joint parameter recovery.
Quasi-alternating links are a generalization of alternating links. They are homologically thin for both Khovanov homology and knot Floer homology. Recent work of Greene and joint work of the first author with Kofman resulted in the classification of quasi-alternating pretzel links in terms of their integer tassel param…
We construct a Kirby diagram of the rational homology ball used in "generalized rational blow-down" developed by Jongil Park. The diagram consists of a dotted circle and a torus knot. The link is simpler, but the parameters are a little complicate. Euclidean Algorithm is used three times in the construction and the pro…
Rational Krigingstat.ME
New kriging method improves mean estimation and uncertainty.
problem Improving mean estimation and uncertainty in kriging.
method Proposes a rational kriging method using generalized least squares and Gaussian process.
result Generalized least squares estimate is more well-behaved than ordinary kriging.
The study classifies manifolds with specific rational cohomology properties.
problem Classifying smooth manifolds with rational cohomology of a sphere.
method Cohomogeneity one actions on smooth manifolds.
result Such manifolds are diffeomorphic to specific known manifolds.
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
Unified and generalized mating frameworks for Kleinian groups and rational maps.
problem Combining two frameworks for mating Kleinian groups with rational maps.
method Extended mating framework to genus zero hyperbolic orbifolds, constructed correspondences, defined parameter space.
result Explicit description and construction of conformal matings and correspondences.
Study counts rational curves on hyperKähler ALE 4-manifolds.
problem Counting rational curves on hyperKähler ALE 4-manifolds.
method Using the period map of the twistor space, count rational curves and specify complex structures.
result The integer function on the parameter space is lower semi-continuous.
New findings on diffusion rates in wind-tree model with rational parameters.
problem Understanding diffusion rates in the wind-tree model with rational parameters.
method Analyzing real numbers in [0,1) as diffusion rates and providing a criterion for Lyapunov spectrum.
result Exhibit an infinite family of wind-tree billiards with the interior of the Lyapunov spectrum being the full square (0,1)^2.
Neural models for NLP typically use large numbers of parameters to reach state-of-the-art performance, which can lead to excessive memory usage and increased runtime. We present a structure learning method for learning sparse, parameter-efficient NLP models. Our method applies group lasso to rational RNNs (Peng et al.,…
We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective parameters in the Einstein metric grows exponentially with dimension.
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groupsmath.DS
Overview of dynamics in algebraic correspondences and their connections.
problem Understanding dynamics in algebraic correspondences and their connections.
method Focus on matings between rational maps and Kleinian groups, highlighting unifying structures.
result Rich dynamics and connections between moduli spaces of rational maps and Kleinian groups.
Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predic…
A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including thos…
Researchers construct explicit bundles for ALF metrics, revealing rational patching matrices for gravitational instantons.
problem Constructing explicit toric Ricci-flat metrics and their associated bundles.
method Explicit construction of patching matrices for ALF metrics and gravitational instantons.
result Rational form of patching matrices for gravitational instantons in the Chen--Teo family.
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie pseudo-group of local feedback transformations. In particular, considered class d…
Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm wit…
Sparse Bayesian learning improves rational approximations for complex-valued models.
problem Efficiently approximate complex-valued models with high non-linearity.
method Sparse Bayesian learning applied to rational approximation of complex-valued models.
result Sparse Bayesian learning reduces computational cost while maintaining accuracy.
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter scaling the uncertainty in the economy around a solution to the deterministic model, i…
Study on cr-invariant variational problem for Legendrian curves in 3-sphere.
problem Lower-order cr-invariant variational problem for Legendrian curves in 3-sphere.
method Deduced Euler-Lagrange equations, investigated closed critical curves, characterized non-constant cr-curvature curves, proved cr-equivalence classes correspondence to rational points.
result Closed critical curves with non-constant cr-curvature are characterized and their cr-equivalence classes are in one-to-one correspondence with rational points of a connected planar domain.
Positive holomorphic sectional curvature on rational surfaces is characterized by Kähler metrics.
problem Characterizing rational surfaces by the existence of a Kähler metric with positive holomorphic sectional curvature.
method Constructing Kähler metrics on projective manifolds obtained from toric manifolds.
result Every projective manifold obtained from a projective toric manifold by a finite sequence of blow-ups at points admits a Kähler metric with positive holomorphic sectional curvature.
Triple torsion, triple cup products, and embedding obstructions for rational homology 3-spheresmath.GT
Identifies a mod- triple cup product for rational homology 3-spheres with specific first homology.
problem Locally flat embeddings in for rational homology 3-spheres
method Using triple torsion linking form and torsion-linking duality
result Identifies the mod- triple cup product for specific rational homology 3-spheres
We consider the following question: Which parameters in the extension of a rational pleating ray across the boundary of $\Cal M$, the Maskit embedding of the Teichmüller space of once punctured tori correspond to a Kleinian group? Using methods of Keen and Series and Wright we prove a local result, stating that on each…
New method detects projective equivalences and symmetries in rational 3D curves.
problem Detecting projective equivalences and symmetries in rational 3D curves.
method Using differential invariants and Möbius transformations to avoid solving large polynomial systems.
result Efficient algorithm for detecting projective equivalences and symmetries without solving large polynomial systems.
We study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball into 4-dimensional rational symplectic manifolds. We compute the rational homotopy groups of that space when the 4-manifold has the form where …
New Lie group approach for envelope surface computation.
problem Efficient computation of envelope surfaces.
method Interpreting surfaces as curves in Lie group spaces, leveraging Lie group and algebra formalisms.
result Explicit rational parameterization of cone envelope surfaces and solution to trimming problem.
Bayesian optimization with RPCE reduces MAP estimation for structural dynamics models.
problem Estimating parameters of structural dynamic models efficiently.
method Bayesian optimization with RPCE surrogate model.
result Effective reduction in model evaluations for MAP estimation.
Reserve-Dependent Surrenderq-fin.MF
We study the modelling and valuation of surrender and other behavioural options in life insurance and pension. We place ourselves in between the two extremes of completely arbitrary intervention and optimal intervention by the policyholder. We present a method that is based on differential equations and that can be use…
We describe a graph parametrization of rational quadratic differentials with presence of a simple pole, whose critical trajectories form a network depending on parameters focusing on the network topological jumps. Obtained bifurcation diagrams are associated with the Stasheff polytopes.
The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.
problem Heat kernel and closed geodesic asymptotics for nilpotent coverings.
method Finite-dimensional rational Floquet-Bloch theory, Pytlik functional, and spectral sums.
result Genuinely local, pointwise higher-order heat-kernel expansions.
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…
Paper develops geometry for Kleinian groups using Farey polynomials.
problem Understanding the geometry of Kleinian groups generated by parabolic elements.
method Sakuma-Weeks triangulations and Farey recursive polynomials.
result Simple recursive algorithm to determine link complement geometry.
Following our result on rationality of the spectral action for Bianchi type-IX cosmological models, which suggests the existence of a rich arithmetic structure in the action, we study the arithmetic and modular properties of the action for an especially interesting family of metrics, namely -invariant Bianchi IX…
For an oriented surface of genus g with b boundary components, we construct a rational map from a subset of C^{6g-6+3b} onto an open algebraic subset of the PSL(2,C)-character variety as an analogue of the Fenchel-Nielsen coordinates. After taking the quotient by an action of a finite group, we obtain a parametrization…
Article explores non-freeness of groups generated by two specific matrices, providing counterexamples and sequences.
problem Tackles the non-freeness of groups generated by two parabolic matrices with rational parameters.
method Uses the orbit test and modulo homomorphisms to provide sufficient conditions and counterexamples.
result Constructs explicit counterexamples and sequences converging to 3, demonstrating non-freeness.
For node level graph encoding, a recent important state-of-art method is the graph convolutional networks (GCN), which nicely integrate local vertex features and graph topology in the spectral domain. However, current studies suffer from several drawbacks: (1) graph CNNs relies on Chebyshev polynomial approximation whi…
We define an invariant β(M) of a finite volume hyperbolic 3-manifold M in the Bloch group B(C) and show it is determined by the simplex parameters of any degree one ideal triangulation of M. β(M) lies in a subgroup of \B(\C) of finite \Q-rank determined by the invariant trace field of M. Moreover, the Chern-Simons inva…
The Availability bias, manifested in the over-representation of extreme eventualities in decision-making, is a well-known cognitive bias, and is generally taken as evidence of human irrationality. In this work, we present the first rational, metacognitive account of the Availability bias, formally articulated at Marr's…
We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (3+1)-dimensional integrable dispersionless systems associated to the Lax pairs which are polynomial and …
The paper constructs new rational homology 3-spheres bounding rational homology 4-balls.
problem Constructing rational homology 3-spheres that bound rational homology 4-balls.
method Exploring plumbed 3-manifolds and using rational homology circles.
result Infinite families of rational homology 3-spheres that bound rational homology 4-balls.
Welfare effects of information and rationality in portfolio decisions under parameter uncertaintyq-fin.MF
We analyze and quantify, in a financial market with parameter uncertainty and for a Constant Relative Risk Aversion investor, the utility effects of two different boundedly rational (i.e., sub-optimal) investment strategies (namely, myopic and unconditional strategies) and compare them between each other and with the u…
Paper proves vanishing terms in a second Poisson bracket for a specific system.
problem Proving polynomiality of coefficients in the dispersion parameter expansion of the second Poisson bracket.
method Bi-Hamiltonian recursion and Liu-Pandharipande relations.
result Proves vanishing terms in the second Poisson bracket expansion.
We solve ElasticNet regularization tuning across multiple instances with provable guarantees.
problem Tuning ElasticNet regularization coefficients across multiple problem instances.
method Characterized ElasticNet loss as a piecewise-rational function, derived structural complexity bounds, and showed generalization and online learning guarantees.
result First general learning-theoretic guarantees for ElasticNet tuning without strong data distribution assumptions.
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this t…