Existence of calibrated local stochastic volatility models proven for non-regular coefficients.
problem Existence of calibrated local stochastic volatility models in finance.
method Investigation of McKean--Vlasov equations with minimal continuity assumptions on coefficients, providing existence and propagation of chaos results.
result Existence of calibrated local stochastic volatility models for appropriate stochastic volatility parameters.
Introduces non-regular spacetime geometry without smooth calculus.
problem Defining gravity without smooth spacetime geometry.
method Discusses non-regular spacetime geometry and curvature without differential calculus.
result Curvature and gravity can be defined without smooth spacetime calculus.
We show that #8(S^2 times S^3) admits two 8-dimensional complex families of inequivalent non-regular Sasakian-Einstein structures. These are the first known non-regular Sasakian-Einstein metrics on this 5-manifold.
Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local Lp space or if g is continuous. In this work we define a mollifier smoothing g_t of g that has the following feature: If g is a Riemannian metric of class C2, then the Levi-Civita connection and the Rieman…
Generalized meshes for non-regular geometries, including fractures.
problem Discretization of partial differential equations in non-regular geometries.
method Introduces generalized meshes with overlapping elements and flexible adjacency relations.
result Discrete differential forms on virtually inflated meshes characterize the trace space of forms in surrounding volumes.
We show that $\scriptstyle{#9(S^2\times S^3)}$ admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound b2(M)≤8 which holds for any regular Sasakian-Einstein $\scriptstyle{…
Classifies complex structures on SL(2,C), finding new non-regular ones.
problem Classifying complex structures on SL(2,C) up to automorphisms.
method Classification via Lie group automorphisms and topological analysis.
result Found one new, non-regular complex structure.
Q-learning with cSMART data assesses cAI tailoring variables.
problem Evaluating moderators in cAI construction.
method Clustered Q-learning with M-out-of-N Cluster Bootstrap.
result Constructs confidence intervals for causal effect moderation.
This paper analyses non-regular ∣2∣-graded geometries, and show that they share many of the properties of regular geometries -- the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as obstruction to flatness of the geometry, the existence of the first two BGG splitting ope…
A complex vector space V is a prehomogeneous G-module if G acts rationally on V with a Zariski-open orbit. The module is called etale if dimV=dimG. We study etale modules for reductive algebraic groups G with one-dimensional center. For such G, even though every etale module is a regular prehomogeneou…
Proposes an exponentially increasing step-size for faster parameter estimation in statistical models.
problem Slow convergence of gradient descent in locally convex loss functions.
method Exponentially increasing step-size in gradient descent algorithm.
result Converges linearly to optimal solution under homogeneous assumptions.
Study shows torsion grows subexponentially in book of I-bundles but can grow exponentially in non-regular covers.
problem Growth rates of torsion in book of I-bundles.
method Analysis of torsion in homology of book of I-bundles using finite-sheeted covers.
result Torsion growth rates differ between regular and non-regular finite-sheeted covers.
A new method solves complex hydroelectricity planning problems.
problem Solving multistage stochastic linear programming for hydrothermal dispatch planning.
method Regularized Linear Decision Rules (AdaLASSO) to reduce overfitting and improve out-of-sample performance.
result Significant reductions in non-zero coefficients and improved spot-price profiles.
We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit non-regular sequence of quadratic polynomials. The corresponding Poincare series turns out to be related to the Rogers-Ramanujan identity.
We examine Higgs bundles for non-compact real forms of SO(4,C) and the isogenous complex group SL(2,C)XSL(2,C). This involves a study of non-regular fibers in the corresponding Hitchin fibrations and provides interesting examples of non-abelian spectral data.
The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.
problem Investigating compatibility conditions on spherically symmetric Finsler metrics.
method Using the inverse problem of calculus of variations, the paper focuses on Landsberg and Berwald types.
result All Landsberg spherically symmetric manifolds in higher dimensions are either Riemannian or have specific geodesic spray formulas.
We provide adaptive inference methods, based on ℓ1 regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular f…
In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit…
Square metrics is an important class of Finsler metrics. Recently, we introduced a special class of non-regular Finsler metrics called singular square metrics. The main purpose of this paper is to provide a necessary and sufficient condition for singular square metrics to be of constant Ricci or flag curvature when dim…
We present explicit constructions of complete Ricci-flat Kahler metrics that are asymptotic to cones over non-regular Sasaki-Einstein manifolds. The metrics are constructed from a complete Kahler-Einstein manifold (V,g_V) of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Ka…
We introduce the notion of a subregular subalgebra, which we believe is useful for classification of subalgebras of Lie algebras. We use it to construct a non-regular invariant generalized complex structure on a Lie group. As an illustration of the study of invariant generalized complex structures, we compute them all …
Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because the models are nonidentifiable and non-regular. In a Bayesian network, the set of …
We show that a group of diffeomorphisms $\D$ on the open unit interval I, equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non regular: the exponential map is not defined for some path of the Lie algebra. this result extends to the group of diffeomorphisms of fi…
The paper tackles sampling from Gibbs measures with constrained support, providing a sampling guarantee.
problem Sampling from Gibbs measures with constrained support, especially in the pre-asymptotic regime.
method Analyzing the spectral gap of Langevin dynamics to provide a non-asymptotic sampling guarantee.
result The low-temperature Gibbs distribution concentrates on a neighborhood of its mode in the pre-asymptotic regime.
LS improves model selection for singular statistical models.
problem Challenges in model selection for singular statistical models.
method Integrates empirical loss from WAIC and sBIC penalty term.
result Enhanced utility for model selection without regularity constraints.
We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive…
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
The stable Khovanov-Rozansky homology of torus knots has been conjecturally described as the Koszul homology of an explicit non-regular sequence of polynomials. We verify this conjecture against newly available computational data for sl(3)-homology. Special attention is paid to torsion. In addition, explicit conjectura…
Complementing the previous paper in the series, this paper classifies ∣2∣-graded parabolic geometries, listing their important properties: the group G0, the graded tangent bundle gr(T) and its algebraïc bracket, the relevant cohomology spaces and the standard Tractor bundle $\mc{T}$. Several of these geometries …
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White's local regularity theorem for mean curvature …
Characterizes spherical Finsler metrics satisfying a specific condition.
problem Spherically symmetric Finsler metrics satisfying the σT-condition. method Complete characterization and subclass investigation within Landsberg category.
result Identifies precise conditions for metrics satisfying the T-condition. This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation. The paper provides explicit formulas for those err…
Study Finsler metrics with vanishing Landsberg curvature.
problem Characterize Finsler metrics with specific curvature properties.
method Derive expressions for curvatures, solve PDEs, construct examples.
result Construct non-regular Landsberg metrics not of Berwald type.
Study on p-Kähler structures on fibrations and Lie groups.
problem Existence of p-Kähler structures on complex manifolds. method Investigation of quasi-regular fibrations and reductive Lie groups with invariant complex structures.
result Construction of non-regular complex structures on Lie algebras sl(2m−1,R) for m≥2. A large portfolio of independent returns is optimized under the variance risk measure with a ban on short positions. The no-short selling constraint acts as an asymmetric ℓ1 regularizer, setting some of the portfolio weights to zero and keeping the out of sample estimator for the variance bounded, avoiding the di…
In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex curves, there is a family of curves and a subsequence such that both the domains and t…
New regularizers tighten convex relaxation bounds for neural networks.
problem Large gap between certifiable and empirical robustness in neural networks.
method Two regularizers to train neural networks yielding tighter convex relaxation bounds.
result Higher certified accuracy with proposed regularizers.
The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on S2×S3 and on $\scriptstyle{(S^2\times S^3)# (S^…
Constructs bihamiltonian structures from Lie algebras for specific types of nilpotent elements.
problem Constructing bihamiltonian structures from Lie algebras.
method Using classical W-algebras and non-regular nilpotent elements of semisimple type. result Leading terms define Dubrovin-Frobenius manifolds and calculate central invariants.
Combinatorial approach to α-Ricci and Lin-Lu-Yau Ricci curvatures on graphs
problem Curvature formulas for α-Ricci and Lin-Lu-Yau Ricci curvatures on graphs method Combinatorial construction of optimal transport plans and exact formulas
result Combinatorial proof of known curvature formulas
We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K--contact structure, we prove that there exists …
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case ∥β∥α>1 is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion…
Classifies special quartic curves up to equivalence.
problem Classifying maximal quartic curves up to equivalence.
method Analyzing intersections of quartic polynomials and their level sets.
result Quartic generalised projective special real manifolds have non-regular boundary behavior.
It has been suggested that adversarial examples cause deep learning models to make incorrect predictions with high confidence. In this work, we take the opposite stance: an overly confident model is more likely to be vulnerable to adversarial examples. This work is one of the most proactive approaches taken to date, as…
We study the Kasparov product on (possibly non-compact and incomplete) Riemannian manifolds. Specifically, we show on a submersion of Riemannian manifolds that the tensor sum of a regular vertically elliptic operator on the total space and an elliptic operator on the base space represents the Kasparov product of the co…
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical i…
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predicti…