arXiv research

Study on geodesics in Cartan group sub-Riemannian problem, proving conjugate time relation to Maxwell time.

Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate time…

Study geodesics on Grushin spaces, proving upper bounds on conjugate times.

Survey on conjugate surfaces in product spaces.

Geodesic flows on certain surfaces are shown to be semi-conjugate to expansive flows.

Study of Lévy flights on Zoll surfaces, revealing geometric information.

The study identifies conjugate and cut points in ideal fluid motion configurations.

Study geodesics and shortest arcs on Lie groups with specific metrics.

The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can signific…

In this paper, we introduce the (co)homology group of a multiple conjugation biquandle. It is the (co)homology group of the prismatic chain complex, which is related to the homology of foams introduced by J. S. Carter, modulo a certain subchain complex. We construct invariants for $S^1$-oriented handlebody-links using …

The paper studies conjugate points on Lie groups with specific metrics.

New method for pricing financial products without no-arbitrage condition.

In this paper we study smooth orientation-preserving free actions of the cyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $\sharp g (S^n \times S^n)\sharp Σ$, where $Σ$ is a homotopy $2n$-sphere. When $n=2$ we obtain a classification up to topological conjugation. When $n=3$ we obtain a classi…

In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal fundamental solut…

Bayesian model predicts oncology demand trends with high accuracy.

Let $(M,g(t))$, $0\le t\le T$, $\partial M\neφ$, be a compact $n$-dimensional manifold, $n\ge 2$, with metric $g(t)$ evolving by the Ricci flow such that the second fundamental form of $\partial M$ with respect to the unit outward normal of $\partial M$ is uniformly bounded below on $\partial M\times [0,T]$. We will pr…

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…

Improved Gaussian process regression with tighter log marginal likelihood bounds.

Study dispersive estimates for Schrödinger and wave equations on a cone with specific metric.

We study conjugate points along homogeneous geodesics in generalized flag manifolds. This is done by analyzing the second variation of the energy of such geodesics. We also give an example of how the homogeneous Ricci flow can evolve in such way to produce conjugate points in the complex projective space $\mathbb{C} P^…

We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.

Global rigidity theorem for metrics on Σ×S1 without conjugate points.

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical man…

The paper tackles efficient computation of optimal transport by approximating conjugates with amortized optimization.

Estimates geodesics on surfaces without conjugate points.

Quotients $Y=X/conj$ by the complex conjugation $conj\: X\to X$ for complex surfaces $X$ defined over $\R$ tend to be completely decomposable when they are simply connected, i.e., split into connected sums $\#_n CP^2\#_m\barCP^2$ if $w_2(Y)\ne0$, or into $\#_n(S^2\times S^2)$ if $w_2(Y)=0$. The author proves this prope…

Develops multi-modal neural network models for improved prediction and uncertainty quantification.

A conjugate Bayesian method detects change points in Hawkes processes efficiently.

New method speeds up inference for non-conjugate Gaussian processes.

In this paper, we classify smooth 5-manifolds with fundamental group isomorphic to $\z/2$ and universal cover diffeomorphic to $S^2 \times S^3$. This gives a classification of smooth free involutions on $S^2 \times S^3$ up to conjugation.

Geometric focusing affects dispersive estimates for Schrödinger and wave equations.

We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of $n$-parallel biquandle operations for any integer $n$, an…

We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely, Frostig and Singer. The result holds for log-depth networks from a rich family of ar…

The paper studies Jacobi fields and conjugate points in projective sprays.

Paper describes how to extend multiple conjugation quandles using maps.

An integral stability estimate is proved for refraction coefficients of two conformal metrics in a plane domain in terms of its travel times. No assumption on absence of conjugate points of geodesics is made.

For a surface group, a new bound is given for conjugator length function.

The study examines Hopfian properties of conjugation quandles and their underlying groups.

Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.

An embedding of the m-times punctured disc into the n-times punctured disc, for n>m, yields an embedding of the braid group on m strands B_m into the braid group on n strands B_n, called a geometric embedding. The main example consists of adding n-m trivial strands to the right of each braid on m strands. We show that …

The questions when two Morse function on closed manifolds are conjugated is investigated. Using the handle decompositions of manifolds the condition of conjugation is formulated. For each Morse function on 3-manifold the ordered generalized Heegaard diagram is built. The criteria of Morse function conjugation are given…

Study conjugate locus in convex 3-manifolds using Jacobi fields.

Conjugate gradient methods improve efficiency for high-dimensional GLMMs.

We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact controllability technique is proposed to solve the time-dependent wave equations. We dis…

Paper finds new criteria for conjugate points in fluid flows.

Study analyzes Lévy process structure on manifolds with conjugate points.

We study the geodesic X-ray transform $X$ on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of $X$ and relate it to the con…

We describe the sample paths of the stochastic field $F = F_t(v,x,q)$ of aggregate utilities parameterized by Pareto weights $v$ and total cash amounts $x$ and stocks' quantities $q$ in an economy. We also describe the sample paths of the stochastic field $G = G_t(u,y,q)$, which is conjugate to $F$ with respect to the …