Related papers: Adelic descent for continuous localizing invariant…
Current deep visual local feature detectors do not model the spatial uncertainty of detected features, producing suboptimal results in downstream applications. In this work, we propose two post-hoc covariance estimates that can be plugged…
The stable pairs theory of local curves in 3-folds (equivariant with respect to the scaling 2-torus) is studied with stationary descendent insertions. Reduction rules are found to lower descendents when higher than the degree. Factorization…
We use the method of sliding paraboloids to establish a Harnack inequality for linear, degenerate and singular elliptic equation with unbounded lower order terms. The equations we consider include uniformly elliptic equations and linearized…
We prove the precise inversion of adjunction formula for finite linear group quotients of complete intersection varieties defined by semi-invariant equations. As an application, we prove the semi-continuity of minimal log discrepancies for…
In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related…
We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…
This paper shows the convergence of adele-valued random walks to an adelic L\'evy process under scaling limits. We use random walks on the $p$-adic numbers to construct random walks initially on the infinite product space, and use survival…
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…
We consider alternating gradient descent (AGD) with fixed step size applied to the asymmetric matrix factorization objective. We show that, for a rank-$r$ matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$, $T = C…
We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…
In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain…
We considered real, p-adic and adelic noncommutative scalar solitons and obtained some new results.
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
We prove existence of an invariant measure on a hypergroup.
We prove the ergodic Closing Lemma for Nonsingular Endomorphisms.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting.…
We provide a new proof for maximal monotonicity of the subdifferential of a convex function.
In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.
We prove a dynamical version of the Mordell-Lang conjecture for subvarieties of the affine space A^g over a p-adic field, endowed with polynomial actions on each coordinate of A^g. We use analytic methods similar to the ones employed by…