相关论文: Finer filtration for matrix-valued cocycle based o…
Let T_\alpha denote the rotation T_{\alpha}x=x+\alpha (mod 1) by an irrational number \alpha on the additive circle T=[0,1). Let \beta_1,..., \beta_d be d\geqslant 1 parameters in [0, 1). One of the goals of this paper is to describe the…
We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in $S^{1}$. In particular, the concept of rotation number of a matrix $g\in Gl^{+}(2,{\R})$ can be generalized to a…
We present a moduli space for similar triangles, then classify triangle maps $f$ that arise from linear maps on this space, with the well-studied pedal map as a special case. Each linear triangle map admits a Markov partition, showing that…
Let $M$ be a representation of an acyclic quiver $Q$ over an infinite field $k$. We establish a deterministic algorithm for computing the Harder-Narasimhan filtration of $M$. The algorithm is polynomial in the dimensions of $M$, the weights…
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
We establish an integration formula for integral foliated simplicial volume along ergodic decompositions. This is analogous to the ergodic decomposition formula for the cost of groups.
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…
This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step…
We prove a version of pointwise Ergodic Theorem for non-stationary random dynamical systems. Also, we discuss two specific examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix…
A possible avenue towards the covariant formulation of the bosonic Matrix Theory is explored. The approach is guided by the known covariant description of the bosonic membrane. We point out various problems with this particular…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
Approximate inference algorithm is one of the fundamental research fields in machine learning. The two dominant theoretical inference frameworks in machine learning are variational inference (VI) and Markov chain Monte Carlo (MCMC).…
We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on the case of prime moduli. These exponential sums arise in the theory of the horocyclic flow on $\mathrm{GL}_n$.
A generalisation of the extended Kalman filter for Stiefel manifold-valued measurements is presented. We provide simulations on the 2-sphere and the space of orthogonal 4-by-2 matrices which show significant improvement of the Extended…
We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations, and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has…
This preliminary report contains a sketch of the proof of the following result: a slowly divergent Teichmuller geodesic satisfying a certain logarithmic law is determined by a uniquely ergodic measured foliation.
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
The bipolar filtration of Cochran, Harvey and Horn presents a framework of the study of deeper structures in the smooth concordance group of topologically slice knots. We show that the graded quotient of the bipolar filtration of…
We extend the definitions of Chern-Schwartz-MacPherson (CSM) cycles of matroids to tropical manifolds. To do this, we provide an alternate description of CSM cycles of matroids which is invariant under integer affine transformations.…