Related papers: Sequential motion planning in connected sums of re…

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…

We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…

In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…

It is shown that a simple graph which is embeddable in the real projective plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the topologically uncontractible embedded graphs of this type are constructible from one of 8…

We provide a simple algebraic construction of the twistor spaces of arbitrary Joyce's self-dual metrics on the 4-manifold H^2 x T^2 that extend smoothly to nCP^2, the connected sum of complex projective planes. Indeed, we explicitly realize…

The possibilities for new or unusual kinds of topological, locally linear periodic maps of non-prime order on closed, simply connected 4-manifolds with positive definite intersection pairings are explored. On the one hand, certain…

A contractive condition is addressed for extended 2-cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. It is…

Additive robotic construction of building-scale discrete bar structures, such as trusses and space frames, is increasingly attractive due to the potential improvements in efficiency, safety, and design possibilities. However, programming…

We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the…

A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning…

The singular chain complex of the iterated loop space is expressed in terms of the cobar construction. After that we consider the spectral sequence of the cobar construction and calculate its first term over Z/p-coefficients and over a…

A topological space is nonseparably connected if it is connected but all of its connected separable subspaces are singletons. We show that each connected first countable space is the image of a nonseparably connected complete metric space…

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refine the classical cup-length estimates. We then define the…

We prove the projective plane $\rp^2$ is an absolute extensor of a finite-dimensional metric space $X$ if and only if the cohomological dimension mod 2 of $X$ does not exceed 1. This solves one of the remaining difficult problems (posed by…

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial…