CG-XMARL v4.1 is a military-grade multi-agent reinforcement learning system for autonomous UAV formation control integrated with DCS World 2.9. The system implements a 3-UAV wedge formation pursuit control architecture with advanced consensus-based virtual structure (CBVS) guidance, hierarchical finite state machines, and a planned HGAT-MAPPO-WM (Hierarchical Graph Attention Transformer with Multi-Agent Proximal Policy Optimization and World Model) neural architecture.
We prove that the single-source shortest-path problem on disk graphs can be solved in $O(n\log n)$ time, and that it can be solved on intersection graphs of fat triangles in $O(n\log^2 n)$ time.
We study the problem of finding the shortest path with increasing chords in a simple polygon. A path has increasing chords if and only if for any points a, b, c, and d that lie on the path in that order, |ad| >= |bc|. In this paper we show that the shortest path with increasing chords is unique and present an algorithm to construct it.
In this short note, we discuss the complexity of the search space for the problem of finding a CSG expression (or CSG tree) corresponding to an input point-cloud and a list of fitted solid primitives.
Given a Laurent polynomial F and its amoeba AF. We relate here the question of the BIBO stability of a multi linear time invariant system with a rational transfer function. We formulate very simple criteria for BIBO strong or weak stability in terms of the position of the origin 0 with respect to the amoeba AF and suggest an algorithmic procedure in order to test such property.
We provide a self contained proof of a result of Dudley [Dud64]} which shows that a bounded convex-body in $\Re^d$ can be $\varepsilon$-approximated, by the intersection of $O_d\bigl(\varepsilon^{-(d-1)/2} \bigr)$ halfspaces, where $O_d$ hides constants that depends on $d$.
We show that the following variant of labeling rotating maps is NP-hard, and present a polynomial approximation scheme for solving it. The input is a set of feature points on a map, to each of which a vertical bar of zero width is assigned. The goal is to choose the largest subsets of the bars such that when the map is rotated and the labels remain vertical, none of the bars intersect. We extend this algorithm to the general case where labels are arbitrary objects.
PurposeThe purpose of this paper is to investigate whether specific corporate governance mechanisms, such as board size, board composition, leverage and firm size, tend to mitigate agency cost occurrence in the USA, Russia and Norway.Design/methodology/approachThe authors analyze the sample of 243 US, 196 Russian and 175 Norwegian joint stock companies for the period 2004-2012. The regression analysis is applied to test the models.FindingsIt is revealed that larger boards increase agency costs (measured by asset utilization ratio and asset liquidity ratio) in all sample companies. The proportion of female members has a very slight positive effect in US companies, a negative influence on agency costs in the Norwegian sample and is not significant in the Russian market. The authors find that the big Russian and US companies in the samples of this paper have lower agency costs.Practical implicationsThe results of this paper show which agency-mitigation mechanisms work more effectively in companies operating in the analyzed countries characterized by specific corporate governance models.Originality/valueThe main contribution of this paper to the empirical literature is that it extends the stream of agency research by introducing new, emerging markets: represented by Scandinavian (depicted by the Norwegian sample) and Russian companies. Considering that each market – US, Norwegian and Russian – represents significant distinguishing features in their institutional framework, the paper provides an important research setting in which corporate governance mechanisms can be analyzed from the perspective of a country’s peculiar characteristics. Unlike other agency cost studies, this paper accounts for the gender diversity component in the companies and contributes to gender diversity issues.
For any natural number $d$ and positive number $\varepsilon$, we present a point set in the $d$-dimensional unit cube $[0,1]^d$ that intersects every axis-aligned box of volume greater than $\varepsilon$. These point sets are very easy to handle and in a vast range for $\varepsilon$ and $d$, we do not know any smaller set with this property.
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices. The complexity of our algorithm is linear in the number of vertices of the projected polytope and we show empirically that the performance is significantly better in comparison to some known efficient algorithms of projection and enumeration.
In this paper, we discuss the algorithm engineering aspects of an O(n^2)-time algorithm [6] for computing a minimum-area convex polygon that intersects a set of n isothetic line segments.
This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4. This paper is the Ph.D thesis written under the direction of Dan Burghelea at OSU.
We show that, for any integer k > 5, the Sparse-Yao graph YY_{6k} (also known as Yao-Yao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k > 7.
Alexis Darrasse, Konstantinos Panagiotou, Olivier Roussel
et al.
This paper is devoted to the construction of Boltzmann samplers according to various distributions, and uses stochastic bias on the parameter of a Boltzmann sampler, to produce a sampler with a different distribution for the size of the output. As a significant application, we produce Boltzmann samplers for words defined by regular specifications containing shuffle operators and linear recursions. This sampler has linear complexity in the size of the output, where the complexity is measured in terms of real-arithmetic operations and evaluations of generating functions.
We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.
We show that the number of unit-area triangles determined by a set of $n$ points in the plane is $O(n^{9/4+ε})$, for any $ε>0$, improving the recent bound $O(n^{44/19})$ of Dumitrescu et al.
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm depends on the special properties of the graph constructed in this way. We survey the art gallery problem, partition into rectangles, minimum-diameter clustering, rectilinear cartogram construction, mesh stripification, angle optimization in tilings, and metric embedding from this perspective.
Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated measuring function.
We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in higher dimensions. The graphs that may be embedded in this way form an interesting subclass of the partial cubes.
This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap's faces are quadrilaterals, with vertices over an underlying integer lattice, and such that the cap convexity is ``radially monotone,'' a type of smoothness constraint. Extensions of Cauchy's arm lemma are used in the proof of non-overlap.