Alpha-Degree Closures for Graphs

Bondy and Chvatal [7] introduced a general and unified approach to a variety of graph-theoretic problems. They defined the k-closure Ck(G), where k is a positive integer, of a graph G of order n as the graph obtained from G by recursively joining pairs of nonadjacent vertices a,b satisfying the condition C(a,b): d(a) + d(b) >= k. From many properties P, they found a suitable k (depending on P and n) such that Ck(G) has property P if and only if G does. For instance, if P is the hamiltonian property, then k=n. In [3], we proved that C(a,b) can be replaced by d(a) + d(b) + |Q(G)| >= k, where Q(G) is a well-defined subset of vertices nonadjacent to a,b. In [4], we proved that, for a (2+k-n)-connected graph, C(a,b) can be replaced by |N(a) U N(b)| + d_ab + e_ab >= k, where e_ab is a well-defined binary variable and d_ab is the minimum degree over all vertices distinct from a,b and non adjacent to them. The condition on connectivity is a necessary one. In this paper, we show that C(a,b) can be replaced by the condition d(a) + d(b) (â_ab - a_ab) >= k, where â_ab and a_ab are respectively the order and independence number of the subgraph G - N(a) U N(b).closure, degree closure, neighborhood closure, dual closure, stability, hamiltonicity, cyclability, degree sequence, matching number, k-leaf-connected

Hyperbolic polyhedral surfaces with regular faces

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ The combinatorial information of these surfaces is shown to be identified with that of Euclidean polyhedral surfaces with negative combinatorial curvature everywhere. We prove that there is a gap between areas of non-smooth hyperbolic polyhedral surfaces and the area of smooth hyperbolic surfaces. The numerical result for the gap is obtained for hyperbolic polyhedral surfaces, homeomorphic to the double torus, whose 1-skeletons are cubic graphs.Comment: 23 pages, 3 figures. arXiv admin note: text overlap with arXiv:1804.1103

Signed Network Modeling Based on Structural Balance Theory

The modeling of networks, specifically generative models, have been shown to provide a plethora of information about the underlying network structures, as well as many other benefits behind their construction. Recently there has been a considerable increase in interest for the better understanding and modeling of networks, but the vast majority of this work has been for unsigned networks. However, many networks can have positive and negative links(or signed networks), especially in online social media, and they inherently have properties not found in unsigned networks due to the added complexity. Specifically, the positive to negative link ratio and the distribution of signed triangles in the networks are properties that are unique to signed networks and would need to be explicitly modeled. This is because their underlying dynamics are not random, but controlled by social theories, such as Structural Balance Theory, which loosely states that users in social networks will prefer triadic relations that involve less tension. Therefore, we propose a model based on Structural Balance Theory and the unsigned Transitive Chung-Lu model for the modeling of signed networks. Our model introduces two parameters that are able to help maintain the positive link ratio and proportion of balanced triangles. Empirical experiments on three real-world signed networks demonstrate the importance of designing models specific to signed networks based on social theories to obtain better performance in maintaining signed network properties while generating synthetic networks.Comment: CIKM 2018: https://dl.acm.org/citation.cfm?id=327174

Escort: A data acquisition and display system to support research testing

Primarily designed to acquire data at steady state test conditions, the system can also monitor slow transients such as those generated in moving to a new test condition. The system configuration makes use of a microcomputer at the test site which acts as a communications multiplexer between the measurement and display devices and a centrally located minicomputer. A variety of measurement and display devices are supported using a modular approach. This allows each system to be configured with the proper combination of devices to meet the specific test requirements, while still leaving the option to add special interfaces when needed. Centralization of the minicomputer improves utilization through sharing. The creation of a pool of minis to provide data acquisition and display services to a variable number of running tests also offers other important advantages

Strategic Joint Production Under Common-Pool Output Quotas: The Case of Fisheries Bycatch

We develop a simple game-theoretic model to explain the production decisions of firms when the production of a marketed good is complementary with the output of an associated good for which no market is available and the output of both goods is regulated by exogenously determined common pool output quotas. This scenario matches that of many fisheries in which regulators attempt to simultaneously manage harvests of targeted species and bycatch of other species through common pool quotas and seasonal closures. Under a competitive equilibrium, individual fishermen fail to fully account for the external effects of their harvest decisions on the season length, leading to excessive discards, drastically shortened seasons, and large shares of un-harvested quota for all but the smallest of fishery sizes. These results are robust for even very efficient (low-bycatch) fishing gears. We examine the sensitivity of our predictions to changes in output prices, discard costs, quota allocations and differing degrees of spatial correlation of target and bycatch species. Finally, we derive the optimal bycatch penalty function and describe its significance in light of various policy alternatives available to regulators.Resource /Energy Economics and Policy,

Using and evaluating the real-time spatial perception system hydra in real-world scenarios

Hydra is a real-time machine perception system released open source in 2022 as a package for Robot Operating System (ROS). Machine perception systems like Hydra may play a role in the engineering of the next generation of spatial AIs for autonomous robots. Hydra is in the preliminary stages of its existence and does not come with intrinsic support for running on custom datasets. This thesis primarily aims to find out whether the promised capabilities of Hydra can be replicated. As well as to establish a workflow and guidelines for what modifications to Hydra are needed to successfully run it

Pushdown Control-Flow Analysis for Free

Traditional control-flow analysis (CFA) for higher-order languages, whether implemented by constraint-solving or abstract interpretation, introduces spurious connections between callers and callees. Two distinct invocations of a function will necessarily pollute one another's return-flow. Recently, three distinct approaches have been published which provide perfect call-stack precision in a computable manner: CFA2, PDCFA, and AAC. Unfortunately, CFA2 and PDCFA are difficult to implement and require significant engineering effort. Furthermore, all three are computationally expensive; for a monovariant analysis, CFA2 is in $O(2^n)$, PDCFA is in $O(n^6)$, and AAC is in $O(n^9 log n)$. In this paper, we describe a new technique that builds on these but is both straightforward to implement and computationally inexpensive. The crucial insight is an unusual state-dependent allocation strategy for the addresses of continuation. Our technique imposes only a constant-factor overhead on the underlying analysis and, with monovariance, costs only O(n3) in the worst case. This paper presents the intuitions behind this development, a proof of the precision of this analysis, and benchmarks demonstrating its efficacy.Comment: in Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, 201