Formulas in connection with parameters related to convexity of paths on three vertices: caterpillars and unit interval graphs

We present formulas to compute the P3 -interval number, the P3 -hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition, we find a connection between the percolation time of a unit interval graph and a parameter involving the diameter of a unit interval graph related to it. Finally, we present a hereditary graph class, defined by forbidden induced subgraphs, such that its percolation time is equal to one.Fil: González, Lucía M.. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Quantitative Models and Implicit Complexity

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resource-bounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logi cs, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes.Comment: 29 page

Evaluasi Kinerja Angkutan Umum Trayek Terminal Oebobo - Terminal Kupang Pp Dan Terminal Kupang - Terminal Noelbaki Pp

Beberapa ruas jalan pada Trayek Terminal Oebobo-Terminal Kupang PP dan trayek Terminal Kupang-Terminal Noelbaki PP, pada jam-jam puncak angkutan umum yang ada cenderung digunakan melebihi kapasitas maksimumnya. Keadaan sebaliknya terjadi pada jam non-puncak, kendaraan umum setengah kosong dan harus melakukan kompetisi dengan angkutan umum lainnya untuk mendapatkan penumpang. Tujuan dari penelitian adalah mengetahui kinerja pelayanan angkutan umum, kebutuhan angkutan umum dan membuat rekomendasi terkait dengan hasil evaluasi kinerja pelayanan pada kedua trayek ini. Dalam penelitian ini indikator kinerja angkutan umum yang dinilai adalah faktor muat, waktu perjalanan, frekuensi pelayanan, waktu antara, waktu tunggu, jumlah kendaraan yang beroperasi, dan waktu pelayanan. Indikator-indikator tersebut diperoleh dari hasil survey dinamis dan survey statis. Dari hasil evaluasi standar pelayanan angkutan umum menurut Dirjen Perhubungan Darat, kinerja pelayanan angkutan umum pada trayek Terminal Oebobo-Terminal Kupang PP dan Terminal Kupang-Terminal Noelbaki PP termasuk kategori baik. Kebutuhan jumlah angkutan umum pada trayek Terminal Oebobo-Terminal Kupang PP adalah 22 unit, sedangkan untuk trayek Terminal Kupang-Terminal Noelbaki PP sebanyak 40 unit. Berdasarkan hasil evaluasi diberikan rekomendasi diantaranya: jumlah angkutan umum yang sudah ada dipertahankan saja atau dikurangi hingga mendekati nilai rata-rata jumlah kendaraan beroperasi setiap hari serta perlunya pembinaan pada pengemudi tentang kesadaran berlalu lintas yang baik di jalan raya. Sometimes in Oebobo Station-Kupang Station route and Kupang Station-Noelbaki Station route, over capacity for public transportation happened in the peak time especially in several roads. While, in peak off time, most of public transportation have no passanger, so they had to compotate with the other transportation the get the passanger. Service operational planning of public transportation should be evaluate as soon as possible to know how about the performance of public transportation services. The goal of this research are to know about public transportation services performance, fleet necessity of public transportation and make recommendations relating to the results of the performance evaluation of services on this route both. The indicators of this research are public transportation performance, load factor, time journey, frequency, time line, passenger time waiting, the quantity of vehicle operated, and time services. All of these indicators get from dinamyc and statistic survey. From the results of the public transport service standards evaluation by the Directorate General of Land Transportation, the performance of public transport services on the Oebobo Station-Kupang Station Route and Kupang Station-Noelbaki Station Route including good categories. The needs of public transport fleet on the Oebobo Station-Kupang Station Route is 22 units, whereas for Kupang Station-Noelbaki Station Route 40 units. Based on the results of the evaluation given recommendations are: for while the number of existing public transport or retained only if necessary, be reduced to close to the average value of the number vehicles in operation each day as well as the need for guidance drivers about traffic awareness good on the highway

Computing the Determinant of the Distance Matrix of a Bicyclic Graph

Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: da Silva Jr., Celso M. Centro Federal de Educação Tecnológica; BrasilFil: Del Vecchio, Renata R.. Universidade Federal Fluminense; BrasilLAGOS 2019: X Latin and American Algorithms, Graphs and Optimization SymposiumBelo HorizonteBrasilUniversidad Federal de Minas Gerai