1. Mathematical Preliminaries. 2. Elements of Computability Theory. 4. The Class P. 5. The Glass NP. 6. The Complexity of Optiimzation Problems. 7. Beyond NP. 8. Space-Complexity Classes. 9. Probabiillistic. 10. Algorithms and Complexity Classes. 11. Interactivite Proof. 12. Systems. 13. Models of Parallel Computer. 14. Parallel Algorithms.

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Introduction to the theory of complexity

To ensure the correctness of network analysis methods, the network (as the input) has to be a sufficiently accurate representation of the underlying data. However, when representing sequential data from complex systems, such as global shipping traffic or Web clickstream traffic as networks, conventional network representations that implicitly assume the Markov property (first-order dependency) can quickly become limiting. This assumption holds that, when movements are simulated on the network, the next movement depends only on the current node, discounting the fact that the movement may depend on several previous steps. However, we show that data derived from many complex systems can show up to fifth-order dependencies. In these cases, the oversimplifying assumption of the first-order network representation can lead to inaccurate network analysis results. To address this problem, we propose the higher-order network (HON) representation that can discover and embed variable orders of dependencies in a network representation. Through a comprehensive empirical evaluation and analysis, we establish several desirable characteristics of HON, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods. We illustrate how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking, and we demonstrate that, by using it as input, HON yields more accurate results without any modification to these tasks.

https://advances.sciencemag.org/content/advances/2/5/e1600028.full.pdf

Representing higher-order dependencies in networks

There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.

The Church-Turing Thesis

This work presents a multi-methodological approach to address the dynamic and stochastic challenges that underlie the problem of international logistic network reconfiguration induced by the One Belt-One Road initiative. A spatial-temporal logistics interaction model integrated with Markov chain is proposed to forecast time-varying logistic distribution flows for a three-layer supply chain framework. Further, numerical forecasts based on two cases of Chinese oil supply chain is carried out to account for the effectiveness of the proposed model. Analytical results suggest various development strategies for the practitioners and the policy makers in optimizing their logistics and transportation decisions in the OBOR context.

Forecasting time-varying logistics distribution flows in the One Belt-One Road strategic context

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Examples dealing with divergent series, infinite sets, and limits are given.

/pdf/a-new-applied-approach-for-executing-computations-with-4trq8jab8d.pdf

A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities

On Parallel Algorithms of some Orthogonal Transforms (S.S. Agaian and D.Z. Gevorkian). An Efficient Algorithm for Finding Peripheral Nodes (I. Arany). Computational Aspects of Assigning Characteristic Semigroup of Asynchronous Automata and Their Extensions (S. Bocian and B. Mikolajczak). Reichenbach's Propositional Logic in Algorithmic Form (P. Borowik). The Complexity of Weighted Multi-Constrained Spanning Tree Problems (P. Camerini, G. Galbiati and F. Maffioli). An Algorithm for Finding SC-Preimages of a Deterministic Finite Automaton (K. Chmiel). On Entropy Decomposition Methods and Algorithm Design (Th. Fischer). An Efficient Algorithm for Dynamic String-Storage Allocation (D. Fox). Covering Intervals with Intervals under Containment Constraints (M.R. Garey and R.Y. Pinter). How to Construct Random Functions (O. Goldreich, S. Goldwasser and S. Micali). Four Pebbles Don't Suffice to Search Planar Infinite Labyrinths (F. Hoffmann). Parallel Algorithms: The Impact of Communication Complexity (F. Hossfeld). Tight Worst-Case Bounds for Bin-Packing Algorithms (A. Ivanyi). Hypergraph Planarity and the Complexity of Drawing Venn Diagrams (D.S. Johnson and H.O. Pollak). Convolutional Charaterization of Computability and Complexity of Computations (S. Jukna). Succinct Data Representations and the Complexity of Computations (S. Jukna). Lattices, Basis Reduction and the Shortest Vector Problem (R. Kannan). The Characterization of Some Complexity Classes by Recursion Schemata (M. Liskiewicz, K. Lorys and M. Piotrow). Some Algorithmic Problems on Lattices (L. Lovasz). Linear Proofs in the Non-Negative Cone (J. Moravek). Characterizing Some Low Arithmetic Classes (J.B. Paris, W.G. Handley and A.J. Wilkie). Constructing a Simplex Form of a Rational Matrix (A. Rycerz and J. Jegier). Computing N with a Few Number of Additions (I. Ruzsa and Zs. Tuza). A Hierarchy of Polynomial Time Basis Reduction Algorithms (C.P. Schnorr). A Topological View of Some Problems in Complexity Theory (M. Sipser). v-Computations on Turing Machines and the Accepted Languages (L. Staiger). On the Greedy Algorithm for an Edge-Partitioning Problem (Gy. Turan). The Complexity of Linear Quadtrees (T.R. Walsh).

Bolyai János Matematikai Társulat

Papers

Theory of algorithms