https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

From the Publisher:
With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter.


0201000296B04062001

The Design and Analysis of Computer Algorithms

Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held. These experiences made me aware that seemingly simple discrete optimization problems could hold the seeds of combinatorial explosions. The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible. Jack Edmonds’ papers and a few key discussions with him drew my attention to the crucial distinction between polynomial-time and superpolynomial-time solvability. I was also influenced by Jack’s emphasis on min-max theorems as a tool for fast verification of optimal solutions, which foreshadowed Steve Cook’s definition of the complexity class NP. Another influence was George Dantzig’s suggestion that integer programming could serve as a universal format for combinatorial optimization problems.

Reducibility Among Combinatorial Problems

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced” means, roughly speaking, that the first problem can be solved deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed.

http://4mhz.de/download.php?file=Cook1971_A4.pdf

The complexity of theorem-proving procedures

We are interested in studying the length of the shortest proof of a propositional tautology in various proof systems as a function of the length of the tautology. The smallest upper bound known for this function is exponential, no matter what the proof system. A question we would like to answer (but have not been able to) is whether this function has a polynomial bound for some proof system. (This question is motivated below.) Our results here are relative results.In §§2 and 3 we indicate that all standard Hilbert type systems (or Frege systems, as we call them) and natural deduction systems are equivalent, up to application of a polynomial, as far as minimum proof length goes. In §4 we introduce extended Frege systems, which allow introduction of abbreviations for formulas. Since these abbreviations can be iterated, they eliminate the need for a possible exponential growth in formula length in a proof, as is illustrated by an example (the pigeonhole principle). In fact, Theorem 4.6 (which is a variation of a theorem of Statman) states that with a penalty of at most a linear increase in the number of lines of a proof in an extended Frege system, no line in the proof need be more than a constant times the length of the formula proved.

/pdf/the-relative-efficiency-of-propositional-proof-systems-50djd7ie3u.pdf

The relative efficiency of propositional proof systems

The class NC consists of problems solvable very fast (in time polynomial in log n ) in parallel with a feasible (polynomial) number of processors. Many natural problems in NC are known; in this paper an attempt is made to identify important subclasses of NC and give interesting examples in each subclass. The notion of NC 1 -reducibility is introduced and used throughout (problem R is NC 1 -reducible to problem S if R can be solved with uniform log-depth circuits using oracles for S ). Problems complete with respect to this reducibility are given for many of the subclasses of NC . A general technique, the “parallel greedy algorithm,” is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in NC 2 (solvable by uniform Boolean circuits of depth O (log 2 n ) and polynomial size). The class LOGCFL is given a new characterization in terms of circuit families. The class DET of problems reducible to integer determinants is defined and many examples given. A new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph. This paper is a revised version of S. A. Cook, (1983, in “Proceedings 1983 Intl. Found. Comut. Sci. Conf.,” Lecture Notes in Computer Science Vol. 158, pp. 78–93, Springer-Verlag, Berlin/New York).

A taxonomy of problems with fast parallel algorithms

A simple ALGOL-like language is defined which includes conditional, while, and procedure call statements as well as blocks. A formal interpretive semantics and a Hoare style axiom system are given for the language. The axiom system is proved to be sound, and in a certain sense complete, relative to the interpretive semantics. The main new results are the completeness theorem, and a careful treatment of the procedure call rules for procedures with global variables in their declarations.

/pdf/soundness-and-completeness-of-an-axiom-system-for-program-3g7csch545.pdf

Stephen A. Cook

Papers

The complexity of theorem-proving procedures

The relative efficiency of propositional proof systems

A taxonomy of problems with fast parallel algorithms

Soundness and completeness of an axiom system for program verification

Review: Alan Cobham, Yehoshua Bar-Hillel, The Intrinsic Computational Difficulty of Functions