Continuous and monotone machines

We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that it is possible to translate back and forth between such machines and names in the standard function encoding used in computable analysis. Put differently, among the operators on Baire space, exactly the partial continuous ones are implementable by continuous machines and the data that such a machine provides is a description of the operator as a sequentially realizable functional. Continuous machines are naturally formulated in type theories and we have formalized our findings in Coq as part of Incone, a Coq library for computable analysis. The correctness proofs use a classical meta-theory with countable choice. Along the way we formally prove some known results such as the existence of a self-modulating modulus of continuity for partial continuous operators on Baire space. To illustrate their versatility we use continuous machines to specify some algorithms that operate on objects that cannot be fully described by finite means, such as real numbers and functions. We present particularly simple algorithms for finding the multiplicative inverse of a real number and for composition of partial continuous operators on Baire space. Some of the simplicity is achieved by utilizing the fact that continuous machines are compatible with multivalued semantics

Continuous Restricted Boltzmann Machines

Restricted Boltzmann machines are a generative neural network. They summarize their input data to build a probabilistic model that can then be used to reconstruct missing data or to classify new data. Unlike discrete Boltzmann machines, where the data are mapped to the space of integers or bitstrings, continuous Boltzmann machines directly use floating point numbers and therefore represent the data with higher fidelity. The primary limitation in using Boltzmann machines for big-data problems is the efficiency of the training algorithm. This paper describes an efficient deterministic algorithm for training continuous machines

Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\frac{4}{3} + \varepsilon$, this result narrows the gap between approximation ratio and inapproximability result by a significant step. Both results are proven by a reduction from the strongly $NP$-complete problem 3-Partition

USING NON-BLASTING TECHNOLOGIES FOR DESTRUCTION OF HARD ROCK IN SURFACE MINING

Determination the effective application field of non-blasting technology and technologies for the hard rock preparation for excavation during surface mining

PHYSICAL & CHEMICAL PROCESES FOR COAL DESTRUCTION IN UNDERGROUND GAS GENERATOR

Estimate the material and thermal balance for providing the chemical reactions in underground gasgenn according to physical spreads of their fluency

PHYSICAL & CHEMICAL PROCESES FOR COAL DESTRUCTION IN UNDERGROUND GAS GENERATOR

Estimate the material and thermal balance for providing the chemical reactions in underground gasgenn according to physical spreads of their fluency

Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the {\epsilon}-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models. Our information-theoretic analysis leads to new expressions for the entropy rate and the rates of related information measures for these very general continuous-time process classes.Comment: 16 pages, 7 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ctrp.ht

Quantum Equivalence and Quantum Signatures in Heat Engines

Quantum heat engines (QHE) are thermal machines where the working substance is quantum. In the extreme case the working medium can be a single particle or a few level quantum system. The study of QHE has shown a remarkable similarity with the standard thermodynamical models, thus raising the issue what is quantum in quantum thermodynamics. Our main result is thermodynamical equivalence of all engine type in the quantum regime of small action. They have the same power, the same heat, the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature, i.e thermodynamic measurements can confirm the presence of quantum coherence in the device. The coherent work extraction mechanism enables power outputs that greatly exceed the power of stochastic (dephased) engines.Comment: v2 contains style and figures improvements. Subsection III.D was adde