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Improvements and Generalizations of Stochastic Knapsack and Multi-Armed Bandit Approximation Algorithms: Full Version
Will Ma
Computer Science , 2013,
Abstract: The multi-armed bandit (MAB) problem features the classical tradeoff between exploration and exploitation. The input specifies several stochastic arms which evolve with each pull, and the goal is to maximize the expected reward after a fixed budget of pulls. The celebrated work of Gittins et al. [GGW89] presumes a condition on the arms called the martingale assumption. Recently, A. Gupta et al. obtained an LP-based 1/48-approximation for the problem with the martingale assumption removed [GKMR11]. We improve the algorithm to a 4/27-approximation, with simpler analysis. Our algorithm also generalizes to the case of MAB superprocesses with (stochastic) multi-period actions. This generalization captures the framework introduced by Guha and Munagala in [GM07a, GM07b], and yields new results for their budgeted learning problems. Also, we obtain a (1/2-eps)-approximation for the variant of MAB where preemption (playing an arm, switching to another arm, then coming back to the first arm) is not allowed. This contains the stochastic knapsack problem of Dean, Goemans, and Vondrak [DGV08] with correlated rewards, where we are given a knapsack of fixed size, a set of jobs each with a joint distribution for its size and reward, and the objective is to maximize expected reward before the knapsack size is exhausted. Our (1/2-eps)-approximation improves the 1/16 and 1/8 approximations of [GKMR11] for correlated stochastic knapsack with cancellation and no cancellation, respectively, providing the first tight algorithm for these problems that matches the integrality gap of 2. We sample probabilities from an exponential-sized dynamic programming solution, whose existence is guaranteed by an LP projection argument. We hope this technique can also be applied to other dynamic programming problems which can be projected down onto a small LP.
Liouville Type Theorems for Lichnerowicz Equations and Ginzburg-Landau Equation: Survey  [PDF]
Li Ma
Advances in Pure Mathematics (APM) , 2011, DOI: 10.4236/apm.2011.13022
Abstract: In this survey paper, we firstly review some existence aspects of Lichnerowicz equation and Ginzburg-Landau equations. We then discuss the uniform bounds for both equations in Rn. In the last part of this report, we consider the Liouville type theorems for Lichnerowicz equation and Ginzburg-Landau equations in Rn via two approaches from the use of maximum principle and the monotonicity formula
Simulation on SO2 and NOX Emission from Coal–Fired Power Plants in North-Eastern North America  [PDF]
Shuangchen Ma
Energy and Power Engineering (EPE) , 2010, DOI: 10.4236/epe.2010.23028
Abstract: MM5-SMOKE-CMAQ regional air quality modeling system was used to simulate pollutants emission from coal–fired power plants in North-Eastern North America. The effects of SO2 and NOX on air quality producing from coal-fired power plants in the summer of 2001 were analyzed. Simulations show the contributions of SO2 and NOX emission from coal-fired power plants using different scenarios, coal-fired power plants from US and Canada contribute 67.2% and 32.8% for total SO2 concentration, 17.6% and 6.0% for total NOX concentration in researched domain. Some control measures for coal-fired power plants were discussed. Further controls for the emissions of SO2 and NOX from coal-fired power plants are necessary to reduce the adverse environmental effects.
The Theory of Vector-Valued Function in Locally Convex Space  [PDF]
Lixin Ma
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.38133
Abstract: In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.
Research of Extent of Well Control of Explored Reserves of Lithologic Deposit in Delta Front Area  [PDF]
Ma Dong
Advances in Materials Physics and Chemistry (AMPC) , 2012, DOI: 10.4236/ampc.2012.24B050
Abstract: Recently the explored reserves submitted in the oil field mainly situate at the end of deposit in delta front area. During the exploitation and production, problems mainly show on lithologic deposit, for example, reserves are low and difficulty of producing is huge. Based on results of sand body dissection of dense well network of developed oil deposit, and combined with explored reserves, this article researches a relation between extent of well control and reserves precision of explored reserves of lithologic deposit in delta front area by well diluted method. This article has significant influence on objectively understanding our unexploited reserves
Mystery of Modern Phillips Curve  [PDF]
Jinpeng Ma
Modern Economy (ME) , 2012, DOI: 10.4236/me.2012.38113
Abstract: The modern Phillips curve is about the relationship between inflation and unemployment and has been the center of a fierce debate in economics over fifty years. This paper reports empirical evidence that uncovers some of its mysteries. The rate of inflation and the unemployment rate are closely related to business cycles. What is of interest is that no two business cycles are exactly alike; however, all business cycles are essentially alike [1,2]. Each expansion is ended by a recession induced by adverse shocks. The U.S. economy suffers from adverse shocks all the time, but not every shock gives rise to a recession. Why do adverse shocks often induce a recession after an expansion that has lasted for a substantial duration? That is, why are double-dip recessions so rare? Here do we find important evidence in the Phillips curve that may help answer this question. We also discuss some issues related to the monetary policy and raise a few open questions about the relationship between unemployment and business cycles.
In Silicon Cloning and Bioinformatics Analysis of the Raphanus Sativus WUS Gene  [PDF]
Ma Guang
Engineering (ENG) , 2013, DOI: 10.4236/eng.2013.510B104
Abstract:

The complete coding sequence ofRaphanus sativusWUS gene was obtained by usingArabidopsis thalianagene se-quence (NM_127349) as a probe in silico cloning. Then the hydrophilicity, secondary structure and advanced structure of WUS protein inRaphanus sativusare analyzed by using bioinformatics methods. The results show that the cDNA was 1298 bp, with no intron, contains an open reading frame of 936bp, encoding 312aa protein. The protein coded byRaphanus sativusgene showed 74% similarity toArabidopsis thaliana.

The Modern Phillips Curve Revisited  [PDF]
Jinpeng Ma
Modern Economy (ME) , 2014, DOI: 10.4236/me.2014.53020
Abstract:

The modern Phillips curve is about the relationship between the average rates of inflation and unemployment. We will provide additional empirical evidence in the US economy from 1948:01 to 2013:03 that helps demonstrate why such a relationship has been built on a wrong methodology, as revealed in Ma [1]. An erroneous approach can lead to a misunderstanding of business cycles and a wrongful implementation of monetary policy. In particular, the way how the two rates may evolve is now at a critical moment for the Fed to decide if an exit from its quantitative easing should be initiated.

Time-resolved laser flash photolysis study on transient reaction between excited triplet state of anthraquinone derivatives (AQS) and 2-deoxythymidine  [PDF]
Jianhua Ma
Natural Science (NS) , 2014, DOI: 10.4236/ns.2014.61001
Abstract:

The transient absorption spectra and kinetics of excited triplet state of anthraquinone derivatives 2-anthraquinonesulfonatesodium (AQS) and 2-deoxythymidine (dT) have been investigated in CH3CN-H2O (97:3) using the time-resolved laser flash photolysis technique (KrF, 248 nm). The absorption spectra of dT radical cation and the radical anion of AQS have been observed. From dynamic and thermodyrnamic analysis, the mechanism of this transient reaction has been initially analysed.

Empirical Identity as an Indicator of Theory Choice  [PDF]
Lei Ma
Open Journal of Philosophy (OJPP) , 2014, DOI: 10.4236/ojpp.2014.44060
Abstract: There are many theories about theory choice in philosophy of science, but no any indicator of scientific theory has been precisely defined, let alone a united index system. By the example of empirical identity, I shall show that a range of scientific indicators to decide theory choice can be precisely defined by some basic concepts. I think that these indicators can provide us a better description of the principles of philosophy of science. The certain pursuit of theories’ empirical identity and novelty leads the cumulative view of scientific progress; under non-cumulative circumstance, it is totally practicable to judge a theory’s empirical identity as well as empirical novelty; empirical identity underdetermines the acceptance of a particular theory. It is possible that all the principles of philosophy of science could be explained again through the system of index of theory choice, thus a more rigorous theory of philosophy of science could be established.
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