Search results for "Bounds"

showing 10 items of 298 documents

On an approximation problem for stochastic integrals where random time nets do not help

2006

Abstract Given a geometric Brownian motion S = ( S t ) t ∈ [ 0 , T ] and a Borel measurable function g : ( 0 , ∞ ) → R such that g ( S T ) ∈ L 2 , we approximate g ( S T ) - E g ( S T ) by ∑ i = 1 n v i - 1 ( S τ i - S τ i - 1 ) where 0 = τ 0 ⩽ ⋯ ⩽ τ n = T is an increasing sequence of stopping times and the v i - 1 are F τ i - 1 -measurable random variables such that E v i - 1 2 ( S τ i - S τ i - 1 ) 2 ∞ ( ( F t ) t ∈ [ 0 , T ] is the augmentation of the natural filtration of the underlying Brownian motion). In case that g is not almost surely linear, we show that one gets a lower bound for the L 2 -approximation rate of 1 / n if one optimizes over all nets consisting of n + 1 stopping time…

Statistics and ProbabilityRandom time netsMeasurable functionStochastic processStochastic integralsApplied MathematicsUpper and lower boundsNatural filtrationCombinatoricsModeling and SimulationStopping timeModelling and SimulationAlmost surelyApproximationBorel measureBrownian motionMathematicsStochastic Processes and their Applications
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On the gonality and the slope of a fibered surface

2018

Abstract Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .

Surface (mathematics)General Mathematics010102 general mathematicsFibrationFibered knot01 natural sciencesUpper and lower boundsCombinatoricsGenus (mathematics)0103 physical sciences010307 mathematical physicsFiber0101 mathematicsMathematicsAdvances in Mathematics
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Learning small programs with additional information

1997

This paper was inspired by [FBW 94]. An arbitrary upper bound on the size of some program for the target function suffices for the learning of some program for this function. In [FBW 94] it was discovered that if “learning” is understood as “identification in the limit,” then in some programming languages it is possible to learn a program of size not exceeding the bound, while in some other programming languages this is not possible.

Theoretical computer sciencebusiness.industryComputer sciencemedia_common.quotation_subjectInductive reasoningMachine learningcomputer.software_genreUpper and lower boundsIdentification (information)Recursive functionsArtificial intelligenceLimit (mathematics)businessFunction (engineering)computermedia_common
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Descriptional and Computational Complexity of the Circuit Representation of Finite Automata

2018

In this paper we continue to investigate the complexity of the circuit representation of DFA—BC-complexity. We compare it with nondeterministic state complexity, obtain upper and lower bounds which differ only by a factor of 4 for a Binary input alphabet. Also we prove that many simple operations (determining if a state is reachable or if an automaton is minimal) are PSPACE-complete for DFA given in circuit representation.

TheoryofComputation_COMPUTATIONBYABSTRACTDEVICESFinite-state machineTheoretical computer scienceComputational complexity theoryComputer science020208 electrical & electronic engineering020206 networking & telecommunications02 engineering and technologyUpper and lower boundsAutomatonNondeterministic algorithmTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSimple (abstract algebra)0202 electrical engineering electronic engineering information engineeringState (computer science)Representation (mathematics)Computer Science::Formal Languages and Automata Theory
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Upper bounds on multiparty communication complexity of shifts

1996

We consider some communication complexity problems which arise when proving lower bounds on the complexity of Boolean functions. In particular, we prove an \(O(\frac{n}{{2\sqrt {\log n} }}\log ^{1/4} n)\)upper bound on 3-party communication complexity of shifts, an O(n e ) upper bound on the multiparty communication complexity of shifts for a polylogarithmic number of parties. These bounds are all significant improvements over ones recently considered “unexpected” by Pudlak [5].

TheoryofComputation_MISCELLANEOUSDiscrete mathematicsCombinatoricsTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYCommunication complexityBinary logarithmBoolean functionUpper and lower boundsMultiparty communicationMathematics
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On the propagation of a perturbation in an anharmonic system

2007

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.

Thermal equilibriumPhysicsAnharmonicityTime evolutionAnharmonic crystals; Propagation velocity; Statistical and Nonlinear Physics; Mathematical PhysicsPerturbation (astronomy)FOS: Physical sciencesStatistical and Nonlinear Physicsanharmonic crystals; propagation velocityMathematical Physics (math-ph)Upper and lower bounds82C05 82D20Classical mechanicsPropagation velocityAnharmonic crystalsSettore MAT/07 - Fisica MatematicaMathematical Physics
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AIs for Dominion Using Monte-Carlo Tree Search

2015

Dominion is a complex game, with hidden information and stochastic elements. This makes creating any artificial intelligence AI challenging. To this date, there is little work in the literature on AI for Dominion, and existing solutions rely upon carefully tuned finite-state solutions. This paper presents two novel AIs for Dominion based on Monte-Carlo Tree Search MCTS methods. This is achieved by employing Upper Confidence Bounds UCB and Upper Confidence Bounds applied to Trees UCT. The proposed solutions are notably better than existing work. The strongest proposal is able to win 67% of games played against a known, good finite-state solution, even when the finite-state solution has the u…

Tree (data structure)business.industryComputer scienceMonte Carlo tree searchConfidence boundsArtificial intelligencebusinessDominion
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Warrant Exercise and Bond Conversion in Large Trader Economies

2006

It is well known that the sequential (premature) exercise of American-type warrants may be advantageous for large warrantholders, even in the absence of regular dividends, because using exercise proceeds to repurchase stock or to expand the firm's scale increases the riskiness of an equity share. We present an upper bound on this advantage and show that this advantage is negligible for a realistic parameter setting. This result, however, does not justify in general the simplifying restriction that warrants or convertible securities are valued as if exercised as a block. It turns out that the option to exercise only a fraction of the outstanding convertibles at the maturity date (partial exe…

WarrantMicroeconomicsEconomyConvertibleBondEconomicsEquity (finance)DividendConvertible bondUpper and lower boundsStock (geology)SSRN Electronic Journal
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Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

2011

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X²Σ and B²Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment. peerReviewed

Wave packetvibraatiotilatGeneral Physics and Astronomyrotaatiotilatvapaat radikaalit01 natural sciencesMolecular physicslaw.inventionsymbols.namesakeNuclear magnetic resonancecoherent antiStokes Raman scatteringlaw0103 physical sciencesCoherent anti-Stokes Raman spectroscopyPhysical and Theoretical Chemistry010306 general physicsta116010304 chemical physicsta114rotationla statesChemistryIntermolecular forcekoherentti anti-Stokes Raman spektroskopiaLaserTime–frequency analysisFemtosecondsymbolshiiliyhdisteetcarbon comboundsnumeerinen analyysivibrational statesRaman scatteringCoherence (physics)The Journal of Chemical Physics
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Sobolev and bounded variation functions on metric measure spaces

2014

International audience

[ MATH ] Mathematics [math]DifferentiabilityEquationsSets010102 general mathematicsTransport[MATH] Mathematics [math]01 natural sciencesDerivationsFine PropertiesFinite Perimeter010104 statistics & probabilityRicci Curvature BoundsLipschitz Functions0101 mathematics[MATH]Mathematics [math]InequalitiesComputingMilieux_MISCELLANEOUS
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