evaluation of similarity models for expected utility violations a body of work proposes a decision cost argument to explain expected utility eu violations based on pair similarity these similarity models suggest various measures over the risky pairs that define decision costs and benefits this paper assesses the empirical modeling success of these similarity measures in explaining risky choice patterns showing eu independence violations we also compare model fit for these similarity models relative to eu and to a selected generalized eu model although the candidate models exhibit some degree of substitutability our results indicate support for models that use relatively simple measures as instruments for similarity

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

preference foundations for nonexpected utility a generalized and simplified technique this paper examines a tradeoff consistency technique for testing and axiomatically founding decision models the technique modifies earlier tradeoff consistency techniques by only considering indifferences not strict preferences the resulting foundations are both more general and more accessible than earlier results and they are so regarding both the technical and the intuitive axioms axiomatizations based on other bisymmetry like conditions also follow as corollaries from the results of this paper the tradeoff technique is applied to three popular theories of individual decision under uncertainty and risk i e expected utility choquet expected utility and prospect theory the conditions used are better suited for empirical measurements of utility than earlier tradeoff conditions and accordingly are easier to test

a quantitative measurement of regret theory this paper introduces a method to measure regret theory a popular theory of decision under uncertainty regret theory allows for violations of transitivity and it may seem paradoxical to quantitatively measure an intransitive theory we adopt the trade off method and show that it is robust to violations of transitivity our method makes no assumptions about the shape of the functions reflecting utility and regret it can be performed at the individual level taking account of preference heterogeneity our data support the main assumption of regret theory that people are disproportionately averse to large regrets even when event splitting effects are controlled for the findings are robust similar results were obtained in two measurements using different stimuli the data support the reliability of the trade off method its measurements could be replicated using different stimuli and were not susceptible to strategic responding

three new tests of independence that differentiate models of risky decision making this paper tests new independence properties to compare three models of risky decision making according to the rank affected multiplicative ram weights model all three properties should be satisfied according to the transfer of attention exchange tax model two should be satisfied and one can be violated however according to cumulative prospect theory cpt all three properties will be violated if the probability weighting function is nonlinear although cpt is flexible enough to accommodate violations of these properties its predicted violations based on previously estimated parameters failed to materialize in 14 choices for which the cpt model disagreed with tax cpt correctly predicted the modal choice in only one case and tax predicted the modal choice in the other 13 new versions of three other paradoxes were also tested and found to refute cpt

common fixed point theorems for contractive maps two common fixed point theorems have been proved by using minimal type commutativity and contractive conditions the last theorem extends known results on compatible maps to a wider class of mappings

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

an explicit time evolution method for acoustic wave propagation cost effective waveform modeling is the key to practical reverse time migration rtm and full waveform inversion fwi implementations we evaluated an explicit time evolution ete method to efficiently simulate wave propagation in acoustic media with high temporal accuracy we started from the constant density acoustic wave equation and obtained an analytical time marching scheme in the wavenumber domain we then formulated an ete scheme in the time space domain by introducing a cosine function approximation although the ete operator appears to be similar to the second order temporal finite difference fd operator the exact nature of the ete formula ensures high accuracy in time we further introduced a set of optimum stencils and coefficients by minimizing evolution errors in a least squares sense our numerical tests indicated that ete can achieve similar waveform accuracy as fd with four times larger time steps meanwhile the compact ete operator keeps the computation efficient the efficiency and capability to handle complex velocity field make ete an attractive engine in acoustic rtm and fwi

an empirical test of gain loss separability in prospect theory we investigate a basic premise of prospect theory that the valuation of gains and losses is separable in prospect theory gain loss separability implies that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble two experimental studies demonstrate a systematic violation of the double matching axiom an axiom that is necessary for gain loss separability we document a reversal between preferences for mixed gambles and the associated gain and loss gambles mixed gamble a is preferred to mixed gamble b but the gain and loss portions of b are preferred to the gain and loss portions of a the observed choice patterns are consistent with a process in which individuals are less sensitive to probability differences when choosing among mixed gambles than when choosing among either gain or loss gambles

the optimized expansion based low rank method for wavefield extrapolation abstractspectral methods are fast becoming an indispensable tool for wavefield extrapolation especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation however for inhomogeneous media we face difficulties in dealing with the mixed space wavenumber domain extrapolation operator efficiently to solve this problem we evaluated an optimized expansion method that can approximate this operator with a low rank variable separation representation the rank defines the number of inverse fourier transforms for each time extrapolation step and thus the lower the rank the faster the extrapolation the method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low rank representation as a result we obtain lower rank representations compared with the standard low rank method within reasonable accuracy and thus cheaper extrapola

a simple behavioral characterization of subjective expected utility subjective expected utility is the most widely used model to represent preferences under uncertainty when objective probabilities of events may not be known this paper presents a new behavioral characterization preference axiomatization of subjective expected utility the latter is derived from a behavioral assumption of cardinal independence also known as standard sequence invariance this axiom requires that a standard sequence of outcomes equally spaced in terms of utility is independent of the conditional event this axiom is a weaker version of the trade off consistency condition of wakker wakker pp 1984 cardinal coordinate independence for expected utility j math psych 28 110 117 the main representation theorem is derived both in the connected topology approach and the algebraic approach when step continuity is replaced with solvability and archimedean axioms

a new time space domain high order finite difference method for the acoustic wave equation a new unified methodology was proposed in finkelstein and kastner 2007 39 to derive spatial finite difference fd coefficients in the joint time space domain to reduce numerical dispersion the key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies we develop this new time space domain fd method further for 1d 2d and 3d acoustic wave modeling using a plane wave theory and the taylor series expansion new spatial fd coefficients are frequency independent though they lead to a frequency dependent numerical solution we prove that the modeling accuracy is 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation however under the same discretization the new 1d method can reach 2m th order accuracy and is always stable the 2d method can reach 2m th order accuracy along eight directions and has better stability similarly the 3d method can reach 2m th order accuracy along 48 directions and also has better stability than the conventional fd method the advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models in addition we study the influence of the fd stencil length on numerical modeling for 1d inhomogeneous media and derive an optimal fd stencil length required to balance the accuracy and efficiency of modeling a new time space domain high order staggered grid fd method for the 1d acoustic wave equation with variable densities is also developed which has similar advantages demonstrated by dispersion analysis stability analysis and modeling experiments the methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering

three dimensional elastic modeling by the fourier method earlier work on three dimensional forward modeling is extended to elastic waves using the equations of con servation of momentum and the stress strain relations for an isotropic elastic medium undergoing infinitesimal deformation in addition to arbitrary compressional or p wave velocity and density variation in lateral and vertical directions elastic modeling permits shear or s wave velocity variation as well the elastic wave equation is solved using a generalization of the method for the acoustic case computation of each time step begins by computing six strain components by per forming nine spatial partial differentiation operations on the three displacement components from the pre vious time step the six strains and two lame constants are linearly combined to yield six stress components

modeling of pseudoacoustic p waves in orthorhombic media with a low rank approximation abstractwavefield extrapolation in pseudoacoustic orthorhombic anisotropic media suffers from wave mode coupling and stability limitations in the parameter range we use the dispersion relation for scalar wave propagation in pseudoacoustic orthorhombic media to model acoustic wavefields the wavenumber domain application of the laplacian operator allows us to propagate the p waves exclusively without imposing any conditions on the parameter range of stability it also allows us to avoid dispersion artifacts commonly associated with evaluating the laplacian operator in space domain using practical finite difference stencils to handle the corresponding space wavenumber mixed domain operator we apply the low rank approximation approach considering the number of parameters necessary to describe orthorhombic anisotropy the low rank approach yields space wavenumber decomposition of the extrapolator operator that is dependent on space location regardless of the parameters a feature necessary for orthorhomb

fourier finite difference migration many existing migration schemes cannot simultaneously handle the two most important problems of migration imaging of steep dips and imaging in media with arbitrary velocity variations in all directions for example phase shift k migration is accurate for nearly all dips but it is limited to very simple velocity functions on the other hand finite difference schemes based on one way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events we propose a new hybrid migration method named fourier finite difference migration wherein the downward continuation operator is split into two downward continuation operators one operator is a phase shift operator for a chosen constant background velocity and the other operator is an optimized finite difference operator for the varying component of the velocity function if there is no variation of velocity then only a phase shift operator will be applied automatically on the other hand if there is a strong variatio

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

a nonreflecting boundary condition for discrete acoustic and elastic wave equations one of the nagging problems which arises in application of discrete solution methods for wave propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh these undesired events eventually override the actual seismic signals which propagate in the modeled region the solution to avoiding boundary effects used to be to enlarge the numerical mesh thus delaying the side reflections and wraparound longer than the range of times involved in the modeling obviously this solution considerably increases the expense of computation more recently nonreflecting boundary conditions were introduced for the finite difference method clayton and enquist 1977 reynolds 1978 these boundary conditions are based on replacing the wave equation in the boundary region by one way wave equations which do not permit energy to propagate from the boundaries into the numerical mesh this approach has been relatively successful except that its effectiveness degrades for event

note on common fixed points under strict contractive conditions the first error occurs in lines 4 7 on page 329 which claim that the inequality d f u ff u max d gu gf u k d f u gu d ff u gf u 2 k d ff u gu d f u gf u 2 kd f u ff u leads to a contradiction however this inequality does not lead to a contradiction unless condition ii is slightly modified to overcome this problem we replace the condition ii of theorem 2 1 by d f x fy max d gx gy k d f x gx d fy gy 2 d fy gx d f x gy 2 1 k 2 ii with the above modification the theorem can be proved along the similar lines as given in the original one with minor changes in accordance with the replaced condition ii

random expected utility we develop and analyze a model of random choice and random expected utility a decision problem is a finite set of lotteries that describe the feasible choices a random choice rule associates with each decision problem a probability measure over choices a random utility function is a probability measure over von neumann morgenstern utility functions we show that a random choice rule maximizes some random utility function if and only if it is mixture continuous monotone the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem extreme lotteries that are not extreme points of the decision problem are chosen with probability 0 and linear satisfies the independence axiom

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

using bounded rationality to improve decentralized design the design of large scale complex engineering systems requires interaction and communication between multiple disciplines and decentralized subsystems game theory has been used previously to model interactions between distributed multidisciplinary design subsystems and predict convergence and equilibrium solutions these game theoretic models assume that designers make perfectly rational decisions by selecting solutions from their rational reaction set for convergent decentralized design problems the intersection of the designers rational reaction set results in a nash equilibrium solution where designers may converge if they were making rational choices however this equilibrium solution is rarely optimal from a multi objective optimization perspective further empirical studies reject the claim that decision makers always make rational choices and the concept of bounded rationality is used to explain such behavior in this paper a framework is proposed that uses the idea of bounded rationality in conjunction with set based design metamodeling and multi objective optimization techniques to improve solutions for convergent decentralized design problems through the use of this framework convergent decentralized design problems converge to solutions that are superior to the nash equilibrium

a k space operator based least squares staggered grid finite difference method for modeling scalar wave propagation abstracttwo staggered grid finite difference sgfd schemes with fourth and sixth order accuracies in time have been developed recently based on new sgfd stencils the sgfd coefficients of the two schemes are determined by a taylor series expansion te approach which is accurate only near a zero wavenumber we have adopted the same sgfd stencils and determined the sgfd coefficients by minimizing the errors between the wavenumber responses of the sgfd operators and the first order k wavenumber space operator in a least squares ls sense we solved the ls problems by performing a weighted pseudoinverse of nonsquare matrices to obtain the sgfd coefficients and to yield ls based sgfd methods we have developed an efficient ls implementation by using a small number of representative wavenumbers which makes the computational time for estimating the coefficients negligible dispersion analysis and numerical examples demonstrate that our ls based sgfd methods can preserve the original temporal accuracy and

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

time evolution of the wave equation using rapid expansion method forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields for the case of spatially varying velocity we have worked on two approaches to evaluate the time evolution of seismic wavefields an exact solution for the constant velocity acoustic wave equation can be used to simulate the pressure response at any time for a spatially varying velocity a one step method can be developed where no intermediate time responses are required using this approach we have solved for the pressure response at intermediate times and have developed a recursive solution the solution has a very high degree of accuracy and can be reduced to various finite difference time derivative methods depending on the approximations used although the two approaches are closely related each has advantages depending on the problem being solved

probability weighting and l moments abstract several popular generalizations of expected utility theory cumulative prospect theory rank dependent utility and yaari s dual model allow for non linear transformation of de cumulative probabilities this paper shows an unexpected connection between probability weighting and the statistical theory of l moments specifically cubic probability weighting results in a linear tradeoff between the expected value the first l moment gini 1912 mean difference statistic the second l moment also known as l scale and the third l moment measuring skewness inverse s shaped probability weighting function crossing the 45 line at a probability 0 5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions

stochastically more risk averse a contextual theory of stochastic discrete choice under risk abstract microeconometric treatments of discrete choice under risk are typically homoscedastic latent variable models specifically choice probabilities are given by preference functional differences given by expected utility rank dependent utility etc embedded in cumulative distribution functions this approach has a problem estimated utility function parameters meant to represent agents degree of risk aversion in the sense of pratt 1964 do not imply a suggested stochastically more risk averse relation within such models a new heteroscedastic model called contextual utility remedies this and estimates in one data set suggest it explains and especially predicts as well as or better than other stochastic models

lowrank seismic wave extrapolation on a staggered grid we evaluated a new spectral method and a new finite difference fd method for seismic wave extrapolation in time using staggered temporal and spatial grids we derived a wave extrapolation operator using a lowrank decomposition for a first order system of wave equations and designed the corresponding fd scheme the proposed methods extend previously proposed lowrank and lowrank fd wave extrapolation methods from the cases of constant density to those of variable density dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion the method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors tests on 2d synthetic examples demonstrated that the proposed method is highly accurate and stable the proposed methods can be used for seismic modeling or reverse time migration

common fixed point theorems under strict contractive conditions in menger spaces abstract the main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property e a in menger probabilistic metric spaces as applications we obtain the corresponding common fixed point theorems under strict contractive in metric spaces

the midweight method to measure attitudes toward risk and ambiguity this paper introduces a parameter free method for measuring the weighting functions of prospect theory and rank dependent utility these weighting functions capture risk attitudes subjective beliefs and ambiguity attitudes our method called the midweight method is based on a convenient way to obtain midpoints in the weighting function scale it can be used both for risk known probabilities and for uncertainty unknown probabilities the resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity i e the difference between uncertainty and risk compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity our method is more efficient and can accommodate violations of expected utility under risk an experiment demonstrates the tractability of our method yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods as predicted by ellsberg this paper was accepted by george wu decision analysis

common fixed points under strict contractive conditions abstract the aim of the present paper is to obtain common fixed point theorems under strict contractive conditions by using a minimal commutativity condition our results extend the recent results due to pant 1998 j math anal appl 226 251 258 1999 soochow j math 25 37 42

risk and rationality uncovering heterogeneity in probability distortion it has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types we present a parsimonious characterization of risk taking behavior by estimating a finite mixture model for three different experimental data sets two swiss and one chinese over a large number of real gains and losses we find two major types of individuals in all three data sets the choices of roughly 80 of the subjects exhibit significant deviations from linear probability weighting of varying strength consistent with prospect theory twenty percent of the subjects weight probabilities near linearly and behave essentially as expected value maximizers moreover individuals are cleanly assigned to one type with probabilities close to unity the reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling

making descriptive use of prospect theory to improve the prescriptive use of expected utility this paper proposes a quantitative modification of standard utility elicitation procedures such as the probability and certainty equivalence methods to correct for commonly observed violations of expected utility traditionally decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities however descriptive violations of expected utility bias utility elicitations that such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that under expected utility should have yielded identical utilities as it is not clear how to correct for these biases without further knowledge of their size or nature most utility elicitations still calculate utilities by means of the expected utility formula this paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory it presents quantitative corrections for the probability and certainty equivalence methods if interactive sessions to correct for biases are not possible then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions in an experiment the discrepancies between the probability and certainty equivalence methods are removed by the authors proposal

back to the st petersburg paradox the conventional parameterizations of cumulative prospect theory do not explain the st petersburg paradox to do so the power coefficient of an individual s utility function must be lower than the power coefficient of an individual s probability weighting function

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

one step extrapolation method for reverse time migration we have proposed a new method a one step extrapolation algorithm to solve the acoustic wave equation by introducing a square root operator the two way wave equation can be formulated as a first order partial differential equation in time which is similar to the one way wave equation to solve the new wave equation we used a stable explicit extrapolation method in the time direction and handled lateral velocity variations in the space and wavenumber domains unlike the conventional explicit finite difference schemes the new method does not suffer from numerical instability or numerical dispersion problems it can be used to design cost effective and high quality reverse time migration or modeling code

fourier finite difference wave propagation we introduce a novel technique for seismic wave extrapolation in time the technique involves cascading a fourier transform operator and a finite difference operator to form a chain operator fourier finite differences ffd we derive the ffd operator from a pseudoanalytical solution of the acoustic wave equation two dimensional synthetic examples demonstrate that the ffd operator can have high accuracy and stability in complex velocity media applying the ffd method to the anisotropic case overcomes some disadvantages of other methods such as the coupling of qp waves and qsv waves the ffd method can be applied to enhance accuracy and stability of seismic imaging by reverse time migration

analysis of higher order finite difference schemes in 3 d reverse time migration the design and usefulness of practical algorithms for 3 d reverse time depth migration is examined while demonstrating data applications of the algorithm we evaluate quantitatively the accuracy of the finite difference operator from second order to eighth order for the scalar wave equation by comparing numerical and analytical solutions the results clearly show the advantage of using higher order finite difference schemes especially from second order to fourth order for space derivatives hence a finite difference method with the accuracy of fourth order in space and second order in time is applied to 3 d full scalar wave equations in reverse time migration considerable savings in cpu and memory are obtained by using larger horizontal grid spacings than the vertical spacings therefore we derive dispersion and stability conditions for such unequal grid spacing the 3 d reverse time migration of data from the hibernia field shows an image improvement over 2 d migrations despite the fact that much of the structure was considered to be approximately 2 d stable nondispersive finite difference methods of higher order can allow for tractable and efficient 3 d reverse time migration solutions

coupled equations for reverse time migration in transversely isotropic media reverse time migration rtm images reflectors by using time extrapolation modeling codes to synthesize source and receiver wavefields in the subsurface asymptotic analysis of wave propagation in transversely isotropic ti media yields a dispersion relation describing coupled p and sv wave modes this dispersion relation can be converted into a fourth order scalar partial differential equation pde increased computational efficiency can be achieved using equivalent coupled second order pdes analysis of the corresponding dispersion relations as matrix eigenvalue systems allows one to characterize all possible coupled linear second order systems equivalent to a given linear fourth order pde and to determine which ones yield optimally efficient finite difference implementations setting the shear velocity along the axis of symmetry to zero yields a simpler approximate ti wave equation that is more efficient to implement this simpler approximation however can become unstable for some plausible combinations of anisotropic parameters the same eigensystem analysis can be applied using finite vertical shear velocity to obtain solutions that avoid these instability problems

fixed point theorems for families of weakly non expansive maps abstract in this paper we present some fixed point theorems for families of weakly non expansive maps under some relatively weaker and more general conditions our results generalize and improve several results due to jungck g jungck fixed points via a generalized local commutativity int j math math sci 25 8 2001 497 507 jachymski j jachymski a generalization of the theorem by rhoades and watson for contractive type mappings math japon 38 6 1993 1095 1102 guo c guo an extension of fixed point theorem of krasnoselski chinese j math p o c 21 1 1993 13 20 rhoades b e rhoades a comparison of various definitions of contractive mappings trans amer math soc 226 1977 257 290 and others

global identification of risk preferences with revealed preference data abstract the concept of parameter identification for a given specification is differentiated from global identification which specification is right first order conditions for production under risk are shown to admit many alternative specification pairs representing risk preferences and either perceived price risk production risk or the deterministic production structure imposing an arbitrary specification on any of the latter three determines which risk preference specification fits a given dataset undermining global identification even when parameter identification is suggested by typical statistics this lack of identification is not relaxed by increasing the number of observations critical implications for estimation of mean variance specifications are derived

a model of probabilistic choice satisfying first order stochastic dominance this paper presents a new model of probabilistic binary choice under risk in this model a decision maker always satisfies first order stochastic dominance if neither lottery stochastically dominates the other alternative a decision maker chooses in a probabilistic manner the proposed model is derived from four standard axioms completeness weak stochastic transitivity continuity and common consequence independence and two relatively new axioms the proposed model provides a better fit to experimental data than do existing models the baseline model can be extended to other domains such as modeling variable consumer demand this paper was accepted by peter wakker decision analysis

coincidence and fixed points in symmetric spaces under strict contractions abstract some common fixed point theorems due to aamri and el moutawakil m aamri d el moutawakil some new common fixed point theorems under strict contractive conditions j math anal appl 270 2002 181 188 and pant and pant r p pant v pant common fixed points under strict contractive conditions j math anal appl 248 2000 327 332 proved for strict contractive mappings in metric spaces are extended to symmetric semi metric spaces under tight conditions some related results are derived besides discussing illustrative examples which establish the utility of results proved in this note

recursive integral time extrapolation methods for waves a comparative review abstractwe compared several families of algorithms for recursive integral time extrapolation rite algorithms for waves in isotropic and anisotropic media these methods allow simulating accurate wave extrapolation with little numerical dispersion even when using larger time steps than are usually possible for conventional finite difference methods these various rite algorithms all share the use of mixed space wavenumber domain operators derived from fourier integral solutions of single mode wave equations we evaluated a taxonomy for rite methods based on how they approximated the influence of medium heterogeneity one family of methods uses mixed domain series expansions to provide accurate approximations to heterogeneous extrapolators even for large time steps we compared several methods for deriving coefficients for such series approximations another family of methods uses interpolation between different homogeneous extrapolations to approximate heterogeneous time extrapolation such methods can b

experience weighted attraction learning in normal form games in experience weighted attraction ewa learning strategies have attractions that reflect initial predispositions are updated based on payoff experience and determine choice probabilities according to some rule e g logit a key feature is a parameter that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded relative to reinforcement of chosen strategies according to received payoffs the other key features are two discount rates and which separately discount previous attractions and an experience weight ewa includes reinforcement learning and weighted fictitious play belief learning as special cases and hybridizes their key elements when 0 and 0 cumulative choice reinforcement results when 1 and levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs using three sets of experimental data parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample estimates of are generally around 50 around 8 1 and varies from 0 to reinforcement and belief learning special cases are generally rejected in favor of ewa though belief models do better in some constant sum games ewa is able to combine the best features of previous approaches allowing attractions to begin and grow flexibly as choice reinforcement does but reinforcing unchosen strategies substantially as belief based models implicitly do

globally optimal finite difference schemes based on least squares abstractspatial finite difference fd coefficients are usually determined by the taylor series expansion te or optimization methods the former can provide high accuracy on a smaller wavenumber or frequency zone and the latter can give moderate accuracy on a larger zone present optimization methods applied to calculate fd coefficients are generally gradient like or global optimization like algorithms and thus iterations are involved they are more computationally expensive and sometimes the global solution may not be found i examined second order spatial derivatives and computed the optimized spatial fd coefficients over the given wavenumber range using the least squares ls method the results indicated that the fd accuracy increased with increasing operator length and decreasing wavenumber range therefore for the given error and operator length globally optimal spatial fd coefficients can be easily obtained some optimal fd coefficients were given i developed schemes to obtain optimized ls

what determines the shape of the probability weighting function under uncertainty decision weights are an important component in recent theories of decision making under uncertainty to better explain these decision weights a two stage approach has been proposed first the probability of an event is judged and then this probability is transformed by the probability weighting function known from decision making under risk we extend the two stage approach by allowing the probability weighting function to depend on the type of uncertainty using this more general approach properties of decision weights can be attributed to properties of probability judgments and or to properties of probability weighting we present an empirical study that shows that it is indeed necessary to allow the probability weighting function to be source dependent the analysis includes an examination of properties of the probability weighting function under uncertainty that have not been considered yet

third order symplectic integration method with inverse time dispersion transform for long term simulation the symplectic integration method is popular in high accuracy numerical simulations when discretizing temporal derivatives however it still suffers from time dispersion error when the temporal interval is coarse especially for long term simulations and large scale models we employ the inverse time dispersion transform itdt to the third order symplectic integration method to reduce the time dispersion error first we adopt the pseudospectral algorithm for the spatial discretization and the third order symplectic integration method for the temporal discretization then we apply the itdt to eliminate time dispersion error from the synthetic data as a post processing method the itdt can be easily cascaded in traditional numerical simulations we implement the itdt in one typical exiting third order symplectic scheme and compare its performances with the performances of the conventional second order scheme and the rapid expansion method theoretical analyses and numerical experiments show that the itdt can significantly reduce the time dispersion error especially for long travel times the implementation of the itdt requires some additional computations on correcting the time dispersion error but it allows us to use the maximum temporal interval under stability conditions thus its final computational efficiency would be higher than that of the traditional symplectic integration method for long term simulations with the aid of the itdt we can obtain much more accurate simulation results but with a lower computational cost we use the inverse time dispersion transform to the 3rd order symplectic integration it can greatly reduce the time dispersion error especially for long travel times it is superior to the conventional 2nd and high order finite difference methods it allows the maximum temporal interval under stability conditions thus is efficient we can obtain more accurate simulation results but with a lower computational cost

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

choice based elicitation and decomposition of decision weights for gains and losses under uncertainty this paper reports the results of an experimental parameter free elicitation and decomposition of decision weights under uncertainty assuming cumulative prospect theory utility functions were elicited for gains and losses at an individual level using the tradeoff method subsequently decision weights were elicited through certainty equivalents of uncertain two outcome prospects furthermore decision weights were decomposed using observable choice instead of invoking other empirical primitives as in previous experimental studies the choice based elicitation of decision weights allows for a quantitative study of their characteristics and also allows among other things for the examination of the sign dependence hypothesis for observed choice under uncertainty our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice based subjective probabilities we also find evidence for sign dependence of decision weights

pseudo analytical finite difference elastic wave extrapolation based on the k space method abstractcost effective elastic wave modeling is the key to practical elastic reverse time migration and full waveform inversion implementations we have developed an efficient elastic pseudo analytical finite difference pafd scheme for elastic wave extrapolation the elastic pafd scheme is based on a modified pseudo spectral method k space method in which a pseudo analytical operator is used to ensure the high accuracy of elastic wave extrapolation however the k space method is motivated for a pure wave mode and thus its application in coupled first order elastic wave equations may cause the elastic pseudo analytical operators to suffer from crosstalk between the p and s wavefields the approaches presented attempt to overcome these shortcomings by introducing two improvements to achieve the goal this is done first by performing a predictor corrector strategy in first order elastic wave equations to eliminate those errors during wave extrapolation considering the massive computational cost in

modeling viewpoint shifts in probabilistic choice a number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory this article presents the development of a new stochastic choice model based on multidimensional scaling this allows decision makers to have multiple viewpoints whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint the implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint this paper also presents the maximum likelihood estimation of the proposed model and reanalyzes tversky s gamble experiment data

acoustic and elastic modeling by optimal time space domain staggered grid finite difference schemes abstractstaggered grid finite difference sfd methods are widely used in modeling seismic wave propagation and the coefficients of finite difference fd operators can be estimated by minimizing dispersion errors using taylor series expansion te or optimization we developed novel optimal time space domain sfd schemes for acoustic and elastic wave equation modeling in our schemes a fourth order multiextreme value objective function with respect to fd coefficients was involved to yield the globally optimal solution with low computational cost we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least squares ls to derive the optimal sfd coefficients by minimizing the relative error of time space domain dispersion relations over a given frequency range to ensure the robustness of our schemes a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold moreover the hybrid absorbin

mixture models of choice under risk this paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals we note that there is heterogeneity in behaviour between individuals and within individuals by heterogeneity between individuals we mean that people are different in terms of both their preference functionals and their parameters for these functionals by heterogeneity within individuals we mean that the behaviour may be different even by the same individual for the same choice problem we propose methods of taking into account all forms of heterogeneity concentrating particularly on using a mixture model to capture the heterogeneity of preference functionals