varieties of nilpotent lie algebras of dimension less than six the set of all nilpotent ide algebra multiplications on a fixed vector space of dimension n over a field k forms an affine variety n isomorphism classes of these lie algebras are orbits in i under the change of basis action of gl n k by examining the orbit structure of n for small n we hope to gain a new perspective on the classification of nilpotent lie algebras in this paper we determine completely the orbit structure of the variety n when n 6 5 and k c we also show that the homomorphic image of a nilpotent lie algebra is in the closure of the orbit of that lie algebra taking the direct product with an abelian lie algebra to make the dimension right some of the orbit structure of n for n 6 and other geometric properties of n were described by vergne in vl v2 v3 recently carles has used vergne s results to study the variety of all lie algebras cl our motivation for studying the classification of nilpotent lie algebras is to gain information about the classification of nilpotent groups the correspondence between nilpotent lie algebras and nilpotent groups is described in go

statistical properties of german dax and chinese indices abstract we investigate statistical properties of the german dax and chinese indices including the volatility distribution autocorrelation function dfa function and return volatility correlation function with both the daily data and minutely data at the minutely time scale the chinese indices may show irregular dynamic behavior at the daily time scale the volatility distribution autocorrelation function and dfa function of the chinese indices are qualitatively similar to those of the german dax while the return volatility correlation function exhibits an anti leverage effect different from the leverage effect of the german dax

adjoint derived location and travel time probabilities for a multidimensional groundwater system backward location and travel time probabilities can be used to determine the former location of contamination in an aquifer for a contaminant parcel that was detected in an aquifer the backward location probability describes its position at some time prior to sampling and the backward travel time probability describes the amount of time required for it to travel to the sampling location from some upgradient position these probabilities which can provide information about the source of contamination are related to adjoint states of resident concentration the governing equations of the backward probabilities are adjoints of the forward governing equation e g the advection dispersion equation we derive these backward governing equations and their boundary and final conditions for both location and travel time probabilities in a multidimensional system each governing equation contains the adjoint of the advection dispersion operator and a load term that defines the particular adjoint state probability the load term depends on both the type of probability location or travel time and the sampling device pumping well or monitoring well with which the contamination was detected the adjoint equation can also be used to efficiently determine forward location and travel time probabilities describing the future location of groundwater contamination a feature most useful for delineating pumping well captures zones we illustrate the use of the backward model for obtaining location and travel time probabilities in a hypothetical two dimensional domain

modeling interactions of trading volumes in financial dynamics abstract a dynamic herding model with interactions of trading volumes is introduced at time t an agent trades with a probability which depends on the ratio of the total trading volume at time t 1 to its own trading volume at its last trade the price return is determined by the volume imbalance and number of trades the model can reproduce the power law distributions of the trading volume number of trades and price return and the probable relation between them the exponents are tunable by adjusting the values of the parameters but show slight deviation from those revealed in empirical studies moreover the time series generated are long range correlated we demonstrate that the results are rather robust and do not depend on the particular form of the trading probability

volatility clustering and scaling for financial time series due to attractor bubbling a microscopic model of financial markets is considered consisting of many interacting agents spins with global coupling and discrete time heat bath dynamics similar to random ising systems the interactions between agents change randomly in time in the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on off intermittency resembling the empirical financial time series with volatility clustering for a proper choice of the model parameters the probability distributions of returns exhibit power law tails with scaling exponents close to the empirical ones

the frobenius semiradical of a lie algebra univ limburg dept math b 3590 diepenbeek belgium ooms ai univ limburg dept math univ campus b 3590 diepenbeek belgium alfons ooms luc ac be

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

robust solutions of linear programming problems contaminated with uncertain data optimal solutions of linear programming problems may become severely infeasible if the nominal data is slightly perturbed we demonstrate this phenomenon by studying 90 lps from the well known netlib collection we then apply the robust optimization methodology ben tal and nemirovski 1 3 el ghaoui et al 5 6 to produce robust solutions of the above lps which are in a sense immuned against uncertainty surprisingly for the netlib problems these robust solutions nearly lose nothing in optimality

on kirillov s lemma for nilpotent lie algebras abstract we establish a sharpening of kirillov s lemma on nilpotent lie algebras with 1 dimensional center and use it to study the structure of 3 step nilpotent lie algebras

non universal scaling and dynamical feedback in generalized models of financial markets abstract we study self organized models for information transmission and herd behavior in financial markets existing models are generalized to take into account the effect of size dependent fragmentation and coagulation probabilities of groups of agents and to include a demand process non universal scaling with a tunable exponent for the group size distribution is found in the resulting system we also show that the fragmentation and coagulation probabilities of groups of agents have a strong influence on the average investment rate of the system

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

microscopic models for long ranged volatility correlations we propose a general interpretation for long range correlation effects in the activity and volatility of financial markets this interpretation is based on the fact that the choice between active and inactive strategies is subordinated to random walk like processes we numerically demonstrate our scenario in the framework of simplified market models such as the minority game model with an inactive strategy or a more sophisticated version that includes some price dynamics we show that real market data can be surprisingly well accounted for by these simple models

stochastic multiplicative processes for financial markets abstract we study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets we find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated levy like distribution and the cross correlation between relative updated wealths is the origin of the nontrivial properties of returns including the power law distribution with exponent outside the stable levy regime and the long range persistence of volatility correlations

a robust geostatistical approach to contaminant source identification 1 estimation under model uncertainty remains a practical concern in many scientific and engineering fields a commonly encountered example in groundwater remediation is the contaminant source identification problem like many other inverse problems contaminant source identification is inherently ill posed and is sensitive to both data and model uncertainties model uncertainties which may be introduced at virtually any stage of a model building process can adversely affect estimator performance if they are not accounted for properly in this paper a robust geostatistical approach rgs which is extended from the geostatistical inversion approach gs is used to solve linear estimation problems the uncertainties in both model and covariance matrices are taken into account in the rgs formulation the nominal correlation structural parameters are estimated using a structural analysis procedure the resulting minimax optimization problem is solved using semidefinite programming techniques the rgs is generic and can be applied to any problem for which the gs is suitable and the upper bound of uncertainty can be quantified the rgs is illustrated for source release history identification in a two dimensional aquifer where the model uncertainty is caused by variability in hydraulic conductivity it is shown that when the model is perfectly known the rgs solution coincides with that of the gs when the model has uncertainty the rgs is robust against unknown variations from a nominal model and its overall performance is better than that of the gs using the same nominal model

recovering the history of a groundwater contaminant plume method of quasi reversibility the method of quasi reversibility qr lattes and lions 1969 has been used previously to solve the diffusion equation with reversed time we develop a quasi reversible solution to a convection dispersion equation by solving the qr diffusion operator in a moving coordinate system the solution procedure is applied to the problem of recovering the history of a groundwater contaminant plume from observations of its present conditions this approach to the plume history problem is potentially superior to the tikhonov regularization approach used by skaggs and kabala 1994 because it is easier to implement and readily allows for space and time dependent transport parameters however our results for a few example problems suggest that the qr procedure is less accurate than the regularization technique thus the easy implementation and improved generality of the qr procedure come at the expense of accuracy this trade off will have to be weighed if the qr technique is to be used

spherical orbits and abelian ideals let g be a connected reductive complex algebraic group with lie algebra lie g g let b be a borel subgroup of g with unipotent radical bu we denote the lie algebra of b and bu by b and bu respectively the group b acts on any ideal of b by means of the adjoint representation after a preliminary section we study a relationship between spherical nilpotent orbits and abelian ideals a of b using the structure theory for these orbits from 10 the principal result of this section is that for an abelian ideal a of b any nilpotent orbit meeting a is a spherical g variety see theorem 2 3 as a consequence of this we obtain a short conceptual proof of a finiteness theorem from 14 namely for a parabolic subgroup p of g and an abelian ideal a of p lie p in the nilpotent radical pu lie pu the group p operates on a with finitely many orbits the proof of this fact in 14 involved long and tedious case by case considerations we also prove a partial converse to the result just mentioned following 4 we say that an ideal of b is ad nilpotent whenever it consists of nilpotent elements in case g is simply laced we show that an ad nilpotent ideal c of b is abelian provided any nilpotent orbit meeting c is spherical see proposition 2 7 in section 3 we consider some properties of ad nilpotent ideals of b in theorem 3 2 we give a description of the normaliser of such ideals this applies in particular to abelian ideals of b a remarkable theorem of doi 10 1006 aima 2000 1959 available online at http www idealibrary com on

nonlinear stochastic exclusion financial dynamics modeling and time dependent intrinsic detrended cross correlation abstract in attempt to reproduce price dynamics of financial markets a stochastic agent based financial price model is proposed and investigated by stochastic exclusion process the exclusion process one of interacting particle systems is usually thought of as modeling particle motion with the conserved number of particles in a continuous time markov process in this work the process is utilized to imitate the trading interactions among the investing agents in order to explain some stylized facts found in financial time series dynamics to better understand the correlation behaviors of the proposed model a new time dependent intrinsic detrended cross correlation tdi dcc is introduced and performed also the autocorrelation analyses are applied in the empirical research furthermore to verify the rationality of the financial price model the actual return series are also considered to be comparatively studied with the simulation ones the comparison results of return behaviors reveal that this financial price dynamics model can reproduce some correlation features of actual stock markets

dynamic scaling behavior of human brain electroencephalogram abstract after filtering out the and peaks in the power spectrum of the human brain electroencephalogram signals y t the probability distribution of the variation y t y t t y t exhibits a dynamic scaling behavior the auto correlation functions persistence probabilities and detrended fluctuation functions of the time series y t all show a nontrivial power law behavior these results indicate that the dynamics of the human brain electroencephalogram is long range correlated in time

minimum relative entropy inversion theory and application to recovering the release history of a groundwater contaminant in this paper we show that given prior information in terms of a lower and upper bound a prior bias and constraints in terms of measured data minimum relative entropy mre yields exact expressions for the posterior probability density function pdf and the expected value of the linear inverse problem in addition we are able to produce any desired confidence intervals in numerical simulations we use the mre approach to recover the release and evolution histories of plume in a one dimensional constant known velocity and dispersivity system for noise free data we find that the reconstructed plume evolution history is indistinguishable from the true history an exact match to the observed data is evident two methods are chosen for dissociating signal from a noisy data set the first uses a modification of mre for uncertain data the second method uses presmoothing by fast fourier transforms and butterworth filters to attempt to remove noise from the signal before the noise free variant of mre inversion is used both methods appear to work very well in recovering the true signal and qualitatively appear superior to that of skaggs and kabala 1994 we also solve for a degenerate case with a very high standard deviation in the noise the recovered model indicates that the mre inverse method did manage to recover the salient features of the source history once the plume source history has been developed future behavior of a plume can then be cast in a probabilistic framework for an example simulation the mre approach not only was able to resolve the source function from noisy data but also was able to correctly predict future behavior

robust truss topology design via semidefinite programming we present and motivate a new model of the truss topology design problem where the rigidity of the resulting truss with respect both to given loading scenarios and small occasional loads is optimized it is shown that the resulting optimization problem is a semidefinite program we derive and analyze several equivalent reformulations of the problem and present illustrative numerical examples

multiscale multifractal dcca and complexity behaviors of return intervals for potts price model abstract to investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events we use a potts dynamic system to construct a random financial time series model of the attitudes of market traders we use multiscale multifractal detrended cross correlation analysis mm dcca and lempel ziv complexity lzc perform numerical research of the return intervals for two significant china s stock market indices and for the proposed model the new mm dcca method is based on the hurst surface and provides more interpretable cross correlations of the dynamic mechanism between different return interval series we scale the lzc method with different exponents to illustrate the complexity of return intervals in different scales empirical studies indicate that the proposed return intervals from the potts system and the real stock market indices hold similar statistical properties

exploiting sparsity in primal dual interior point methods for semidefinite programming the helmberg rendl vanderbei wolkowicz kojima shindoh hara monteiro and nesterov todd search directions have been used in many primal dual interior point methods for semidefinite programs this paper proposes an efficient method for computing the two directions when the semidefinite program to be solved is large scale and sparse

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

comparison of inverse methods for reconstructing the release history of a groundwater contamination source inverse methods can be used to reconstruct the release history of a known source of groundwater contamination from concentration data describing the present day spatial distribution of the contaminant plume using hypothetical release history functions and contaminant plumes we evaluate the relative effectiveness of two proposed inverse methods tikhonov regularization tr and minimum relative entropy mre inversion in reconstructing the release history of a conservative contaminant in a one dimensional domain skaggs and kabala 1994 woodbury and ulrych 1996 we also address issues of reproducibility of the solution and the appropriateness of models for simulating random measurement error the results show that if error free plume concentration data are available both methods perform well in reconstructing a smooth source history function with error free data the mre method is more robust than tr in reconstructing a nonsmooth source history function however the tr method is more robust if the data contain measurement error two error models were evaluated in this study and we found that the particular error model does not affect the reliability of the solutions the results for the tr method have somewhat greater reproducibility because in some cases its input parameters are less subjective than those of the mre method however the mre solution can identify regions where the data give little or no information about the source history function while the tr solution cannot

intermittency in an interacting generalization of the geometric brownian motion model we propose a minimal interacting generalization of the geometric brownian motion model which turns out to be formally equivalent to a model describing the dynamics of networks of analogue neurons for sufficiently strong interactions such systems may have many meta stable states transitions between meta stable states are associated with macroscopic reorganizations of the system which can be triggered by random external forcing such a system will exhibit intermittent dynamics within a large part of its parameter space we propose market dynamics as a possible application of this model in which case random external forcing would correspond to the arrival of important information the emergence of a model of interacting prices of the type considered here can be argued to follow naturally from a general argument based on integrating out all non price degrees of freedom from the dynamics of a hypothetical complete description of economic dependences

diffusion entropy analysis on the scaling behavior of financial markets abstract in this paper the diffusion entropy technique is applied to investigate the scaling behavior of financial markets the scaling behaviors of four representative stock markets dow jones industrial average standardp with the scale invariance exponents all in the interval 0 92 0 95 we also estimate the local scaling exponents which indicate the financial time series is homogenous perfectly in addition a parsimonious percolation model for stock markets is proposed of which the scaling behavior agrees with the real life markets well

volatility behavior of visibility graph emd financial time series from ising interacting system abstract a financial market dynamics model is developed and investigated by stochastic ising system where the ising model is the most popular ferromagnetic model in statistical physics systems applying two graph based analysis and multiscale entropy method we investigate and compare the statistical volatility behavior of return time series and the corresponding imf series derived from the empirical mode decomposition emd method and the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model further we find that the degree distribution of visibility graph for the simulation series has the power law tails and the assortative network exhibits the mixing pattern property all these features are in agreement with the real market data the research confirms that the financial model established by the ising system is reasonable

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

complexity and multifractal behaviors of multiscale continuum percolation financial system for chinese stock markets abstract a new financial agent based time series model is developed and investigated by multiscale continuum percolation system which can be viewed as an extended version of continuum percolation system in this financial model for different parameters of proportion and density two poisson point processes where the radii of points represent the ability of receiving or transmitting information among investors are applied to model a random stock price process in an attempt to investigate the fluctuation dynamics of the financial market to validate its effectiveness and rationality we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets further the multiscale sample entropy analysis is employed to study the complexity of the returns and the cross sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series the empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent

the polynomiality of the poisson center and semi center of a lie algebra and dixmier s fourth problem abstract let g be a finite dimensional lie algebra over an algebraically closed field k of characteristic zero we provide necessary and also some sufficient conditions in order for its poisson center and semi center to be polynomial algebras over k this occurs for instance if g is quadratic of index 2 with g g g and also if g is nilpotent of index at most 2 the converse holds for filiform lie algebras of type l n q n r n and w n we show how dixmier s fourth problem for an algebraic lie algebra g can be reduced to that of its canonical truncation g moreover dixmier s statement holds for all lie algebras of dimension at most eight the nonsolvable ones among them possess a polynomial poisson center and semi center

volatility aggregation intensity energy futures series on stochastic finite range exclusion dynamics abstract the stochastic finite range exclusion process one of statistical physics systems is introduced to construct a new agent based financial price model to study the mechanism of market dynamics a novel volatility aggregation intensity vai time series describing the fluctuation aggregation intensity of the volatility series is developed for further investigating the nonlinear volatility behaviors in energy markets for studying the proposed vai series and the proposed price model the new york mercantile exchange energy futures data is selected and analyzed further cross correlation analysis auto correlation analysis with multiscale and multifractal detrended fluctuation analysis are applied to analyze the correlation volatility clustering and multifractal natures of the vai time series the empirical results show that the proposed model has the parallel behaviors with the authentic markets indicating that it is rational and available the new concept of vai series is of great value and can enrich the study of volatility behaviors in energy markets to some extent

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

a gibbs sampler for inequality constrained geostatistical interpolation and inverse modeling 1 interpolation and inverse modeling problems are ubiquitous in environmental sciences in many applications the parameters being estimated or mapped have physical constraints such as nonnegativity e g concentration hydraulic conductivity solubility limits censored data e g due to dry wells or detection limits and other physical boundaries or missing data geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters but these methods typically cannot enforce physical constraints this paper describes a statistically rigorous and computationally efficient gibbs sampler a markov chain monte carlo technique based on an a priori truncated gaussian distribution model which allows for multiple and variable physical constraints to be enforced within a geostatistical framework sample interpolation and inverse modeling applications confirm that estimates uncertainty bounds and conditional simulations reflect the specified constraints leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters being estimated in addition especially in inverse modeling applications a posteriori confidence bounds are narrower even in areas where constraints are not imposed the method is applicable in multiple dimensions for data with or without measurement error and with any variogram model

a constrained robust least squares approach for contaminant release history identification 1 contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty model uncertainty was rarely considered in the previous studies in this work a robust framework for solving contaminant source recovery problems is introduced the contaminant source identification problem is first cast into one of solving uncertain linear equations where the response matrix is constructed using a superposition technique the formulation presented here is general and is applicable to any porous media flow and transport solvers the robust least squares rls estimator which originated in the field of robust identification directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data in this work a new variant of rls the constrained robust least squares crls is formulated for solving uncertain linear equations crls allows for additional constraints such as nonnegativity to be imposed the performance of crls is demonstrated through one and two dimensional test problems when the system is ill conditioned and uncertain it is found that crls gave much better performance than its classical counterpart the nonnegative least squares the source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications

on commutative polarizations let l be a finite dimensional lie algebra over a field k of characteristic zero and let u l be its enveloping algebra with quotient division ring d l let p be a commutative lie subalgebra of l in o2 the necessary and sufficient condition on p was given in order for d p to be a maximal commutative subfield of d l in particular this condition is satisfied if p is a commutative polarization cp with respect to any regular f l and the converse holds if l is ad algebraic the purpose of this paper is to study lie algebras admitting these cp s and to demonstrate their widespread occurrence first we have the following characterisation if l is completely solvable p is a cp of l if and only if there exists a descending chain of lie subalgebras

crossover in the cont bouchaud percolation model for market fluctuations abstract monte carlo simulations of the cont bouchaud herding model for stock market traders show power law distributions for short times and exponential truncation for longer time intervals if they are made at the percolation threshold in two to seven dimensions

the gelfand kirillov conjecture for semi direct products of lie algebras let g be an n dimensional lie algebra over a field k of characteristic zero and let w be a g module such that dimw n sufficient conditions are given in order for the semi direct product g w to satisfy the gelfand kirillov conjecture this implies that this conjecture holds for an important class of frobenius lie algebras special attention is devoted to the case where g sl 2 k

minority games with score dependent and agent dependent payoffs score dependent and agent dependent payoffs of the strategies are introduced into the standard minority game the intrinsic periodicity is consequently removed and the stylized facts arise such as long range volatility correlations and fat tails in the distribution of the returns the agent dependence of the payoffs is essential in producing the long range volatility correlations the new payoffs lead to a better performance in the dynamic behavior nonlocal in time and can coexist with the inactive strategy we also observe that the standard deviation ensuremath sigma 2 n is significantly reduced thus the efficiency of the system is distinctly improved based on this observation we give a qualitative explanation for the long range volatility correlations

7 dimensional nilpotent lie algebras all 7 dimensional nilpotent lie algebras over c are determined by elementary methods a multiplication table is given for each isomorphism class distinguishing features are given proving that the algebras are pairwise nonisomorphic moduli are given for the infinite families which are indexed by the value of a complex parameter

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

similarities and differences between physics and economics in this opening talk we discuss some of the similarities between work being done by economists and by physicists seeking to contribute to economics we also mention some of the dierences in the approaches taken and justify these dierent approaches by developing the argument that by approaching the same problem from dierent points of view new results might emerge in particular we review some recent results for example the 1nding that there are two new universal scaling models in economics i the 3uctuation of price changes of any stock market is characterized by a pdf which is a simple power law with exponent 4 that extends over 10 2 standard deviations a factor of 10 8 on the y axis ii for a wide range of economic organizations the histogram that shows how size of organization is inversely correlated to 3uc tuations in size with an exponent 1 6 neither of these two new laws has a 1rm theoretical foundation we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic 1eld leads to large 3uctuations c 2001 published by elsevier science b v

statistical volatility duration and complexity of financial dynamics on sierpinski gasket lattice percolation abstract a novel agent based financial dynamics is established based on the percolation system on sierpinski gasket lattice to reproduce the statistical characteristics of financial markets sierpinski gasket lattice is a fractal like graph which corresponds to the fractal well known sierpinski gasket modeling a financial dynamics on sierpinski gasket lattice is a new approach in financial micro mechanism construction in an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time which describe the trend of volatility of return time series in financial markets furthermore a new method cmcid is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale the results show that the pairs of real data and simulated data have synchronization and the synchronization becomes stronger when the scale increases and the power law distribution is employed to investigate the corresponding statistical properties which shows that the proposed model shares a common power law distribution with regard to monotonous volatility duration the empirical results show that the simulated series from the financial model and the historical data share common statistical properties which indicate that the proposed model is reasonable in terms of volatility behavior

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

multiscale synchrony behaviors of paired financial time series by 3d multi continuum percolation abstract multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated in an attempt to study the cross correlation relationships between two stock markets a random stock price model is developed by a new system called three dimensional 3d multi continuum percolation system which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series we assume that the price fluctuations are caused by the spread of investment information the cluster of 3d multi continuum percolation represents the cluster of investors who share the same investment attitude in this paper we focus on the paired return series the paired volatility series and the paired intrinsic mode functions which are decomposed by empirical mode decomposition a new cross recurrence quantification analysis is put forward combining with multiscale cross sample entropy to investigate the multiscale synchrony of these paired series from the proposed model the corresponding research is also carried out for two china stock markets as comparison

on simple novikov algebras and their irreducible modules abstract we give a complete classification of finite dimensional simple novikov algebras and their irreducible modules over an algebraically closed field with prime characteristic moreover we introduce novikov poisson algebras and their tensor theory our tensor theory enables us to understand better certain finite dimensional simple novikov algebras and their irreducible modules

some p v equivalences and a classification of 2 simple prehomogeneous vector spaces of type a classification of 2 simple prehomogeneous vector spaces is completed by using some p v equivalences together with 3 some part is very different from the previous classification of the irreducible or simple cases 1 2 and some new method is necessary this result shows the difficult point of a classification problem of reductive prehomogeneous vector spaces introduction in m sato and t kimura 1 all irreducible prehomogeneous vector spaces abbreviated irreducible p v s are classified up to castling equivalence and it is proved that any irreducible p v is castling equivalent to a 2 simple p v or to sl m x sl m x gl 2 a1 x a1 x a1 with m 2 3 therefore as a step to a classification of the general case it is natural to classify all nonirreducible 2 simple p v s in this paper we shall classify all 2 simple p v s of type ii and give the complete list of them up to strong equivalence in the sense of definition 4 p 36 in 1 however we need various p v equivalences cf propositions 1 7 1 12 1 34 1 36 1 37 theorem 1 16 and its corollary corollary 1 26 definition 1 31 remark 1 32 to carry out the classification and hence first we shall prove them we also investigate the regularity in some cases since all 2 simple p v s of type i are already classified in 3 this completes the classification of all 2 simple p v s here we say that g p v or simply g p is a 2 simple p v if it is a prehomogeneous vector space of the following form g gl 1 k s t xg x g2 where g1 and g2 are simple algebraic groups p the composition of the scalar multiplications gl l k s on each irreducible component and the representation p p1 p 1 pk p k a1 s 1 1 t1 t ofthegroupg1 x g2 where pi aj resp p tj are nontrivial irreducible representations of g1 resp g2 we write g p v instead of g p v for simplicity to avoid confusion we write instead of clearly each gl 1 x g1 x g2 pi p i 1 k is an irreducible 2 simple p v if at least one of them is a nontrivial p v see definition 1 1 we call it a 2 simple p v of type i on the other hand if all of them are trivial p v s we call it a 2 simple p v of type ii in this case we have g2 sl n received by the editors march 3 1986 and in revised form july 30 1986 1980 mathematics subject classification 1985 revision primary 11r20 11r29 secondary 11n25 11r18 01988 american mathematical society 0002 9947 88 1 00 25 per page

computing invariants and semi invariants by means of frobenius lie algebras abstract let u be the enveloping algebra of a finite dimensional lie algebra over a field k of characteristic zero z u its center and sz u its semi center a sufficient condition is given in order for sz u to be a polynomial algebra over k surprisingly this condition holds for many lie algebras especially among those for which the radical is nilpotent in which case sz u z u in particular it allows the explicit description of z u for more than half of all complex indecomposable nilpotent lie algebras of dimension at most 7

persistence probabilities of the german dax and shanghai index abstract we present a relatively detailed analysis of the persistence probability distributions in financial dynamics compared with the auto correlation function the persistence probability distributions describe dynamic correlations nonlocal in time universal and non universal behaviors of the german dax and shanghai index are analyzed and numerical simulations of some microscopic models are also performed around the fixed point z 0 0 the interacting herding model produces the scaling behavior of the real markets

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

a generalized dynamic herding model with feed back interactions abstract a dynamic feed back interaction is introduced to the eguiluz zimmermann model phys rev lett 85 2000 5659 in application to financial dynamics transmission of information at time t is supposed to depend on the variation of the financial index at t 1 the generated time series is strongly correlated in time at criticality both static and dynamic behavior are investigated

on certain maximal subfields in the quotient division ring of an enveloping algebra univ limburg dept math b 3590 diepenbeek belgium ooms ai univ limburg dept math b 3590 diepenbeek belgium

the poisson center and polynomial maximal poisson commutative subalgebras especially for nilpotent lie algebras of dimension at most seven abstract let g be a finite dimensional lie algebra over an algebraically closed field k of characteristic zero we collect some general results on the poisson center of s g including some simple criteria regarding its polynomiality and also on certain poisson commutative subalgebras of s g these facts are then used to complete our previous work on the subject ooms 2009 o5 5 i e to give an explicit description for the poisson center of all indecomposable nilpotent lie algebras of dimension at most seven among other things we also provide a polynomial maximal poisson commutative subalgebra of s g enjoying additional properties as a by product we show that a conjecture by milovanov is valid in this situation these results easily carry over to the enveloping algebra u g

volatility driven market in a generalized lotka voltera formalism abstract the generalized lotka voltera glv formalism has been introduced in order to explain the power law distributions in the individual wealth w i t pareto law and financial markets returns fluctuations r as a result of the auto catalytic multiplicative random character of the individual capital dynamics as long as the multiplicative random factor is extracted from the same probability distribution for all the individuals the exponent of the power laws turns out to be independent on the time variations of the average this explains also the stability over the past century of experimentally measured pareto exponent in contrast to the scaling properties of the single time unconditional probability distributions the auto correlations between observables measured at different times are not correctly reproduced by the original glv if the variance 2 of is time independent in the glv formalism the volatility r 2 auto correlations decay exponentially while the measurements in real markets indicate a power law with a very small exponent we show in the present paper that by making the variance of the individual wealth changes 2 a function of the market volatility r 2 one correctly reproduces the market volatility long range correlations moreover we show that this non trivial feedback loop between the market price volatility and the variance of the investors wealth leads to non trivial patterns in the overall market trends if the feedback is too strong it may even endanger the market stability

robust convex quadratically constrained programs in this paper we study robust convex quadratically constrained programs a subset of the class of robust convex programs introduced by ben tal and nemirovski 4 in contrast to 4 where it is shown that such robust problems can be formulated as semidefinite programs our focus in this paper is to identify uncertainty sets that allow this class of problems to be formulated as second order cone programs socp we propose three classes of uncertainty sets for which the robust problem can be reformulated as an explicit socp and present examples where these classes of uncertainty sets are natural

estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling 1 as the incidence of groundwater contamination continues to grow a number of inverse modeling methods have been developed to address forensic groundwater problems in this work the geostatistical approach to inverse modeling is extended to allow for the recovery of the antecedent distribution of a contaminant at a given point back in time which is critical to the assessment of historical exposure to contamination such problems are typically strongly underdetermined with a large number of points at which the distribution is to be estimated to address this challenge the computational efficiency of the new method is increased through the application of the adjoint state method in addition the adjoint problem is presented in a format that allows for the reuse of existing groundwater flow and transport codes as modules in the inverse modeling algorithm as demonstrated in the presented applications the geostatistical approach combined with the adjoint state method allow for a historical multidimensional contaminant distribution to be recovered even in heterogeneous media where a numerical solution is required for the forward problem