general relaxation schemes in multigrid algorithms for higher order singularity methods abstract relaxation schemes based on an approximate and incomplete factorization technique af are described these af schemes allow one to construct a fast multigrid method for solving integral equations of the second as well as of the first kind novel items are the smoothing factors found for integral equations of the first kind and the comparison with similar results for equations of the second kind application of the mg algorithm shows convergence of a second order accurate panel method to the level of the truncation error within two multigrid cycles

hyperinflation in brazil israel and nicaragua revisited abstract the aim of the present work is to address the description of hyperinflation regimens in economy the spirals of hyperinflation developed in brazil israel and nicaragua are revisited this new analysis of data indicates that the episodes occurred in brazil and nicaragua can be understood within the frame of the model available in the literature which is based on a nonlinear feedback nlf characterized by an exponent 0 in the nlf model the accumulated consumer price index carries a finite time singularity of the type 1 t c t 1 determining a critical time t c at which the economy would crash it is shown that in the case of brazil the entire episode cannot be described with a unique set of parameters because the time series was strongly affected by a change of policy this fact gives support to the so called lucas critique who stated that model s parameters usually change once policy changes on the other hand such a model is not able to provide any t c in the case of the weaker hyperinflation occurred in israel it is shown that in this case the fit of data yields 0 this limit leads to the linear feedback formulation which does not predict any t c an extension for the nlf model is suggested

bounded queries approximations and the boolean hierarchy this paper investigates nondeterministic bounded query classes in relation to the complexity of np hard approximation problems and the boolean hierarchy nondeterministic bounded query classes turn out be rather suitable for describing the complexity of np hard approximation problems the results in this paper take advantage of this machine based model to prove that in many cases np approximation problems have the upward collapse property that is a reduction between np approximation problems of apparently different complexity at a lower level results in a similar reduction at a higher level for example if maxclique reduces to log n approximating maxclique using many one reductions then the traveling salesman problem tsp is equivalent to maxclique under many one reductions several upward collapse theorems are presented in this paper the proofs of these theorems rely heavily on the machinery provided by the nondeterministic bounded query classes in fact these results depend on a surprising connection between the boolean hierarchy and nondeterministic bounded query classes

extending downward collapse from 1 versus 2 queries to m versus m 1 queries the top part of figure 1 1 shows some classes from the truth table bounded query and boolean hierarchies it is well known that if either of these hierarchies collapses at a given level then all higher levels of that hierarchy collapse to that same level this is a standard upward translation of equality that has been known for over a decade the issue of whether these hierarchies can translate equality downwards has proven vastly more challenging in particular with regard to figure 1 1 consider the following claim psigkmtt psigkmponett implies diffmsigk codiffmsigk bh sigmak this claim if true says that equality translates downwards between levels of the bounded query hierarchy and the boolean hierarchy levels that before the fact are immediately below them until recently it was not known whether ever held except for the degenerate cases m 0 and k 0 then hemaspaandra hemaspaandra and hempel siam j comput 28 1999 pp 383 393 proved that holds for all m for k 2 buhrman and fortnow j comput system sci 59 1999 pp 182 199 then showed that when k 2 holds for the case m 1 in this paper we prove that for the case k 2 holds for all values of m since there is an oracle relative to which for k 1 holds for all m fails see buhrman and fortnow our achievement of the k 2 case cannot be strengthened to k 1 by any relativizable proof technique the new downward translation we obtain also tightens the collapse in the polynomial hierarchy implied by a collapse in the bounded query hierarchy of the second level of the polynomial hierarchy

non extensive behavior of a stock market index at microscopic time scales abstract this paper presents an empirical investigation of the intraday brazilian stock market price fluctuations considering q gaussian distributions that emerge from a non extensive statistical mechanics our results show that when price returns are measured over intervals less than one hour the empirical distributions are well fitted by q gaussians with exponential damped tails scaling behavior is also observed for these microscopic time intervals we find that the time evolution of the return distributions is according to a super diffusive q gaussian stationary process within a nonlinear fokker planck equation this regime breaks down due to the exponential fall off of the tails which in turn governs the transient dynamics to the long term macroscopic gaussian regime this exponentially damped non extensive modeling provides a new framework to investigate the dynamics of other stock markets intraday price fluctuations

the boolean hierarchy ii applications the boolean hierarchy i structural properties j cai et al siam j comput 17 1988 pp 1232 252 explores the structure of the boolean hierarchy the closure of np with respect to boolean

the mechanism of double exponential growth in hyper inflation abstract analyzing historical data of price indices we find an extraordinary growth phenomenon in several examples of hyper inflation in which price changes are approximated nicely by double exponential functions of time in order to explain such behavior we introduce the general coarse graining technique in physics the monte carlo renormalization group method to the price dynamics starting from a microscopic stochastic equation describing dealers actions in open markets we obtain a macroscopic noiseless equation of price consistent with the observation the effect of auto catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double exponential behavior

new statistic for financial return distributions power law or exponential we introduce a new statistical tool the tp statistic and te statistic designed specifically to compare the behavior of the sample tail of distributions with power law and exponential tails as a function of the lower threshold u one important property of these statistics is that they converge to zero for power laws or for exponentials correspondingly regardless of the value of the exponent or of the form parameter this is particularly useful for testing the structure of a distribution power law or not exponential or not independently of the possibility of quantifying the values of the parameters we apply these statistics to the distribution of returns of one century of daily data for the dow jones industrial average and over 1 year of 5 min data of the nasdaq composite index our analysis confirms previous works showing the tendency for the tails to resemble more and more a power law for the highest quantiles but we can detect clear deviations that suggest that the structure of the tails of the distributions of returns is more complex than usually assumed it is clearly more complex that just a power law our new tp and te statistic should also be useful for other applications in the natural sciences as a powerful non parametric test for power laws and exponentials

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

a downward collapse within the polynomial hierarchy downward collapse also known as upward separation refers to cases where the equality of two larger classes implies the equality of two smaller classes we provide an unqualified downward collapse result completely within the polynomial hierarchy in particular we prove that for k 2 if rm p sigma p k 1 rm p sigma p k 2 then sigma p k pi p k rm ph we extend this to obtain a more general downward collapse result

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

transonic panel method for the full potential equation applied to multicomponent airfoils the panel method approach is extended to obtain numerical solutions of the full potential equation for transonic flow this extension is accomplished by adding a field distribution of source singularities to the conventional distribution of singularities over the boundaries of the field the unknown source distribution in the field is determined by solving the full potential equation shock waves are captured automatically by splitting the transformed flux components and applying upwind differencing to the monotonic supersonic parts the transonic panel method limits the space discretization to those parts of the flow domain in which the nonlinear compressibility effects are non negligible the method is tested by computing the potential flow over single and multicomponent airfoils

a threshold model for australian stock exchange equities abstract in this paper we present a threshold model to describe the phenomena of zero return enhancement that is present in australian stock exchange data we examine the intraday behaviour of the asx data and construct a new measure for the market activity using principal component analysis we use this measure to create a business time scale that keeps the level of zero return enhancement constant throughout trading hours operating in this new time scale we fit the model to data for small and large time scales and find that the model affords an excellent approximation of the distribution of stock returns

a gpu based multi level algorithm for boundary value problems abstract a novel geometric single grid multi level gsgml algorithm is presented for the numerical solution of boundary value problems bvps the algorithm is specifically designed for parallel scalability with high occupancy of streaming processors inside many core architectures like the graphics processing unit gpu the algorithm consists of iterative superposed operations on a single grid and is composed of two full grid routines a restriction and a coarsened interpolation relaxation the restriction is a local average of scalar or vector fields and the interpolation relaxation is a simultaneous application of coarsened finite difference operators and interpolations in complementary subsets of the grid the routines are scheduled in a saw like refining cycle convergence to machine precision is achieved repeating the full cycle using residuals and superposition the algorithm is attractive for its computational simplicity and provides a competitive gpu based fast solver for elliptic partial differential equations like the poisson helmholtz equation applications shown in this work include the deformation of two dimensional grids the computation of three dimensional streamlines for a singular trifoil knot vortex and the calculation of three dimensional electric potentials in heterogeneous dielectric media

on truth table reducibility to sat we show that polynomial time truth table reducibility via boolean circuits to sat is the same as logspace truth table reducibility via boolean formulas to sat and the same as logspace turing reducibility to sat in addition we prove that a constant number of rounds of parallel queries to sat is equivalent to one round of parallel queries we give an oracle relative to which 2p is not equal to the class of predicates polynomial time truth table reducible to sat

a multilevel formulation of the method of moments em scattering the modeling of electromagnetic scattering and radiation problems using the method of moments mom is limited to resonant frequencies because of the extensive computational requirements of solving large matrix equations in this study a multilevel formulation of mom which allows substantial computational savings and thus extends the application of mom to higher frequencies is presented using a hierarchy of discretization levels the multilevel technique extracts different modal components of the solution by focusing on a specific portion of the spectrum of the solution at a given level the fundamental features of this process for the mom solution of the electric field integral equation efie are developed and implemented this multilevel mom allows the rapid evaluation of the current distributions on a variety of 2 d scatterers with thousands of unknowns in fewer than ten cycles and in fractions of the normal cpu times the method is stable fast suitable for multiple excitations and adaptable as a solve module for almost any mom code

a characteristic time scale in dollar yen exchange rates abstract here we analyze tick data of yen dollar exchange using random walk methods we find that there exists a characteristic time scale approximately at 10 min according to the results at time scales shorter than 10 min the market exhibits anti persistence meaning that it self organizes so as to restore a given tendency for time scales longer than 10 min the market approaches a behavior appropriate to pure brownian motion

a second step towards complexity theoretic analogs of rice s theorem abstract rice s theorem states that every nontrivial language property of the recursively enumerable sets is undecidable borchert and stephan 1997 initiated the search for complexity theoretic analogs of rice s theorem in particular they proved that every nontrivial counting property of circuits is up hard and that a number of closely related problems are spp hard the present paper studies whether their up hardness result itself can be improved to spp hardness we show that their up hardness result cannot be strengthened to spp hardness unless unlikely complexity class containments hold nonetheless we prove that every p constructibly bi infinite counting property of circuits is spp hard we also raise their general lower bound from unambiguous nondeterminism to constant ambiguity nondeterminism

unambiguous computation boolean hierarchies and sparse turing complete sets this paper studies for up two topics that have been intensely studied for np boolean hierarchies and the consequences of the existence of sparse turing complete sets unfortunately as is often the case the results for np draw on special properties of np that do not seem to carry over straightforwardly to up for example it is known for np and more generally for any class containing sigma and emptyset and closed under union and intersection that the symmetric difference hierarchy the boolean hierarchy and the boolean closure all are equal we prove that closure under union is not needed for this claim for any class cal k that contains sigma and emptyset and is closed under intersection e g up us and fewp the symmetric difference hierarchy over cal k the boolean hierarchy over cal k and the boolean closure of cal k all are equal on the other hand we show that two hierarchies the hausdorff hierarchy and the nested difference hierarchy which in the np case are equal to the boolean closure fail to be equal for the up case in some relativized worlds regarding sparse turing complete sets for up we prove that if up has sparse turing complete sets then the levels of the unambiguous polynomial hierarchy are simpler than one would otherwise expect they collapse one level in terms of their location in the promise unambiguous polynomial hierarchy we obtain related results under the weaker assumption that up has sparse turing hard sets

properties of low variability periods in financial time series abstract properties of low variability periods in the time series are analysed the theoretical approach is used to show the relationship between the multi scaling of low variability periods and multi affinity of the time series it is shown that this technically simple method is capable of revealing more details about time series than the traditional multi affine analysis we have applied this scaling analysis to financial time series a number of daily currency and stock index time series the results show a good scaling behaviour for different model parameters the analysis of high frequency usd eur exchange rate data confirmed the theoretical expectations

analysis of high resolution foreign exchange data of usd jpy for 13 years we analyze high resolution foreign exchange data consisting of 20 million data points of usd jpy for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations a conditional probability density analysis clearly shows the existence of trend following movements at time scale of 8 ticks about 1 minute

fluctuation scaling of quotation activities in the foreign exchange market abstract we study the scaling behavior of quotation activities for various currency pairs in the foreign exchange market the components centrality is estimated from multiple time series and visualized as a currency pair network the power law relationship between a mean of quotation activity and its standard deviation for each currency pair is found the scaling exponent and the ratio between common and specific fluctuations increase with the length of the observation time window t the result means that although for t 1 min the market dynamics are governed by specific processes and at a longer time scale t 100 min the common information flow becomes more important we point out that quotation activities are not independently poissonian for t 1 min and temporally or mutually correlated activities of quotations can happen even at this time scale a stochastic model for the foreign exchange market based on a bipartite graph representation is proposed

reasoning with power defaults this paper introduces power default reasoning pdr a framework for non monotonic reasoning based on the domain theoretic idea of modeling default rules with partial information in a higher order setting pdr lifts a non monotonic operator at the base syntactic level to a well behaved almost monotonic operator in the higher order space of the smyth power domain effectively a space of sets of models working in the model space allows us to prove the dichotomy theorem and the extension splitting theorem leading to a more well behaved logic and modulo the usual complexity conjectures a less complex logic than standard default logic specifically we prove that skeptical normal default inference is a problem complete for co np 3 in the boolean hierarchy for strict propositional logic and np 4 complete in general these results by changing the underlying semantics contrasts favorably with similar results of gottlob j logic comput 2 3 1992 397 425 who proves that standard skeptical default reasoning is 2p complete furthermore we show that the skeptical non monotonic consequence relation defined using our domain theoretic semantics obeys all of the laws for preferential consequence relations defined by kraus lehmann and magidor in particular we get the property of being able to reason by cases and the so called law of cautious monotony both of these laws fail for the standard propositional default logic of reiter artificial intelligence 13 1980 81 132 but hold in pdr as a consequence of the dichotomy theorem and the extension splitting theorem

separating complexity classes with tally oracles abstract long and selman 1986 proved that for most familiar pairs of complexity classes separating the classes with a tally oracle is no easier than truly separating the classes refuting a claim in the literature we prove for the first time that for many familiar pairs of complexity classes separating the classes with a tally oracle is easier than truly separating the classes

lower bounds and the hardness of counting properties rice s theorem states that all nontrivial language properties of recursively enumerable sets are undecidable borchert and stephan math logic quart 46 4 2000 489 504 started the search for complexity theoretic analogs of rice s theorem and proved that every nontrivial counting property of boolean circuits is up hard hemaspaandra and rothe theoret comput sci 244 1 2 2000 205 217 improved the up hardness lower bound to upo 1 hardness the present paper raises the lower bound for nontrivial counting properties from upo 1 hardness to fewp hardness i e from constant ambiguity nondeterminism to polynomial ambiguity nondeterminism furthermore we prove that no relativizable technique can raise this lower bound to fewp 1 ttp hardness we also prove a rice style theorem for np namely that every nontrivial language property of np sets is np hard and for a broad class of leaf language classes we prove a sufficient condition for the natural analog of rice s theorem to hold

frequency analysis of tick quotes on the foreign exchange market and agent based modeling a spectral distance approach abstract high frequency financial data of the foreign exchange market eur chf eur gbp eur jpy eur nok eur sek eur usd nzd usd usd cad usd chf usd jpy usd nok and usd sek are analyzed by utilizing the kullback leibler divergence between two normalized spectrograms of the tick frequency and the generalized jensen shannon divergence among them the temporal structure variations of the similarity between currency pairs is detected and characterized a simple agent based model in which n market participants exchange m currency pairs is proposed the equation for the tick frequency is approximately derived theoretically based on the analysis of this model the spectral distance of the tick frequency is associated with the similarity of the behavior perception and decision of the market participants in exchanging these currency pairs

oracles that compute values this paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in npmv the class of all multivalued partial functions that are computable nondeterministically in polynomial time concerning deterministic polynomial time reducibilities it is shown that a multivalued partial function is polynomial time computable with k adaptive queries to npmv if and only if it is polynomial time computable via 2k 1 nonadaptive queries to npmv a characteristic function is polynomial time computable with k adaptive queries to npmv if and only if it is polynomial time computable with k adaptive queries to np unless the boolean hierarchy collapses for every k k adaptive nonadaptive queries to npmv are different than k 1 adaptive nonadaptive queries to npmv nondeterministic reducibilities lowness and the difference hierarchy over npmv are also studied the difference hierarchy for partial functions does not collapse unless the boolean hierarchy collapses but surprisingly the levels of the difference and bounded query hierarchies do not interleave as is the case for sets unless the polynomial hierarchy collapses