relative tensor triangular chow groups for coherent algebras abstract we apply the machinery of relative tensor triangular chow groups to the action of d qcoh x the derived category of quasi coherent sheaves on a noetherian scheme x on the derived category of quasi coherent a modules d qcoh a where a is a not necessarily commutative coherent o x algebra when a is commutative we recover the tensor triangular chow groups of spec a we also obtain concrete descriptions for integral group algebras and hereditary orders over curves and we investigate the relation of these invariants to the classical ideal class group of an order an important tool for these computations is a new description of relative tensor triangular chow groups as the image of a map in the k theoretic localization sequence associated to a certain verdier localization

stock return distributions tests of scaling and universality from three distinct stock markets define the log return of stock price st over a time interval t rrtt log st tlog st1 analyses of returns of individual stocks 2 3 and stock indices 4 have shown that the cumulative distribution of returns is well fit by a power law asymptotic behavior with tail exponent r pr x xr 1

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

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

effect of nonlinear correlations on the statistics of return intervals in multifractal data sets we study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations we find that nonlinear correlations in the record lead to a power law i decay of the autocorrelation function of the return intervals ii increase in the conditional return period and iii decay in the probability density function of the return intervals we show explicitly that all the observed quantities depend both on the threshold value and system size and hence there is no simple scaling observed we also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation

models for singularity categories abstract in this article we construct various models for singularity categories of modules over differential graded rings the main technique is the connection between abelian model structures cotorsion pairs and deconstructible classes and our constructions are based on more general results about localization and transfer of abelian model structures we indicate how recollements of triangulated categories can be obtained model categorically discussing in detail krause s recollement k ac inj r k inj r d r in the special case of curved mixed z graded complexes we show that one of our singular models is quillen equivalent to positselski s contraderived model for the homotopy category of matrix factorizations

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

smashing localizations of rings of weak global dimension at most one abstract we show for a ring r of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in r if moreover r is commutative we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms we also classify smashing localizations of the derived category of any valuation domain and provide an easy criterion for the telescope conjecture tc for any commutative ring of weak global dimension at most one as a consequence we show that the tc holds for any commutative von neumann regular ring r and it holds precisely for those prufer domains which are strongly discrete

complex network based time series analysis abstract recent works show that complex network theory may be a powerful tool in time series analysis we propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series an original stock time series the corresponding return series and its amplitude series are considered the degree distribution of the original series can be well fitted with a power law while that of the return series can be well fitted with a gaussian function the degree distribution of the amplitude series contains two asymmetric gaussian branches reconstruction of networks from time series is a common problem in diverse research the proposed strategy may be a reasonable solution to this problem

visibility graph approach to exchange rate series abstract by means of a visibility graph we investigate six important exchange rate series it is found that the series convert into scale free and hierarchically structured networks the relationship between the scaling exponents of the degree distributions and the hurst exponents obeys the analytical prediction for fractal brownian motions the visibility graph can be used to obtain reliable values of hurst exponents of the series the characteristics are explained by using the multifractal structures of the series the exchange rate of euro to japanese yen is widely used to evaluate risk and to estimate trends in speculative investments interestingly the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series

resolutions in factorization categories building upon ideas of eisenbud buchweitz positselski and others we introduce the notion of a factorization category we then develop some essential tools for working with factorization categories including constructions of resolutions of factorizations from resolutions of their components and derived functors using these resolutions we lift fully faithfulness and equivalence statements from derived categories of abelian categories to derived categories of factorizations some immediate geometric consequences include a realization of the derived category of a projective hypersurface as matrix factorizations over a noncommutative algebra and recover of a theorem of baranovsky and pecharich

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

statistical properties of visibility graph of energy dissipation rates in three dimensional fully developed turbulence abstract we study the statistical properties of complex networks constructed from time series of energy dissipation rates in three dimensional fully developed turbulence using the visibility algorithm the degree distribution is found to have a power law tail with the tail exponent 3 0 the exponential relation between the number of the boxes n b and the box size l b based on the edge covering box counting method illustrates that the network is not self similar which is also confirmed by the hub hub attraction according to the visibility algorithm in addition it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent 1 163 0 005

abstract representation theory of dynkin quivers of type a abstract we study the representation theory of dynkin quivers of type a in abstract stable homotopy theories including those associated to fields rings schemes differential graded algebras and ring spectra reflection functors partial coxeter functors and serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules certain explicitly constructed spectral bimodules in fact these universal tilting modules are spectral refinements of classical tilting complexes as a consequence we obtain split epimorphisms from the spectral picard groupoid to derived picard groupoids over arbitrary fields these results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators as further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field this includes yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral serre duality result finally using abstract representation theory of linearly oriented a n quivers we construct canonical higher triangulations in stable derivators and hence a posteriori in stable model categories and stable categories

scale invariance and universality of economic fluctuations in recent years physicists have begun to apply concepts and methods of statistical physics to study economic problems and the neologism econophysics is increasingly used to refer to this work much recent work is focused on understanding the statistical properties of time series one reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic time series viewed from a dierent perspective might yield new results this manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on economics we shall see that while scale invariance has been tested for many years universality is relatively less frequently discussed this article reviews the results of two recent studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier in size by as much as eight orders of magnitude ii quantifying business rm uctuations we analyze the computstat database comprising all publicly traded united states manufacturing companies within the years 1974 1993 we nd that the distributions of growth rates is dierent for dierent bins of rm size with a width that varies inversely with a power of rm size similar variation is found for other complex organizations including country size university research budget size and size of species of bird populations c 2000 elsevier science b v all rights reserved

dynamic asset trees and black monday abstract the minimum spanning tree based on the concept of ultrametricity is constructed from the correlation matrix of stock returns the dynamics of this asset tree can be characterised by its normalised length and the mean occupation layer as measured from an appropriately chosen centre called the central node we show how the tree length shrinks during a stock market crisis black monday in this case and how a strong reconfiguration takes place resulting in topological shrinking of the tree

visibility graph analysis of economy policy uncertainty indices abstract uncertainty plays an important role in the global economy in this paper the economic policy uncertainty epu indices of the united states and china are selected as the proxy variable corresponding to the uncertainty of national economic policy by adopting the visibility graph algorithm the four economic policy uncertainty indices of the united states and china are mapped into complex networks and the topological properties of the corresponding networks are studied the hurst exponents of all the four indices are within 0 5 1 which implies that the economic policy uncertainty is persistent the degree distributions of the epu networks have power law tails and thus the networks are scale free the average clustering coefficients of the four epu networks are high and close to each other while these networks exhibit weak assortative mixing we also find that the epu network in united states based on daily data shows the small world feature since the average shortest path length increases logarithmically with the network size such that l n 0 626 ln n 0 405 our research highlights the possibility to study the epu from the view angle of complex networks

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

a characterization of bases of tropical kernels in terms of cramer s rule abstract the tropical kernel of a min plus matrix is a linear space it has a finite basis that is uniquely determined up to scalar multiplication in this paper we give a characterization of vectors in a basis of the kernel using the tropical analogue of cramer s rule we first show that each finite vector in a basis can be obtained by applying cramer s rule to a submatrix consisting of certain rows of the original matrix we prove the main results by presenting an algorithm for choosing such rows further we extend the result for kernel vectors that contain infinity in its entries

cartesian modules over representations of small categories we introduce the new concept of cartesian module over a pseudofunctor r from a small category to the category of small preadditive categories already the case when r is a strict functor taking values in the category of commutative rings is sucient

inverse statistics in stock markets universality and idiosyncracy abstract investigations of inverse statistics a concept borrowed from turbulence in stock markets exemplified with filtered dow jones industrial average sp physica a 324 2003 338 343 int j mod phys b 17 2003 4003 4012 we have performed extensive analyses based on unfiltered daily indices and stock prices as well as high frequency 5 min records in numerous stock markets all over the world our analysis confirms that the power law distribution of exit times with an exponent of about 1 5 is universal for all the data sets analyzed in addition all data sets show that the power law scaling in the optimal investment horizon holds but with idiosyncratic exponents specifically 1 5 for the daily data in most of the developed stock markets and the 5 min high frequency data while the values for the daily indexes and stock prices in emerging markets are significantly less than 1 5 we show that there is little chance that the discrepancy in is due to the difference in sample sizes of the two kinds of stock markets

gorenstein complexes and recollements from cotorsion pairs we describe a general correspondence between injective resp projective recollements of triangulated categories and injective resp projective cotorsion pairs this provides a model category description of these recollement situations our applications focus on displaying several recollements that glue together various full subcategories of k r the homotopy category of chain complexes of modules over a general ring r when r is left noetherian these recollements involve complexes built from the gorenstein injective modules when r is a left coherent ring for which all flat modules have finite projective dimension we obtain the duals these results extend to a general ring r by replacing the gorenstein modules with the gorenstein ac modules introduced in 9 we also see that in any abelian category with enough injectives the gorenstein injective objects enjoy a maximality property in that they contain every other class making up the right half of an injective cotorsion pair

statistical properties of world investment networks abstract we have performed a detailed investigation on the world investment networks constructed from the coordinated portfolio investment survey cpis data of the international monetary fund ranging from 2001 to 2006 the distributions of degrees and node strengths are scale free the weight distributions can be well modeled by the weibull distribution the maximum flow spanning trees of the world investment networks possess two universal allometric scaling relations independent of time and the investment type the topological scaling exponent is 1 17 0 02 and the flow scaling exponent is 1 03 0 01

singularity categories and singular equivalences for resolving subcategories let mathcal x be a resolving subcategory of an abelian category in this paper we investigate the singularity category mathsf d sg underline mathcal x mathsf d b mathsf mod underline mathcal x mathsf k b mathsf proj mathsf mod underline mathcal x of the stable category underline mathcal x of mathcal x we consider when the singularity category is triangle equivalent to the stable category of gorenstein projective objects and when the stable categories of two resolving subcategories have triangle equivalent singularity categories applying this to the module category of a gorenstein ring we prove that the complete intersections over which the stable categories of resolving subcategories have trivial singularity categories are the simple hypersurface singularities of type mathsf a 1 we also generalize several results of yoshino on totally reflexive modules

exact model structures and recollements abstract we show how to obtain recollements of triangulated categories using the theory of exact model structures from 13 after noting how the theory relates to well known notions in the simplest case of frobenius categories we apply these ideas to recollements of homotopy categories of chain complexes in short we give model categorical explanations for the classical verdier localization recollement as well as several recollement situations due to neeman and murfet

visibility graph analysis of heart rate time series and bio marker of congestive heart failure abstract study of rr interval time series for congestive heart failure had been an area of study with different methods including non linear methods in this article the cardiac dynamics of heart beat are explored in the light of complex network analysis viz visibility graph method heart beat rr interval time series data taken from physionet database 46 47 belonging to two groups of subjects diseased congestive heart failure 29 in number and normal 54 in number are analyzed with the technique the overall results show that a quantitative parameter can significantly differentiate between the diseased subjects and the normal subjects as well as different stages of the disease further the data when split into periods of around 1 hour each and analyzed separately also shows the same consistent differences this quantitative parameter obtained using the visibility graph analysis thereby can be used as a potential bio marker as well as a subsequent alarm generation mechanism for predicting the onset of congestive heart failure

ambiguities in recurrence based complex network representations of time series recently different approaches have been proposed for studying basic properties of time series from a complex network perspective in this work the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail we discuss the main requirements that permit a feasible system theoretic interpretation of network topology in terms of dynamically invariant phase space properties possible artifacts induced by disregarding these requirements are pointed out and systematically studied finally a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed

universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices the investigations of financial markets from a complex network perspective have unveiled many phenomenological properties in which the majority of these studies map the financial markets into one complex network in this work we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph a universal allometric scaling law is uncovered in the minimal spanning trees whose scaling exponent is independent of the stock market and the length of the stock index in contrast the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors there are marked discrepancies in the allometric scaling behaviors between the stock indices and the brownian motions using surrogate time series we find that these discrepancies are caused by the fat tailedness of the return distribution and the nonlinear long term correlation

triangulated equivalence between a homotopy category and a triangulated quotient category abstract given two complete hereditary cotorsion pairs q r and q r in a bicomplete abelian category g such that q q and q r q r becker showed that there exists a hereditary abelian model structure m q w r on g where w is a thick subcategory of g we prove that the homotopy category ho m of m is triangulated equivalent to the triangulated quotient category d b g q r k b q r where d b g q r is the subcategory of d b g consisting of all homology bounded complexes with both finite q dimension and r dimension and k b q r is the bounded homotopy category of q r core objects applications are given in the category of modules it is shown that the homotopy category of the gorenstein flat resp ding projective and gorenstein ac projective model structure on the category of modules established by gillespie and his coauthors can be realized as a certain triangulated quotient category

characterizing pseudoperiodic time series through the complex network approach recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network j zhang m small phys rev lett 96 2006 238701 essentially this is a transformation from the time domain to the network domain which allows for the dynamics of the time series to be studied via organization of the network in this paper we focus on the deterministic chaotic rossler time series and stochastic noisy periodic data that yield substantially different structures of networks in particular we test an extensive range of network topology statistics which have not been discussed in previous work but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles our goal is to find out how they reflect and quantify different aspects of specific dynamics and how they can be used to distinguish different dynamical regimes for example we find that the joint degree distribution appears to fundamentally characterize spatial organizations of cycles in phase space and this is quantified via an assortativity coefficient we applied network statistics to electrocardiograms of a healthy individual and an arrythmia patient such time series are typically pseudoperiodic but are noisy and nonstationary and degrade traditional phase space based methods these time series are however better differentiated by our network based statistics

gorenstein homological algebra and universal coefficient theorems we study criteria for a ring or more generally for a small category to be gorenstein and for a module over it to be of finite projective dimension the goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones among the universal coefficient theorems covered by our methods we find besides all the classic examples several exotic examples arising from the kk theory of c algebras and also neeman s brown adams representability theorem for compactly generated categories

on exact categories and applications to triangulated adjoints and model structures abstract we show that quillen s small object argument works for exact categories under very mild conditions this has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures in particular the interplay of different exact structures on the category of complexes of quasi coherent sheaves leads to a streamlined and generalized version of recent results obtained by estrada gillespie guil asensio hovey jorgensen neeman murfet prest trlifaj and possibly others

cotorsion pairs model category structures and representation theory we make a general study of quillen model structures on abelian categories we show that they are closely related to cotorsion pairs which were introduced by salce sal79 and have been much studied recently by enochs and coauthors ej00 this gives a method of constructing model structures on abelian categories which we illustrate by building two model structures on the category of modules over a possibly noncommutative gorenstein ring the homotopy category of these model structures is a generalization of the stable module category much used in modular representation theory this stable module category has also been studied by benson ben97

koszul duality for lie algebroids abstract this paper studies the role of dg lie algebroids in derived deformation theory more precisely we provide an equivalence between the homotopy theories of formal moduli problems and dg lie algebroids over a commutative dg algebra of characteristic zero at the level of linear objects we show that the category of representations of a dg lie algebroid is an extension of the category of quasi coherent sheaves on the corresponding formal moduli problem we describe this extension geometrically in terms of pro coherent sheaves

tilting theory via stable homotopy theory we show that certain tilting results for quivers are formal consequences of stability and as such are part of a formal calculus available in any abstract stable homotopy theory thus these results are for example valid over arbitrary ground rings for quasi coherent modules on schemes in the differential graded context in stable homotopy theory and also in the equivariant motivic or parametrized variant thereof in further work we will continue developing this calculus and obtain additional abstract tilting results here we also deduce an additional characterization of stability based on goodwillie s strongly co cartesian n cubes as applications we construct abstract auslander reiten translations and abstract serre functors for the trivalent source and verify the relative fractionally calabi yau property this is used to offer a new perspective on may s axioms for monoidal triangulated categories