correlation study of the athens stock exchange we study the year after year properties of three different portfolios traded in the athens stock exchange ase for the time period 1987 2004 we use the minimum spanning tree mst technique and the random matrix theory rmt which make it possible to examine at the same time the temporal evolution of the portfolios and of the market as a whole the first four moments of the distribution of correlations and the normalized tree lengths of the mst show a similar behaviour for all three portfolios however by studying topological properties of the mst such as the node degree k we are able to identify changes to the mst associated to each portfolio that are due to a crisis in the market like the one that happened during the period 1999 2001 we also see that while the effect of the market to the information content of the correlation matrix for all three portfolios is almost the same the market is affected differently by different economic sectors at different time periods r 2007 elsevier b v all rights reserved

cross correlations in volume space differences between buy and sell volumes abstract we study the cross correlations of buy and sell volumes on the korean stock market in high frequency we observe that the pulling effects of volumes are as small as that of returns the properties of the correlations of buy and sell volumes differ they are explained by the degree of synchronization of stock volumes further the pulling effects on the minimal spanning tree are studied in minimal spanning trees with directed links the large pulling effects are clustered at the center not uniformly distributed the epps effect of buy and sell volumes are observed the reversal of the cross correlations of buy and sell volumes is also detected

dependence structure of the korean stock market in high frequency data abstract this paper analyzes the evolution of the dependence structure for various time window intervals known as epps effect using the trade and quote data of 663 actively traded stocks in korean stock market it is found that the random matrix theory analysis could not represent the dependence structure of the stock market in the microstructure regime the cook johnson copula is introduced as a parsimonious alternative method to handle this problem and the existence of the epps effect is confirmed for the 663 stocks using high frequency data it was also found that large capitalization companies tend to have a stronger dependence structure except for the largest capitalization group since the phenomenon of price level resistance leads to the weak dependence structure in the largest capitalization group in addition grouping the industry as a sub portfolio is an appropriate approach for hour interval traders whereas this approach is not a strategy recommended for high frequency traders

minimal surfaces in minimally convex domains in this paper we prove that every conformal minimal immersion of a compact bordered riemann surface m into a minimally convex domain d r can be approximated uniformly on compacts in m m bm by proper complete conformal minimal immersions m d see theorems 1 1 1 7 and 1 9 we also obtain a rigidity theorem for complete immersed minimal surfaces of finite total curvature contained in a minimally convex domain in r see theorem 1 16 and we characterize the minimal surface hull of a compact set k in r for any n 3 by sequences of conformal minimal disks whose boundaries converge to k in the measure theoretic sense see corollary 5 6

quantifying and interpreting collective behavior in financial markets firms having similar business activities are correlated we analyze two different cross correlation matrices c constructed from i 30 min price fluctuations of 1000 us stocks for the two year period 1994 95 and ii one day price fluctuations of 422 us stocks for the 35 year period 1962 96 we find that the eigenvectors of c corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets these subsets are similar to business sectors and are stable for extended periods of time we find that price fluctuations of these subsets are characterized by power law decaying time correlations reminiscent of strongly interacting systems the internal structure of a complex system manifests itself in correlations among its constituents in complex physical systems interactions between constituents cause collective modes having special statistical properties which reflect the underlying dynamics can we quantify collective movement of stock prices in analogous terms to address this question we analyze the equal time correlation matrix c constructed from the price fluctuations of a large number of stocks first we find that the collective modes for the stock market problem partition the set of all stocks studied into distinct subsets typically these subsets are formed by combinations of related industries and in some cases they go beyond grouping by industry due to company diversification the traditional partitioning of firms into subsets by products and services is difficult and sometimes arbitrary and thus our results could be viewed as a statistical alternative to traditional industry classification 1 furthermore we find that the price fluctuations of the collective modes display long range power law time correla

random matrix theory and fund of funds portfolio optimisation abstract the proprietary nature of hedge fund investing means that it is common practise for managers to release minimal information about their returns the construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise in this paper random matrix theory rmt is applied to a cross correlation matrix c constructed using hedge fund returns data the analysis reveals a number of eigenvalues that deviate from the spectrum suggested by rmt the components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers the inverse participation ratio is used to quantify the number of components that participate in each eigenvector finally the correlation matrix is cleaned by separating the noisy part from the non noisy part of c this technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio leading to an improved risk profile for a fund of hedge funds

spectral analysis of time dependent market adjusted return correlation matrix abstract we present an adjusted method for calculating the eigenvalues of a time dependent return correlation matrix in a moving window first we compare the normalized maximum eigenvalue time series of the market adjusted return correlation matrix to that of the logarithmic return correlation matrix on an 18 year dataset of 310 s p 500 listed stocks for small and large window or memory sizes we observe that the resulting new eigenvalue time series is more stationary than the time series obtained without the adjustment second we perform this analysis while sweeping the window size 5 100 500 in order to examine the dependence on the choice of window size this approach demonstrates the multi modality of the eigenvalue distributions we find that the three dimensional distribution of the eigenvalue time series for our market adjusted return is significantly more stationary than that produced by classic method finally our model offers an approximate polarization domain characterized by a smooth l shaped strip the polarization with large amplitude is revealed while there is persistence in agreement of individual stock returns movement with market with small amplitude most of the time

a new method to estimate the noise in financial correlation matrices companies belonging to the same industrial branch are subject to similar economical influences hence the time series of their stocks can show similar trends implying a correlation financial correlation matrices measure the unsystematic correlations between time series of stocks such information is important for risk management it has been found by laloux et al that the correlation matrices are noise dressed a major reason being the finiteness of the time series we present a new and alternative method to estimate this noise we introduce a power mapping of the elements in the correlation matrix which suppresses the noise and thereby effectively prolongs the time series neither further data processing nor additional input is needed to develop and test our method we use a model suggested by noh which can be viewed as a special case of a factor model in economics we perform numerical simulations for the time series and obtain correlation matrices we support the numerics by a qualitative analytical discussion with our approach different correlation structures buried under this noise can be detected our method is general and can be applied to all systems in which time series are measured

the optimal all partial sums algorithm in commutative semigroups and its applications for image thresholding segmentation the design and analysis of multidimensional all partial sums aps algorithms are considered we employ the sequence length as the performance measurement criterion for aps algorithms and corresponding thresholding methods which is more sophisticated than asymptotic time complexity under the straight line program computation model with this criterion we propose the piling algorithm to minimize the sequence length then we show this algorithm is an optimal aps algorithm in commutative semigroups in the worst case the experimental results also show the algorithmic efficiency of the piling algorithm furthermore the theoretical works of aps algorithm will help to construct the higher dimensional thresholding methods

algorithms of maximum likelihood data clustering with applications abstract we address the problem of data clustering by introducing an unsupervised parameter free approach based on maximum likelihood principle starting from the observation that data sets belonging to the same cluster share a common information we construct an expression for the likelihood of any possible cluster structure the likelihood in turn depends only on the pearson s coefficient of the data we discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations compared to standard clustering methods our approach has the advantages that i it is parameter free ii the number of clusters need not be fixed in advance and iii the interpretation of the results is transparent in order to test our approach and compare it with standard clustering algorithms we analyze two very different data sets time series of financial market returns and gene expression data we find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability

the calabi yau conjectures for embedded surfaces in this talk i will discuss the proof of the calabi yau conjectures for embedded surfaces this is joint work with bill minicozzi cm9 the calabi yau conjectures about surfaces date back to the 1960s much work has been done on them over the past four decades in particular examples of jorge xavier from 1980 and nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces i e injective immersions they are in fact true their original form was given in 1965 in ca where e calabi made the following two conjectures about minimal surfaces see also s s chern page 212 of ch conjecture 1 prove that a complete minimal hypersurface in r must be unbounded calabi continued it is known that there are no compact minimal submanifolds of r or of any simply connected complete riemannian manifold with sectional curvature 0 a more ambitious conjecture is conjecture 2 a complete minimal hypersurface in r has an unbounded projection in every n 2 dimensional flat subspace

spectral methods and cluster structure in correlation based networks abstract we investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks for this we use daily return data from the nyse and focus specifically on the spectral properties of weight w i j c i j i j and diffusion matrices d i j w i j s j i j where c i j is the correlation matrix and s i j w i j the strength of node j the eigenvalues and corresponding eigenvectors of the weight matrix are ranked in descending order as in the earlier observations the first eigenvector stands for a measure of the market correlations its components are to first approximation equal to the strengths of the nodes and there is a second order roughly linear correction the high ranking eigenvectors excluding the highest ranking one are usually assigned to market sectors and industrial branches our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge in addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering it turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included thus no natural threshold value for that ratio seems to exist we suggest that these observations can be of use for other correlation based networks as well

pl equivariant surgery and invariant decompositions of 3 manifolds using normal surface theory h j2 we introduce the notion of least weight normal surfaces the weight of a normal surface is a nonnegative integer invariant of the normal isotopy class of the surface if we focus on a particular class of normal surfaces and choose representatives which minimize the weight over the class then we have least weight normal surfaces it is remarkable how these least weight normal surfaces exhibit many of the same useful properties as least area minimal surfaces they provide a piecewise linear pl environment to obtain the recent topological results coming from the analysis and geometry of least area surfaces in an impressive series of papers meeks and yau m y i m y z m y 3 m y m y meeks simon and yau m s y scott s meeks and scott m s and freedman hass and scott f h s introduced the analysis and geometry of least area surfaces into the study of topological questions about 3 manifolds the consequences have led to the resolution of many outstanding problems in the topology of 3 manifolds since most of the problems being solved with these new techniques are topological in nature it has been felt that there should be a more topological approach to the proofs of these results besides the bulk of the work in the theory of

cross correlation dynamics in financial time series abstract the dynamics of the equal time cross correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows empirical results for the s p 500 and the dow jones euro stoxx 50 indices reveal that the dynamics of the small eigenvalues of the cross correlation matrix over these time windows oppose those of the largest eigenvalue this behaviour is shown to be independent of the size of the time window and the number of stocks examined a basic one factor model is then proposed which captures the main dynamical features of the eigenvalue spectrum of the empirical data through the addition of perturbations to the one factor model leading to a market plus sectors model additional sectoral features are added resulting in an inverse participation ratio comparable to that found for empirical data by partitioning the eigenvalue time series we then show that negative index returns drawdowns are associated with periods where the largest eigenvalue is greatest while positive index returns drawups are associated with periods where the largest eigenvalue is smallest the study of correlation dynamics provides some insight on the collective behaviour of traders with varying strategies

structure of a financial cross correlation matrix under attack abstract we investigate the structure of a perturbed stock market in terms of correlation matrices for the purpose of perturbing a stock market two distinct methods are used namely local and global perturbation the former involves replacing a correlation coefficient of the cross correlation matrix with one calculated from two gaussian distributed time series while the latter reconstructs the cross correlation matrix just after replacing the original return series with gaussian distributed time series concerning the local case it is a technical study only and there is no attempt to model reality the term global means the overall effect of the replacement on other untouched returns through statistical analyses such as random matrix theory rmt network theory and the correlation coefficient distributions we show that the global structure of a stock market is vulnerable to perturbation however apart from in the analysis of inverse participation ratios iprs the vulnerability becomes dull under a small scale perturbation this means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small scale perturbation in contrast when going down to the structure of business sectors we confirm that correlation based business sectors are regrouped in terms of iprs this result gives a clue about monitoring the effect of hidden intentions which are revealed via portfolios taken mostly by large investors

a bridge principle for minimal and constant mean curvature submanifolds of rn on demontre un principe de pont qui generalise l etablissement du theoreme de meeks yau la dimension ainsi que la codimension de n 1 et n 2 peuvent etre arbitraires et on ne suppose pas la stabilite on demontre un principe de pont pour des hypersurfaces de courbure moyenne constante

data driven estimates of the number of clusters in multivariate time series an important problem in unsupervised data clustering is how to determine the number of clusters here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series two nonparametric and purely data driven algorithms are expounded and compared the first exploits the eigenvalue spectra of surrogate data while the second employs the eigenvector components of the interrelation matrix compared to the first algorithm the second approach is computationally faster and not limited to linear interrelation measures

the reaction of stock markets to crashes and events a comparison study between emerging and mature markets using wavelet transforms abstract we study here the behaviour of the first three eigenvalues 1 2 3 and their ratios 1 2 1 3 2 3 of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets it has been known for some time that the largest eigenvalue 1 contains information on the risk associated with the particular assets of which the covariance matrix is comprised here we wish to ascertain whether the subdominant eigenvalues 2 3 hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets to do this we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component our results appear to indicate that mature markets respond to crashes differently to emerging ones in that emerging markets may take up to two months to recover while major markets take less than a month to do so in addition the results appears to show that the subdominant eigenvalues 2 3 give additional information on market movement especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics

the space of embedded minimal surfaces of fixed genus in a 3 manifold v fixed genus this paper is the fifth and final in a series on embedded minimal surfaces following our earlier papers on disks we prove here two main structure theorems for itnonsimply connected embedded minimal surfaces of any given fixed genus the first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely oriented double spiral staircases the second gives a pair of pants decomposition of any such surface when there are small necks cutting the surface along a collection of short curves after the cutting we are left with graphical pieces that are defined over a disk with either one or two sub disks removed a topological disk with two sub disks removed is called a pair of pants both of these structures occur as different extremes in the two parameter family of minimal surfaces known as the riemann examples

scale invariance and criticality in financial markets abstract we discuss the evidences supporting the view of financial markets as system operating close to a critical point from the theoretical side this picture is based on detailed knowledge of the behavior of minority games these are models of heterogeneous agents interacting through a market mechanism which can be solved analytically with tools of statistical mechanics from the empirical side we extend these evidences showing that market sector structure is itself scale invariant scale invariant features also appear in the classification of states in the time domain

interest rates factor model abstract interdependence of the interest rates of the us the uk and japan is analyzed in this work by means of spectral analysis and network methods a predominant effective factor in the interest rate market is which country floats a bond issue and a minor effective factor is time to maturity of bonds power law cross correlation among different countries is analyzed by the detrended cross correlation analysis method long range cross correlation is found between the first factors of interest rate while there is no cross correlation between some of the second factors the tail dependency is indicated by tail indices from archimedean copulas including an empirical copula in contrast to other pairs the us uk first factor pair has tail dependencies in both the upper tail and lower tail dynamic properties of interest rate are modeled by a stochastic volatility model the properties of mean reverting and volatility clustering are observed and reflected in this model the proposed simulation method combines the dependence structures and the factor dynamics model it simultaneously describes the interest rates of different countries

emergence of correlations between securities at short time scales abstract the correlation matrix is the key element in optimal portfolio allocation and risk management in particular the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode sectors and style factors we investigate how these eigenvalues depend on the time scale of securities returns in the u s market for this purpose one minute returns of the largest 533 u s stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties we reveal the emergence of several dominant eigenvalues as the time scale increases a simple lead lag factor model is proposed to capture and reproduce the observed time scale dependence of eigenvalues using this model the relaxation time of the eigenvalues emergence is estimated to be around one minute for all the dominant eigenmodes including the market mode as a consequence the use of five minute returns time series for inferring correlations between stocks turns out to be a good compromise between statistical abundance of data points and well established correlations our findings evidence that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales

embeddedness of minimal surfaces with total boundary curvature at most 4 pi this paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 47r must be smoothly embedded related results are proved for varifolds and for soap film surfaces

economic fluctuations and statistical physics quantifying extremely rare and less rare events in finance one challenge of economics is that the systems treated by these sciences have no perfect metronome in time and no perfect spatial architecture crystalline or otherwise nonetheless as if by magic out of nothing but randomness one finds remarkably fine tuned processes in time we present an overview of recent research joining practitioners of economic theory and statistical physics to try to better understand puzzles regarding economic fluctuations one of these puzzles is how to describe outliers phenomena that lie outside of patterns of statistical regularity we review evidence consistent with the possibility that such outliers may not exist this possibility is supported by recent analysis of databases containing information about each trade of every stock r 2007 elsevier b v all rights reserved

a general existence theorem for embedded minimal surfaces with free boundary in this paper we prove a general existence theorem for properly embedded minimal surfaces with free boundary in any compact riemannian 3 manifold m with boundary m these minimal surfaces are either disjoint from m or meet m orthogonally the main feature of our result is that there is no assumptions on the curvature of m or convexity of m we prove the boundary regularity of the minimal surfaces at their free boundaries furthermore we define a topological invariant the filling genus for compact 3 manifolds with boundary and show that we can bound the genus of the minimal surface constructed above in terms of the filling genus of the ambient manifold m our proof employs a variant of the min max construction used by colding and de lellis on closed embedded minimal surfaces which were first developed by almgren and pitts 2014 wiley periodicals inc

embeddedness of the solutions to the h plateau problem abstract we generalize meeks and yau s embeddedness result on the solutions of the plateau problem to constant mean curvature disks we show that any minimizing h disk in an h 0 convex domain is embedded for any h 0 h 0 in particular for the unit ball b in r 3 this implies that for any h 0 1 any jordan curve in b bounds an embedded h disk in b

minimal surfaces in quasi fuchsian 3 manifolds in this paper we prove that if a quasi fuchsian 3 manifold m contains a closed geodesic with complex length fancyscript l l i theta such that theta l gg 1 where l 0 and then it contains at least two incompressible minimal surfaces near the geodesic

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

composition of the first principal component of a stock index a comparison between sp500 and vnindex abstract we analyzed the components of the eigenvector corresponding to the largest eigenvalue of a cross correlation matrix of stock price change the 1 st eigenvector using the principle components pcs analysis method we found that the components of the 1 st eigenvector are not uniformly distributed in fact they are proportional to the correlations of individual stocks and the 1st pc and could be negative if the corresponding stock is in average negatively correlated to other stocks by analyzing data from the world stock index in a developed country sp500 and an emerging one such as vietnam vnindex from 2013 to 2017 we found negative components in the 1 st eigenvector in the vnindex and their distribution is also broader than that of sp500 furthermore we found that the largest components correspond to stocks of financial services brokerage or investment advisory firms firms in both indices those stocks are found to be center hubs in a minimum spanning tree mst analysis and play an important role whenever a systemic breakdown happens finally we found a phenomenological linear dependence between the components of the 1 st eigenvector and the average stock correlation in both indices and derived an approximation of this dependency using empirical stylized facts of the data this result provides an estimation of how the pc1 is composed

dynamics of implied volatility surfaces from random matrix theory abstract we analyze the dynamics of the implied volatility surface of kospi 200 futures options from random matrix theory to extract the informative data we use random matrix criteria implied volatility data have a colossal eigenvalue and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction we discern the marketwide knowledge of the implied volatility surface movement such as the level skew and smile effect these dynamics has the ergodic property and long range autocorrelation we also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics and confirm the existence of leverage effect even in the short time interval

a fast recurring two dimensional entropic thresholding algorithm thresholding is an important form of image segmentation and is used in the processing of images for many applications one of the criteria to select a suitable threshold is the maximization of the two dimensional 2 d entropies based on the 2 d gray level local average gray level histogram the rationale of this approach is introduced in order to reduce the computation time of entropy function a fast recurring algorithm for 2 d entropic thresholding method is presented the experimental results show that the processing time to obtain the threshold vector from 2 d histogram is reduced from 30 to 0 15 s

the existence of embedded minimal surfaces and the problem of uniqueness it was in the early nineteen thirties that douglas and radd solved the plateau problem for a rectifiable jordan curve in euclidean space the minimal surfaces that they obtained are realized by conformal harmonic maps from the unit disk in 1948 morrey generalized the theorem of douglas and radd to minimal surfaces in a homogeneously regular riemannian manifold in both cases the solutions are defective as they may possess branch points it was not until 1968 that osserman 24 was able to prove that interior branch points do not exist on the douglas radd morrey solution osserman s theorem in this full generality was proved by alt 2 3 and gulliver 8 if the jordan curve is real analytic gulliver and lesley 9 showed that the solution surface is free of branch points even on its boundary hence at least in this case we know that the douglas radd morrey solution is an immersion and represents a classical surface however the douglas radd morrey solution may in general have selfintersections it was then a classical problem to find conditions on the jordan curve to guarantee that the solution is an embedded disk in 1932 radd was the first to produce a general condition of this type he proved that if the curve can be projected onto a convex curve in the plane then it bounds a unique embedded minimal disk which is a graph over this plane it was not until the seventies that there was further progress on the problem of embeddedness osserman had conjectured that if a jordan curve is extreme that is lies on the boundary of its convex hull then the douglas rad6 solution is embedded gulliver and spruck 10 proved this conjecture under the additional assumption that the absolute total curvature of the jordan curve is less than 4 z right after this work tomi and tromba 32 showed that an extreme curve must bound an embedded minimal disk which need not be stable in 1976 almgren and simon 1 established the existence for such a curve of an embedded stable minimal disk which need not be a douglas radd solution finally in the same year the authors 18 proved that any douglas rad6 solution must be embedded

dynamics of cross correlations in the stock market co movements of stock price uctuations are described by the cross correlation matrix c the application of random matrix theory rmt allows to distinguish between spurious correlations in c due to measurement noise and true correlations containing economically meaningful information by calculating cross correlations for di3erent time windows we study the time dependence of eigenvectors of c which are related to economic sectors and the time evolution of the largest eigenvalue which describes the average correlation strength we use these results to forecast cross correlations and test the quality of our forecast by constructing investments in the stock market which expose the invested capital to a minimum level of risk only c

triply periodic constant mean curvature surfaces abstract given a closed flat 3 torus n for each h 0 and each non negative integer g we obtain area estimates for closed surfaces with genus g and constant mean curvature h embedded in n this result contrasts with the theorem of traizet 31 who proved that every flat 3 torus admits for every positive integer g with g 2 connected closed embedded minimal surfaces of genus g with arbitrarily large area

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

the asymptotic behavior of properly embedded minimal surfaces of finite topology while advances have been made in recent years in the study of properly embedded minimal surfaces of finite topology in r3 3 5 8 9 11 12 13 23 progress has depended in an essential manner on the special structure of such surfaces with finite total curvature a properly immersed minimal surface with finite total curvature is conformally a compact riemann surface punctured in a finite number of points and its gauss map extends to the compact surface as a meromorphic function 22 in particular all the topological ends are conformally equivalent to a punctured disk and there is a well defined limit tangent plane at each end outside of a sufficiently large compact set such an end is a multisheeted graph over the limit tangent plane and if the end is embedded it is asymptotic to either a plane or a half catenoid see e g schoen 24 for a survey of results on properly immersed surfaces of finite total curvature see 9 1 without the assumption of finite total curvature these results are not true in general as an indication of the relative lack of information consider that it is unknown whether or not the helicoid is the only simply connected minimal surface that is properly embedded and nonplanar a question raised by osserman the helicoid has infinite total curvature and a single annular end if a surface has finite topology then all of its ends are annular any general theory of properly embedded minimal surfaces of finite topology must include an understanding of the behavior of these ends in this paper we prove

correlation and network analysis of global financial indices random matrix theory rmt and network methods are applied to investigate the correlation and network properties of 20 financial indices the results are compared before and during the financial crisis of 2008 in the rmt method the components of eigenvectors corresponding to the second largest eigenvalue form two clusters of indices in the positive and negative directions the components of these two clusters switch in opposite directions during the crisis the network analysis uses the fruchterman reingold layout to find clusters in the network of indices at different thresholds at a threshold of 0 6 before the crisis financial indices corresponding to the americas europe and asia pacific form separate clusters on the other hand during the crisis at the same threshold the american and european indices combine together to form a strongly linked cluster while the asia pacific indices form a separate weakly linked cluster if the value of the threshold is further increased to 0 9 then the european indices france germany and the united kingdom are found to be the most tightly linked indices the structure of the minimum spanning tree of financial indices is more starlike before the crisis and it changes to become more chainlike during the crisis the average linkage hierarchical clustering algorithm is used to find a clearer cluster structure in the network of financial indices the cophenetic correlation coefficients are calculated and found to increase significantly which indicates that the hierarchy increases during the financial crisis these results show that there is substantial change in the structure of the organization of financial indices during a financial crisis

a thresholding method based on two dimensional renyi s entropy in this paper we present a new thresholding technique based on two dimensional renyi s entropy the two dimensional renyi s entropy was obtained from the two dimensional histogram which was determined by using the gray value of the pixels and the local average gray value of the pixels this new method extends a method due to sahoo et al pattern recognition 30 1997 71 and includes a previously proposed global thresholding method due to abutaleb pattern recognition 47 1989 22 further our method extends a global thresholding method due to chang et al ieee trans image process 4 1995 370 to the two dimensional setting the effectiveness of the proposed method is demonstrated by using examples from the real world and synthetic images

the space of embedded minimal surfaces of fixed genus in a 3 manifold iv locally simply connected this paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3manifold the key is to understand the structure of an embedded minimal disk in a ball in r3 this was undertaken in cm3 cm4 and the global version of it will be completed here see the discussion around figure 12 for the local case and cm15 for some more details our main results are theorem 0 1 the lamination theorem and theorem 0 2 the one sided curvature estimate the lamination theorem is stated in the global case where the lamination is in fact a foliation the first four papers of this series show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multivalued graph this is done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase like the helicoid to prove that such a disk is a double spiral staircase we showed in the first three papers of the series that it is built out of n valued graphs where n is a fixed number in this paper we will deal with how the multi valued graphs fit together and in particular prove regularity of the set of points of large curvature the axis of the double spiral staircase the first theorem is the global version of the statement that every embedded minimal disk is a double spiral staircase

the space of embedded minimal surfaces of fixed genus in a 3 manifold iii planar domains this paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3 manifold in cm3 cm5 we describe the case where the surfaces are topologically disks on any fixed small scale although the focus of this paper general planar domains is more in line with cm6 we will prove a result here namely corollary iii 3 5 below which is needed in cm5 even for the case of disks roughly speaking there are two main themes in this paper the first is that stability leads to improved curvature estimates this allows us to find large graphical regions these graphical regions lead to two possibilities

localized motion in random matrix decomposition of complex financial systems abstract with the random matrix theory we decompose the multi dimensional time series of complex financial systems into a set of orthogonal eigenmode functions which are classified into the market mode sector mode and random mode in particular the localized motion generated by the business sectors plays an important role in financial systems both the business sectors and their impact on the stock market are identified from the localized motion we clarify that the localized motion induces different characteristics of the time correlations for the stock market index and individual stocks with a variation of a two factor model we reproduce the return volatility correlations of the eigenmodes

embedded self similar shrinkers of genus 0 we conrm a well known conjecture that the round sphere is the only compact embedded self similar shrinking solution of mean curvature ow in r 3 with genus 0 more generally we show that the only properly embedded self similar shrinkers in r 3 with vanishing intersection form are the sphere the cylinder and the plane this answers two questions posed by t ilmanen

fast adaptive pnn based thresholding algorithms abstract thresholding is a fundamental operation in image processing based on the pairwise nearest neighbor technique and the variance criterion this theme presents two fast adaptive thresholding algorithms the proposed first algorithm takes o m k m time where k denotes the number of thresholds specified by the user m denotes the size of the compact image histogram and the parameter has the constraint 1 m on a set of different real images experimental results reveal that the proposed first algorithm is faster than the previous three algorithms considerably while having a good feature preserving capability the previous three mentioned algorithms need o m k time given a specific peak signal to noise ratio psnr we further present the second thresholding algorithm to determine the number of thresholds as few as possible in order to obtain a thresholded image satisfying the given psnr the proposed second algorithm takes o m k m n time where n and denote the image size and the fewest number of thresholds required respectively some experiments are carried out to demonstrate the thresholded images that are encouraging since the time complexities required in our proposed two thresholding algorithms are polynomial they could meet the real time demand in image preprocessing

quantifying economic fluctuations abstract this manuscript is a brief summary of a talk designed to address the question of whether two of the pillars of the field of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on interpreting empirical data on economic fluctuations using this conceptual framework as a guide we empirically quantify the relation between trading activity measured by the number of transactions n and the price change g t for a given stock over a time interval t t t we relate the time dependent standard deviation of price changes volatility to two microscopic quantities the number of transactions n t in t and the variance w2 t of the price changes for all transactions in t we find that the long ranged volatility correlations are largely due to those of n we then argue that the tail exponent of the distribution of n is insufficient to account for the tail exponent of p g x since n and w display only weak inter dependency our results show that the fat tails of the distribution p g x arises from w finally we review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory rmt rmt makes predictions for universal properties that do not depend on the interactions between the elements comprising the system and deviations from rmt provide clues regarding system specific properties we compare the statistics of the cross correlation matrix c whose elements cij are the correlation coefficients of price fluctuations of stock i and j against a random matrix having the same symmetry properties it is found that rmt methods can distinguish random and non random parts of c the non random part of c which deviates from rmt results provides information regarding genuine collective behavior among stocks 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 field leads to large fluctuations and we discuss a curious symmetry breaking a feature qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature

an analysis of cross correlations in an emerging market abstract we apply random matrix theory to compare correlation matrix estimators c obtained from emerging market data the correlation matrices are constructed from 10 years of daily data for stocks listed on the johannesburg stock exchange jse from january 1993 to december 2002 we test the spectral properties of c against random matrix predictions and find some agreement between the distributions of eigenvalues nearest neighbour spacings distributions of eigenvector components and the inverse participation ratios for eigenvectors we show that interpolating both missing data and illiquid trading days with a zero order hold increases agreement with rmt predictions for the more realistic estimation of correlations in an emerging market we suggest a pairwise measured data correlation matrix for the data set used this approach suggests greater temporal stability for the leading eigenvectors an interpretation of eigenvectors in terms of trading strategies is given as opposed to classification by economic sectors

similarities between stock price correlation networks and co main product networks threshold scenarios abstract because of the high yields and high risks associated with the stock market investors can hold diversified portfolios with low relativity of stocks to reduce unsystematic risk the current literature analyzes single factors affecting the relativity of stocks but in this paper we analyze the correlations between different factors to provide multiple perspectives of and about investment portfolios this study analyzes the relationships between the similarities of the main products of listed companies and the varying degrees of correlations of stock price by examining different threshold scenarios of the energy industry between 2012 and 2016 and then constructing stock price correlation threshold networks and co main product networks to analyze the similarities in their structures the results indicate that two factors are significantly correlated in 97 5 of the scenarios and that these factors are the most strongly correlated when the threshold is between 0 5 and 0 7 the two networks exhibit a high degree of similarity in degree weighted degree and community division main product similarity used as supplementary information for stock relativity research plays a role similar to stock price correlations in certain scenarios furthermore compared with stock price correlations the similarity of main products is simpler and more intuitive this paper proposes a new method to study stock relativity based on different threshold scenarios thus it could serve as a reference for investors when developing portfolio strategies from multiple perspectives

stable minimal surfaces in m ℝ in 4 we developed the theory of properly embedded minimal surfaces in m r where m is a compact riemannian surface one of the first results in 4 is that a properly embedded noncompact minimal surface in m r of bounded gaussian curvature is quasiperiodic in the following sense given any sequence of vertical translates n of a subsequence of the n converges on compact subsets of m r to another properly embedded minimal surface by the curvature estimates of schoen 8 every properly embedded stable minimal surface in m r has bounded curvature therefore every properly embedded noncompact stable minimal surface in m r is quasiperiodic this quasiperiodicity property will be essential in proving the next theorem throughout this paper m denotes a compact riemannian surface

network trending leadership followership and neutrality among companies a random matrix approach abstract in this article we analyze the cross correlation between returns of different stocks to answer the following important questions the first one is if there exists collective behavior in a financial market how could we detect it and the second question is is there a particular company among the companies of a market as the leader of the collective behavior or is there no specified leadership governing the system similar to some complex systems we use the method of random matrix theory to answer the mentioned questions cross correlation matrix of index returns of four different markets is analyzed the participation ratio quantity related to each matrices eigenvectors and the eigenvalue spectrum is calculated we introduce shuffled matrix created of cross correlation matrix in such a way that the elements of the later one are displaced randomly comparing the participation ratio quantities obtained from a correlation matrix of a market and its related shuffled one on the bulk distribution region of the eigenvalues we detect a meaningful deviation between the mentioned quantities indicating the collective behavior of the companies forming the market by calculating the relative deviation of participation ratios we obtain a measure to compare the markets according to their collective behavior answering the second question we show there are three groups of companies the first group having higher impact on the market trend called leaders the second group is followers and the third one is the companies who have not a considerable role in the trend the results can be utilized in portfolio construction