a truthful constant approximation for maximizing the minimum load on related machines abstract designing truthful mechanisms for scheduling on related machines is a very important problem in single parameter mechanism design we consider the covering objective that is we are interested in maximizing the minimum completion time of a machine this problem falls into the class of problems where the optimal allocation can be truthfully implemented a major open issue for this class is whether truthfulness affects the polynomial time implementation we provide the first constant factor approximation for deterministic truthful mechanisms in particular we come up with an approximation guarantee of 2 e significantly improving on the previous upper bound of min m 2 e s m s 1

truthful optimization using mechanisms with verification we study the question of whether optimization problems can be solved exactly in the presence of economic constraints such as truthfulness of selfish agents in general imposing these extra constraints makes it impossible to optimize even in exponential time to reconcile optimization and economic incentives we focus on so called mechanisms with verification and show that under this general mechanism design paradigm it is indeed possible to optimize and to be truthful our truthful mechanisms minimize any cost function that is monotone nondecreasing in email protected costs under the technical hypothesis that the possible declarations of the selfish agents belong to a finite set our results also extend to the multidimensional scenario of compound agents in the case in which the single dimensions are one parameter we also show how to implement truthfully and efficiently classical approximation algorithms for cost functions that behave smoothly in the presence of input rounding our results are applied to a number of very general scheduling problems to obtain the first truthful mechanisms for them finally the issue of designing mechanisms with verification for infinite domains is studied showing the limitations that the imposition of the taxation principle yields

new irreversibility measure and complexity analysis based on singular value decomposition abstract visibility graph algorithm is a powerful tool for visualization and analysis of complex dynamical system kullback leibler divergence kld based on the horizontal visibility graph algorithm has received largely extensive attention in the field of irreversibility analysis in this paper we will propose a new irreversibility measure built on the multi scale theory i e the kld based on singular value decomposition kld svd furthermore since matrix singular value can reflect the basic characteristics of the complex system we further bring forward the definition of shannon entropy with singular value decomposition se svd after considering that the shannon entropy has been well defined as a complexity measure in order to show the advantages of these two new measures in detecting the complexity of systems several simulation and real data experiments are chosen to examine the performance of them through these results we find that the average and variance of kld svd corresponding to each time series is less than that of the kld moreover kld svd s volatility is significantly weaker than kld s as there is a conceptual link between predictability and irreversibility we can argue that kld svd algorithm implies the higher predictability and lower confusion on the other hand se svd can do well in revealing the internal complexity of the different time series meanwhile it is useful to mention that se svd is robust against noise efficiently

truthful mechanisms with implicit payment computation it is widely believed that computing payments needed to induce truthful bidding is somehow harder than simply computing the allocation we show that the opposite is true creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation rule our main result is a general procedure to take a monotone allocation rule for a single parameter domain and transform it via a black box reduction into a randomized mechanism that is truthful in expectation and individually rational for every realization the mechanism implements the same outcome as the original allocation rule with probability arbitrarily close to 1 and requires evaluating that allocation rule only once we also provide an extension of this result to multiparameter domains and cycle monotone allocation rules under mild star convexity and nonnegativity hypotheses on the type space and allocation rule respectively because our reduction is simple versatile and general it has many applications to mechanism design problems in which re evaluating the allocation rule is either burdensome or informationally impossible applying our result to the multiarmed bandit problem we obtain truthful randomized mechanisms whose regret matches the information theoretic lower bound up to logarithmic factors even though prior work showed this is impossible for truthful deterministic mechanisms we also present applications to offline mechanism design showing that randomization can circumvent a communication complexity lower bound for deterministic payments computation and that it can also be used to create truthful shortest path auctions that approximate the welfare of the vcg allocation arbitrarily well while having the same running time complexity as dijkstra s algorithm

footswitch system for measurement of the temporal parameters of gait gait analysis relies upon accurate measurement of initial and end foot contact times these times act as a reference point for correlating all other gait data and as a mean of distinguishing normal and pathologic gait we have developed a simple inexpensive footswitch system that provides accurate estimates of the start and end of stance phase for sequential steps the estimates of the beginning and end of stance phase do not require custom footwear extensive calibration or precise placement of the sensor within the shoe the system is based on a commercially available transducer and can be readily reproduced for use in a laboratory setting for less than 50 we describe this system as well as its validation to assess the accuracy of this footswitch system we compared footswitch based estimates of initial and end foot contact times with those obtained using a force platform as 10 people took 30 steps 10 each at slow normal and fast walking rates across a force platform both estimates coincided within 10 ms mean 0 3 ms n 300 for the start of stance phase and within 22 ms mean 1 8 ms n 300 for the end of stance phase for stance duration the differences ranged from 24 to 28 ms mean 1 10 ms n 300 in combination these measures can be used to estimate stance duration to within 3 of force plate determined values for steps with stance durations ranging from 446 to 1594 ms estimates of swing and stride duration also are within 5 of force plate determined values this system should therefore prove to be a useful tool for augmenting laboratory based investigations of gait

truthful mechanisms for two range values variant of unrelated scheduling in this paper we consider a restricted variant of the scheduling problem where the machines are the strategic players for this multi parameter mechanism design problem the only known truthful mechanisms use task independent allocation algorithms and only have approximation ratio o m n nisan a ronen algorithmic mechanism design extended abstract in stoc 99 proceedings of the thirty first annual acm symposium on theory of computing acm new york ny usa 1999 pp 129 140 a mu alem m schapira setting lower bounds on truthfulness extended abstract in soda 07 proceedings of the eighteenth annual acm siam symposium on discrete algorithms society for industrial and applied mathematics philadelphia pa usa 2007 pp 1143 1152 p lu c yu an improved randomized truthful mechanism for scheduling unrelated machines in 25th international symposium on theoretical aspects of computer science stacs 2008 pp 527 538 p lu c yu randomized truthful mechanisms for scheduling unrelated machines in c h papadimitriou s zhang eds proceedings of wine in lecture notes in computer science vol 5385 springer 2008 pp 402 413 lavi and swamy first use the cycle monotone condition and design a 3 approximation truthful mechanism for a two value variant in r lavi c swamy truthful mechanism design for multi dimensional scheduling via cycle monotonicity in ec 07 proceedings of the 8th acm conference on electronic commerce acm new york ny usa 2007 pp 252 261 where the processing time of task j on machine i say t i j can only be either a lower value l j or a higher value h j we consider a generalized variant where t i j lies in l j l j 1 e h j h j 1 e and e is a parameter satisfying some condition we consider two special cases case a when h j l j 2 j and case b when h j l j 2 j and give randomized truthful mechanisms with approximation ratio 4 1 e for both cases based on these two cases results we are also able to deal with the general case of our two range values scheduling problem we use a combination of two mechanisms which is also a novel method in mechanism design for scheduling problems and finally we give a randomized truthful mechanism with approximation ratio 7 1 e although the generalization seems a little incremental we actually use a very novel technique in the key step of proving truthfulness for case a as well as a new mechanism scheme for case b besides the results in this paper are the first truthful mechanisms with constant approximation ratios when a machine player can report infinitely possible values which is quite different from the two value variant in which only finite values are available furthermore together with lavi and swamy s work our results suggest that such a task dependent approach can really do much better for the scheduling unrelated machines problem

a unified approach to truthful scheduling on related machines we present a unified framework for designing deterministic monotone polynomial time approximation schemes ptass for a wide class of scheduling problems on uniformly related machines this class includes among others minimizing the makespan maximizing the minimum load and minimizing the p norm of the machine loads vector previously this kind of result was only known for the makespan objective monotone algorithms have the property that an increase in the speed of a machine cannot decrease the amount of work assigned to it our results imply the existence of a truthful mechanism that can be implemented in polynomial time where the social goal is approximated within arbitrary precision

a comprehensive segmentation analysis of crude oil market based on time irreversibility abstract in this paper we perform a comprehensive entropic segmentation analysis of crude oil future prices from 1983 to 2014 which used the jensen shannon divergence as the statistical distance between segments and analyze the results from original series s and series begin at 1986 marked as s to find common segments which have same boundaries then we apply time irreversibility analysis of each segment to divide all segments into two groups according to their asymmetry degree based on the temporal distribution of the common segments and high asymmetry segments we figure out that these two types of segments appear alternately and do not overlap basically in daily group while the common portions are also high asymmetry segments in weekly group in addition the temporal distribution of the common segments is fairly close to the time of crises wars or other events because the hit from severe events to oil price makes these common segments quite different from their adjacent segments the common segments can be confirmed in daily group series or weekly group series due to the large divergence between common segments and their neighbors while the identification of high asymmetry segments is helpful to know the segments which are not affected badly by the events and can recover to steady states automatically finally we rearrange the segments by merging the connected common segments or high asymmetry segments into a segment and conjoin the connected segments which are neither common nor high asymmetric

robust screening under ambiguity we consider the problem of screening where a seller puts up for sale an indivisible good and a buyer with a valuation unknown to the seller wishes to acquire the good we assume that the buyer valuations are represented as discrete types drawn from some distribution which is also unknown to the seller the seller is averse to possible mis specification of types distribution and considers the unknown type density as member of an ambiguity set and seeks an optimal pricing mechanism in a worst case sense we specify four choices for the ambiguity set and derive the optimal mechanism in each case

regret minimization for reserve prices in second price auctions we show a regret minimization algorithm for setting the reserve price in a sequence of second price auctions under the assumption that all bids are independently drawn from the same unknown and arbitrary distribution our algorithm is computationally efficient and achieves a regret of o t in a sequence of t auctions this holds even when the number of bidders is stochastic with a known distribution

multifractal stationary random measures and multifractal random walks with log infinitely divisible scaling laws we define a large class of continuous time multifractal random measures and processes with arbitrary log infinitely divisible exact or asymptotic scaling law these processes generalize within a unified framework both the recently defined log normal multifractal random walk j f muzy j delour and e bacry eur j phys b 17 537 2000 e bacry j delour and j f muzy phys rev e 64 026103 2001 and the log poisson product of cylindrical pulses j barral and b b mandelbrot cowles foundation discussion paper no 1287 2001 unpublished our construction is based on some continuous stochastic multiplication as introduced in f schmitt and d marsan eur j phys b 20 3 2001 from coarse to fine scales that can be seen as a continuous interpolation of discrete multiplicative cascades we prove the stochastic convergence of the defined processes and study their main statistical properties the question of genericity universality of limit multifractal processes is addressed within this new framework we finally provide a method for numerical simulations and discuss some specific examples

quadrantal multi scale distribution entropy analysis of heartbeat interval series based on a modified poincare plot abstract the poincare plot is one of the most important approaches in human cardiac rhythm analysis however further investigations are still needed to concentrate on techniques that can characterize the dispersion of the points displayed by a poincare plot based on a modified poincare plot we provide a novel measurement named distribution entropy de and propose a quadrantal multi scale distribution entropy analysis qmde for the quantitative descriptions of the scatter distribution patterns in various regions and temporal scales we apply this method to the heartbeat interval series derived from healthy subjects and congestive heart failure chf sufferers respectively and find that the discriminations between them are most significant in the first quadrant which implies significant impacts on vagal regulation brought about by chf we also investigate the day night differences of young healthy people and it is shown that the results present a clearly circadian rhythm especially in the first quadrant in addition the multi scale analysis indicates that the results of healthy subjects and chf sufferers fluctuate in different trends with variation of the scale factor the same phenomenon also appears in circadian rhythm investigations of young healthy subjects which implies that the cardiac dynamic system is affected differently in various temporal scales by physiological or pathological factors

an algorithm for computing solutions of variational problems with global convexity constraints we present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions the main motivation behind the numerical method is to compute solutions to adverse selection problems within a principal agent framework problems such as product lines design optimal taxation structured derivatives design etc can be studied through the scope of these models we develop a method to estimate their optimal pricing schedules

replica free evaluation of the neuronal population information with mixed continuous and discrete stimuli from the linear to the asymptotic regime recent studies have explored theoretically the ability of populations of neurons to carry information about a set of stimuli both in the case of purely discrete or purely continuous stimuli and in the case of multidimensional continuous angular and discrete correlates in the presence of additional quenched disorder in the distribution an analytical expression for the mutual information has been obtained in the limit of large noise by means of the replica trick here we show that the same results can actually be obtained in most cases without the use of replicas by means of a much simpler expansion of the logarithm fitting the theoretical model to real neuronal data we show that the introduction of correlations in the quenched disorder improves the fit suggesting a possible role of signal correlations actually detected in real data in a redundant code we show that even in the more difficult analysis of the asymptotic regime an explicit expression for the mutual information can be obtained without resorting to the replica trick despite the presence of quenched disorder both with a gaussian and with a more realistic thresholded gaussian model when the stimuli are mixed continuous and discrete we find that with both models the information seem to grow logarithmically to infinity with the number of neurons and with the inverse of the noise even though the exact general dependence cannot be derived explicitly for the thresholded gaussian model in the large noise limit lower values of information were obtained with the thresholded gaussian model for a fixed value of the noise and of the population size on the contrary in the asymptotic regime with very low values of the noise a lower information value is obtained with the gaussian model

asymmetric first price auctions a perturbation approach we use perturbation analysis to obtain explicit approximations of the equilibrium bids in asymmetric first price auctions withn bidders in which bidders valuations are independently drawn from different distribution functions several applications are presented explicit approximations of the seller s expected revenue the maximal bid the optimal reserve price inefficiency and a consequence of stochastic dominance we also suggest an improved numerical method for calculating the seller s expected revenue

adaptive anisotropic and hierarchical cones of discrete convex functions we introduce a new class of adaptive methods for optimization problems posed on the cone of convex functions among the various mathematical problems which possess such a formulation the monopolist problem rochet and chone econometrica 66 783 826 1998 ekeland and moreno bromberg numer math 115 45 69 2010 arising in economics is our main motivation consider a two dimensional domain omega sampled on a grid x x of n points we show that the cone mathrm conv x conv x of restrictions to x x of convex functions on omega is typically characterized by approx n 2 n2 linear inequalities a direct computational use of this description therefore has a prohibitive complexity we thus introduce a hierarchy of sub cones mathrm conv mathcal v conv v of mathrm conv x conv x associated to stencils mathcal v v which can be adaptively locally and anisotropically refined we show using the arithmetic structure of the grid that the trace u x u x of any convex function u on omega is contained in a cone mathrm conv mathcal v conv v defined by only mathcal o n ln 2 n o nln2n linear constraints in average over grid orientations numerical experiments for the monopolist problem based on adaptive stencil refinement strategies show that the proposed method offers an unrivaled accuracy complexity trade off in comparison with existing methods we also obtain as a side product of our theory a new average complexity result on edge flipping based mesh generation

correlation differences in heartbeat fluctuations during rest and exercise we study the heartbeat activity of healthy individuals at rest and during exercise we focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise for exercise the interval series is anticorrelated at short time scales and correlated at intermediate time scales while for rest we observe the opposite crossover pattern from strong correlations in the short time regime to weaker correlations at larger scales we also suggest a physiologically motivated stochastic scenario to provide an intuitive explanation of the scaling differences between rest and exercise

multifractality of stock markets based on cumulative distribution function and multiscale multifractal analysis abstract considering the diverse application of multifractal techniques in natural scientific disciplines this work underscores the versatility of multiscale multifractal detrended fluctuation analysis mma method to investigate artificial and real world data sets the modified mma method based on cumulative distribution function is proposed with the objective of quantifying the scaling exponent and multifractality of nonstationary time series it is demonstrated that our approach can provide a more stable and faithful description of multifractal properties in comprehensive range rather than fixing the window length and slide length our analyzes based on cdf mma method reveal significant differences in the multifractal characteristics in the temporal dynamics between us and chinese stock markets suggesting that these two stock markets might be regulated by very different mechanism the cdf mma method is important for evidencing the stable and fine structure of multiscale and multifractal scaling behaviors and can be useful to deepen and broaden our understanding of scaling exponents and multifractal characteristics

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

optimal design for multi item auctions a robust optimization approach in this paper we revisit the auction design problem for multi item auctions with budget constrained buyers by introducing a robust optimization approach to model a concepts such as incentive compatibility and individual rationality that are naturally expressed in the language of robust optimization and b the auctioneer s beliefs on the buyers valuations of the items rather than using probability distributions the classical probabilistic approach or an adversarial model to model valuations we introduce an uncertainty set based model for these valuations we construct these uncertainty sets to incorporate historical information available to the auctioneer in a way that is consistent with limit theorems of probability theory or knowledge of the probability distribution in this setting we formulate the auction design problem as a robust optimization problem and provide a characterization of the optimal solution as an auction with reservation prices thus extending the work of myerson myerson rb

optimal mechanism design for a sequencing problem with two dimensional types we study the design of mechanisms for a sequencing problem where the types of job agents consist of processing times and waiting costs that are private to the jobs in the bayes nash setting we seek to find a sequencing rule and incentive compatible payments that minimize the total expected payments that have to be made to the agents it is known that the problem can be efficiently solved when jobs have single dimensional types here we address the problem with two dimensional types we show that the problem can be solved in polynomial time by linear programming techniques answering an open problem formulated by heydenreich et al our implementation is randomized and truthful in expectation remarkably it also works when types are correlated across jobs the main steps are a compactification of an exponential size linear programming formulation and a convex decomposition algorithm that allows us to implement the optimal linear programming solution in addition by means of computational experiments we generate some new insights into the implementability in different equilibria

minimizing within convex bodies using a convex hull method we present numerical methods to solve optimization problems on the space of convex functions or among convex bodies hence convexity is a constraint on the admissible objects whereas the functionals are not required to be convex to deal with this our method mixes geometrical and numerical algorithms we give several applications arising from classical problems in geometry and analysis alexandrov s problem of finding a convex body of prescribed surface function cheeger s problem of a subdomain minimizing the ratio surface area on volume newton s problem of the body of minimal resistance in particular for the latter application the minimizers are still unknown except in some particular classes we give approximate solutions better than the theoretical known ones hence demonstrating that the minimizers do not belong to these classes

perishability of data dynamic pricing under varying coefficient models we consider a firm that sells a large number of products to its customers in an online fashion each product is described by a high dimensional feature vector and the market value of a product is assumed to be linear in the values of its features parameters of the valuation model are unknown and can change over time the firm sequentially observes a product s features and can use the historical sales data binary sale no sale feedbacks to set the price of current product with the objective of maximizing the collected revenue we measure the performance of a dynamic pricing policy via regret which is the expected revenue loss compared to a clairvoyant that knows the sequence of model parameters in advance we propose a pricing policy based on projected stochastic gradient descent psgd and characterize its regret in terms of time t features dimension d and the temporal variability in the model parameters t we consider two settings in the first one feature vectors are chosen antagonistically by nature and we prove that the regret of psgd pricing policy is of order o t t 1t t t in the second setting referred to as stochastic features model the feature vectors are drawn independently from an unknown distribution we show that in this case the regret of psgd pricing policy is of order o d2 log t t 1t t t d

fuzzy formulation of auctions and optimal sequencing for multiple auctions abstract current research on auctions is mainly based on the game theory in the first part of this paper we propose a fuzzy set based formulation of auctions we define fuzzy sets to represent the seller and buyers valuations bid possibilities and win possibilities analyzing the properties of these fuzzy sets we study fuzzy versions of discriminating and nondiscriminating bidding strategies for each bidder in a single object auction by using bellman and zadeh s concept of confluence of fuzzy decisions instead of the game theoretic nash equilibrium the monotonically decreasing membership function replaces of the corresponding distribution density function in milgrom and weber s auction theory in the second part of the paper we develop a soft computing approach to maximize the seller s revenue in multiple object auctions through the use of object sequencing the proposed sequencing approach is based on fuzzy rule quantification numerical experience shows the potential of the proposed approach for application in practical auctions

evaluation of missing ordinal pattern and its fractional distribution entropy abstract the number of missing ordinal patterns nmp receives extensive attention in this paper we change the perspective and study nmp about time delay and multi scale theory we first highlight the surrogate framework to see if the nmp for a series is statistically different from that of iterative amplitude adjusted fourier transform iaaft surrogates as time delay and scales changes furthermore by means of the fractional calculus we combine nmp with distribution entropy to study the fractional distribution entropy with nmp in order to show the advantages of these methods several simulated data and electrocardiograph ecg signals are chosen to examine the performance of them through experiments we find that nmp about time delay and multi scale theory shows an excellent characteristic in the nonlinearity analysis of different time series especially when applied to ecg signals moreover the results of the fractional distribution entropy show that it can explore the complexity of dynamical systems effectively

mutual information of population codes and distance measures in probability space we studied the mutual information between a stimulus and a system consisting of stochastic statistically independent elements that respond to a stimulus using statistical mechanical methods the properties of the mutual information mi in the limit of a large system size n are calculated for continuous valued stimuli the mi increases logarithmically with n and is related to the log of the fisher information of the system for discrete stimuli the mi saturates exponentially with n we find that the exponent of saturation of the mi is the chernoff distance between response probabilities that are induced by different stimuli

extracting fractal components from time series abstract we present a technique for extracting random fractal components from a given time series in the frequency domain the method was based on characteristics of the fractal time series that the original and the renormalized coarse grained time series had a random phase relationship an ordinary fft based cross spectral method was used to measure the phase relationship the method was tested on simulated data with known fractal and or simple harmonic properties and with a mixture of these the percent fractal components derived by this technique were closely matched to the theoretical values we set the extracted fractal power showed power law dependence expressed as spectral exponent by which we could calculate the hurst exponent h of the time series from it was also shown that the calculated h for the simulated time series gave good estimates for the true h of the random fractal process

envelope theorems for arbitrary choice sets the standard envelope theorems apply to choice sets with convex and topological structure providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative this paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function we also provide conditions for the value function to be variously absolutely continuous left and right differentiable or fully differentiable these results are applied to mechanism design convex programming continuous optimization problems saddle point problems problems with parameterized constraints and optimal stopping problems

fractal ion channel behavior generates fractal firing patterns in neuronal models fractal behavior has been observed in both ion channel gating and neuronal spiking patterns but a causal relationship between the two has not yet been established here we examine the effects of fractal ion channel activity in modifications of two classical neuronal models fitzhugh nagumo fhn and hodgkin huxley hh for the modified fhn model the recovery variable was represented as a population of ion channels with either fractal or markov gating characteristics fractal gating characteristics changed the form of the interspike interval histogram isih and also induced fractal behavior in the firing rate for the hh model the k conductance was represented as a collection of ion channels with either quasifractal or markov gating properties fractal gating induced fractal rate behavior without changing the isih we conclude that fractal ion channel gating activity is sufficient to account for fractal rate firing behavior

approximating optimization problems over convex functions many problems of theoretical and practical interest involve finding an optimum over a family of convex functions for instance finding the projection on the convex functions in hk and optimizing functionals arising from some problems in economics in the continuous setting and assuming smoothness the convexity constraints may be given locally by asking the hessian matrix to be positive semidefinite but in making discrete approximations two difficulties arise the continuous solutions may be not smooth and functions with positive semidefinite discrete hessian need not be convex in a discrete sense previous work has concentrated on non local descriptions of convexity making the number of constraints to grow super linearly with the number of nodes even in dimension 2 and these descriptions are very difficult to extend to higher dimensions in this paper we propose a finite difference approximation using positive semidefinite programs and discrete hessians and prove convergence under very general conditions even when the continuous solution is not smooth working on any dimension and requiring a linear number of constraints in the number of nodes using semidefinite programming codes we show concrete examples of approximations to problems in two and three dimensions

multiple testing strategy for the detection of temporal irreversibility in stationary time series we propose a strategy for the detection of temporal irreversibility in stationary time series based on multiple bidimensional tests the test is helpful to evaluate the displacement of irreversibility toward high dimensions the test can be used independently of the theoretical functionals actually utilized to check irreversibility the method was applied to simulated nonlinear signals generated by the delayed henon map and a two loop negative feedback model to show how the presence of a delay could produce the displacement of irreversibility toward higher dimensions the method was applied also to series of a biological variable i e heart period that is known to be regulated by multiple feedback loops simulations and real data support the need of exploring progressively increasing embedding dimensions when assessing temporal irreversibility

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

regularity of solutions for some variational problems subject to a convexity constraint we first study the minimizers in the class of convex functions of an elliptic functional with nonhomogeneous dirichlet boundary conditions we prove c1 regularity of the minimizers under the assumption that the upper envelope of admissible functions is c1 this condition is optimal at least when the functional depends only on the gradient 3 we then give various extensions of this result in particular we consider a problem without boundary conditions arising in an economic model introduced by rochet and chone in 4

modeling heart rate variability in healthy humans a turbulence analogy many complex systems share similar statistical characteristics in this letter a turbulence analogy is proposed for the long term heart rate variability of healthy humans based on such an analogy the equivalence of an inertial range is found and a cascade model which captures the statistical properties of the heart rate data is given

bifurcations in a nonlinear model of the baroreceptor cardiac reflex abstract we investigate the dynamic properties of a nonlinear model of the human cardio baroreceptor control loop as a new feature we use a phase effectiveness curve to describe the experimentally well known phase dependency of the cardiac pacemaker s sensitivity to neural activity we show that an increase of sympathetic time delays leads via a hopf bifurcation to sustained heart rate oscillations for increasing baroreflex sensitivity or for repetitive vagal stimulation we observe period doubling toroidal oscillations chaos and entrainment between the rhythms of the heart and the control loop the bifurcations depend crucially on the involvement of the cardiac pacemaker s phase dependency we compare the model output with experimental data from electrically stimulated anesthetized dogs and discuss possible implications for cardiac arrhythmias

genericity and robustness of full surplus extraction we study whether priors that admit full surplus extraction fse are generic an issue that becomes a gauge to evaluate the validity of the current mechanism design paradigm we consider the space of priors on the universal type space and thereby relax the assumption of a fixed finite number of types made by cremer and mclean 1988 we show that fse priors are topologically generic contrary to the result of heifetz and neeman 2006 that fse is generically impossible both geometrically and measure theoretically instead of using the bdp approach or convex combinations of priors adopted in heifetz and neeman 2006 we prove our genericity results by showing a robustness property of cremer mclean mechanisms

magnitude and sign scaling in power law correlated time series a time series can be decomposed into two sub series a magnitude series and a sign series here we analyze separately the scaling properties of the magnitude series and the sign series using the increment time series of cardiac interbeat intervals as an example we 6nd that time series having identical distributions and long range correlation properties can exhibit quite di8erent temporal organizations of the magnitude and sign sub series from the cases we study it follows that the long range correlations in the magnitude series indicate nonlinear behavior speci6cally our results suggest that the correlation exponent of the magnitude series is a monotonically increasing function of the multifractal spectrum width of the original series on the other hand the sign series mainly relates to linear properties of the original series we also show that the magnitude and sign series of the heart interbeat interval series can be used for diagnosis purposes c

multidimensional mechanism design finite dimensional approximations and efficient computation multidimensional mechanism design problems have proven difficult to solve by extending techniques from the one dimensional case this paper considers mechanism design problems with multidimensional types when the seller s cost function is not separable across buyers by adapting results obtained by border border k 1991 implementation of reduced form auctions a geometric approach econometrica59 1175 1187 we transform the seller s problem into a representation that only involves interim variables and eliminates the dimensionality dependence on the number of buyers we show that the associated infinite dimensional optimization problem posed by the theoretical model can be approximated arbitrarily well by a sequence of finite dimensional linear programming problems we provide an efficient i e terminating in polynomial time in the problem size method to compute the separation oracle associated with the border constraints and incentive compatibility constraints this implies that our finite dimensional approximation is solvable in polynomial time finally we illustrate how the numerical solutions of the finite dimensional approximations can provide insights into the nature of optimal solutions to the infinite dimensional problem in particular cases

combination of equiprobable symbolization and time reversal asymmetry for heartbeat interval series analysis symbolic dynamics method and time reversal asymmetry analysis are both important approaches in the study of heartbeat interval series however there is limited research work reported on combining these two methods we provide a method of time reversal asymmetry analysis which focuses on the differences between the forward and backward embedding m words after the operation of equiprobable symbolization to investigate the total amplitude as well as the distribution features of the difference four indices are proposed based on the application to simulation series we found that these measures can successfully detect time reversal asymmetry in chaos series with application to human heartbeat interval series rr series it is suggested that the distribution features of the forward backward difference can sensitively capture the dynamical changes caused by diseases or aging in particular the index e d which reflects the random degree of the forward backward difference distribution can significantly discriminate healthy subjects from diseased ones we conclude that rr series from healthy subjects show more asymmetry in temporal structure on the original time scale from the perspective of equiprobable symbolization whereas diseases account for loss of this asymmetry

weak monotonicity characterizes deterministic dominant strategy implementation we characterize dominant strategy incentive compatibility with multidimensional types a deterministic social choice function is dominant strategy incentive compatible if and only if it is weakly monotone w mon the w mon requirement is the following if changing one agent s type while keeping the types of other agents fixed changes the outcome under the social choice function then the resulting difference in utilities of the new and original outcomes evaluated at the new type of this agent must be no less than this difference in utilities evaluated at the original type of this agent

theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions in a recent study the initial rise of the mutual information between the firing rates of n neurons and a set of p discrete stimuli has been analytically evaluated under the assumption that neurons fire independently of one another to each stimulus and that each conditional distribution of firing rates is gaussian yet real stimuli or behavioral correlates are high dimensional with both discrete and continuously varying features moreover the gaussian approximation implies negative firing rates which is biologically implausible here we generalize the analysis to the case where the stimulus or behavioral correlate has both a discrete and a continuous dimension like orientation and shape could be in a visual stimulus or type and direction in a motor action the functional relationship between the firing patterns and the continuous correlate is expressed through the tuning curve of the neuron using two different parameters to modulate its width and its flatness in the case of large noise we evaluate the mutual information up to the quadratic approximation as a function of population size we also show that in the limit of large n and assuming that neurons can discriminate between continuous values with a resolution delta theta the mutual information grows to infinity like ln 1 delta theta when delta theta goes to zero then we consider a more realistic distribution of firing rates truncated at zero and we prove that the resulting correction with respect to the gaussian firing rates can be expressed simply as a renormalization of the noise parameter finally we demonstrate the effect of averaging the distribution across the discrete dimension evaluating the mutual information only with respect to the continuously varying correlate

optimal dynamic auctions and simple index rules a monopolist seller has multiple units of an indivisible good to sell over a discrete finite time horizon buyers with unit demand arrive over time and each buyer privately knows her arrival time her value for a unit and her deadline we study whether the seller s optimal allocation rule is a simple index rule each buyer is assigned an index and the allocation rule is calculated by a dynamic knapsack algorithm using those indices simple indicates that the index of a buyer depends only on local information i e the distribution information for that time period if buyer deadlines are public such simple index rules are optimal if the standard increasing hazard rate condition on the distribution of valuations holds and given two buyers with the same deadline the later arriving one has a lower hazard rate implying stochastically higher valuations when buyer deadlines are private this condition is neither sufficient nor necessary if the rule we identify is not feasible then the optimal allocation rule is not a simple index rule and cannot be calculated by backward induction

multi affine model for the velocity distribution in fully turbulent flows a simple multi affine model for the velocity distribution in fully developed turbulent flows is introduced to capture the essential features of the underlying geometry of the velocity field the authors show that in this model the various relevant quantities characterizing different aspects of turbulence can be readily calculated a simultaneous good agreement is found with the available experimental data for the velocity structure functions the dq spectra obtained from studies of the velocity derivatives and the exponent describing the scaling of the spectrum of the kinetic energy fluctuations their results are obtained analytically assuming a single free parameter the fractal dimension of the region where the dominating contribution to dissipation comes from is estimated to be d approximately 2 88

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

automated design of revenue maximizing combinatorial auctions designing optimal that is revenue maximizing combinatorial auctions cas is an important elusive problem it is unsolved even for two bidders and two items for sale rather than pursuing the manual approach of attempting to characterize the optimal ca we introduce a family of cas and then seek a high revenue auction within that family the family is based on bidder weighting and allocation boosting we coin such cas virtual valuations combinatorial auctions vvcas vvcas are the vickrey clarke groves vcg mechanism executed on virtual valuations that are affine transformations of the bidders valuations the auction family is parameterized by the coefficients in the transformations the problem of designing a ca is thereby reduced to search in the parameter space of vvca or the more general space of affine maximizer auctions we first construct vvcas with logarithmic approximation guarantees in canonical special settings 1 limited supply with additive valuations and 2 unlimited supply in the ma

the price of envy freeness in machine scheduling we consider k envy free assignments for scheduling problems in which the completion time of each machine is not k times larger than the one she could achieve by getting the jobs of another machine for a given factor k 1 we introduce and investigate the notion of price of k envy freeness defined as the ratio between the makespan of the best k envy free assignment and that of an optimal allocation achievable without envy freeness constraints we provide exact or asymptotically tight bounds on the price of k envy freeness for all the basic scheduling models that is unrelated related and identical machines moreover we show how to efficiently compute such allocations with a worsening multiplicative factor being at most the best approximation ratio for the minimum makespan problem guaranteed by a polynomial time algorithm for each specific model finally we extend our results to the case of restricted assignments and to the objective of minimizing the sum of the completion times of all the machines

truth revelation in approximately efficient combinatorial auctions some important classical mechanisms considered in microeconomics and game theory require the solution of a difficult optimization problem this is true of mechanisms for combinatorial auctions which have in recent years assumed practical importance and in particular of the gold standard for combinatorial auctions the generalized vickrey auction gva traditional analysis of these mechanisms in particular their truth revelation properties assumes that the optimization problems are solved precisely in reality these optimization problems can usually be solved only in an approximate fashion we investigate the impact on such mechanisms of replacing exact solutions by approximate ones specifically we look at a particular greedy optimization method we show that the gva payment scheme does not provide for a truth revealing mechanism we introduce another scheme that does guarantee truthfulness for a restricted class of players we demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that for our restricted class of players they imply that truthful strategies are dominant those properties have applicability beyond the specific auction studied

conforming approximation of convex functions with the finite element method we consider the interior approximation of convex functions with convex finite element functions the main motivation for this study is the investigation of a novel discretization of optimization problems with convexity constraints by the finite element method under a mild assumption on the family of meshes we show that the conforming approximation is convergent if the finite elements are at least piecewise quadratic we further provide similar results under additional constraints on the function values or on the gradient the theoretical findings are illustrated by numerical examples

multifractal spectra of multi affine functions abstract self affine functions f x with multiscaling height correlations cq x xqhq are described in terms of the standard multifractal formalism with a modified assumption for the partition the corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones according to our calculations the f type spectra are not uniquely determined by the hq spectrum but depend on the particular choice which is made for the dependence of n on x where n is the number of points over which the average is taken our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process

global holder estimates for 2d linearized monge ampere equations with right hand side in divergence form abstract we establish global holder estimates for solutions to inhomogeneous linearized monge ampere equations in two dimensions with the right hand side being the divergence of a bounded vector field these equations arise in the semi geostrophic equations in meteorology and in the approximation of convex functionals subject to a convexity constraint using fourth order abreu type equations our estimates hold under natural assumptions on the domain boundary data and monge ampere measure being bounded away from zero and infinity they are an affine invariant and degenerate version of global holder estimates by murthy stampacchia and trudinger for second order elliptic equations in divergence form

testing stationarity in time series we propose a procedure for testing stationarity of time series by combining a test for time independence of the probability density with one of the spectral density the potentials of this test procedure are demonstrated by its application to various types of numerically simulated time series ranging from simple linear stochastic processes to high dimensional transient chaos problems of practical implementation are discussed in particular the relation between the lengths of the time series and its maximal relevant time scales stationarity is then tested for experimental data from geophysics and physiology exchange rates are found to be stationary on time scales of decades in the sense that their spectral densities do not significantly change

optimal contract design in the joint economic lot size problem with multi dimensional asymmetric information abstract previous work has studied the classical joint economic lot size model as an adverse selection problem with asymmetric cost information solving this problem is challenging due to the presence of countervailing incentives and two dimensional information asymmetry under which the classical single crossing condition does not need to hold in the present work we advance the existing knowledge about the problem on hand by conducting its optimality analysis which leads to a better informed and an easier problem solution first we refine the existing closed form solution which simplifies problem solving and its analysis second we prove that karush kuhn tucker conditions are necessary for optimality and demonstrate that the problem may in general possess non optimal stationary points due to non convexity third we prove that certain types of stationary points are always dominated which eases the analytical solution of the problem fourth we derive a simple optimality condition stating that a weak pareto efficiency of the buyer s possible cost structures implies optimality of any stationary point it simplifies the analytical solution approach and ensures a successful solution of the problem by means of conventional numerical techniques e g with a general purpose solver we further establish properties of optimal solutions and indicate how these are related with the classical results on adverse selection

tractable stochastic analysis in high dimensions via robust optimization modern probability theory whose foundation is based on the axioms set forth by kolmogorov is currently the major tool for performance analysis in stochastic systems while it offers insights in understanding such systems probability theory in contrast to optimization has not been developed with computational tractability as an objective when the dimension increases correspondingly some of its major areas of application remain unsolved when the underlying systems become multidimensional queueing networks auction design in multi item multi bidder auctions network information theory pricing multi dimensional options among others we propose a new approach to analyze stochastic systems based on robust optimization the key idea is to replace the kolmogorov axioms and the concept of random variables as primitives of probability theory with uncertainty sets that are derived from some of the asymptotic implications of probability theory like the central limit theorem in addition we observe that several desired system properties such as incentive compatibility and individual rationality in auction design are naturally expressed in the language of robust optimization in this way the performance analysis questions become highly structured optimization problems linear semidefinite mixed integer for which there exist efficient practical algorithms that are capable of solving problems in high dimensions we demonstrate that the proposed approach achieves computationally tractable methods for a analyzing queueing networks b designing multi item multi bidder auctions with budget constraints and c pricing multi dimensional options

optimization and mechanism design mechanism design is about optimizing the allocation of resources when the parameters needed to determine an optimal allocation are privately held by the agents who will consume the resources an agent s report of her information will influence the resulting allocation which in turn will affect her utility in such a situation how can one simultaneously elicit the information that is privately held and choose the optimal allocation this paper illustrates how standard results in linear programming play a role in the analysis of mechanism design problems it is not a comprehensive survey rather it focuses on two variations of a particular problem the allocation of a single object

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

analysis of heartbeat asymmetry based on multi scale time irreversibility test abstract we investigate the asymmetry of heart rate control system and suggest a simple index to quantify this asymmetry by performing high dimensional time irreversibility tests to heartbeat interval time series over multiple scales the results provide strong evidence to the concept that the asymmetry is an intrinsic property of heart rate control system as a simple and visual method it is proved to be effective in classifying physiologic and synthetic subjects while the maximum scale is selected within a proper range and also provides a new way to analyze the time irreversibility for other high dimensional systems

on the generic im possibility of full surplus extraction in mechanism design a number of studies most notably cremer and mclean 1985 1988 have shown that in harsanyi type spaces of a fixed finite size it is generically possible to design mechanisms that extract all the surplus from players and as a consequence implement any outcome as if the players private information were commonly known in contrast we show that within the set of common priors on the universal type space the subset of priors that permit the extraction of the players full surplus is shy shyness is an otion of smallness for convex subsets of infinite dimensional topological vector spaces in our case the set of common priors which generalizes the usual notion of zero lebesgue measure in finite dimensional spaces

dynamic mechanism design a myersonian approach we study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods we make three contributions first we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent s equilibrium expected payoff with respect to his current type it combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by impulse response functions the formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms second we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule revenue equivalence third we characterize perfect bayesian equilibrium implementable allocation rules in markov environments which yields tractable sufficient conditions that facilitate novel applications we illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods bandit auctions

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

on convex functions and the finite element method many problems of theoretical and practical interest involve finding a convex or concave function for instance optimization problems such as finding the projection on the convex functions in h k omega or some problems in economics in the continuous setting and assuming smoothness the convexity constraints may be given locally by asking the hessian matrix to be positive semidefinite but in making discrete approximations two difficulties arise the continuous solutions may be not smooth and an adequate discrete version of the hessian must be given in this paper we propose a finite element description of the hessian and prove convergence under very general conditions even when the continuous solution is not smooth working on any dimension and requiring a linear number of constraints in the number of nodes using semidefinite programming codes we show concrete examples of approximations to optimization problems

games with incomplete information played by bayesian players i iii this article originally appeared in management science november 1967 volume 14 number 3 pp 159 182 published by the institute of management sciences the paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation such as the payoff functions the strategies available to various players the information other players have about the game etc however each player has a subjective probability distribution over the alternative possibilities in most of the paper it is assumed that these probability distributions entertained by the different players are mutually consistent in the sense that they can be regarded as conditional probability distributions derived from a certain basic probability distribution over the parameters unknown to the various players but later the theory is extended also to cases where the different players subjective probability distributions fail to satisfy this consistency assumption in cases where the consistency assumption holds the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution and the outcome of this lottery will decide which particular subgame will be played i e what the actual values of the relevant parameters will be in the game yet each player will receive only partial information about the outcome of the lottery and about the values of these parameters however every player will know the basic probability distribution governing the lottery thus technically the resulting game will be a game with complete information it is called the bayes equivalent of the original game part i of the paper describes the basic model and discusses various intuitive interpretations for the latter part ii shows that the nash equilibrium points of the bayes equivalent game yield bayesian equilibrium points for the original game finally part iii considers the main properties of the basic probability distribution

a numerical approach to variational problems subject to convexity constraint we describe an algorithm to approximate the minimizer of an elliptic functional in the form int omega j x u nabla u on the set cal c of convex functions u in an appropriate functional space x such problems arise for instance in mathematical economics 4 a special case gives the convex envelope u 0 of a given function u 0 let t n be any quasiuniform sequence of meshes whose diameter goes to zero and i n the corresponding affine interpolation operators we prove that the minimizer over cal c is the limit of the sequence u n where u n minimizes the functional over i n cal c we give an implementable characterization of i n cal c then the finite dimensional problem turns out to be a minimization problem with linear constraints

representational capacity of a set of independent neurons the capacity with which a system of independent neuron like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses both discrete noiseless and continuous noisy neurons are analyzed in both cases the information grows monotonically with the number of neurons considered under the assumption that neurons are independent the mutual information rises linearly from zero and approaches exponentially its maximum value we find the dependence of the initial slope on the number of stimuli and on the sparseness of the representation

multi to one dimensional optimal transport we consider the monge kantorovich problem of transporting a probability density on m to another on the line so as to optimize a given cost function we introduce a nestedness criterion relating the cost to the densities under which it becomes possible to solve this problem uniquely by constructing an optimal map one level set at a time this map is continuous if the target density has connected support we use level set dynamics to develop and quantify a local regularity theory for this map and the kantorovich potentials solving the dual linear program we identify obstructions to global regularity through examples more specifically fix probability densities f and g on open sets x m and y n with m n 1 consider transporting f onto g so as to minimize the cost s x y we give a nondegeneracy condition on s c1 1 that ensures the set of x paired with g a e y y lie in a codimension n submanifold of x specializing to the case m n 1 we discover a nestedness criterion relating s to f g that allows us to construct a unique optimal solution in the form of a map f x y when s c2 w3 1 and g and f are bounded the kantorovich dual potentials u satisfy cloc1 1 y and the normal velocity v of f 1 y with respect to changes in y is given by v x syy dxsy x f x positivity of v locally implies a lipschitz bound on f moreover c2 if f 1 y intersects x c1 transversally on subsets where this nondegeneracy positivity and transversality can be quantified for each integer r 1 the norms of u cr 1 1 and f cr 1 are controlled by these bounds g log f x cr 1 1 x w2 1 s cr 1 1 and the smallness of f 1 y we give examples showing regularity extends from x to part of x but not from y to y we also show that when s remains nested for all f g the problem in m reduces to a supermodular problem in 2017 wiley periodicals inc

truthful generalized assignments via stable matching in the generalized assignment problem gap a set of jobs seek to be assigned to a set of machines for every job machine pair there are a specific value and an accommodated capacity for the assignment the objective is to find an assignment that maximizes the total sum of values given that the capacity constraint of every machine is satisfied the gap is a classic optimization problem and has been studied extensively from the algorithmic perspective dughmi and ghosh dughmi s ghosh a 2010 truthful assignment without money acm conf electronic commerce acm new york 325 334 proposed the game theoretical framework in which every job is owned by a selfish agent who aims to maximize the value of his own assignment they gave a logarithmic approximation truthful in expectation mechanism and left open the problem whether there exists a truthful mechanism with a constant approximation factor in this paper we give an affirmative answer to this question and provide a constant approximation mechanism

ironing sweeping and multidimensional screening we provide existence proofs and characterization results for the multidimensional version of the multiproduct monopolist problem of mussa and rosen 1978 these results are also directly applicable to the multidimensional nonlinear pricing problems studied by wilson 1993 and armstrong 1996 we establish that bunching is robust in these multidimensional screening problems even with very regular distributions of types this comes from a strong conflict between participation constraints and second order incentive compatibility conditions we consequently design a new technique the sweeping procedure for dealing with bunching in multidimensional contexts this technique extends the ironing procedure of mussa and rosen 1978 to several dimensions we illustrate it on two examples we first solve a linear quadratic version of the bidimensional nonlinear pricing problem where consumers types are exponentially distributed the solution involves pure bundling for consumers with low demands the second example is the bidimensional version of the mussa and rosen problem when consumers types are uniformly distributed on a square the solution is such that the seller offers a full differentiation of products in the upper part of the qualities spectrum but only limited choice for lower qualities this seems to be a quite general pattern for multidimensional screening problems the sweeping procedure is potentially applicable to other multidimensional screening problems

characterization of flow pattern transitions for horizontal liquid liquid pipe flows by using multi scale distribution entropy in coupled 3d phase space abstract horizontal oil water two phase flows often exist in many industrial processes uncovering the dynamic mechanism of the flow pattern transition is of great significance for modeling the flow parameters in this study we propose a method called multi scale distribution entropy msde in a coupled 3d phase space and use it to characterize the flow pattern transitions in horizontal oil water two phase flows firstly the proposed msde is validated with lorenz system and arfima processes interestingly it is found that the msde is dramatically associated with the cross correlations of the coupled time series then through conducting the experiment of horizontal oil water two phase flows the upstream and downstream flow information is collected using a conductance cross correlation velocity probe the coupled cross correlated signals are investigated using the msde method and the results indicate that the msde is an effective tool uncovering the complex dynamic behaviors of flow pattern transitions

strongly polynomial time truthful mechanisms in one shot one of the main challenges in algorithmic mechanism design is to turn existing efficient algorithmic solutions into efficient truthful mechanisms building a truthful mechanism is indeed a difficult process since the underlying algorithm must obey certain monotonicity properties and suitable payment functions need to be computed this task usually represents the bottleneck in the overall time complexity we provide a general technique for building truthful mechanisms that provide optimal solutions in strongly polynomial time we show that the entire mechanism can be obtained if one is able to express write a strongly polynomial time algorithm for the corresponding optimization problem as a suitable combination of simpler algorithms this approach applies to a wide class of mechanism design graph problems where each selfish agent corresponds to a weighted edge in a graph the weight of the edge is the cost of using that edge our technique can be applied to several optimization problems which prior results cannot handle e g min max optimization problems as an application we design the first strongly polynomial time truthful mechanism for the minimum diameter spanning tree problem by obtaining it directly from an existing algorithm for solving this problem for this non utilitarian min max problem no truthful mechanism was known even considering those running in exponential time indeed exact algorithms do not necessarily yield truthful mechanisms also standard techniques for payment computations may result in a running time which is not polynomial in the size of the input graph the overall running time of our mechanism instead is polynomial in the number n of nodes and m of edges and it is only a factor o n a n n away from the best known canonical centralized algorithm

simultaneous ad auctions we consider a model with two simultaneous vcg ad auctions a and b where each advertiser chooses to participate in a single ad auction we prove the existence and uniqueness of a symmetric equilibrium in that model moreover when the click rates in a are pointwise higher than those in b we prove that the expected revenue in a is greater than the expected revenue in b in this equilibrium in contrast we show that this revenue ranking does not hold when advertisers can participate in both auctions

efficient computation of optimal auctions via reduced forms we study an optimal auction problem for selecting a subset of agents to receive an item or service whereby each agent s service can be configured the agent has multidimensional preferences over c

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

monotonicity and implementability consider an environment with a finite number of alternatives and agents with private values and quasilinear utility functions a domain of valuation functions for an agent is a monotonicity domain if every finite valued monotone randomized allocation rule defined on it is implementable in dominant strategies we fully characterize the set of all monotonicity domains

characterization of revenue equivalence the property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints the characterization holds for any possibly infinite outcome space and many of the known results are immediate consequences moreover revenue equivalence can be identified in cases where existing theorems are silent

multiscale aspects of cardiac control abstract we report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics we first review recent progress using wavelet based multifractal analysis magnitude and sign decomposition analysis and a new segmentation algorithm to quantify multiscale features of heartbeat interval series we then investigate how heartbeat dynamics change with circadian influences and under pathologic conditions and we discuss their possible relation to the underlaying cardiac control mechanisms the analytic tools we discuss may be used on a wider range of physiologic signals

non linear pricing by convex duality we consider the pricing problem of a risk neutral monopolist who produces at a cost and offers an infinitely divisible good to a single potential buyer that can be of a finite number of single dimensional types the buyer has a non linear utility function that is differentiable strictly concave and strictly increasing using a simple reformulation and shortest path problem duality as in vohra 2011 we transform the initial non convex pricing problem of the monopolist into an equivalent optimization problem yielding a closed form pricing formula under a regularity assumption on the probability distribution of buyer types we examine the solution of the problem when the regularity condition is relaxed in different ways or when the production function is non linear and convex for arbitrary type distributions we offer a complete solution procedure

optimal auction design this paper considers the problem faced by a seller who has a single object to sell to one of several possible buyers when the seller has imperfect information about how much the buyers might be willing to pay for the object the seller s problem is to design an auction game which has a nash equilibrium giving him the highest possible expected utility optimal auctions are derived in this paper for a wide class of auction design problems

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected