algorithms for the coalitional manipulation problem we investigate the problem of coalitional manipulation in elections which is known to be hard in a variety of voting rules we put forward efficient algorithms for the problem in borda maximin and plurality with runoff and analyze their windows of error specifically given an instance on which an algorithm fails we bound the additional power the manipulators need in order to succeed we finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation

a novel characterization of the complexity class θkp based on counting and comparison abstract the complexity class 2 p which is the class of languages recognizable by deterministic turing machines in polynomial time with at most logarithmic many calls to an np oracle received extensive attention in the literature its complete problems can be characterized by different specific tasks such as deciding whether the optimum solution of an np problem is unique or whether it is in some sense odd e g whether its size is an odd number in this paper we introduce a new characterization of this class and its generalization k p to the k th level of the polynomial hierarchy we show that problems in k p are also those whose solution involves deciding for two given sets a and b of instances of two k 1 p complete or k 1 p complete problems whether the number of yes instances in a is greater than those in b moreover based on this new characterization we provide a novel sufficient condition for k p hardness we also define the general problem comp valid k which is proven here k 1 p complete comp valid k is the problem of deciding given two sets a and b of quantified boolean formulas with at most k alternating quantifiers whether the number of valid formulas in a is greater than those in b notably the problem comp sat of deciding whether a set contains more satisfiable boolean formulas than another set which is a particular case of comp valid 1 demonstrates itself as a very intuitive 2 p complete problem nonetheless to our knowledge it eluded its formal definition to date in fact given its strict adherence to the count and compare semantics here introduced comp valid k is among the most suitable tools to prove k p hardness of problems involving the counting and comparison of the number of yes instances in two sets we support this by showing that the 2 p hardness of the max voting scheme over mcp nets is easily obtained via the new characterization of k p introduced in this paper

systems of frequency distributions for water and environmental engineering abstract a wide spectrum of frequency distributions are used in hydrologic hydraulic environmental and water resources engineering these distributions may have different origins are based on different hypotheses and belong to different generating systems review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include 1 differential equations 2 distribution elasticity 3 genetic theory 4 generating functions 5 transformations 6 bessel function 7 expansions and 8 entropy maximization this paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems it also proposes based on empirical evidence another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering

bounded query classes polynomial time machines having restricted access to an np oracle are investigated restricted access means that the number of queries to the oracle is restricted or the way in which the queries are made is restricted e g queries made during truth table reductions very different kinds of such restrictions result in the same or comparable complexity classes in particular the class p text np o log n can be characterized in very different ways furthermore the boolean hierarchy is generalized in such a way that it is possible to characterize p text np and p text np o log n in terms of the generalization

exact analysis of dodgson elections lewis carroll s 1876 voting system is complete for parallel access to np in 1876 lewis carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters preferences becomes a condorcet winner a candidate who beats all other candidates in pairwise majority rule elections bartholdi tovey and trick provided a lower bound np hardness on the computational complexity of determining the election winner in carroll s system we provide a stronger lower bound and an upper bound that matches our lower bound in particular determining the winner in carroll s system is complete for parallel access to np that is it is complete for theta 2 p for which it becomes the most natural complete problem known it follows that determining the winner in carroll s elections is not np complete unless the polynomial hierarchy collapses

a note on pareto tails and lognormal body of us cities size distribution abstract luckstead and devadoss 2017 fitted a distribution made up of lower tail pareto lognormal body and upper tail pareto to city sizes in the us here we propose a class of distributions providing better fits the fits are assessed in terms of akaike information criterion bayesian information criterion and probability plots

some new classes of complex symmetric operators we say that an operator t e b h is complex symmetric if there exists a conjugate linear isometric involution c so that t ct c we prove that binormal operators operators that are algebraic of degree two including all idempotents and large classes of rank one perturbations of normal operators are complex symmetric from an abstract viewpoint these results explain why the compressed shift and volterra integration operator are complex symmetric finally we attempt to describe all complex symmetric partial isometries obtaining the sharpest possible statement given only the data dim ker t dim ker t

on the graph laplacian and the rankability of data abstract recently anderson et al 2019 proposed the concept of rankability which refers to a dataset s inherent ability to produce a meaningful ranking of its items in the same paper they proposed a rankability measure that is based on an integer program for computing the minimum number of edge changes made to a directed graph in order to obtain a complete dominance graph i e an acyclic tournament graph in this article we prove a spectral degree characterization of complete dominance graphs and apply this characterization to produce a new measure of rankability that is cost effective and more widely applicable we support the details of our algorithm with several results regarding the conditioning of the laplacian spectrum of complete dominance graphs and the hausdorff distance between their laplacian spectrum and that of an arbitrary directed graph with weights between zero and one finally we analyze the rankability of datasets from the world of chess and college football

the complexity of manipulative attacks in nearly single peaked electorates many electoral control and manipulation problems which we will refer to in general as manipulative actions problems are np hard in the general case it has recently been noted that many of these problems fall into polynomial time if the electorate is single peaked i e is polarized along some axis issue however real world electorates are not truly single peaked there are usually some mavericks and so real world electorates tend merely to be nearly single peaked this paper studies the complexity of manipulative action algorithms for elections over nearly single peaked electorates we do this for many notions of nearness and for a broad range of election systems we provide instances where even one maverick jumps the manipulative action complexity up to np hardness but we also provide many instances where some number of mavericks can be tolerated without increasing the manipulative action complexity

when are elections with few candidates hard to manipulate in multiagent settings where the agents have different preferences preference aggregation is a central issue voting is a general method for preference aggregation but seminal results have shown that all general voting protocols are manipulable one could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard especially among computational agents it is reasonable to measure this hardness by computational complexity some earlier work has been done in this area but it was assumed that the number of voters and candidates is unbounded such hardness results lose relevance when the number of candidates is small because manipulation algorithms that are exponential only in the number of candidates and only slightly so might be available we give such an algorithm for an individual agent to manipulate the single transferable vote stv protocol which has been shown hard to manipulate in the above sense this motivates the core of this article which derives hardness results for realistic elections where the number of candidates is a small constant but the number of voters can be large the main manipulation question we study is that of coalitional manipulation by weighted voters we show that for simpler manipulation problems manipulation cannot be hard with few candidates we study both constructive manipulation making a given candidate win and destructive manipulation making a given candidate not win we characterize the exact number of candidates for which manipulation becomes hard for the plurality borda stv copeland maximin veto plurality with runoff regular cup and randomized cup protocols we also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others votes but not vice versa to our knowledge these are the first results on the hardness of manipulation when there is uncertainty about the others votes

more complicated questions about maxima and minima and some closures of np abstract starting from np complete problems defined by questions of the kind max m and min m we consider problems defined by more complicated questions about these maxima and minima as for example max m min m and is max odd this continues a work started by papadimitriou and yannakakis 1982 it is shown that these and other problems are complete in certain subclasses of the boolean closure of np and other classes in the interesting area below the class p 2 of the polynomial time hierarchy special methods are developed to prove such completeness results for this it is necessary to establish some properties of the classes in question which might be interesting in their own right

mixed integer programming with convex concave constraints fixed parameter tractability and applications to multicovering and voting abstract a classic result of lenstra math oper res 1983 says that an integer linear program can be solved in fixed parameter tractable fpt time for the parameterization by the number of variables we extend this result by incorporating piecewise linear convex or concave functions to our mixed integer programs this general technique allows us to analyze the parameterized complexity of a number of classic np hard computational problems in particular we prove that weighted set multicover is in fpt when parameterized by the number of elements to cover and that there exists an fpt time approximation scheme for multiset multicover for the same parameter this is our most technical result further we use our general technique to prove that a number of problems from computational social choice e g problems related to bribery and control in elections are in fpt when parameterized by the number of candidates for bribery this resolves a nearly 10 year old family of open problems and for weighted electoral control of approval voting this improves some previously known xp memberships to fpt memberships

comparisons of log normal mixture and pareto tails gb2 or log normal body of romania s all cities size distribution abstract modeling demographic data has been on the agenda of statisticians for many years some of the distributions used are pareto reverse pareto q exponential and log normal models an approach to this problem is to consider three statistical models one for the upper tail one for the middle range and another for the lower tail this paper deals with the size distribution of urban and rural agglomerations in romania for the 1992 2017 period by comparing the recently introduced three log normal mixture 3ln pareto tails log normal ptln and threshold double pareto generalized beta of second kind tdpgb2 models the tdpgb2 statistical model has the ptln distribution as a limiting case the maximum likelihood estimates of the distributions are computed and goodness of fit tests are performed using the kolmogorov smirnov ks cramer von mises cm and anderson darling ad statistics also we use the vuong and bayes factor log likelihood tests using both graphical and formal statistical tests our results rigorously confirm that the 3ln model is statistically equivalent to ptln and tdpgb2 distributions the preferred model being the ptln probability law both the ptln and tdpgb2 distributions have pareto tails but the 3ln model does not all the three models prove to be very well suited parameterizations of romania s city size data

computing functions with parallel queries to np the class 2p of languages polynomial time truth table reducible to sets in np has a wide range of different characterizations we consider several functional versions of 2p based on these characterizations we show that in this way the three function classes fllognp fplognp and fp np are obtained in contrast to the language case the function classes seem to all be different we give evidence in support of this fact by showing that fllognp coincides with any of the other classes then l p and that the equality of the classes fplognp and fp np would imply that the number of nondeterministic bits needed for the computation of any problem in np can be reduced by a polylogarithmic factor and that the problem can be computed deterministically with a subexponential time bound of order 2no 1 log log n

a general functional form for approximating the lorenz curve abstract the purpose of this paper is to present several descriptive approximations of empirical lorenz curves each of these hypothetical forms is less restrictive than those considered before we compare these alternative forms by goodness of fit f tests of nested forms and measurement of the gini coefficient

complex symmetric weighted composition operators in several variables abstract in this paper we study the complex symmetric weighted composition operators on the hilbert space h s of analytic functions over the open unit ball with reproducing kernels k w s z 1 z w s where s n we completely characterize complex symmetric weighted composition operators with respect to two important conjugations j v and j which include hermitian weighted composition operators and normal weighted composition operators appeared in 17 surprisingly they are essential representatives of general conjugations of the form c j where c is unitary and j symmetric indeed these complex symmetric weighted composition operators can only be divided into two classes the size estimates and some other properties of these complex symmetric weighted composition operators are obtained moreover involutive weighted composition operators are completely characterized too as an application we construct concrete conjugations for the involutive composition operators which solves a problem raised by garcia and hammond in a general case

the exponentiated generalized birnbaum saunders distribution a new distribution called the exponentiated generalized birnbaum saunders distribution is proposed and studied the new distribution is quite flexible to model survival data reliability problems fatigue life studies and hydrological data it can have decreasing increasing upside down bathtub bathtub shaped increasing decreasing increasing and decreasing increasing decreasing hazard rate functions we provide a comprehensive account of the mathematical properties of the new distribution and various structural quantities are derived we discuss maximum likelihood estimation of the model parameters for uncensored and censored data two empirical applications of the new model to real data are presented for illustrative purposes

size distribution of u s lower tail cities abstract studies that analyzed the size distribution of u s cities have mainly focused on the upper tail and showed that these cities adhere to zipf s law however even though a large number of cities are in the lower tail very few studies have examined the distribution of these small cities because of data limitations we apply reverse pareto and reverse general pareto distributions to analyze u s lower tail cities our results show the power law behavior of lower tail u s cities is accurately represented by both the reverse pareto and general pareto

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

city size distributions for india and china this paper studies the size distributions of urban agglomerations for india and china we have estimated the scaling exponent for zipf s law with the indian census data for the years of 1981 2001 and the chinese census data for 1990 and 2000 along with the biased linear fit estimate the maximum likelihood estimate for the pareto and tsallis q exponential distribution has been computed for india the scaling exponent is in the range of 1 88 2 06 and for china it is in the interval 1 82 2 29 the goodness of fit tests of the estimated distributions are performed using the kolmogorov smirnov statistic

complexity of and algorithms for the manipulation of borda nanson s and baldwin s voting rules we investigate manipulation of the borda voting rule as well as two elimination style voting rules nanson s and baldwin s voting rules which are based on borda voting we argue that these rules have a number of desirable computational properties for unweighted borda voting we prove that it is np hard for a coalition of two manipulators to compute a manipulation this resolves a long standing open problem in the computational complexity of manipulating common voting rules we prove that manipulation of baldwin s and nanson s rules is computationally more difficult than manipulation of borda as it is np hard for a single manipulator to compute a manipulation in addition for baldwin s and nanson s rules with weighted votes we prove that it is np hard for a coalition of manipulators to compute a manipulation with a small number of candidates because of these np hardness results we compute manipulations using heuristic algorithms that attempt to minimise the number of manipulators we propose several new heuristic methods experiments show that these methods significantly outperform the previously best known heuristic method for the borda rule our results suggest that whilst computing a manipulation of the borda rule is np hard computational complexity may provide only a weak barrier against manipulation in practice in contrast to the borda rule our experiments with baldwin s and nanson s rules demonstrate that both of them are often more difficult to manipulate in practice these results suggest that elimination style voting rules deserve further study

a quantitative version of the gibbard satterthwaite theorem for three alternatives the gibbard satterthwaite theorem states that every nondictatorial election rule among at least three alternatives can be strategically manipulated we prove a quantitative version of the gibbard satterthwaite theorem a random manipulation by a single random voter will succeed with a nonnegligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range

complex symmetric monomial toeplitz operators on the unit ball abstract monomial toeplitz operators t z p z q on the weighted bergman space of the unit ball in c n are natural extension of the weighted shift operators in higher dimensions dim ker t z p z q may occur for non trivial case thus complex symmetric phenomena will appear in this paper we completely characterize when the monomial toeplitz operator t z p z q on the weighted bergman space is j a symmetric where j a f z f a z with the symmetric unitary n n matrix a moreover we also determine all possible forms of a such that t z p z q is j a symmetric as an application we construct the weakly closed unital commutative algebra generated by complex symmetric toeplitz operators

the complexity of kemeny elections kemeny proposed a voting scheme which is distinguished by the fact that it is the unique voting scheme that is neutral consistent and condorcet bartholdi tovey and trick showed that determining the winner in kemeny s system is np hard we provide a stronger lower bound and an upper bound matching the lower bound namely we show that determining the winner in kemeny s system is complete for p np the class of sets solvable via parallel access to np

two remarks on the power of counting the relationship between the polynomial hierarchy and valiant s class p is at present unknown we show that some low portions of the polynomial hierarchy namely deterministic polynomial algorithms using an np oracle at most a logarithmic number of times can be simulated by one p computation we also show that the class of problems solvable by polynomial time nondeterministic turing machines which accept whenever there is an odd number of accepting computations is idempotent that is closed under usage of oracles from the same class

on the approximability of dodgson and young elections the voting rules proposed by dodgson and young are both designed to find an alternative closest to being a condorcet winner according to two different notions of proximity the score of a given alternative is known to be hard to compute under either rule in this paper we put forward two algorithms for approximating the dodgson score a combinatorial greedy algorithm and an lp based algorithm both of which yield an approximation ratio of h m 1 where m is the number of alternatives and h m 1 is the m 1 st harmonic number we also prove that our algorithms are optimal within a factor of 2 unless problems in np have quasi polynomial time algorithms despite the intuitive appeal of the greedy algorithm we argue that the lp based algorithm has an advantage from a social choice point of view further we demonstrate that computing any reasonable approximation of the ranking produced by dodgson s rule is np hard this result provides a complexity theoretic explanation of sharp discrepancies that have been observed in the social choice theory literature when comparing dodgson elections with simpler voting rules finally we show that the problem of calculating the young score is np hard to approximate by any factor this leads to an inapproximability result for the young ranking

pareto versus lognormal a maximum entropy test it is commonly found that distributions that seem to be lognormal over a broad range change to a power law pareto distribution for the last few percentiles the distributions of many physical natural and social events earthquake size species abundance income and wealth as well as file city and firm sizes display this structure we present a test for the occurrence of power law tails in statistical distributions based on maximum entropy this methodology allows one to identify the true data generating processes even in the case when it is neither lognormal nor pareto the maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems our results provide support for the theory that distributions with lognormal body and pareto tail can be generated as mixtures of lognormally distributed units

the power law distribution for the income of poor households abstract this study proposes a reverse pareto model to describe the power law behavior for the lower tail data of income distribution and illustrates an application on malaysian and italian household income data a robust method based on probability integral transform statistic is used for estimating the shape parameter of the reverse pareto model to allow for the existence of outlying observations in the lower tail data besides that the optimal threshold of reverse pareto is determined by using kolmogorov smirnov statistic it is found that the fitted reverse pareto adequately describes the lower tail data of both datasets suggesting that the power law behavior is obeyed in addition the estimated optimal threshold of reverse pareto model can be utilized as an alternative measure for the relative poverty line based on the reverse pareto model the lorenz curve gini and theil coefficients are determined and it is found that low income inequality is observed for the period of the study the fitted lorenz curve shows that nearly 80 of the total household income is owned by the bottom 80 whereas the remaining total household income is owned by the top 20 finally comparison of the reverse pareto model with some alternative distributions such as shifted reverse exponential shifted reverse stretched exponential and shifted reverse lognormal in terms of model fitting for the lower tail data is also conducted the results show that the reverse pareto model outperform all the other models

parameterized computational complexity of control problems in voting systems voting systems are common tools in a variety of areas this paper studies parameterized computational complexity of control of plurality condorcet and approval voting systems respectively the types of controls considered include adding or deleting candidates or voters under constructive or destructive setting we obtain the following results 1 constructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 2 destructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 3 constructive control by adding voters in condorcet voting is w 1 hard with respect to the parameter number of added voters 4 constructive control by deleting voters in condorcet voting is w 1 hard with respect to the parameter number of deleted voters 5 constructive control by adding voters in approval voting is w 1 hard with respect to the parameter number of added voters and 6 constructive control by deleting voters in approval voting is w 2 hard with respect to the parameter number of deleted voters

geometrically concave univariate distributions in this paper our aim is to show that if a probability density function is geometrically concave convex then the corresponding cumulative distribution function and the survival function are geometrically concave convex too under some assumptions the proofs are based on the so called monotone form of l hospital s rule and permit us to extend our results to the case of the concavity convexity with respect to holder means to illustrate the applications of the main results we discuss in details the geometrical concavity of the probability density function cumulative distribution function and survival function of some common continuous univariate distributions moreover at the end of the paper we present a simple alternative proof to schweizer s problem related to the mulholland s generalization of minkowski s inequality

on the evaluation of election outcomes under uncertainty we investigate the extent to which it is possible to compute the probability of a particular candidate winning an election given imperfect information about the preferences of the electorate we assume that for each voter we have a probability distribution over a set of preference orderings thus for each voter we have a number of possible preference orderings we do not know which of these orderings actually represents the preferences of the voter but for each ordering we know the probability that it does for the case where the number of candidates is a constant we are able to give a polynomial time algorithm to compute the probability that a given candidate will win we present experimental results obtained with an implementation of the algorithm illustrating how the email protected s performance in practice is better than its predicted theoretical bound however when the number of candidates is not bounded we prove that the problem becomes p hard for the plurality k approval borda copeland and bucklin voting rules we further show that even evaluating if a candidate has any chance of winning is np complete for the plurality voting rule in the case where voters may have different weights with unweighted voters we give a polynomial algorithm for plurality and show that the problem is hard for many other voting rules finally we give a monte carlo approximation algorithm for computing the probability of a candidate winning in any settings with an error that is as small as desired

the learnability of voting rules scoring rules and voting trees are two broad and concisely representable classes of voting rules scoring rules award points to alternatives according to their position in the preferences of the voters while voting trees are iterative procedures that select an alternative based on pairwise comparisons in this paper we investigate the pac learnability of these classes of rules we demonstrate that the class of scoring rules as functions from preferences into alternatives is efficiently learnable in the pac model with respect to voting trees while in general a learning algorithm would require an exponential number of samples we show that if the number of leaves is polynomial in the size of the set of alternatives then a polynomial training set suffices we apply these results in an emerging theory automated design of voting rules by learning

complex symmetric operators and applications ii a bounded linear operator t on a complex hilbert space h is called complex symmetric if t ct c where c is a conjugation an isometric antilinear involution of h we prove that t cj t where j is an auxiliary conjugation commuting with t t t we consider numerous examples including the poincare neumann singular integral bounded operator and the jordan model operator compressed shift the decomposition t cj t also extends to the class of unbounded c selfadjoint operators originally introduced by glazman in this context it provides a method for estimating the norms of the resolvents of certain unbounded operators

universality in the tail of musical note rank distribution abstract although power laws have been used to fit rank distributions in many different contexts they usually fail at the tails languages as sequences of symbols have been a popular subject for ranking distributions and for this purpose music can be treated as such here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution which arises in the ranking of multiplicative stochastic processes the parameters a and b are obtained for classical jazz and rock music revealing interesting features specially we have obtained a clear trend in the values of the parameters for major and minor tonal modes finally we discuss the distribution of notes for each octave and its connection with the ranking of the notes

an ordered family of lorenz curves abstract a general method for building parametric functional families of lorenz curves generated from an initial lorenz curve which satisfies some regularity conditions is presented it is shown that these families can be ordered in a manner which leads to a hierarchy of lorenz curves the method starts from a generating lorenz curve l 0 p and builds the family by increasing the number of parameters which can be easily interpreted in terms of the elasticities of l 0 p the method is applied to a family we term the pareto family since they use the pareto lorenz curves as their generating curves the family is shown to contain an important number of classical lorenz curves used in the existing literature several properties of this family are analyzed these include the population function inequality measures and lorenz orderings a general method for the estimation of these family is given and applied to the pareto family finally an application is presented for data from various countries the results are very robust across data sources the pareto models fit very well in a number of applications

complex symmetric partial isometries an operator t b h is complex symmetric if there exists a conjugate linear isometric involution c h h so that t ct c we provide a concrete description of all complex symmetric partial isometries in particular we prove that any partial isometry on a hilbert space of dimension 4 is complex symmetric

a generalization of the beta distribution with applications abstract this paper introduces a five parameter beta distribution gb which nests the generalized beta and gamma distributions and includes more than thirty distributions as limiting or special cases the generalized beta leads to an exponential generalized beta egb distribution which includes generalized forms of the logistics exponential gompertz and gumbell distributions and the normal as special cases the egb family of distributiosn provides the basis for partially adaptive estimation of econometric models with possibly skewed and leptokurtic error distributions applications of the models to investigating the distribution of income stock returns and in regression analysis are considered

control of condorcet voting complexity and a relation algebraic approach abstract we study the constructive variant of the control problem for condorcet voting where control is done by deleting voters we prove that this problem remains np hard if instead of condorcet winners the alternatives in the uncovered set win furthermore we present a relation algebraic model of condorcet voting and relation algebraic specifications of the dominance relation and the solutions of the control problem all our relation algebraic specifications immediately can be translated into the programming language of the obdd based computer system relview our approach is very flexible and especially appropriate for prototyping and experimentation and as such very instructive for educational purposes it can easily be applied to other voting rules and control problems

parameterized complexity of candidate control in elections and related digraph problems there are different ways for an external agent to influence the outcome of an election we concentrate on control by adding or deleting candidates our main focus is to investigate the parameterized complexity of various control problems for different voting systems to this end we introduce natural digraph problems that may be of independent interest they help in determining the parameterized complexity of control for different voting systems including llull copeland and plurality voting devising several parameterized reductions we provide an overview of the parameterized complexity of the digraph and control problems with respect to natural parameters such as adding deleting only a bounded number of candidates or having only few voters

parameterized computational complexity of dodgson and young elections abstract we show that the two np complete problems of dodgson score and young score have differing computational complexities when the winner is close to being a condorcet winner on the one hand we present an efficient fixed parameter algorithm for determining a condorcet winner in dodgson elections by a minimum number of switches in the votes on the other hand we prove that the corresponding problem for young elections where one has to delete votes instead of performing switches is w 2 complete in addition we study dodgson elections that allow ties between the candidates and give fixed parameter tractability as well as w 2 completeness results depending on the cost model for switching ties

multiply broken power law densities as survival functions an alternative to pareto and lognormal fits abstract survival functions defined by multiply broken power law densities are introduced to model firm size data sets of four historical censuses reported in montebruno et al physica a 523 2019 858 the survival functions complementary cumulative distributions are obtained by least squares regression the probability distributions are inferred from the analytic survival functions the mean firm growth the growth volatility and entropy evolution are calculated over a 30 year period covered by the censuses a representation of the survival functions as single power law density with varying exponent depending on firm size is derived index functions i e rescaled logarithmic derivatives of survival functions are used to demonstrate that neither pareto power laws nor lognormal densities can accurately reproduce the tails of the firm size distributions like the survival functions the empirical rank size relations of the four censuses also admit representation by broken power law densities a generating mechanism for empirically obtained broken power law densities based on the fokker planck equation is proposed as well

ranking chain sum orders ranking information is an important topic in information sciences internet searching voting systems and sports in the full information approach a ranking is a total order of the candidates we compare two rankings by pairwise comparisons under the nearest neighbor kendall tau distance and study the distance and rank aggregation problems in many settings the information is incomplete and a ranking is given by a partial order a bucket order is obtained if a ranking allows ties and treats tied candidates as equivalent then the distance and rank aggregation problems can be solved efficiently in almost linear time a chain sum order is complementary to a bucket order and consists of a set of disjoint total orders its width and height is the number and the maximum size of the total orders respectively we show that the distance and rank aggregation problems of a total order and a chain sum order of bounded width or of height at most two can be solved in polynomial time and are np complete for a total and a chain sum order of height at least 12 both problems remain np complete for a total and a heap order which is the partial order obtained from a single elimination tournament in sports however the problems are fixed parameter tractable with respect to the distance and the ulam distance but are fixed parameter intractable with respect to the order dimension

pareto tails and lognormal body of us cities size distribution abstract we consider a distribution which consists of lower tail pareto lognormal body and upper tail pareto to estimate the size distribution of all us cities this distribution fits the data more accurately than a distribution that comprises of only lognormal and the upper tail pareto

on complex symmetric toeplitz operators abstract in this paper we give a characterization of a complex symmetric toeplitz operator t on the hardy space h 2 moreover if t is a complex symmetric toeplitz operator we provide a necessary and sufficient condition for t to be normal finally we investigate these t with finite symbols

the size distributions of all indian cities abstract we apply five distributions lognormal double pareto lognormal lognormal upper tail pareto pareto tails lognormal and pareto tails lognormal with differentiability restrictions to estimate the size distribution of all indian cities since india contains numerous small cities it is important to explicitly model the lower tail behavior for studying the distribution of all indian cities our results rigorously confirm using both graphical and formal statistical tests that among these five distributions pareto tails lognormal is a better suited parametrization of the indian city size data verifying that the indian city size distribution exhibits a strong reverse pareto in the lower tail lognormal in the mid range body and pareto in the upper tail

on the closure of the complex symmetric operators compact operators and weighted shifts abstract we study the closure cso of the set cso of all complex symmetric operators on a separable infinite dimensional complex hilbert space among other things we prove that every compact operator in cso is complex symmetric using a construction of kakutani as motivation we also describe many properties of weighted shifts in cso cso in particular we show that weighted shifts which demonstrate a type of approximate self similarity belong to cso cso as a byproduct of our treatment of weighted shifts we explain several ways in which our result on compact operators is optimal

kolmogorov characterizations of complexity classes abstract this paper completely characterizes the k p levels of the polynomial hierarchy in terms of kolmogorov complexity from the characterization it follows that the k p and k p levels of the polynomial hierarchy are equal if and only if every k p language is accepted by some k p machine whose pronouncements query answers are kolmogorov simple analogous results are obtained for the exponential hierarchy

q exponential distribution in urban agglomeration usually the studies of distributions of city populations have been reduced to power laws in such analyses a common practice is to consider cities with more than one hundred thousand inhabitants here we argue that the distribution of cities for all ranges of populations can be well described by using a q exponential distribution this function which reproduces the zipf mandelbrot law is related to the generalized nonextensive statistical mechanics and satisfies an anomalous decay equation

exact algorithms for weighted and unweighted borda manipulation problems we derive exact combinatorial algorithms for both weighed and unweighted borda manipulation problems we derive an fpt algorithm for the unweighted borda manipulation problem with respect to the number of candidates we prove that borda manipulation with two manipulators is polynomial time solvable in single peaked elections we propose o m 2 m t 1 time and o t m 1 t t 1 m time algorithms for the weighted and the unweighted borda manipulation problems respectively where t is the number of manipulators and m is the number of candidates in particular for t 2 our algorithm for the unweighted case runs in o 3 m time affirmatively resolving one open problem posed by betzler et al 2 as a byproduct of our results we show that the unweighted borda manipulation problem admits an algorithm with running time o 2 9 m 2 log m based on an integer linear programming technique finally we prove that the unweighted borda manipulation problem is polynomial time solvable in single peaked elections in contrast to the np hardness in the general case

on the complexity of unique solutions on montre que le probleme de savoir si un cas du probleme du commis voyageur a une solution uniquement optimale est complet pour 2 p

a robust and efficient estimator for the tail index of inverse pareto distribution abstract based on the probability integral transform statistic finkelstein et al 2006 have proposed a robust estimator for the shape parameter of pareto distribution in this paper based on the same method a robust and efficient estimator for the shape parameter of the inverse pareto distribution is developed assuming that the threshold parameter is known to study the robustness properties of this new estimator we derive the asymptotic variance breakdown point and gross error sensitivity however since the inverse pareto distribution is literally an inverse of the pareto distribution some derivations and proofs for the probability integral transform statistic estimator presented in this paper are found closely related to those provided by finkelstein et al 2006 the performance of this new estimator and the maximum likelihood estimator is assessed through a simulation study for the application an inverse pareto distribution is fitted to the lower tail data of malaysian household incomes for the year of 2014 involving the proposed estimator in order to allow for the presence of outliers based on the inverse pareto model the parametric lorenz curve is fitted and the gini coefficient is estimated to measure the income inequality of poor households in malaysia