new bounds on classical and quantum one way communication complexity in this paper we provide new bounds on classical and quantum distributional communication complexity in the two party one way model of communication in the classical one way model our bound extends the well known upper bound of kremer nisan and ron i kremer n nisan d ron on randomized one round communication complexity in proceedings of the 27th acm symposium on theory of computing stoc 1995 pp 596 605 to include non product distributions let email protected 0 1 2 be a constant we show that for a boolean function f xxy 0 1 and a non product distribution m on xxy d e 1 m f o i x y 1 vc f where d e 1 m f represents the one way distributional communication complexity of f with error at most e under m vc f represents the vapnik chervonenkis dimension of f and i x y represents the mutual information under m between the random inputs of the two parties for a non boolean function f xxy 1 k k 2 an integer we show a similar upper bound on d e 1 m f in terms of k i x y and the pseudo dimension of f deffk a generalization of the vc dimension for non boolean functions in the quantum one way model we provide a lower bound on the distributional communication complexity under product distributions of a function f in terms of the well studied complexity measure of f referred to as the rectangle bound or the corruption bound of f we show for a non boolean total function f xxy z and a product distribution m on xxy q e 3 8 1 m f email protected rec e 1 m f where q e 3 8 1 m f represents the quantum one way distributional communication complexity of f with error at most e 3 8 under m and rec e 1 m f represents the one way rectangle bound of f with error at most e under m similarly for a non boolean partial function f xxy email protected and a product distribution m on xxy we show q e 6 2 1 5 4 1 m f email protected rec e 1 m f

scale sensitive dimensions uniform convergence and learnability learnability in valiant s pac learning model has been shown to be strongly related to the existence of uniform laws of large numbers these laws define a distribution free convergence property of means to expectations uniformly over classes of random variables classes of real valued functions enjoying such a property are also known as uniform glivenko cantelli classes in this paper we prove through a generalization of sauer s lemma that may be interesting in its own right a new characterization of uniform glivenko cantelli classes our characterization yields dudley gine and zinn s previous characterization as a corollary furthermore it is the first based on a gine and zinn s previous characterization as a corollary furthermore it is the first based on a simple combinatorial quantity generalizing the vapnik chervonenkis dimension we apply this result to obtain the weakest combinatorial condition known to imply pac learnability in the statistical regression or agnostic framework furthermore we find a characterization of learnability in the probabilistic concept model solving an open problem posed by kearns and schapire these results show that the accuracy parameter plays a crucial role in determining the effective complexity of the learner s hypothesis class

the space complexity of recognizing well parenthesized expressions in the streaming model the index function revisited we show an p n t lower bound for the space required by any unidirectional constanterror randomized t pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well parenthesized this proves a conjecture due to magniez mathieu and nayak 2009 and rigorously establishes the peculiar power of bi directional streams over unidirectional ones observed in the algorithms they present the lower bound is obtained by analysing the information that is necessarily revealed by the players about their respective inputs in a two party communication protocol for a variant of the index function

quantum de finetti theorems under local measurements with applications quantum de finetti theorems are a useful tool in the study of correlations in quantum multipartite states in this paper we prove two new quantum de finetti theorems both showing that under tests formed by local measurements in each of the subsystems one can get an exponential improvement in the error dependence on the dimension of the subsystems we also obtain similar results for non signaling probability distributions we give several applications of the results to quantum complexity theory polynomial optimization and quantum information theory the proofs of the new quantum de finetti theorems are based on information theory in particular on the chain rule of mutual information the results constitute improvements and generalizations of a recent de finetti theorem due to brandao christandl and yard

studying the human brain anatomical network via diffusion weighted mri and graph theory our goal is to study the human brain anatomical network for this the anatomical connection probabilities acp between 90 cortical and subcortical brain gray matter areas are estimated from diffusion weighted magnetic resonance imaging dw mri techniques the acp between any two areas gives the probability that those areas are connected at least by a single nervous fiber then the brain is modeled as a non directed weighted graph with continuous arc weights given by the acp matrix based on this approach complex networks properties such as small world attributes efficiency degree distribution vulnerability betweenness centrality and motifs composition are studied the analysis was carried out for 20 right handed healthy subjects mean age 31 10 s d 7 43 according to the results all networks have small world and broad scale characteristics additionally human brain anatomical networks present bigger local efficiency and smaller global efficiency than the corresponding random networks in a vulnerability and betweenness centrality analysis the most indispensable and critical anatomical areas were identified putamens precuneus insulas superior parietals and superior frontals interestingly some areas have a negative vulnerability e g superior temporal poles pallidums supramarginals and hechls which suggest that even at the cost of losing in global anatomical efficiency these structures were maintained through the evolutionary processes due to their important functions finally symmetrical characteristic building blocks motifs of size 3 and 4 were calculated obtaining that motifs of size 4 are the expanded version of motif of size 3 these results are in agreement with previous anatomical studies in the cat and macaque cerebral cortex

how to construct random functions a constructive theory of randomness for functions based on computational complexity is developed and a pseudorandom function generator is presented this generator is a deterministic polynomial time algorithm that transforms pairs g r where g is any one way function and r is a random k bit string to polynomial time computable functions r 1 2 k 1 2 k these r s cannot be distinguished from random functions by any probabilistic polynomial time algorithm that asks and receives the value of a function at arguments of its choice the result has applications in cryptography random constructions and complexity theory

the learnability of quantum states traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n but using ideas from computational learning theory we show that one can do exponentially better in a statistical setting in particular to predict the outcomes of most measurements drawn from an arbitrary probability distribution one needs only a number of sample measurements that grows linearly with n this theorem has the conceptual implication that quantum states despite being exponentially long vectors are nevertheless reasonable in a learning theory sense the theorem also has two applications to quantum computing first a new simulation of quantum one way communication protocols and second the use of trusted classical advice to verify untrusted quantum advice

age related changes in modular organization of human brain functional networks graph theory allows us to quantify any complex system e g in social sciences biology or technology that can be abstractly described as a set of nodes and links here we derived human brain functional networks from fmri measurements of endogenous low frequency correlated oscillations in 90 cortical and subcortical regions for two groups of healthy young and older participants we investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks newman s modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra and inter modular connectivity both young and older brain networks demonstrated significantly non random modularity the young brain network was decomposed into 3 major modules central and posterior modules which comprised mainly nodes with few inter modular connections and a dorsal fronto cingulo parietal module which comprised mainly nodes with extensive inter modular connections the mean network in the older group also included posterior superior central and dorsal fronto striato thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced whereas the number of connector nodes in posterior and central modules was increased

quantum computing postselection and probabilistic polynomial time i study the class of problems efficiently solvable by a quantum computer given the ability to postselect on the outcomes of measurements i prove that this class coincides with a classical complexity class called pp or probabilistic polynomial time using this result i show that several simple changes to the axioms of quantum mechanics would let us solve pp complete problems efficiently the result also implies as an easy corollary a celebrated theorem of beigel reingold and spielman that pp is closed under intersection as well as a generalization of that theorem due to fortnow and reingold this illustrates that quantum computing can yield new and simpler proofs of major results about classical computation

the connectivity of functional cores reveals different degrees of segregation and integration in the brain at rest the principles of functional specialization and integration in the resting brain are implemented in a complex system of specialized networks that share some degree of interaction recent studies have identified wider functional modules compared to previously defined networks and reported a small world architecture of brain activity in which central nodes balance the pressure to evolve segregated pathways with the integration of local systems the accurate identification of such central nodes is crucial but might be challenging for several reasons e g inter subject variability and physiological pathological network plasticity and recent works reported partially inconsistent results concerning the properties of these cortical hubs here we applied a whole brain data driven approach to extract cortical functional cores and examined their connectivity from a resting state fmri experiment on healthy subjects two main statistically significant cores centered on the posterior cingulate cortex and the supplementary motor area were extracted and their functional connectivity maps thresholded at three statistical levels revealed the presence of two complex systems one system is consistent with the default mode network dmn and gradually connects to visual regions the other centered on motor regions and gradually connects to more sensory specific portions of cortex these two large scale networks eventually converged to regions belonging to the medial aspect of the dmn potentially allowing inter network interactions

test retest reliability of resting state connectivity network characteristics using fmri and graph theoretical measures characterizing the brain connectome using neuroimaging data and measures derived from graph theory emerged as a new approach that has been applied to brain maturation cognitive function and neuropsychiatric disorders for a broad application of this method especially for clinical populations and longitudinal studies the reliability of this approach and its robustness to confounding factors need to be explored here we investigated test retest reliability of graph metrics of functional networks derived from functional magnetic resonance imaging fmri recorded in 33 healthy subjects during rest we constructed undirected networks based on the anatomic automatic labeling aal atlas template and calculated several commonly used measures from the field of graph theory focusing on the influence of different strategies for confound correction for each subject method and session we computed the following graph metrics clustering coefficient characteristic path length local and global efficiency assortativity modularity hierarchy and the small worldness scalar reliability of each graph metric was assessed using the intraclass correlation coefficient icc overall iccs ranged from low to high 0 to 0 763 depending on the method and metric methodologically the use of a broader frequency band 0 008 0 15 hz yielded highest reliability indices mean icc 0 484 followed by the use of global regression mean icc 0 399 in general the second order metrics small worldness hierarchy assortativity studied here tended to be more robust than first order metrics in conclusion our study provides methodological recommendations which allow the computation of sufficiently robust markers of network organization using graph metrics derived from fmri data at rest

a general lower bound on the number of examples needed for learning abstract we prove a lower bound of 1 ln 1 vcdim c on the number of random examples required for distribution free learning of a concept class c where vcdim c is the vapnik chervonenkis dimension and and are the accuracy and confidence parameters this improves the previous best lower bound of 1 ln 1 vcdim c and comes close to the known general upper bound of o 1 ln 1 vcdim c ln 1 for consistent algorithms we show that for many interesting concept classes including k cnf and k dnf our bound is actually tight to within a constant factor

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

dense quantum coding and quantum finite automata we consider the possibility of encoding m classical bits into many fewer n quantum bits qubits so that an arbitrary bit from the original m bits can be recovered with good probability we show that nontrivial quantum codes exist that have no classical counterparts on the other hand we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding the proof is based on an entropy coalescence principle that is obtained by viewing holevo s theorem from a new perspective in the existing implementations of quantum computing qubits are a very expensive resource moreover it is difficult to reinitialize existing bits during the computation in particular reinitialization is impossible in nmr quantum computing which is perhaps the most advanced implementation of quantum computing at the moment this motivates the study of quantum computation with restricted memory and no reinitialization that is of quantum finite automata it was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata here we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata

constant depth circuits fourier transform and learnability in this paper boolean functions in 4c0 are studied using harmonic analysis on the cube the main result is that an aco boolean function has almost all of its power spectrum on the low order coefficients an important ingredient of the proof is hastad s switching lemma 8 this result implies several new properties of functions in 4c functions in ac have low average sensitivity they may be approximated well by a real polynomial of low degree and they cannot be pseudorandom function generators perhaps the most interesting application is an o n poiyiog n time algorithm for learning func tions in aco the algorithm observes the behavior of an ac function on o npo y og n randomly chosen inputs and derives a good approximation for the fourier transform of the function this approximation allows the algorithm to predict with high probability the value of the function on other randomly chosen inputs

testing product states quantum merlin arthur games and tensor optimization we give a test that can distinguish efficiently between product states of n quantum systems and states that are far from product if applied to a state whose maximum overlap with a product state is 1 e the test passes with probability 1 e regardless of n or the local dimensions of the individual systems the test uses two copies of we prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarizing channel a key application of the test is to quantum merlin arthur games with multiple merlins where we obtain several structural results that had been previously conjectured including the fact that efficient soundness amplification is possible and that two merlins can simulate many merlins qma k qma 2 for k 2 building on a previous result of aaronson et al this implies that there is an efficient quantum algorithm to verify 3 sat with constant soundness given two unentangled proofs of o n qubits we also show how qma 2 with log sized proofs is equivalent to a large number of problems some related to quantum information such as testing separability of mixed states as well as problems without any apparent connection to quantum mechanics such as computing injective tensor norms of 3 index tensors as a consequence we obtain many hardness of approximation results as well as potential algorithmic applications of methods for approximating qma 2 acceptance probabilities finally our test can also be used to construct an efficient test for determining whether a unitary operator is a tensor product which is a generalization of classical linearity testing

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

negative edges and soft thresholding in complex network analysis of resting state functional connectivity data complex network analyses of functional connectivity have consistently revealed non random modular small world scale free like behavior of hard thresholded networks constructed from the right tail of the similarity histogram in the present study we determined network properties resulting from edges constrained to specific ranges across the full correlation histogram in particular the left negative most tail and their dependence on the confound signal removal strategy employed in the absence of global signal correction left tail networks comprised predominantly long range connections associated with weak correlations and were characterized by substantially reduced modularity and clustering negative assortativity and 1 deconvolution of specific confound signals white matter csf and motion resulted in the most robust within subject reproducibility of global network parameters iccs 0 5 global signal removal altered the network topology in the left tail with the clustering coefficient and assortativity converging to zero networks constructed from the absolute value of the correlation coefficient were thus compromised following global signal removal since the different right tail and left tail topologies were mixed these findings informed the construction of soft thresholded networks replacing the hard thresholding or binarization operation with a continuous mapping of all correlation values to edge weights suppressing rather than removing weaker connections and avoiding issues related to network fragmentation a power law adjacency function with 12 yielded modular networks whose parameters agreed well with corresponding hard thresholded values that were reproducible in repeated sessions across many months and evidenced small world like and scale free like properties

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples