independent valued minimax pathological or beneficial minimax search which is used by most game playing programs is considered pathological when deeper searches produce worse evaluations than shallower ones this phenomenon was first observed in theoretical analyses under seemingly reasonable conditions it was most commonly explained by the lack of dependence between nearby positions in the analyses if nearby positions have similar values as is typically the case in real games the pathology no longer occurs in this paper we show that the pathology can be eliminated even without position value dependence by assigning enough different values to the positions and modeling the heuristic error as normally distributed noise that is independent of the depth in the game tree this leads to the conclusion that minimax is less prone to the pathology than was previously thought and indicates the importance of the number of different position values

information processing in complex networks graph entropy and information functionals this paper introduces a general framework for defining the entropy of a graph our definition is based on a local information graph and on information functionals derived from the topological structure of a given graph more precisely an information functional quantifies structural information of a graph based on a derived probability distribution such a probability distribution leads directly to an entropy of a graph then the structural information content of a graph will be is interpreted and defined as the derived graph entropy another major contribution of this paper is the investigation of relationships between graph entropies in addition to this we provide numerical results demonstrating not only the feasibility of our method which has polynomial time complexity but also its usefulness with regard to practical applications aiming to an understanding of information processing in complex networks

geometrically accurate efficient and flexible quadrature techniques for the tetrahedral finite cell method abstract we illustrate the importance of geometrically accurate volume quadrature for obtaining optimal accuracy with non boundary fitted finite element discretizations when the problem domain is defined by sharp boundaries we consider the tetrahedral finite cell method tetfcm and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher order geometric parametrizations of cut tetrahedral elements the element wise parametrization procedure relies on the identification of the intersection topology and a series of higher order mappings based on lagrange polynomials we demonstrate with several 3d examples that geometrically faithful local parametrization ensures optimal accuracy while significantly reducing the number of quadrature points with respect to recursive subdivision on the other hand we highlight the strength of subdivision quadrature in the context of a patient specific workflow for the simulation based performance analysis of coupled bone implant configurations in particular we show that accuracy flexibility and computational efficiency of the tetfcm critically depend on flexibly applying the two different quadrature variants for fuzzy imaging data and sharp boundary representations respectively

prediction of the mechanical response of the femur with uncertain elastic properties abstract a mandatory requirement for any reliable prediction of the mechanical response of bones based on quantitative computer tomography is an accurate relationship between material properties usually young s modulus e and bone density many such e relationships are available based on different experiments on femur specimens with a large spread due to uncertainties the first goal of this study is to pool and analyze the relevant available experimental data and develop a stochastic e relationship this analysis highlights that there is no experimental data available to cover the entire density range of the human femur and that some popular e relationships are based on data that contains extreme scatter while others are based on a very limited amount of information the second goal is to use the newly developed stochastic e relationship in high order finite element analyses feas for the computation of strains and displacements in two human proximal femurs mimicking in vitro experiments when compared with the experimental observations the fea predictions using the median of the stochastic e relationship follow the underlying distribution of the stochastic e relationship thus most deviations of the fea predictions from experimental observations can possibly be explained by uncertain elastic properties of the femur

autonomous fes afe a stride toward personalized medicine abstract finite element analysis fea introduced more than half a century ago requires a qualified analyst to generate the necessary input data verify the output and post process the analysis results for a meaningful conclusion the required expertise and labor efforts have precluded the use of fea in daily medical practice by orthopedic surgeons for example patient specific analyses of the mechanical response of human bones may have a tremendous impact in clinical practice should they be easily accessible by orthopedic surgeons recent scientific advancements such as low dose ct scans machine learning and high order fea which facilitates an inherent methodology for assessing numerical accuracy allow a fully autonomous process for assessing bone strength and fracture risk this autonomous process that we shall refer to here as autonomous finite element afe analysis introduces a paradigm shift in the use of fea we shall describe herein a novel process that utilizes afe to produce a patient specific assessment of bone strength the process consists of an automatic segmentation of femurs from ct scans by convolution neural networks an automatic mesh generation and application of boundary conditions based on anatomical points a high order fe analysis with numerical error control and finally an automatic report with a clear assessment of bone fracture risk one specific application of afe is the determination of the risk of fracture for patients with tumors of the femur and whether a prophylactic surgery is needed to the best of our knowledge this is the first ce accredited afe application being used by orthopedic surgeons in clinical practice

the effect of mobility on minimaxing of game trees with random leaf values abstract random minimaxing introduced by beal and smith icca j 17 1994 3 9 is the process of using a random static evaluation function for scoring the leaf nodes of a full width game tree and then computing the best move using the standard minimax procedure the experiments carried out by beal and smith using random minimaxing in chess showed that the strength of play increases as the depth of the lookahead is increased we investigate random minimaxing from a combinatorial point of view in an attempt to gain a better understanding of the utility of the minimax procedure and a theoretical justification for the results of beal and smith s experiments the concept of domination is central to our theory intuitively one move by white dominates another move when choosing the former move would give less choice for black when it is black s turn to move and subsequently more choice for white when it is white s turn to move we view domination as a measure of mobility and show that when one move dominates another then its probability of being chosen is higher we then investigate when the probability of a good move relative to the probability of a bad move increases with the depth of search we show that there exist situations when increased depth of search is beneficial but that this is not always the case under the assumption that each move is either good or bad we are able to state sufficient conditions to ensure that increasing the depth of search increases the strength of play of random minimaxing if the semantics of the game under consideration match these assumptions then it is fair to say that random minimaxing appears to follow a reasonably intelligent strategy in practice domination does not always occur so it remains an open problem to find a more general measure of mobility in the absence of domination

partial order bounding a new approach to evaluation in game tree search abstract in computer game playing the established method for constructing an evaluation function uses a scalar value computed as a weighted sum of features this paper advocates the use of partial order evaluation and describes an efficient new search method called partial order bounding pob previous tree search algorithms using a partial order evaluation have attempted to propagate partially ordered values through the search tree which leads to many problems in practice such as the complexity of backing up sets of incomparable evaluations pob compares partially ordered values only in the leaves of a game tree and backs up boolean values through the tree a closely related new algorithm linear extension partial order bounding le pob uses a standard scalar alpha beta search with values from a suitably chosen linear extension of the partial order evaluation as an application the effectiveness of partial order evaluation is shown in the case of modeling capturing races called semeai in the game of go

offdiagonal complexity a computationally quick complexity measure for graphs and networks abstract a vast variety of biological social and economical networks shows topologies drastically differing from random graphs yet the quantitative characterization remains unsatisfactory from a conceptual point of view motivated from the discussion of small scale free networks a biased link distribution entropy is defined which takes an extremum for a power law distribution this approach is extended to the node node link cross distribution whose nondiagonal elements characterize the graph structure beyond link distribution cluster coefficient and average path length from here a simple and computationally cheap complexity measure can be defined this offdiagonal complexity odc is proposed as a novel measure to characterize the complexity of an undirected graph or network while both for regular lattices and fully connected networks odc is zero it takes a moderately low value for a random graph and shows high values for apparently complex structures as scale free networks and hierarchical trees the odc approach is applied to the helicobacter pylori protein interaction network and randomly rewired surrogates

weakly enforced essential boundary conditions for nurbs embedded and trimmed nurbs geometries on the basis of the finite cell method summary enforcing essential boundary conditions plays a central role in immersed boundary methods nitsche s idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints we formulate an extension of nitsche s method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the b spline and non uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries furthermore we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3d geometries with several benchmark problems we demonstrate the overall good convergence behavior of the proposed method and its good accuracy we provide extensive studies on the stability of the method its influence parameters and numerical properties and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two a newly composed boundary integration concept further enhances the modeling process and allows a flexible discretization independent introduction of boundary conditions finally we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non uniform rational basis spline geometries copyright 2013 john wiley sons ltd

sharp lower bounds on the narumi katayama index of graph operations abstract the narumi katayama index nk g of a simple graph g is equal to the product of the degrees of the vertices of g in this paper we present sharp lower bounds on the narumi katayama index of several graph operations such as union join suspension rooted product cluster corona product direct product cartesian product strong product generalized hierarchical product composition disjunctive product and symmetric difference in terms of the narumi katayama indices and the orders of their components using these results the narumi katayama index of several classes of graphs will be computed

a hybrid binomial inverse hypergeometric probability distribution theory and applications abstract in this paper we define a novel probability distribution triggered by a due date setting problem from a multi item single level production system as a result we derive a recurrence relation for the underlying distribution function and finally we also infer the novel discrete distribution function we underpin our analytical findings by numerical results when computing the distribution function the expected value as well as the variance in order to apply and translate our apparatus to other problems we come up with an application when determining due dates for a production system with sequence dependent setup costs

real time heuristic search abstract we apply the two player game assumptions of limited search horizon and commitment to moves in constant time to single agent heuristic search problems we present a variation of minimax lookahead search and an analog to alpha beta pruning that significantly improves the efficiency of the algorithm paradoxically the search horizon reachable with this algorithm increases with increasing branching factor in addition we present a new algorithm called real time a for interleaving planning and execution we prove that the algorithm makes locally optimal decisions and is guaranteed to find a solution we also present a learning version of this algorithm that improves its performance over successive problem solving trials by learning more accurate heuristic values and prove that the learned values converge to their exact values along every optimal path these algorithms effectively solve significantly larger problems than have previously been solvable using heuristic evaluation functions

an incremental negamax algorithm abstract in certain models of game trees with erroneous evaluation functions the minimax algorithm does not reduce errors even under favourable assumptions about the size of the errors and the frequency of their occurrence we present an incremental negamax algorithm which uses estimates of all nodes in the tree rather than only those of the leaves to determine the root value under the assumption of independently occurring and sufficiently small errors the algorithm is shown to have exponentially reduced error probabilities with respect to the height of the tree

femoral strength is better predicted by finite element models than qct and dxa clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in vivo were available a group of 51 human femurs age range 21 93 23 females 28 males were evaluated for bone density and geometry using quantitative computed tomography qct and dual energy x ray absorptiometry dxa regional bone density and dimensions obtained from qct and dxa were used to develop statistical models to predict femoral strength ex vivo the qct data also formed the basis of a three dimensional finite element fe models to predict structural stiffness the femurs were separated into two groups a model training set n 25 was used to develop statistical models to predict ultimate load and a test set n 26 was used to validate these models the main goal of this study was to test the ability of dxa qct and fe techniques to predict fracture load non invasively in a simple load configuration which produces predominantly femoral neck fractures the load configuration simulated the single stance phase portion of normal gait in 87 of the specimens clinical appearing sub capital fractures were produced the training test study design provided a tool to validate that the predictive models were reliable when used on specimens with unknown strength characteristics the fe method explained at least 20 more of the variance in strength than the dxa models planned refinements of the fe technique are expected to further improve these results three dimensional fe models are a promising method for predicting fracture load and may be useful in monitoring strength changes in vivo

the multi player version of minimax displays game tree pathology abstract it is widely believed that by searching deeper in the game tree the decision maker is more likely to make a better decision dana nau and others have discovered pathology theorems that show the opposite searching deeper in the game tree causes the quality of the ultimate decision to become worse not better the models for these theorems assume that the search procedure is minimax and the games are two player zero sum this report extends nau s pathology theorem to multi player game trees searched with maxn the multi player version of minimax thus two player zero sum game trees and multi player game trees are shown to have an important feature in common

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

best first minimax search we describe a very simple selective search algorithm for two player games called best first minimax it always expands next the node at the end of the expected line of play which determines the minimax value of the root it uses the same information as alpha beta minimax and takes roughly the same time per node generation we present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth but at significant time cost our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move pruning subtrees below moves not chosen by either player we also show how to efficiently generate a class of incremental random game trees on uniform random game trees best first minimax outperforms alpha beta when both algorithms are given the same amount of computation on random trees with random branching factors best first outperforms alpha beta for shallow depths but eventually loses at greater depths we obtain similar results in the game of othello finally we present a hybrid best first extension algorithm that combines alpha beta with best first minimax and performs significantly better than alpha beta in both domains even at greater depths in othello it beats alpha beta in two out of three games

the tetrahedral finite cell method higher order immersogeometric analysis on adaptive non boundary fitted meshes the finite cell method fcm is an immersed domain finite element method that combines higher order non boundary fitted meshes weak enforcement of dirichlet boundary conditions and adaptive quadrature based on recursive subdivision due to its ability to improve the geometric resolution of intersected elements it can be characterized as an immersogeometric method in this paper we extend the fcm so far only used with cartesian hexahedral elements to higher order non boundary fitted tetrahedral meshes based on a reformulation of the octree based subdivision algorithm for tetrahedral elements we show that the resulting tetfcm scheme is fully accurate in an immersogeometric sense that is the solution fields achieve optimal and exponential rates of convergence for h and p refinement if the immersed geometry is resolved with sufficient accuracy tetfcm can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase field fracture analysis of a human femur bone

benefits of using multivalued functions for minimaxing abstract minimaxing has been very successful in game playing practice although a complete explanation of why it has been that successful has not yet been given in particular it has not been shown why it should be useful as it is in practice to use multivalued evaluation functions such functions have many distinct values as their result and can discriminate between positions according to the heuristic knowledge represented in these values in this paper we modify a basic pathological model by adding two assumptions regarding multivalued evaluation functions these assumptions non uniformity of error distribution and dependency of heuristic values directly relate to the properties of multivalued evaluation functions as used in practice simulation studies of our multivalued model have exhibited sharp error reductions for deeper searches using minimaxing this behavior corresponds to observations in practice the error reductions are primarily due to the improved evaluation quality as search depth increases this phenomenon of lower probability of static evaluation errors with increasing search depth is revealed through our model although the same evaluation function is used at all levels of the tree and although its general error probability is independent of the depth essentially with increasing search depth the evaluation function is more frequently used on such positions which can be more reliably evaluated by a multivalued function with the assumed properties this effect together with the ability to discriminate between positions of different goodness leads to the benefits of using multivalued evaluation functions of appropriate granularity for minimaxing

validation of subject specific automated p fe analysis of the proximal femur abstract background the use of subject specific finite element fe models in clinical practice requires a high level of automation and validation in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 a novel method for generating high order finite element p fe models from ct scans was presented and validated by experimental observations on two fresh frozen femurs harvested from a 30 year old male and 21 year old female herein we substantiate the validation process by enlarging the experimental database 54 year old female femur improving the method and examine its robustness under different ct scan conditions approach a fresh frozen femur of a 54 year old female was scanned under two different environments in air and immersed in water dry and wet ct thereafter the proximal femur was quasi statically loaded in vitro by a 1000 n load the two qct scans were manipulated to generate p fe models that mimic the experimental conditions we compared p fe displacements and strains of the wet ct model to the dry ct model and to the experimental results in addition the material assignment strategy was reinvestigated the inhomogeneous young s modulus was represented in the fe model using two different methods directly extracted from the ct data and using continuous spatial functions as in yosibash et al 2007a reliable simulations of the human proximal femur by high order finite element analysis validated by experimental observations j biomechanics 40 3688 3699 results excellent agreement between dry and wet fe models was found for both displacements and strains i e the method is insensitive to ct conditions and may be used in vivo good agreement was also found between fe results and experimental observations the spatial functions representing young s modulus are local and do not influence strains and displacements prediction finally the p fe results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer aided decision making

a history of graph entropy measures this survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures setting the scene with a review of classical measures for determining the structural information content of graphs we discuss graph entropy measures which play an important role in a variety of problem areas including biology chemistry and sociology in addition we examine relationships between selected entropy measures illustrating differences quantitatively with concrete examples

accuracy of finite element predictions in sideways load configurations for the proximal human femur abstract in undetermined subject specific finite element models have been used to predict stress state and fracture risk in individual patients while many studies analysed quasi axial loading configurations only few works simulated sideways load configurations such as those arising in a fall the majority among these latter directly predicted bone strength without assessing elastic strain prediction accuracy the aim of the present work was to evaluate if a subject specific finite element modelling technique from ct data that accurately predicted strains in quasi axial loading configurations is suitable to accurately predict strains also when applying low magnitude loads in sideways configurations to this aim a combined numerical experimental study was performed to compare finite element predicted strains with strain gauge measurements from three cadaver proximal femurs instrumented with sixteen strain rosettes and tested non destructively under twelve loading configurations spanning a wide cone 0 30 for both adduction and internal rotation angles of sideways fall scenarios the results of the present study evidenced a satisfactory agreement between experimentally measured and predicted strains r2 greater than 0 9 rmse lower than 10 and displacements the achieved strain prediction accuracy is comparable to those obtained in state of the art studies in quasi axial loading configurations still the presence of the highest strain prediction errors around 30 in the lateral neck aspect would deserve attention in future studies targeting bone failure less

depth first iterative deepening an optimal admissible tree search abstract the complexities of various search algorithms are considered in terms of time space and cost of solution path it is known that breadth first search requires too much space and depth first search can use too much time and doesn t always find a cheapest path a depth first iterative deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches the algorithm has been used successfully in chess programs has been effectively combined with bi directional search and has been applied to best first heuristic search as well this heuristic depth first iterative deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the fifteen puzzle within practical resource limits

on the nature of pathology in game searching abstract game playing programs usually process the estimates attached to game positions through repeated minimax operations as if these were true terminal payoffs this process introduces a spurious noise which degrades the quality of the decisions and in the extreme case may cause a pathological phenomenon the deeper we search the worse we play using a probabilistic game model this paper examines the nature of this distortion quantifies its magnitude determines the conditions when its damage is curtailed and explains why search depth pathology the extreme manifestation of minimax distortion is rarely observed in common games

asymptotic properties of levelregular decision trees with randomly evaluated leaves game trees are an important model of decision making situations both in artificial intelligence and decision analysis the model most frequently investigated in theoretical research consists of a uniform tree of heighh and a constant branching factorb where the terminal positions are assigned the values of independent identically distributed random variables 1 3 10 our paper investigates two generalizations

comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop tower testing abstract current screening techniques based on areal bone mineral density abmd measurements are unable to identify the majority of people who sustain hip fractures biomechanical examination of such events may help determine what predisposes a hip to be susceptible to fracture recently drop tower simulations of in vitro sideways falls have allowed the study of the mechanical response of the proximal human femur at realistic impact speeds this technique has created an opportunity to validate explicit finite element fe models against dynamic test data this study compared the outcomes of 15 human femoral specimens fractured using a drop tower with complementary specimen specific explicit fe analysis correlation coefficient and root mean square error rmse were found to be moderate for whole bone stiffness comparison r2 0 3476 and 22 85 respectively no correlation was found between experimentally and computationally predicted peak force however energy absorption comparison produced moderate correlation and rmse r2 0 4781 and 29 14 respectively by comparing predicted strain maps to high speed video data we demonstrated the ability of the fe models to detect vulnerable portions of the bones based on our observations we conclude that there exists a need to extend the current apparent level material models for bone to cover higher strain rates than previously tested experimentally

when is it better not to look ahead in situations where one needs to make a sequence of decisions it is often believed that looking ahead will help produce better decisions however it was shown 30 years ago that there are pathological situations in which looking ahead is counterproductive two long standing open questions are a what combinations of factors have the biggest influence on whether lookahead pathology occurs and b whether it occurs in real world decision making this paper includes simulation results for several synthetic game tree models and experimental results for three well known board games two chess endgames kalah with some modifications to facilitate experimentation and the 8 puzzle the simulations show the interplay between lookahead pathology and several factors that affect it and the experiments confirm the trends predicted by the simulation models the experiments also show that lookahead pathology is more common than has been thought all three games contain situations where it occurs

the last player theorem game trees are an important model of decision making situations both in artificial intelligence and decision analysis but many of the properties of game trees are not well understood one of these properties is known as biasing when a minimax search is done to an odd search depth all moves tend to look good and when it is done to an even search depth all modes tend to look bad one explanation sometimes proposed for biasing is that whenever a player makes a move his position is strengthened and that the evaluation function used in the minimax search reflects this however the mathematical results in this paper suggest that biasing may instead be due to the errors made by the evaluation function

walk entropies in graphs abstract entropies based on walks in graphs and in their line graphs are defined they are based on the summation over diagonal and off diagonal elements of the exponential of the adjacency matrix known as the network communicability the walk entropies are strongly related to the walk regularity of graphs and line graphs they are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies a homogeneous weighting of the edges of the graph is used to simulate the effects of the temperature over the entropies defined in particular the walk entropy of graphs is non monotonic for regular but non walk regular graphs in contrast to non regular graphs

information theoretic measures of uhg graphs with low computational complexity we introduce a novel graph class we call universal hierarchical graphs uhg whose topology can be found numerously in problems representing e g temporal spacial or general process structures of systems for this graph class we show that we can naturally assign two probability distributions for nodes and for edges which lead us directly to the definition of the entropy and joint entropy and hence mutual information establishing an information theory for this graph class furthermore we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy also we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples

uncertainty quantification for personalized analyses of human proximal femurs computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads which affect the simulation results to quantify the influence we developed a probabilistic framework based on polynomial chaos pc that propagates stochastic input variables through any computational model we considered a stochastic e relationship and a stochastic hip contact force representing realistic variability of experimental data their influence on the prediction of principal strains 1 and 3 was quantified for one human proximal femur including sensitivity and reliability analysis large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck with coefficients of variation of 40 between 60 and 80 of the variance in 1 and 3 are attributable to the uncertainty in the e relationship while 10 are caused by the load magnitude and 5 30 by the load direction principal strain directions were unaffected by material and loading uncertainties the antero superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure however all were very small pf 0 001 in summary uncertainty quantification with pc has been demonstrated to efficiently and accurately describe the influence of very different stochastic inputs which increases the credibility and explanatory power of personalized analyses of human proximal femurs