lower bounds for randomized k serverand motion planning algorithms in this paper the authors prove lower bounds on the competitive ratio of randomized algorithms for two on line problems the k server problem suggested by manasse mcgeoch and sleator competitive algorithms for on line problems j algorithms 11 1990 pp 208 230 and an on line motion planning problem due to papadimitriou and yannakakis shortest paths without a map lecture notes in comput sci 372 springer verlag new york 1989 pp 610 620 the authors prove against an oblivious adversary an omega log k lower bound on the competitive ratio of any randomized on line k server algorithm in any sufficiently large metric space an omega log log k lower bound on the competitive ratio of any randomized on line k server algorithm in any metric space with at least k 1 points and an omega log log n lower bound on the competitive ratio of any on line motion planning algorithm for a scene with n obstacles previously no superconstant lower bound on the competitive ratio of randomized on line algorithms was known for any of these problems

the theory of non linear elastic ship water interaction dynamics non linear mathematical models are developed to provide formulations of the equations of motion describing the dynamical interaction behaviour between an incompressible or compressible ideal fluid and a moving or fixed elastic or rigid structure the general theoretical approach is based on the fundamental equations of continuum mechanics the concept of hamilton s principle and suitably formulated variational principles the resultant mathematical model expressed in a fixed or a moving frame of reference allows the theoretical establishment of non linear problems associated with ship dynamics and offshore engineering through applications of the variational principles this is demonstrated by rigorously deriving the governing equations of motion for general non linear ship water interaction problems in particular the theory is applied to a rigid ship travelling in calm water or in waves a bottom fixed rigid rod or tower excited by an incident wave and a two dimensional elastic beam travelling in waves

competitive exploration of rectilinear polygons exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem typical for online problems is that decisions must be made based on past events without complete information about the future in our case the robots do not have complete information about the environment competitive analysis can be used to measure the performance of methods solving online problems the competitive ratio of such a method is the ratio between the method s performance and the performance of the best method having full knowledge of the future we prove constant competitive strategies and lower bounds for exploring a simple rectilinear polygon in the l1 metric

shape spectrum based view grouping and matching of 3d free form objects we address the problem of constructing view aspects of 3d free form objects for efficient matching during recognition we introduce a novel view representation based on shape spectrum features and propose a general and powerful technique for organizing multiple views of objects of complex shape and geometry into compact and homogeneous clusters our view grouping technique obviates the need for surface segmentation and edge detection experiments on 6 400 synthetically generated views of 20 free form objects and 100 real range images of 10 sculpted objects demonstrate the good performance of our shape spectrum based model view selection technique

on computing structural changes in evolving surfaces and their appearance as a surface undergoes a one parameter family of deformations its shape and its appearance change smoothly except at certain critical parameter values where abrupt structural changes occur this paper considers the case of surfaces defined as the zero set of smooth density functions undergoing a gaussian diffusion process and addresses the problem of computing the critical parameter values corresponding to structural changes in the parabolic curves of a surface and in its aspect graph an algorithm based on homotopy continuation and curve tracing is proposed in the case of polynomial density functions whose zero set is an algebraic surface it has been implemented and examples are presented

tree exploration with advice we study the amount of knowledge about the network that is required in order to efficiently solve a task concerning this network the impact of available information on the efficiency of solving network problems such as communication or exploration has been investigated before but assumptions concerned availability of particular items of information about the network such as the size the diameter or a map of the network in contrast our approach is quantitative we investigate the minimum number of bits of information bits of advice that has to be given to an algorithm in order to perform a task with given efficiency we illustrate this quantitative approach to available knowledge by the task of tree exploration a mobile entity robot has to traverse all edges of an unknown tree using as few edge traversals as possible the quality of an exploration algorithm a is measured by its competitive ratio i e by comparing its cost number of edge traversals to the length of the shortest path containing all edges of the tree depth first search has competitive ratio 2 and in the absence of any information about the tree no algorithm can beat this value we determine the minimum number of bits of advice that has to be given to an exploration algorithm in order to achieve competitive ratio strictly smaller than 2 our main result establishes an exact threshold number of bits of advice that turns out to be roughly loglogd where d is the diameter of the tree more precisely for any constant c we construct an exploration algorithm with competitive ratio smaller than 2 using at most loglogd c bits of advice and we show that every algorithm using loglogd g d bits of advice for any function g unbounded from above has competitive ratio at least 2

comments on efficiently computing and representing aspect graphs of polyhedral objects this correspondence is originated by the definition of aspect given in the above paper by gigus canny seidel ibid vol 13 no 6 1991 on the computation of aspect graphs of polyhedra simple examples are presented which show that the data stored according to this definition can be unsuitable for identifying an object or its attitude through a topological match a definition is suggested which does not incur the problems pointed out

a unified approach for the formulation of interaction problems by the boundary element method a unified formulation is presented based on boundary element method in a form suitable for performing the interaction analyses by substructure method for solid solid and soil structure problems the proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem such as unit displacement or load problem as required in conventional methods it eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions to explain the formulation it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input where both the inclusion and surrounding medium are treated as viscoelastic it is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation then the formulation is extended to other types of interaction problems a multi inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half space it is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis but also in the analysis involving diffraction of waves in a medium containing holes copyright 2005 john wiley sons ltd

online searching with turn cost we consider the problem of searching for an object on a line at an unknown distance opt from the original position of the searcher in the presence of a cost of d for each time the searcher changes direction this is a generalization of the well studied linear search problem we describe a strategy that is guaranteed to find the object at a cost of at most 9 opt 2d which has the optimal competitive ratio 9 with respect to opt plus the minimum corresponding additive term our argument for upper and lower bound uses an infinite linear program which we solve by experimental solution of an infinite series of approximating finite linear programs estimating the limits and solving the resulting recurrences for an explicit proof of optimality we feel that this technique is interesting in its own right and should help solve other searching problems in particular we consider the star search or cowpath problem with turn cost where the hidden object is placed on one of m rays emanating from the original position of the searcher for this problem we give a tight bound of 1 2mm m 1 m 1 opt m m m 1 m 1 1 d we also discuss tradeoffs between the corresponding coefficients and we consider randomized strategies on the line

learnability stability and uniform convergence the problem of characterizing learnability is the most basic question of statistical learning theory a fundamental and long standing answer at least for the case of supervised classification and regression is that learnability is equivalent to uniform convergence of the empirical risk to the population risk and that if a problem is learnable it is learnable via empirical risk minimization in this paper we consider the general learning setting introduced by vapnik which includes most statistical learning problems as special cases we show that in this setting there are non trivial learning problems where uniform convergence does not hold empirical risk minimization fails and yet they are learnable using alternative mechanisms instead of uniform convergence we identify stability as the key necessary and sufficient condition for learnability moreover we show that the conditions for learnability in the general setting are significantly more complex than in supervised classification and regression

a comparison of localized finite element formulations for two dimensional wave diffraction and radiation problems two of the most promising localized finite element methods are compared the boundary series element method in which a series of eigenfunctions is used to represent the far field solution and the boundary integral element method in which an integral equation is satisfied at the boundary between localized finite element and outer regions the methods are applied to water of arbitrary depth the theory of the two methods is summarized and typical numerical results are discussed consideration is given to the well known hydrodynamical reciprocal relations and to the phenomenon of irregular frequencies the relative merits of the two methods are established

an alternative proof for the equivalence of searcher and 2 searcher it was conjectured in 1992 that the 2 searcher who has two flashlights has the same searching capability as the searcher who has an omni directional light source park et al proved this conjecture affirmatively in 2001 but their proof is rather complicated and not easy to understand in this paper we present an alternative proof which we believe is conceptually more transparent and easier to understand for this purpose we introduce a tool called the 2 link visibility diagram that represents 2 link visibility which has other applications

a mixed finite element method for the dynamic analysis of coupled fluid solid interaction problems on the basis of a variational principle a mixed finite element approach is developed to describe the linear dynamics of coupled fluid structure interactions the variables of acceleration in the elastic solid and pressure in the fluid are adopted as the arguments of the variational principle these are chosen since they directly relate to many practical fluid structure interaction dynamic problems involving free surface disturbances e g a dam water system a fuel cell in an aircraft etc matrix equations describing the motions are presented and four methods of solution discussed each simplifying and approximating the matrix equations for easier application to solve various types of engineering problems this is demonstrated by analysing a selection of fluid structure interaction problems of practical interest the examples illustrate the general principle and application of the described functional approach without need to resort to more complex dynamic problems which can be analysed in a similar manner

structure of indicator function classes with finite vapnik chervonenkis dimensions the vapnik chervonenkis vc dimension is used to measure the complexity of a function class and plays an important role in a variety of fields including artificial neural networks and machine learning one major concern is the relationship between the vc dimension and inherent characteristics of the corresponding function class according to sauer s lemma if the vc dimension of an indicator function class f is equal to d the cardinality of the set fs1n will not be larger than d 0dcnd therefore there naturally arises a question about the vc dimension of an indicator function class what kinds of elements will be contained in the function class f if f has a finite vc dimension in this brief we answer the above question first we investigate the structure of the function class f when the cardinality of the set fs1n reaches the maximum value d 0dcnd based on the derived result we then figure out what kinds of elements will be contained in f if f has a finite vc dimension

piecemeal graph exploration by a mobile robot we study how a mobile robot can learn an unknown environment in a piecemeal manner the robot s goal is to learn a complete map of its environment while satisfying the constraint that it must return every so often to its starting position for refueling say the environment is modeled as an arbitrary undirected graph which is initially unknown to the robot we assume that the robot can distinguish vertices and edges that it has already explored we present a surprisingly efficient algorithm for piecemeal learning an unknown undirected graph g v e in which the robot explores every vertex and edge in the graph by traversing at most o e v1 o 1 edges this nearly linear algorithm improves on the best previous algorithm in which the robot traverses at most o e v2 edges we also give an application of piecemeal learning to the problem of searching a graph for a treasure

hybrid dimensionality reduction method based on support vector machine and independent component analysis this paper presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk supervised criterion and data independence unsupervised criterion classification accuracy is used as a metric to evaluate the performance of the method by minimizing the structural risk projection originated from the decision boundaries directly improves the classification performance from a supervised perspective from an unsupervised perspective projection can also be obtained based on maximum independence among features or attributes in data to indirectly achieve better classification accuracy over more intrinsic representation of the data orthogonality interrelates the two sets of projections such that minimum redundancy exists between the projections leading to more effective dimensionality reduction experimental results show that the proposed hybrid dimensionality reduction method that satisfies both criteria simultaneously provides higher classification performance especially for noisy data sets in relatively lower dimensional space than various existing methods

the localized finite element method and its application to the two dimensional sea keeping problem we study the various convergence properties of the localized finite element method which is devoted to the numerical solution of linear problems set in unbounded domains the problem under consideration is the so called sea keeping problem i e the determination of the motion of ships undergoing the action of an incident swell but in fact the method applies to numerous other problems copyright 1988 society for industrial and applied mathematics

rademacher penalties and structural risk minimization we suggest a penalty function to be used in various problems of structural risk minimization this penalty is data dependent and is based on the sup norm of the so called rademacher process indexed by the underlying class of functions sets the standard complexity penalties used in learning problems and based on the vc dimensions of the classes are conservative upper bounds in a probabilistic sense uniformly over the set of all underlying distributions for the penalty we suggest thus for a particular distribution of training examples one can expect better performance of learning algorithms with the data driven rademacher penalties we obtain oracle inequalities for the theoretical risk of estimators obtained by structural minimization of the empirical risk with rademacher penalties the inequalities imply some form of optimality of the empirical risk minimizers we also suggest an iterative approach to structural risk minimization with rademacher penalties in which the hierarchy of classes is not given in advance but is determined in the data driven iterative process of risk minimization we prove probabilistic oracle inequalities for the theoretical risk of the estimators based on this approach as well

computing occlusion free viewpoints this paper presents methods to compute the locus of all viewpoints from which features on known polyhedral objects can be viewed in their entirety without being occluded by anything in the environment convex and concave polyhedra with or without holes and the viewing model of perspective projection are employed in this work initially properties of the occlusion free and occluded loci of viewpoints are determined based on these properties two methods to construct these loci together with their complexity analysis are presented in the first method a boundary representation of the occlusion free locus is obtained in the second method the locus of occluded viewpoints is expressed in terms of a constructive solid geometry representation that consists of a union of component solids implementation results and comparison of the two methods are given

computing the aspect graph for line drawings of polyhedral objects an algorithm for computing the aspect graph for polyhedral objects is described the aspects graph is a representation of three dimensional objects by a set of two dimensional views the set of viewpoints on the gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same at the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes it is shown that for polyhedral objects there are two fundamental visual events 1 the projections of an edge and a vertex coincide and 2 the projections of three nonadjacent edges intersect at a point the geometry of the object is reflected in the locus of the accidental viewpoints the algorithm computes the partition together with a representative view for each region of the partition

the polygon exploration problem we present an on line strategy that enables a mobile robot with vision to explore an unknown simple polygon we prove that the resulting tour is less than 26 5 times as long as the shortest watchman tour that could be computed off line our analysis is doubly founded on a novel geometric structure called angle hull let d be a connected region inside a simple polygon p we define the angle hull of d cal ah d to be the set of all points in p that can see two points of d at a right angle we show that the perimeter of cal ah d cannot exceed in length the perimeter of d by more than a factor of 2 this upper bound is tight

how bad may learning curves be in this paper we motivate the need for estimating bounds on learning curves of average case learning algorithms when they perform the worst on training samples we then apply the method of reducing learning problems to hypothesis testing ones to investigate the learning curves of a so called ill disposed learning algorithm in terms of a system complexity the boolean interpolation dimension since the ill disposed algorithm behaves worse than ordinal ones and the boolean interpolation dimension is generally bounded by the number of system weights the results can apply to interpreting or to bounding the worst case learning curve in real learning situations this study leads to a new understanding of the worst case generalization in real learning situations which differs significantly from that in the uniform learnable setting via vapnik chervonenkis vc dimension analysis we illustrate the results with some numerical simulations

fast multigrid method for solving incompressible hydrodynamic problems with free surfaces we develop of a finite volume multigrid euler scheme for solving three dimensional fully nonlinear ship wave problems the flowfield and the a priori unknown free surface location are calculated by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow the evolution of the free surface boundary condition is linked to the evolution of the bulk flow via a novel iteration strategy that allows temporary leakage through the surface before the solution is converged the method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow a multigrid algorithm is used to accelerate convergence to a steady state

optimality and competitiveness of exploring polygons by mobile robots a mobile robot represented by a point moving along a polygonal line in the plane has to explore an unknown polygon and return to the starting point the robot has a sensing area which can be a circle or a square centered at the robot this area shifts while the robot moves inside the polygon and at each point of its trajectory the robot sees explores all points for which the segment between the robot and the point is contained in the polygon and in the sensing area we focus on two tasks exploring the entire polygon and exploring only its boundary we consider several scenarios both shapes of the sensing area and the manhattan and the euclidean metrics we focus on two quality benchmarks for exploration performance optimality the length of the trajectory of the robot is equal to that of the optimal robot knowing the polygon and competitiveness the length of the trajectory of the robot is at most a constant multiple of that of the optimal robot knowing the polygon most of our results concern rectilinear polygons we show that optimal exploration is possible in only one scenario that of exploring the boundary by a robot with square sensing area starting at the boundary and using the manhattan metric for this case we give an optimal exploration algorithm and in all other scenarios we prove impossibility of optimal exploration for competitiveness the situation is more optimistic we show a competitive exploration algorithm for rectilinear polygons whenever the sensing area is a square for both tasks regardless of the metric and of the starting point finally we show a competitive exploration algorithm for arbitrary convex polygons for both shapes of the sensing area regardless of the metric and of the starting point

hydrodynamic forces on submerged oscillating cylinders at forward speed the hydrodynamic problem of submerged oscillating cylinders at forward speed is analysed by linearized potential theory the numerical method used combines a finite element approximation of the velocity potential in a region surrounding the cylinder with a boundary integral equation representation of the outer region this method avoids the calculation of the second order derivatives of the steady potential due to forward speed which appear in the body surface condition for the unsteady potential due to the oscillation of the cylinder numerical results from the present method for test cases of a circular cylinder in an unbounded fluid and below a free surface are in excellent agreement with the analytical solutions further results for elliptic cylinders are provided and the influence of forward speed on the hydrodynamic force on a submerged cylinder is investigated

the global artificial boundary conditions for numerical simulations of the flow around a submerged body we consider the numerical approximations of the two dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface one vertical segment is introduced as the upstream artificial boundary and two vertical segments are introduced as the downstream artificial boundaries on the artificial boundaries a sequence of high order global artificial boundary conditions are given then the original problem is reduced to a problem defined on a finite computational domain which is equivalent to a variational problem after solving the variational problem by the finite element method we obtain the numerical approximation of the original problem the numerical examples show that the artificial boundary conditions given in this paper are very effective

computing exact aspect graphs of curved objects algebraic surfaces this article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface orthographic projection is assumed the algorithm is based on a catalog of visual events available from singularity theory it uses curve tracing cell decomposition homotopy continuation and ray tracing to construct the regions of the view sphere delineated by visual event curves the algorithm has been fully implemented and examples are presented

a fast iterative method to compute the flow around a submerged body the authors develop an efficient iterative method for computing steady linearized potential flow around a submerged body moving in a liquid of finite constant depth in this paper they restrict the presentation to the two dimensional problem but the method is readily generalizable to the three dimensional case i e the flow in a canal the problem is indefinite which makes the convergence of most iterative methods unstable to circumvent this difficulty the authors decompose the problem into two more easily solvable subproblems and form a schwarz type iteration to solve the original problem the first subproblem is definite and can therefore be solved by standard iterative methods the second subproblem is indefinite but has no body it is therefore easily and efficiently solvable by separation of variables the authors prove that the iteration converges for sufficiently small froude numbers in addition they present numerical results for a second order accurate discretization of the problem they demonstrate that the iterative method converges rapidly and that the convergences rate improves when the froude number decreases they also verify numerically that the convergence rate is essentially independent of the grid size 20 refs 6 figs 10 tabs

optimal graph exploration without good maps a robot has to visit all nodes and traverse all edges of an unknown undirected connected graph using as few edge traversals as possible the quality of an exploration algorithm a is measured by comparing its cost number of edge traversals to that of the optimal algorithm having full knowledge of the graph the ratio between these costs maximized over all starting nodes in the graph and over all graphs in a given class u is called the overhead of algorithm a for the class u of graphs we consider three scenarios providing the robot with varying amount of information the robot may either know nothing about the explored graph or have an unlabeled isomorphic copy of it an unanchored map or have such a copy with a marked starting node an anchored map for all of the above scenarios we construct natural exploration algorithms that have smallest or in one case close to smallest overhead while for the class of all graphs depth first search turns out to be an optimal algorithm for all scenarios the situation for trees is much different we show that under the scenario without any knowledge dfs is still optimal for trees but this is not the case if a map is available under the scenario with an unanchored map we show that optimal overhead is at least 3 but strictly below 2 and thus dfs is not optimal under the scenario with an anchored map we construct an optimal algorithm for trees and show that its overhead is 3 2 we also consider exploration of the class of lines simple paths in this case depth first search remains optimal for the scenario without any knowledge with overhead 2 under the scenario with an unanchored map we construct an optimal algorithm and show that its overhead is 3 finally under the scenario with an anchored map we construct an optimal algorithm and show that its overhead is 7 5 an important contribution of this paper is establishing lower bounds that prove optimality of these exploration algorithms

empirical measure of multiclass generalization performance the k winner machine case combining the k winner machine kwm model with empirical measurements of a classifier s vapnik chervonenkis vc dimension gives two major results first analytical derivations refine the theory that characterizes the generalization performances of binary classifiers second a straightforward extension of the theoretical framework yields bounds to the generalization error for multiclass problems

shortest paths without a map we study several versions of the shortest path problem when the map is not known in advanced but is specified dynamically we are seeking dynamic decision rules that optimize the worst case ratio of the distance covered to the length of the statically optimal path we describe optimal decision rules for two cases layered graphs of bounded width and two dimensional scenes with unit square obstacles the optimal rules turn out to be intuitive common sense heuristics for slightly more general graphs and scenes we show that no bounded ratio is possible we also show that the computational problem of devising a strategy that achieves a given worst case ratio to the optimum path in a graph is a universal two person game and thus pspace complete whereas optimizing the expected ratio is p hard

discretized vapnik chervonenkis dimension for analyzing complexity of real function classes in this paper we introduce the discretized vapnik chervonenkis vc dimension for studying the complexity of a real function class and then analyze properties of real function classes and neural networks we first prove that a countable traversal set is enough to achieve the vc dimension for a real function class whereas its classical definition states that the traversal set is the output range of the function class based on this result we propose the discretized vc dimension defined by using a countable traversal set consisting of rational numbers in the range of a real function class by using the discretized vc dimension we show that if a real function class has a finite vc dimension only a finite traversal set is needed to achieve the vc dimension we then point out that the real function classes which have the infinite vc dimension can be grouped into two categories type a and type b subsequently based on the obtained results we discuss the relationship between the vc dimension of an indicator output network and that of the real output network when both networks have the same structure except for the output activation functions finally we present the risk bound based on the discretized vc dimension for a real function class that has infinite vc dimension and is of type a we prove that with such a function class the empirical risk minimization erm principle for the function class is still consistent with overwhelming probability this is a development of the existing knowledge that the erm learning is consistent if and only if the function class has a finite vc dimension

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

stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise in this work we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation rm d x t rm div left frac nabla x t nabla x t right rm d t x t rm d w t rm in 0 infty times mathcal o where mathcal o is a bounded and open domain in mathbb r n n geqq 1 and w t is a wiener process of the form w t sum infty k 1 mu k e k beta k t e k in c 2 overline mathcal o cap h 1 0 mathcal o and beta k k in mathbb n are independent brownian motions this is a stochastic diffusion equation with a highly singular diffusivity term one main result established here is that for all initial conditions in l 2 mathcal o it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality thus one obtains a stochastic version of the minimal total variation flow the new approach developed here also allows us to prove the finite time extinction of solutions in dimensions 1 leqq n leqq3 which is another main result of this work

vc dimension of exterior visibility in this paper we study the vapnik chervonenkis vc dimension of set systems arising in 2d polygonal and 3d polyhedral configurations where a subset consists of all points visible from one camera in the past it has been shown that the vc dimension of planar visibility systems is bounded by 23 if the cameras are allowed to be anywhere inside a polygon without holes here we consider the case of exterior visibility where the cameras lie on a constrained area outside the polygon and have to observe the entire boundary we present results for the cases of cameras lying on a circle containing a polygon vc dimension 2 or lying outside the convex hull of a polygon vc dimension 5 the main result of this paper concerns the 3d case we prove that the vc dimension is unbounded if the cameras lie on a sphere containing the polyhedron hence the term exterior visibility

ito s formula in umd banach spaces and regularity of solutions of the zakai equation using the theory of stochastic integration for processes with values in a umd banach space developed recently by the authors an ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in umd banach spaces the abstract results are applied to prove regularity in space and time of the solutions of the zakai equation

the scale space aspect graph currently the aspect graph is computed from the theoretical standpoint of perfect resolution in object shape the viewpoint and the projected image this means that the aspect graph may include details that an observer could never see in practice introducing the notion of scale into the aspect graph framework provides a mechanism for selecting a level of detail that is large enough to merit explicit representation this effectively allows control over the number of nodes retained in the aspect graph this paper introduces the concept of the scale space aspect graph defines three different interpretations of the scale dimension and presents a detailed example for a simple class of objects with scale defined in terms of the spatial extent of features in the image

computing the flow around a submerged body using composite grids the subject of this paper is an accurate numerical method for solving the linear two dimensional steady potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below the free surface the differential equation is discretized by a second order accurate finite difference scheme on a composite grid the composite grid consists of two overlapping component grids one curvilinear grid close to the body and one cartesian grid which covers the surrounding liquid to solve the problem numerically the infinite domain is truncated to finite length the inflow and outflow boundary conditions are formed by making an eigenfunction expansion of the solution ahead of and behind the body each eigenfunction is required to be bounded and satisfy the upstream condition at infinity this is imposed by functional relations between the solution and its normal derivative at the inflow and outflow boundaries the method is carefully validated and the computed solutions are found to be in very good agreement with existing results

visibility occlusion and the aspect graph this chapter studies the ways in which the topology of the image of a polyhedron changes with changing viewpoint we catalog the ways that the topological appearance or aspect can change this enables us to find maximal regions of viewpoints of the same aspect we use these techniques to construct the viewpoint space partition vsp a partition of viewpoint space into maximal regions of constant aspect and its dual the aspect graph here we present tight bounds on the maximum size of the vsp and the aspect graph and give algorithms for their construction first in the convex case and then in the general case in particular we give bounds on the maximum size of n 2 and n 6 under an orthographic projection viewing model and of n 3 and n 9 under a perspective viewing model the algorithms make use of a new representation of the appearance of polyhedra from all viewpoints called the aspect representation or asp we believe that this representation is one of the significant contributions of this paper

on the piano movers problem v the case of a rod moving in three dimensional space amidst polyhedral obstacles this paper a fifth in a series solves some additional 3 d special cases of the piano movers problem which arises in robotics the main problem solved in this paper is that of planning the motion of a rod moving amidst polyhedral obstacles we present polynomial time motion planning algorithms for this case using the connectivity graph technique described in the preceding papers we also study certain more general polyhedral problems which arise in the motion planning problem considered here but have application to other similar problems application of these techniques to the problem of planning the motion of a general polyhedral body moving in 3 space amidst polyhedral obstacles is also described

the power of a pebble exploring and mapping an unknown environment is a fundamental problem that is studied in a variety of contexts many results have focused on finding efficient solutions to restricted versions of the problem in this paper we consider a model that makes very limited assumptions about the environment and solve the mapping problem in this general setting we model the environment by an unknown directed graph g and consider the problem of a robot exploring and mapping g the edges emanating from each vertex are numbered from 1 to d but we do not assume that the vertices of g are labeled since the robot has no way of distinguishing between vertices it has no hope of succeeding unless it is given some means of distinguishing between vertices for this reason we provide the robot with a pebble a device that it can place on a vertex and use to identify the vertex later in this paper we show 1 if the robot knows an upper bound on the number of vertices then it can learn the graph efficiently with only one pebble 2 if the robot does not know an upper bound on the number of vertices n then log log n pebbles are both necessary and sufficient in both cases our algorithms are deterministic

constructing arrangements of lines and hyperplanes with applications a finite set of lines partitions the euclidean plane into a cell complex similarly a finite set of d 1 dimensional hyperplanes partitions d dimensional euclidean space an algorithm is presented that constructs a representation for the cell complex defined by n hyperplanes in optimal o n d time in d dimensions it relies on a combinatorial result that is of interest in its own right the algorithm is shown to lead to new methods for computing lambda matrices constructing all higher order voronoi diagrams halfspatial range estimation degeneracy testing and finding minimum measure simplices in all five applications the new algorithms are asymptotically faster than previous results and in several cases are the only known methods that generalize to arbitrary dimensions the algorithm also implies an upper bound of 2 cn d c a positive constant for the number of combinatorially distinct arrangements of n hyperplanes in e d

fundamental viscous solutions or transient oseenlets associated with a body manoeuvring in a viscous fluid a viscous boundary element method involving a convolution integral formulation is developed to determine directly the fluid actions and velocity flow field associated with a body manoeuvring in a viscous fluid the proposed general approach is analogous to a potential flow singularity distribution panel method with the singularity replaced by a fundamental viscous solution from the developed nonlinear mathematical model based on an integral identity relation it is seen that the oseen equation its variant or modified form is central to the theoretical development of the fundamental viscous solution analytical expressions are presented for the fundamental solutions or transient oseenlets appropriate to two dimensional and three dimensional steady and unsteady transient manoeuvring problems involving prescribed translational rotational and their combined motions the examples considered and hence the fundamental viscous solutions relate to model towing tank experiments i e steady state rotating arm planar motion mechanism oscillatory tests etc used extensively to derive fluid action data on manoeuvring ships and submersibles examples of combined translational and rotational motions are investigated and these relate to an elementary idealization of a propeller rotating in an axial flow and an idealization of a body moving ahead with parasitic oscillatory roll motion the predicted fluid flow patterns associated with the various fundamental solutions are presented and these clearly illustrate the generation shedding and decay of vortices in the wakes

a computational model of view degeneracy we quantify the observation by kender and freudenstein 1987 that degenerate views occupy a significant fraction of the viewing sphere surrounding an object for a perspective camera geometry we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object for a typical recognition system parameterization view degeneracies typically occur with probabilities of 20 percent and depending on the parameterization as high as 50 percent we discuss the impact of view degeneracy on the problem of object recognition and for a particular recognition framework relate the cost of object disambiguation to the probability of view degeneracy to reduce this cost we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view in order to validate both our view degeneracy model as well as our active focal length control model a set of experiments are reported using a real recognition system operating on real images

on the additive properties of the fat shattering dimension the properties of the vc dimension under various compositions are well understood but this is much less the case for classes of continuous functions in this brief we show that a commonly used scale sensitive dimension v y is much less well behaved under minkowski summation than its vc cousin while the fat shattering dimension retains some compositional similarity to the vc dimension as an application we analyze the fat shattering dimension of trigonometric functions and series

the artificial boundary conditions for computing the flow around a submerged body in this paper we consider the numerical simulations of the steady linearized potential flow around a body which moves in a liquid of finite constant depth at constant speed and distance below a free surface two vertical segments are introduced as the artificial boundary to limit the unbounded physical domain to a bounded computational domain a series of approximate artificial boundary conditions at the given artificial boundary are designed by imposing the continuity of the solution and its normal derivative then the original problem is reduced to a problem defined in a bounded computational domain which is solved numerically by the finite element method the numerical examples show that our artificial boundary conditions are very effective

an optimal competitive strategy for walking in streets a simple polygon p with two distinguished vertices s and t is called a street if the two boundary chains from s to t are mutually weakly visible we present an on line strategy that walks from s to t in any unknown street on a path at most sqrt 2 times longer than the shortest path this matches the best lower bound previously known and settles an open problem in the area of competitive path planning the result was simultaneously and independently obtained by the first three authors and by the last two authors both papers c icking r klein and e langetepe proceedings of the 16th symposium on theoretical aspects in computer science lecture notes in comput sci 1563 springer verlag berlin 1999 pp 110 120 and s schuierer and i semrau proceedings of the 16th symposium on theoretical aspects of computer science pp 121 131 were presented at stacs 99 the present paper contains a joint full version

training multilayer perceptron classifiers based on a modified support vector method in this paper we describe a training method for one hidden layer multilayer perceptron classifier which is based on the idea of support vector machines svm an upper bound on the vapnik chervonenkis vc dimension is iteratively minimized over the interconnection matrix of the hidden layer and its bias vector the output weights are determined according to the support vector method but without making use of the classifier form which is related to mercer s condition the method is illustrated on a two spiral classification problem

reduced order modeling of fluid structure interaction and vortex induced vibration systems using an extension of jourdain s principle abstract a first principles variational approach is proposed for reduced order modeling of fluid structure interaction fsi systems specifically vortex induced vibration viv fsi has to be taken into account in the design and analysis of many engineering applications yet a comprehensive theoretical development where analytical equations are derived from first principles is nonexistent an approach where jourdain s principle is modified and extended for fsi is used to derive reduced order models from an extended variational formulation where assumptions are explicitly stated two viv models are considered an elastically supported inverted pendulum and a translating cylinder both immersed in a flow and allowed to move transversely to the flow direction their reduced order models are obtained in the form of i a single governing equation and ii two general coupled equations as well as the coupled lift oscillator model comparisons are made with three existing models based on our theoretical results and especially the reduced order model we conclude that the first principles development herein is a viable framework for the modeling of complex fluid structure interaction problems such as vortex induced oscillations

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

three dimensional weak visibility complexity and applications abstract in this paper we study the complexity of 3d weak visibility we obtain an o n 8 time and n 6 space algorithm to compute the weakly visible region of a triangle f from another triangle g among general scenes which are a set of n disjoint triangles we also consider the cases when the scenes are rectilinear objects and polyhedral terrains we show that in these special situations the weakly visible regions can be computed much faster in o n 6 time and o n 4 space with these results we obtain the first known polynomial time algorithm to decide whether or not a simple polyhedron is weakly internally or externally visible

stochastic nonlinear schrodinger equations abstract this paper is devoted to the well posedness of stochastic nonlinear schrodinger equations in the energy space h 1 r d and is a continuation of our recent work barbu et al 2014 we allow general complex coefficients in the noise thus covering both the conservative and non conservative case the latter being important to include quantum measurement effects in the underlying physical model we consider both focusing and defocusing nonlinearities and prove global well posedness in h 1 r d including also the pathwise continuous dependence on initial conditions with exponents of the nonlinearity in exactly the same sharp range as in the deterministic case in particular in the special conservative case this work improves earlier results in de bouard and debussche 2003 where the critical exponents could not be reached for d 6 in the defocusing and for d 4 in the focusing case respectively moreover the local existence uniqueness and blowup alternative are also established for the energy critical case the approach presented here is mainly based on the rescaling approach already used in barbu et al 2014 to study the l 2 case and also on the strichartz estimates established in marzuola et al 2008 for large perturbations of the laplacian

on inviscid limits for the stochastic navier stokes equations and related models we study inviscid limits of invariant measures for the 2d stochastic navier stokes equations as shown by kuksin j stat phys 115 1 2 469 492 2004 the noise scaling sqrt nu is the only one which leads to non trivial limiting measures which are invariant for the 2d euler equations using a moser type iteration for stochastic drift diffusion equations we show that any limiting measure mu 0 is in fact supported on bounded vorticities relationships of mu 0 to the long term dynamics of 2d euler in l infty with the weak topology are discussed we also obtain a drift independent modulus of continuity for a stationary deterministic model problem which leads us to conjecture that in fact mu 0 is supported on c 0 moreover in view of the batchelor krainchnan 2d turbulence theory we consider inviscid limits for a weakly damped stochastic navier stokes equation in this setting we show that only an order zero noise scaling with respect to leads to a nontrivial limiting measure in the inviscid limit

competitive online approximation of the optimal search ratio how efficiently can we search an unknown environment for a goal in an unknown position how much would it help if the environment were known we answer these questions for simple polygons and for undirected graphs by providing online search strategies that are as good as the best offline search algorithms up to a constant factor for other settings we prove that no such online algorithms exist we introduce a natural measure which gives reasonable results and is more realistic than pure pessimistic competitive analysis

computing the generalized aspect graph for objects with moving parts algorithms for computing the aspect graph representation are generalized to include a larger more realistic domain of objects known as articulated assemblies those objects composed of rigid parts with articulated connections allowed between parts the generalization suggests two slightly different representations one that directly summarizes the possible general views of the object and another hierarchical form summarizing the possible general configurations and their respective views algorithms are outlined for computing both representations the generalized aspect graphs of assemblies formed using translational connections are examined

model complexity control for regression using vc generalization bounds it is well known that for a given sample size there exists a model of optimal complexity corresponding to the smallest prediction generalization error hence any method for learning from finite samples needs to have some provisions for complexity control existing implementations of complexity control include penalization or regularization weight decay in neural networks and various greedy procedures aka constructive growing or pruning methods there are numerous proposals for determining optimal model complexity aka model selection based on various asymptotic analytic estimates of the prediction risk and on resampling approaches nonasymptotic bounds on the prediction risk based on vapnik chervonenkis vc theory have been proposed by vapnik this paper describes application of vc bounds to regression problems with the usual squared loss an empirical study is performed for settings where the vc bounds can be rigorously applied i e linear models and penalized linear models where the vc dimension can be accurately estimated and the empirical risk can be reliably minimized empirical comparisons between model selection using vc bounds and classical methods are performed for various noise levels sample size target functions and types of approximating functions our results demonstrate the advantages of vc based complexity control with finite samples

a numerical method to calculate the two dimensional flow around an underwater obstacle the linear two dimensional steady potential flow around a body travelling in a liquid of finite constant depth at constant speed and distance below a free surface is considered the analytical solutions ahead of and behind the body are used to form functional relations between the potential and its normal derivative these relations are imposed as boundary conditions for the problem close to the body to satisfy the radiation condition one more relation is imposed ahead of the body than behind it a second order accurate finite difference discretization of the problem is also analyzed an analogous theory is developed which results in matrix relations as boundary conditions for the problem close to the body

efficiently computing and representing aspect graphs of polyhedral objects an efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented the aspect graph is an approach to representing 3 d objects by a set of 2 d views for the purpose of object recognition in this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change the viewing data of an object is the partition of the viewpoint space together with a representative view in each region the algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection

how to learn an unknown environment i the rectilinear case we consider the problem faced by a robot that must explore and learn an unknown room with obstacles in it we seek algorithms that achieve a bounded ratio of the worst case distance traversed in order to see all visible points of the environment thus creating a map divided by the optimum distance needed to verify the map if we had it in the beginning the situation is complicated by the fact that the latter off line problem the problem of optimally verifying a map is np hard although we show that there is no such competitive algorithm for general obstacle courses we give a competitive algorithm for the case of a polygonal room with a bounded number of obstacles in it we restrict ourselves to the rectilinear case where each side of the obstacles and the room is parallel to one of the coordinates and the robot must also move either parallel or perpendicular to the sides in a subsequent paper we will discuss the extension to polygons of general shapes we also discuss the off line problem for simple rectilinear polygons and find an optimal solution in the l 1 metric in polynomial time in the case where the entry and the exit are different points

topological recognition of polyhedral objects from multiple views abstract the aspect graph ag has been proposed as a viewer centered tool for object recognition although the aspects could be used for recognition from one image the full information stored in the ag aspects and visual events suggests a multiple views possibly active approach the topological nature of the ag also suggests a topological match of images of the unknown object and stored aspects in this paper we present a theoretical investigation on the use of the ag for topological recognition from multiple views of polyhedral objects first we discuss the topological matching process and give a suitable topological definition of aspect moreover since topological identification is approximate we tackle the problem of understanding the ability of the ag to topologically discriminate different objects more precisely we address the question how similar are two polyhedra with the same ag the isomorphism of polyhedra is chosen as the reference similarity condition the cases of general and convex polyhedra are discussed under perspective and parallel projections in practice it could be difficult to identify the visual events from the images of the unknown object thus we also compare isomorphism and the similarity induced by i a topologically reduced aspect graph ii the set of topologically different aspects neglecting visual events

computing exact aspect graphs of curved objects solid of revolution this paper introduces a new approach to computing the exact orthographic aspect graph of curved objects curves corresponding to various visual events partition the view sphere into regions where the image structure is stable a catalog of these events for piecewise smooth objects is available from singularity theory for a solid of revolution whose generator is an algebraic curve each visual event is characterized by a system of polynomial equations whose roots can be computed by continuation methods within each region the stable image structure is characterized by a variation of cylindrical algebraic decomposition and ray tracing this approach has been implemented and several examples are presented

stochastic nonlinear schrodinger equations no blow up in the non conservative case abstract this paper is devoted to the study of noise effects on blow up solutions to stochastic nonlinear schrodinger equations it is a continuation of our recent work 2 where the local well posedness is established in h 1 also in the non conservative critical case here we prove that in the non conservative focusing mass super critical case by adding a large multiplicative gaussian noise with high probability one can prevent the blow up on any given bounded time interval 0 t 0 t moreover in the case of spatially independent noise the explosion even can be prevented with high probability on the whole time interval 0 the noise effects obtained here are completely different from those in the conservative case studied in 5

tight bounds for undirected graph exploration with pebbles and multiple agents we study the problem of deterministically exploring an undirected and initially unknown graph with n vertices either by a single agent equipped with a set of pebbles or by a set of collaborating agents the vertices of the graph are unlabeled and cannot be distinguished by the agents but the edges incident to a vertex have locally distinct labels the graph is explored when all vertices have been visited by at least one agent in this setting it is known that for a single agent without pebbles log n bits of memory are necessary and sufficient to explore any graph with at most n vertices we are interested in how the memory requirement decreases as the agent may mark vertices by dropping and retrieving distinguishable pebbles or when multiple agents jointly explore the graph we give tight results for both questions showing that for a single agent with constant memory log log n pebbles are necessary and sufficient for exploration we further prove that using collaborating agents instead of pebbles does not help as log log n agents with constant memory each are necessary and sufficient for exploration for the upper bounds we devise an algorithm for a single agent with constant memory that explores any n vertex graph using o log log n pebbles even when n is not known a priori the algorithm terminates after polynomial time and returns to the starting vertex we further show that the algorithm can be realized with additional constant memory agents rather than pebbles implying that o log log n agents with constant memory can explore any n vertex graph for the lower bound we show that the number of agents needed for exploring any graph with at most n vertices is already log log n when we allow each agent to have at most o log n 1 e bits of memory for any e 0 our argument also implies that a single agent with sublogarithmic memory needs log log n pebbles to explore any n vertex graph

vc theory of large margin multi category classifiers in the context of discriminant analysis vapnik s statistical learning theory has mainly been developed in three directions the computation of dichotomies with binary valued functions the computation of dichotomies with real valued functions and the computation of polytomies with functions taking their values in finite sets typically the set of categories itself the case of classes of vector valued functions used to compute polytomies has seldom been considered independently which is unsatisfactory for three main reasons first this case encompasses the other ones second it cannot be treated appropriately through a naive extension of the results devoted to the computation of dichotomies third most of the classification problems met in practice involve multiple categories in this paper a vc theory of large margin multi category classifiers is introduced central in this theory are generalized vc dimensions called the dimensions first a uniform convergence bound on the risk of the classifiers of interest is derived the capacity measure involved in this bound is a covering number this covering number can be upper bounded in terms of the dimensions thanks to generalizations of sauer s lemma as is illustrated in the specific case of the scale sensitive natarajan dimension a bound on this latter dimension is then computed for the class of functions on which multi class svms are based this makes it possible to apply the structural risk minimization inductive principle to those machines

ito s formula for the lp norm of stochastic w 1 _ p valued processes we prove ito s formula for the lp norm of a stochastic w 1 p valued processes appearing in the theory of spdes in divergence form

a nearly optimal sensor placement algorithm for boundary coverage locating visual sensors in 2d can be often modeled as an art gallery problem tasks such as surveillance require observing or covering the interior of a polygon with a minimum number of sensors or guards for other tasks such as inspection and image based rendering observing the boundaries of the environment is sufficient as interior covering ic also edge covering ec is np hard and no finite algorithm is known for its exact solution approximate ec solutions are provided by many heuristic algorithms but their performances with respect to optimality minimum number of sensors is unknown in this paper we propose a new ec sensors location technique the algorithm is incremental and converges toward the optimal solution it refines an initial approximation provided by an integer covering algorithm iec where each edge is observed entirely by at least one sensor a lower bound for the number of sensors specific of the polygon considered is used at each step for evaluating the quality of the current solution and a set of rules are provided for performing a local refinement to reduce the computational burden the algorithm has been implemented and tests over hundreds of random polygons show that it supplies solutions very close to and often coincident with the lower bound and then suboptimal or optimal in addition the approximate starting solutions provided by the iec algorithms are on the average close to optimum the tight lower bound can also be used for testing other ec sensor location algorithms running times allow dealing with polygons with up to a few hundreds of edges which appears adequate for many practical cases an enhanced version of the algorithm also taking into account range and incidence constraints has also been implemented and tested

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

broadcast in the rendezvous model in many large distributed or mobile networks broadcast algorithms are used to update information stored at the nodes in this paper we propose a new model of communication based on rendezvous and analyze a multi hop distributed algorithm to broadcast a message in a synchronous setting in the rendezvous model two neighbors u and v can communicate if and only if u calls v and v calls u simultaneously thus nodes u and v obtain a rendezvous at a meeting point if m is the number of meeting points the network can be modeled by a graph of n vertices and m edges at each round every vertex chooses a random neighbor and there is a rendezvous if an edge has been chosen by its two extremities rendezvous enable an exchange of information between the two entities we get sharp lower and upper bounds on the time complexity in terms of number of rounds to broadcast we show that for any graph the expected number of rounds is between ln n and o n2 for these two bounds we prove that there exist some graphs for which the expected number of rounds is either o ln n or n2 for specific topologies additional bounds are given

local rademacher complexities we propose new bounds on the error of learning algorithms in terms of a data dependent notion of complexity the estimates we establish give optimal rates and are based on a local and empirical version of rademacher averages in the sense that the rademacher averages are computed from the data on a subset of functions with small empirical error we present some applications to classification and prediction with convex function classes and with kernel classes in particular

a near tight approximation algorithm for the robot localization problem localization is a fundamental problem in robotics the kidnapped robot possesses a compass and map of its environment it must determine its location at a minimum cost of travel distance the problem is np hard g dudek k romanik and s whitesides siam j comput 27 1998 pp 583 604 even to minimize within factor c log n c tovey and s koenig proceedings of the national conference on artificial intelligence austin tx 2000 pp 819 824 where n is the map size no approximation algorithm has been known we give an o log 3n factor algorithm the key idea is to plan travel in a majority rule map which eliminates uncertainty and permits a link to the frac 1 2 group steiner not group steiner problem the approximation factor is not far from optimal we prove a c log 2 epsilon n lower bound assuming np not subseteq ztime n polylog n for the grid graphs commonly used in practice we also extend the algorithm to polygonal maps by discretizing the problem using novel geometric techniques

reconstructing visibility graphs with simple robots we consider the problem of finding a minimalistic configuration of sensors that enable a simple robot inside an initially unknown polygon p on n vertices to reconstruct the visibility graph of p the robot can sense features of its environment through its sensors and it is allowed to move from vertex to vertex we aim at understanding which sensorial capabilities are sufficient for the reconstruction of the visibility graph of p we are able to show that the combinatorial visibilities at every vertex do not contain enough information even when combined with the knowledge of the exact interior angle at each vertex using sensors that can put distant vertices into a spatial relation on the other hand can in some cases enable our robot to reconstruct the visibility graph of p we show that this is true for a sensor that can distinguish whether the angle between the lines toward two visible vertices is convex or reflex as long as the robot is capable of identifying the vertex it last visited we also show that measuring angles exactly is enough if the robot has a compass