lie theory for nilpotent l algebras the deligne groupoid is a functor from nilpotent differential graded lie algebras concentrated in positive degrees to groupoids in the special case of lie algebras over a field of characteristic zero it gives the associated simply connected lie group we generalize the deligne groupoid to a functor from l algebras concentrated in degree n to n groupoids we actually construct the nerve of the n groupoid which is an enriched kan complex the construction of gamma is quite explicit it is based on dupont s proof of the de rham theorem and yields higher dimensional analogues of holonomy and of the campbell hausdorff formula in the case of abelian l algebras i e chain complexes the functor is the dold kan simplicial set

asymptotically optimal anomaly detection via sequential testing sequential detection of independent anomalous processes among k processes is considered at each time only m 1 leq m leq k processes can be observed and the observations from each chosen process follow two different distributions depending on whether the process is normal or abnormal each anomalous process incurs a cost per unit time until its anomaly is identified and fixed switching across processes and state declarations are allowed at all times while decisions are based on all past observations and actions the objective is a sequential search strategy that minimizes the total expected cost incurred by all the processes during the detection process under reliability constraints we develop index type algorithms for the case with both known observation distributions and the case when the observation distributions have unknown parameters we show that the proposed algorithms are asymptotically optimal in terms of minimizing the total expected cost as the error constraints approach zero simulation results demonstrate strong performance in the finite regime

randomized sensor selection in sequential hypothesis testing we consider the problem of sensor selection for time optimal detection of a hypothesis we consider a group of sensors transmitting their observations to a fusion center the fusion center considers the output of only one randomly chosen sensor at the time and performs a sequential hypothesis test we study a sequential multiple hypothesis test with randomized sensor selection strategy we incorporate the random processing times of the sensors to determine the asymptotic performance characteristics of this test for three distinct performance metrics we show that for a generic set of sensors and binary hypothesis the time optimal policy requires the fusion center to consider at most two sensors we also show that for the case of multiple hypothesis the time optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses

gross fibrations syz mirror symmetry and open gromov witten invariants for toric calabi yau orbifolds given a toric calabi yau orbifold x whose underlying toric variety is semi projective we construct and study a non toric lagrangian torus bration on x which we call the gross bration we apply the strominger yau zaslow recipe to the gross bration of a toric modication of x to construct its instanton corrected mirror where the instanton corrections come from genus 0 open orbifold gromov witten invariants which are virtual counts of holomorphic orbi disks inx bounded by bers of the gross bration we explicitly evaluate all these invariants by rst proving an open closed equality and then employing the toric mirror theorem for suitable toric parital compactications of x our calculations are then applied to 1 prove a conjecture of gross siebert on a relation between genus 0 open orbifold gromov witten invariants and mirror maps ofx this is called the open mirror theorem which leads to an enumerative meaning of mirror maps and 2 demonstrate how open orbifold gromov witten invariants for toric calabi yau orb ifolds change under toric crepant resolutions this is an open analogue of ruan s crepant resolution conjecture

formal completions and idempotent completions of triangulated categories of singularities abstract the main goal of this paper is to prove that the idempotent completions of triangulated categories of singularities of two schemes are equivalent if the formal completions of these schemes along singularities are isomorphic we also discuss thomason s theorem on dense subcategories and a relation to the negative k theory

inverse geometry heat transfer problem based on a radial basis functions geometry representation summary we present a methodology for solving a nonlinear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is de ned the representation of the geometry is based on radial basis functions rbfs and the nonlinear inverse problem is solved using the iteratively regularized gauss newton method in our work we consider not only the problem with no geometry restrictions but also the bound constrained problem the methodology is used for the industrial application of estimating the location of the 1150 c isotherm in a blast furnace hearth based on measurements of the thermocouples located inside it we validate the solution of the algorithm against simulated measurements with different levels of noise and study its behavior on different regularization matrices finally we study the error behavior of the solution copyright c 2004 john wiley sons ltd

active sequential hypothesis testing consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration due to the sequential nature of the problem the decision maker relies on his current information state to adaptively select the most informative sensing action among the available ones in this paper using results in dynamic programming lower bounds for the optimal total cost are established the lower bounds characterize the fundamental limits on the maximum achievable information acquisition rate and the optimal reliability moreover upper bounds are obtained via an analysis of two heuristic policies for dynamic selection of actions it is shown that the first proposed heuristic achieves asymptotic optimality where the notion of asymptotic optimality due to chernoff implies that the relative difference between the total cost achieved by the proposed policy and the optimal total cost approaches zero as the penalty of wrong declaration hence the number of collected samples increases the second heuristic is shown to achieve asymptotic optimality only in a limited setting such as the problem of a noisy dynamic search however by considering the dependency on the number of hypotheses under a technical condition this second heuristic is shown to achieve a nonzero information acquisition rate establishing a lower bound for the maximum achievable rate and error exponent in the case of a noisy dynamic search with size independent noise the obtained nonzero rate and error exponent are shown to be maximum

neural dissimilarity indices that predict oddball detection in behaviour neuroscientists have recently shown that images that are difficult to find in visual search elicit similar patterns of firing across a population of recorded neurons the l 1 distance between firing rate vectors associated with two images was strongly correlated with the inverse of decision time in behavior but why should decision times be correlated with l 1 distance what is the decision theoretic basis in our decision theoretic formulation we model visual search as an active sequential hypothesis testing problem with switching costs our analysis suggests an appropriate neuronal dissimilarity index which correlates equally strongly with the inverse of decision time as the l 1 distance we also consider a number of other possibilities such as the relative entropy kullback leibler divergence and the chernoff entropy of the firing rate distributions a more stringent test of equality of means which would have provided a strong backing for our modeling fails for our proposed as well as the other already discussed dissimilarity indices however test statistics from the equality of means test when used to rank the indices in terms of their ability to explain the observed results places our proposed dissimilarity index at the top followed by relative entropy chernoff entropy and the l 1 indices computations of the different indices require an estimate of the relative entropy between two poisson point processes an estimator is developed and is shown to have near unbiased performance for almost all operating regions

deformation theory of objects in homotopy and derived categories ii pro representability of the deformation functor abstract this is the second paper in a series in part i we developed deformation theory of objects in homotopy and derived categories of dg categories here we extend these derived deformation functors to an appropriate bicategory of artinian dg algebras and prove that these extended functors are pro representable in a strong sense

quickest detection in multiple on off processes we consider the quickest detection of idle periods in multiple on off processes at each time only one process can be observed and the observations are random realizations drawn from two different distributions depending on the current state on or off of the chosen process the objective is to catch an idle period in any of the on off processes as quickly as possible subject to a reliability constraint we show that this problem presents a fresh twist to the classic problem of quickest change detection that considers only one stochastic process a bayesian formulation of the problem is developed for both infinite and finite number of processes based on the theory of partially observable markov decision process pomdp while a general pomdp is pspace hard we show that the optimal decision rule has a simple threshold structure for the infinite case for the finite case basic properties of the optimal decision rule are established and a low complexity threshold policy is proposed which converges to the optimal decision rule for the infinite case as the number of processes increases this problem finds applications in spectrum sensing in cognitive radio networks where a secondary user searches for idle channels in the spectrum

quickest search over multiple sequences the problem of sequentially finding an independent and identically distributed sequence that is drawn from a probability distribution q1 by searching over multiple sequences some of which are drawn from q1 and the others of which are drawn from a different distribution q0 is considered in the problem considered the number of sequences with distribution q1 is assumed to be a random variable whose value is unknown within a bayesian formulation a sequential decision rule is derived that optimizes a trade off between the probability of false alarm and the number of samples needed for the decision in the case in which one can observe one sequence at a time it is shown that the cumulative sum cusum test which is well known to be optimal for a non bayesian statistical change point detection formulation is optimal for the problem under study specifically the cusum test is run on the first sequence if a reset event occurs in the cusum test then the sequence under examination is abandoned and the rule switches to the next sequence if the cusum test stops then the rule declares that the sequence under examination when the test stops is generated by q1 the result is derived by assuming that there are infinitely many sequences so that a sequence that has been examined once is not retested if there are finitely many sequences the result is also valid under a memorylessness condition expressions for the performance of the optimal sequential decision rule are also developed the general case in which multiple sequences can be examined simultaneously is considered the optimal solution for this general scenario is derived

resolutions in factorization categories building upon ideas of eisenbud buchweitz positselski and others we introduce the notion of a factorization category we then develop some essential tools for working with factorization categories including constructions of resolutions of factorizations from resolutions of their components and derived functors using these resolutions we lift fully faithfulness and equivalence statements from derived categories of abelian categories to derived categories of factorizations some immediate geometric consequences include a realization of the derived category of a projective hypersurface as matrix factorizations over a noncommutative algebra and recover of a theorem of baranovsky and pecharich

structured threshold policies for dynamic sensor scheduling a partially observed markov decision process approach we consider the optimal sensor scheduling problem formulated as a partially observed markov decision process pomdp due to operational constraints at each time instant the scheduler can dynamically select one out of a finite number of sensors and record a noisy measurement of an underlying markov chain the aim is to compute the optimal measurement scheduling policy so as to minimize a cost function comprising of estimation errors and measurement costs the formulation results in a nonstandard pomdp that is nonlinear in the information state we give sufficient conditions on the cost function dynamics of the markov chain and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to a monotone likelihood ratio mlr ordering as a result the computational complexity of implementing the optimal scheduling policy is inexpensive we then present stochastic approximation algorithms for estimating the best linear mlr order threshold policy

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

searching for anomalies over composite hypotheses the problem of detecting anomalies in multiple processes is considered we consider a composite hypothesis case in which the measurements drawn when observing a process follow a common distribution with an unknown parameter vector whose value lies in normal or abnormal parameter spaces depending on its state the objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint we develop a deterministic search algorithm with the following desired properties first when no additional side information on the process states is known the proposed algorithm is asymptotically optimal in terms of minimizing the detection delay as the error probability approaches zero second when the parameter value under the null hypothesis is known and equal for all normal processes the proposed algorithm is asymptotically optimal as well with better detection time determined by the true null state third when the parameter value under the null hypothesis is unknown but is known to be equal for all normal processes the proposed algorithm is consistent in terms of achieving error probability that decays to zero with the detection delay finally an explicit upper bound on the error probability under the proposed algorithm is established for the finite sample regime extensive experiments on synthetic dataset and darpa intrusion detection dataset are conducted demonstrating strong performance of the proposed algorithm over existing methods

quickest detection in coupled systems this work considers the problem of quickest detection of signals in a coupled system of n sensors which receive continuous sequential observations from the environment it is assumed that the signals which are modeled by general ito processes are coupled across sensors but that their onset times may differ from sensor to sensor two main cases are considered in the first one signal strengths are the same across sensors while in the second one they differ by a constant the objective is the optimal detection of the first time at which any sensor in the system receives a signal the problem is formulated as a stochastic optimization problem in which an extended minimal kullback leibler divergence criterion is used as a measure of detection delay with a constraint on the mean time to the first false alarm the case in which the sensors employ cumulative sum cusum strategies is considered and it is proved that the minimum of n cusums is asymptotically optimal as the mean time to the first false

chern characters and hirzebruch riemann roch formula for matrix factorizations we study the category of matrix factorizations for an isolated hypersurface singularity we compute the canonical bilinear form on the hochschild homology of this category we find explicit expressions for the chern character and the boundary bulk maps and derive an analogue of the hirzebruch riemann roch formula for the euler characteristic of the hom space between a pair of matrix factorizations we also establish g equivariant versions of these results

homological mirror symmetry for calabi yau hypersurfaces in projective space we prove homological mirror symmetry for a smooth d dimensional calabi yau hypersurface in projective space for any d 3 for example d 3 is the quintic threefold the main techniques involved in the proof are the construction of an immersed lagrangian sphere in the d dimensional pair of pants the introduction of the relative fukaya category and an understanding of its grading structure a description of the behaviour of this category with respect to branched covers via an orbifold fukaya cate gory a morse bott model for the relative fukaya category that allows one to make explicit computations and the introduction of certain graded categories of matrix factorizations mirror to the relative fukaya category

controlled sensing for multihypothesis testing the problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings in the fixed sample size setting for binary hypothesis testing the optimal exponent for the maximal error probability corresponds to the maximum chernoff information over the choice of controls and a pure stationary open loop control policy is asymptotically optimal within the larger class of all causal control policies for multihypothesis testing in the fixed sample size setting lower and upper bounds on the optimal error exponent are derived it is also shown through an example with three hypotheses that the optimal causal control policy can be strictly better than the optimal open loop control policy in the sequential setting a test based on earlier work by chernoff for binary hypothesis testing is shown to be first order asymptotically optimal for multihypothesis testing in a strong sense using the notion of decision making risk in place of the overall probability of error another test is also designed to meet hard risk constrains while retaining asymptotic optimality the role of past information and randomization in designing optimal control policies is discussed

multi parameter regularization techniques for ill conditioned linear systems when a system of linear equations is ill conditioned regularization techniques provide a quite useful tool for trying to overcome the numerical inherent difficulties the ill conditioned system is replaced by another one whose solution depends on a regularization term formed by a scalar and a matrix which are to be chosen in this paper we consider the case of several regularizations terms added simultaneously thus overcoming the problem of the best choice of the regularization matrix the error of this procedure is analyzed and numerical results prove its efficiency

shape identification for natural convection problems using the adjoint variable method an inverse geometry problem is investigated to identify the boundary shape of a domain from temperature measurements on the other boundary where the temperature field is dominated by natural convection the potential applications of the present investigation are the determination of a phase change isotherm in the bridgman crystal growth or the thermal tomography which detects flaws in materials nondestructively the inverse problem is posed as a minimization problem of the performance function which is the sum of square residuals between calculated and observed temperature by means of a conjugate gradient method employing the adjoint variable method the present method is found to identify the domains reasonably accurately even with noisy temperature measurements

localized mirror functor for lagrangian immersions and homological mirrorsymmetry for mathbb p 1_ a b c this paper gives a new way of constructing landau ginzburg mirrors using deformation theory of lagrangian immersions motivated by the works of seidel strominger yau zaslow and fukaya oh ohta ono moreover we construct a canonical functor from the fukaya category to the mirror category of matrix factorizations this functor derives homological mirror symmetry under some explicit assumptions as an application the construction is applied to spheres with three orbifold points to produce their quantum corrected mirrors and derive homological mirror symmetry furthermore we discover an enumerative meaning of the inverse mirror map for elliptic curve quotients

homological mirror symmetry for curves of higher genus abstract this paper is devoted to homological mirror symmetry conjecture for curves of higher genus it was proposed by katzarkov as a generalization of original kontsevich s conjecture a version of this conjecture in the case of the genus two curve was proved by seidel 25 based on the paper of seidel we prove the conjecture in the same version for curves of genus g 3 namely we relate the fukaya category of a genus g curve to the category of singularities of zero fiber in the mirror dual landau ginzburg model we also prove a kind of reconstruction theorem for hypersurface singularities namely formal type of hypersurface singularity i e a formal power series up to a formal change of variables can be reconstructed with some technical assumptions from its d z 2 g category of landau ginzburg branes the precise statement is theorem 1 2

optimal index policies for anomaly localization in resource constrained cyber systems abstract the problem of anomaly localization in a resource constrained cyber system is considered each anomalous component of the system incurs a cost per unit time until its anomaly is identified and fixed different anomalous components may incur different costs depending on their criticality to the system due to resource constraints only one component can be probed at each given time the observations from a probed component are realizations drawn from two different distributions depending on whether the component is normal or anomalous the objective is a probing strategy that minimizes the total expected cost incurred by all the components during the detection process under reliability constraints we consider both independent and exclusive models in the former each component can be abnormal with a certain probability independent of other components in the latter one and only one component is abnormal we develop optimal index policies under both models the proposed index policies apply to a more general case where a subset more than one of the components can be probed simultaneously the problem under study also finds applications in spectrum scanning in cognitive radio networks and event detection in sensor networks

homological mirror symmetry for punctured spheres we prove that the wrapped fukaya category of a punctured sphere s with an arbitrary number of points removed is equivalent to the triangulated category of singularities of a mirror landau ginzburg model proving one side of the homological mirror symmetry conjecture in this case by investigating fractional gradings on these categories we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the landau ginzburg model

contraction algebra and singularity of three dimensional flopping contraction donovan and wemyss duke math j 165 8 1397 1474 2016 introduced the contraction algebra of flopping curves in threefold they conjectured that the contraction algebra determines the formal neighborhood of the underlying singularity of the contraction in this paper we prove that the contraction algebra together with its natural a infty structure constructed in hua and toda int math res not rnw333 2017 determine the formal neighborhood of the singularity

discrimination of two channels by adaptive methods and its application to quantum system the optimal exponential error rate for adaptive discrimination of two channels is discussed in this problem adaptive choice of input signal is allowed this problem is discussed in various settings it is proved that adaptive choice does not improve the exponential error rate in these settings these results are applied to quantum state discrimination

fast multiband spectrum scanning for cognitive radio systems this paper considers the problem of how to quickly and accurately determine the availability of each spectrum band for a multi band primary system using one or few sensors such problem is referred to as spectrum scanning two cases of practical interest are studied 1 a single sensor case in which only one spectrum band is observed at one time and 2 a multiple sensor case in which multiple spectrum bands are observed simultaneously for each case scenarios with and without a scanning delay constraint are investigated using mathematical tools from optimal stopping theory optimal spectrum scanning algorithms are developed to minimize a cost function that strikes a desirable trade off between detection performance and sensing delay in the non delay constrained case it is shown that the optimal scanning algorithm is a concatenated sequential probability ratio test c sprt in the delay constrained case the optimal scanning algorithm has a high implementation complexity and truncation algorithms are developed as alternative low complexity options numerical examples are provided to illustrate the effectiveness of the proposed algorithms

lagrangian floer potential of orbifold spheres abstract for each sphere with three orbifold points we construct an algorithm to compute the open gromov witten potential which serves as the quantum corrected landau ginzburg mirror and is an infinite series in general this gives the first class of general type geometries whose full potentials can be computed as a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients furthermore we prove that the open gromov witten potential is convergent even in the general type cases and has an isolated singularity at the origin which is an important ingredient of proving homological mirror symmetry

quickest linear search over correlated sequences consider a set of random sequences each consisting of independent and identically distributed random variables drawn from one of the two known distributions f 0 and f 1 the underlying distributions of different sequences are correlated induced by an inherent physical coupling in the mechanisms generating these sequences the objective is to design the quickest data adaptive and sequential search procedure for identifying one sequence generated according to f 1 the optimal design involves striking a balance between the average delay in reaching a decision and the rate of false alarms as two opposing figures of merit optimal and asymptotically optimal decision rules are derived which can take radically different forms depending on the correlation structure performance and sampling complexity analyses are provided to delineate the tradeoff between decision delay and quality the generalization to parallel sampling in which multiple sequences are sampled at the same time is also investigated

quickest change detection of a markov process across a sensor array recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption in this work a more general scenario is considered where the change propagates across the sensors and its propagation can be modeled as a markov process a centralized bayesian version of this problem is considered with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process the problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework insights into the structure of the optimal stopping rule are presented in the limiting case of rare disruptions it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened under a certain condition on the kullback leibler k l divergence between the post and the pre change densities it is established that the threshold test is asymptotically optimal in the vanishing false alarm probability regime it is shown via numerical studies that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single sensor test or a test that incorrectly assumes that the change propagates instantaneously

active hypothesis testing for anomaly detection the problem of detecting a single anomalous process among a finite number m of processes is considered at each time a subset of the processes can be observed and the observations from each chosen process follow two different distributions depending on whether the process is normal or abnormal the objective is a sequential search strategy that minimizes the expected detection time subject to an error probability constraint this problem can be considered as a special case of active hypothesis testing first considered by chernoff where a randomized strategy referred to as the chernoff test was proposed and shown to be asymptotically as the error probability approaches zero optimal for the special case considered in this paper we show that a simple deterministic test achieves asymptotic optimality and offers better performance in the finite regime we further extend the problem to the case where multiple anomalous processes are present in particular we examine the case where only an upper bound on the number of anomalous processes is known

divergence estimation for multidimensional densities via k nearest neighbor distances a new universal estimator of divergence is presented for multidimensional continuous densities based on k nearest neighbor k nn distances assuming independent and identically distributed i i d samples the new estimator is proved to be asymptotically unbiased and mean square consistent in experiments with high dimensional data the k nn approach generally exhibits faster convergence than previous algorithms it is also shown that the speed of convergence of the k nn method can be further improved by an adaptive choice of k

towards mirror symmetry for varieties of general type abstract the goal of this paper is to propose a theory of mirror symmetry for varieties of general type using landau ginzburg mirrors as motivation we describe the mirror of a hypersurface of general type and more generally varieties of non negative kodaira dimension as the critical locus of the zero fibre of a certain landau ginzburg potential the critical locus carries a perverse sheaf of vanishing cycles our main result shows that one obtains the interchange of hodge numbers expected in mirror symmetry this exchange is between the hodge numbers of the hypersurface and certain hodge numbers defined using a mixed hodge structure on the hypercohomology of the perverse sheaf

a sequential procedure for multihypothesis testing the sequential testing of more than two hypotheses has important applications in direct sequence spread spectrum signal acquisition multiple resolution element radar and other areas a useful sequential test which we term the msprt is studied in this paper the test is shown to be a generalization of the sequential probability ratio test under bayesian assumptions it is argued that the msprt approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large bounds on error probabilities are derived and asymptotic expressions for the stopping time and error probabilities are given a design procedure is presented for determining the parameters of the msprt two examples involving gaussian densities are included and comparisons are made between simulation results and asymptotic expressions comparisons with bayesian fixed sample size tests are also made and it is found that the msprt requires two to three times fewer samples on average

on the fukaya categories of higher genus surfaces abstract we construct the fukaya category of a closed surface equipped with an area form using only elementary essentially combinatorial methods we also compute the grothendieck group of its derived category

parameterization of planar curves immersed in triangulations with application to finite elements we construct a method for the parameterization of a class of planar piecewise c2 curves over a collection of edges in an ambient triangulation the map from the collection of edges to the curve is the closest point projection a distinguishing feature of the method is that edges in the ambient triangulation need not interpolate the curve we formulate conditions on the ambient triangulations so that the resulting parameterization over its selected edges is i bijective ii maps simple connected collection of edges to simple connected components of the curve and iii is c1 within each edge of the collection these properties of the parameterization make it particularly useful in the construction of high order finite element approximation spaces on planar curves immersed in triangulations we discuss this application and illustrate it with numerical examples the parameterization method applies to a large class of planar curves including most ones of interest in engineering and computer graphics applications and to a large family of triangulations including acute angled triangulations copyright 2011 john wiley sons ltd

on the derived categories of degree d hypersurface fibrations we provide descriptions of the derived categories of degree d hypersurface fibrations which generalize a result of kuznetsov for quadric fibrations and give a relative version of a well known theorem of orlov using a local generator and morita theory we re interpret the resulting matrix factorization category as a derived equivalent sheaf of dg algebras on the base then applying homological perturbation methods we obtain a sheaf of a infty algebras which gives a new description of homological projective duals for relative d veronese embeddings recovering the sheaf of clifford algebras obtained by kuznetsov in the case when d 2

on the iteratively regularized gauss newton method for solving nonlinear ill posed problems the iteratively regularized gauss newton method is applied to compute the stable solutions to nonlinear ill posed problems f x y when the data y is given approximately by y with y y in this method the iterative sequence x k is defined successively by x k 1 x k k i f x k f x k 1 f x k f x k y k x k x 0 where x 0 x 0 is an initial guess of the exact solution x and k is a given decreasing sequence of positive numbers admitting suitable properties when x k is used to approximate x the stopping index should be designated properly in this paper an a posteriori stopping rule is suggested to choose the stopping index of iteration and with the integer k determined by this rule it is proved that x k x c inf x k x k k 0 1 with a constant c independent of where x k denotes the iterative solution corresponding to the noise free case as a consequence of this result the convergence of x k is obtained and moreover the rate of convergence is derived when x 0 x satisfies a suitable source wise representation the results of this paper suggest that the iteratively regularized gauss newton method combined with our stopping rule defines a regularization method of optimal order for each 0 v 1 numerical examples for parameter estimation of a differential equation are given to test the theoretical results