theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

a probabilistic plan recognition algorithm based on plan tree grammars we present the phatt algorithm for plan recognition unlike previous approaches to plan recognition phatt is based on a model of plan execution we show that this clarifies several difficult issues in plan recognition including the execution of multiple interleaved root goals partially ordered plans and failing to observe actions we present the phatt algorithm s theoretical basis and an implementation based on tree structures we also investigate the algorithm s complexity both analytically and empirically finally we present phatt s integrated constraint reasoning for parametrized actions and temporal constraints

twisted fourier mukai functors due to a theorem by orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of fourier mukai type we extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor as an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties

d equivalence and k equivalence let x and y be smooth projective varieties over they are called d equivalent if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories and k equivalent if they are birationally equivalent and the pull backs of their canonical divisors to a common resolution coincide we expect that the two equivalences coincide for birationally equivalent varieties we shall provide a partial answer to the above problem in this paper

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

image segmentation with a unified graphical model we propose a unified graphical model that can represent both the causal and noncausal relationships among random variables and apply it to the image segmentation problem specifically we first propose to employ conditional random field crf to model the spatial relationships among image superpixel regions and their measurements we then introduce a multilayer bayesian network bn to model the causal dependencies that naturally exist among different image entities including image regions edges and vertices the crf model and the bn model are then systematically and seamlessly combined through the theories of factor graph to form a unified probabilistic graphical model that captures the complex relationships among different image entities using the unified graphical model image segmentation can be performed through a principled probabilistic inference experimental results on the weizmann horse data set on the voc2006 cow data set and on the msrc2 multiclass data set demonstrate that our approach achieves favorable results compared to state of the art approaches as well as those that use either the bn model or crf model alone

mathieu subspaces of associative algebras abstract motivated by the mathieu conjecture mathieu 1997 m the image conjecture zhao 2010 z3 and the well known jacobian conjecture keller 1939 k see also bass et al 1982 bcw and van den essen 2000 e1 the notion of mathieu subspaces as a natural generalization of the notion of ideals has been introduced recently in zhao 2010 z4 for associative algebras in this paper we first study algebraic elements in the radicals of mathieu subspaces of associative algebras over fields and prove some properties and characterizations of mathieu subspaces with algebraic radicals we then give some characterizations or classifications for strongly simple algebras the algebras with no non trivial mathieu subspaces over arbitrary commutative rings and for quasi stable algebras the algebras all of whose subspaces that do not contain the identity element of the algebra are mathieu subspaces over arbitrary fields furthermore co dimension one mathieu subspaces and the minimal non trivial mathieu subspaces of the matrix algebras over fields are also completely determined

hessian nilpotent polynomials and the jacobian conjecture let z z 1 z n and let a n i 1 2 z 2 i be the laplace operator the main goal of the paper is to show that the well known jacobian conjecture without any additional conditions is equivalent to what we call the vanishing conjecture for any homogeneous polynomial p z of degree d 4 if m p m z 0 for all m 1 then m p m 1 z 0 when m 0 or equivalently m p m 1 z 0 when m 3 2 3 n 2 1 it is also shown in this paper that the condition m p m z 0 m 1 above is equivalent to the condition that p z is hessian nilpotent i e the hessian matrix hes p z 2 p z i z j is nilpotent the goal is achieved by using the recent breakthrough work of m de bondt a van den essen and various results obtained in this paper on hessian nilpotent polynomials some further results on hessian nilpotent polynomials and the vanishing conjecture above are also derived

causality and model abstraction abstract much of science and engineering is concerned with characterizing processes by equations describing the relations that hold among parameters of objects and govern their behavior over time in formal descriptions of processes in terms of parameters and equations the notion of causality is rarely made explicit formal treatments of the foundations of sciences have avoided discussions of causation and spoken only of functional relations among variables nevertheless the notion of causality plays an important role in our understanding of phenomena even when we describe the behavior of a system formally in terms of acausal mathematical relations we often give an informal intuitive explanation of why the system behaves the way it does in terms of cause effect relations in this paper we will present an operational definition of causal ordering the definition allows us to extract causal dependency relations among variables implicit in a model of a system when a model is represented as a set of acausal mathematical relations our approach is based on the theory of causal ordering first presented by simon 22 the paper shows how to use the theory and its extension in reasoning about physical systems further the paper studies the relation of the theory to the problems of model aggregation

images of commuting differential operators of order one with constant leading coefficients abstract we first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients we then propose what we call the image conjecture on these differential operators and show that the jacobian conjecture bass et al 1982 bcw van den essen 2000 e de bondt 2009 bo hence also the dixmier conjecture dixmier 1968 d and the vanishing conjecture zhao 2007 z3 of differential operators with constant coefficients are actually equivalent to certain special cases of the image conjecture a connection of the image conjecture and hence also the jacobian conjecture with multidimensional laplace transformations of polynomials is also discussed

the dixmier conjecture and the shape of possible counterexamples we establish a lower bound for the size of possible counterexamples of the dixmier conjecture we prove that b 15 where b is the minimum of the greatest common divisor of the total degrees of p and q where p q runs over the counterexamples of the dixmier conjecture 2013 elsevier inc

on the image conjecture abstract the image conjecture was formulated by the third author who showed that it implied his vanishing conjecture which is equivalent to the famous jacobian conjecture we prove various cases of the image conjecture and show that how it leads to another fascinating and elusive assertion that we here dub the factorial conjecture various cases of the factorial conjecture are proved

causality in device behavior abstract this paper shows how formal characterizations of causality and of the method of comparative statics long used in econometrics thermodynamics and other domains can be applied to clarify and make rigorous the qualitative causal calculus recently proposed by de kleer and brown 2 the formalization shows exactly what assumptions are required to carry out causal analysis of a system of interdependent variables in equilibrium and to propagate disturbances through such a system the intuitive concepts of causality captured by de kleer and brown provide a rough approximation to the standard analytic techniques that are used in the treatment of simultaneous algebraic and differential equations

reconstruction and finiteness results for fourier mukai partners abstract we develop some methods for studying the fourier mukai partners of an algebraic variety as applications we prove that abelian varieties have finitely many fourier mukai partners and that they are uniquely determined by their derived category of coherent d modules we also generalize a famous theorem due to bondal and orlov

automated modeling of complex systems to answer prediction questions abstract a question about the behavior of a complex physical system can be answered by simulating the system the challenge is building a model of the system that is appropriate for answering the question if the model omits relevant aspects of the system the predicted behavior may be wrong if on the other hand the model includes many aspects that are irrelevant to the question it may be difficult to simulate and explain the leading approach to automated modeling compositional modeling constructs a simplest adequate model for a question from building blocks model fragments that are designed by knowledge engineers this paper presents a new compositional modeling algorithm that constructs models from simpler building blocks the individual influences among system variables and addresses important modeling issues that previous programs left to the knowledge engineer in the most rigorous test of a modeling algorithm to date we implemented our algorithm applied it to a large knowledge base for plant physiology and asked a domain expert to evaluate the models it produced

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

the strong factorial conjecture abstract in this paper we present an unexpected link between the factorial conjecture 8 and furter s rigidity conjecture 13 the factorial conjecture in dimension m asserts that if a polynomial f in m variables x i over c is such that l f k 0 for all k 1 then f 0 where l is the c linear map from c x 1 x m to c defined by l x 1 l 1 x m l m l 1 l m the rigidity conjecture asserts that a univariate polynomial map a x with complex coefficients of degree at most m 1 such that a x x mod x 2 is equal to x if m consecutive coefficients of the formal inverse for the composition of a x are zero

a note on the correctness of the causal ordering algorithm in this paper we examine in detail the algorithm of simon h a simon causal ordering and identifiability in w c hood t c koopmans eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley sons inc new york 1953 pp 49 74 chapter iii called the causal ordering algorithm coa used for constructing the causal ordering of a system given a complete specification of the system in terms of a set of structural equations that govern the variables in the system this algorithm constructs a graphical characterization of the model in a form that we call a partial causal graph simon argued in h a simon causal ordering and identifiability in w c hood t c koopmans eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley sons inc new york 1953 pp 49 74 chapter iii and subsequent papers that a graph so generated explicates causal structure among variables in the model we formalize this claim further by proving that any causal model based on a one to one correspondence between equations and variables must be consistent with the coa

causal ordering comparative statics and near decomposability abstract the notion of causal ordering has been explicated for systems in the form of sets of linear algebraic equations and also for dynamic models consisting of linear differential equations since we often wish to aggregate or disaggregate models of systems or to consider the static equilibrium of a dynamic model the question arises as to how these transformations from one model of a system to another affect the causal ordering of variables the present paper provides some answers to this question

the sensitivity of belief networks to imprecise probabilities an experimental investigation abstract bayesian belief networks are being increasingly used as a knowledge representation for reasoning under uncertainty some researchers have questioned the practicality of obtaining the numerical probabilities with sufficient precision to create belief networks for large scale applications in this work we investigate how precise the probabilities need to be by measuring how imprecision in the probabilities affects diagnostic performance we conducted a series of experiments on a set of real world belief networks for medical diagnosis in liver and bile disease we examined the effects on diagnostic performance of 1 varying the mappings from qualitative frequency weights into numerical probabilities 2 adding random noise to the numerical probabilities 3 simplifying from quaternary domains for diseases and findings absent mild moderate and severe to binary domains absent and present and 4 using test cases that contain diseases outside the network we found that even extreme differences in the probability mappings and large amounts of noise lead to only modest reductions in diagnostic performance we found no significant effect of the simplification from quaternary to binary representation we also found that outside diseases degraded performance modestly overall these findings indicate that even highly imprecise input probabilities may not impair diagnostic performance significantly and that simple binary representations may often be adequate these findings of robustness suggest that belief networks are a practical representation without requiring undue precision

interactive construction of graphical decision models based on causal mechanisms abstract we propose a framework for building graphical decision models from individual causal mechanisms our approach is based on the work of simon simon h a 1953 causal ordering and identifiability in hood w c koopmans t c eds studies in econometric method cowles commission for research in economics monograph no 14 john wiley and sons inc new york ny pp 49 74 ch iii who proposed a causal ordering algorithm for explicating causal asymmetries among variables in a self contained set of structural equations we extend the causal ordering algorithm to under constrained sets of structural equations common during the process of problem structuring we demonstrate that the causal ordering explicated by our extension is an intermediate representation of a modeler s understanding of a problem and that the process of model construction consists of assembling mechanisms into self contained causal models we describe i ma g e ni e an interactive modeling tool that supports mechanism based model construction and demonstrate empirically that it can effectively assist users in constructing graphical decision models

fourier mukai transformations on k3 surfaces with ρ 1 and atkin lehner involutions abstract we show that there is a surjection from the fourier mukai transformations on projective k3 surfaces with the picard number x 1 to so called the group of atkin lehner involutions this was expected in hosono lian oguiso and yau s paper

the refinement of probabilistic rule sets sociopathic interactions abstract probabilistic rules in a classification expert system can result in a sociopathic knowledge base as a consequence of the assumption of conditional independence between observations and rule modularity a sociopathic knowledge base has the property that all the rules are individually judged to be correct rules yet a subset of the knowledge base gives better classification accuracy than the original knowledge base independent of the amount of computational resources that are available this paper describes how sociopathic interactions cause rule induction and refinement methods to converge to local optima with respect to maximizing classification accuracy the problem of optimally refining sociopathic knowledge bases is modeled as a bipartite graph minimization problem and shown to be np hard a heuristic rule refinement algorithm for sociopathic reduction called socio reducer is presented experimental results in a medical diagnosis domain show that it can reduce the diagnosis error rate by 10 5

the lned and lfed conjectures for algebraic algebras abstract let k be a field of characteristic zero and a a k algebra such that all the k subalgebras generated by finitely many elements of a are finite dimensional over k a k e derivation of a is a k linear map of the form i for some k algebra endomorphism of a where i denotes the identity map of a in this paper we first show that for all locally finite k derivations d and locally finite k algebra automorphisms of a the images of d and i do not contain any nonzero idempotent of a we then use this result to show some cases of the lfed and lned conjectures proposed in 21 more precisely we show the lned conjecture for a and the lfed conjecture for all locally finite k derivations of a and all locally finite k e derivations of the form i with being surjective in particular both conjectures are proved for all finite dimensional k algebras furthermore some finite extensions of derivations and automorphism to inner derivations and inner automorphisms respectively have also been established this result is not only crucial in the proofs of the results above but also interesting on its own right

images of derivations of polynomial algebras with divergence zero abstract in this paper we show that the image of a derivation d of k x y with divergence zero is not necessarily a mathieu subspace where k is a field of characteristic zero which gives a negative answer to question 4 1 proposed by van den essen wright and zhao in 4 note that the 2 dimensional jacobian conjecture is equivalent to saying that the image of any derivation d of k x y with divergence zero and 1 im d is a mathieu subspace

a note on the complexity of the causal ordering problem in this note we provide a concise report on the complexity of the causal ordering problem originally introduced by simon to reason about causal dependencies implicit in systems of mathematical equations we show that simon s classical algorithm to infer causal ordering is np hard an intractability previously guessed but never proven we present then a detailed account based on nayak s suggested algorithmic solution the best available which is dominated by computing transitive closure bounded in time by o v s where s e v is the input system structure composed of a set e of equations over a set v of variables with number of variable appearances density s we also comment on the potential of causal ordering for emerging applications in large scale hypothesis management and analytics

incompatibility of diophantine equations arising from the strong factorial conjecture abstract in the present article we establish new evidence in support of the strong factorial conjecture of edo and van den essen 2 by proving it in several special cases for example we show that the conjecture holds for powers of linear forms and sums of prime powers of the variables finally we show one way of constructing new examples of polynomials satisfying the conjecture using known examples

on the length of polynomial automorphisms of the affine plane the automorphism group of the affine plane is a mysterious and challenging object although we know that it is an amalgamated product of two well known subgroups many questions are still unsolved moreover the group has the structure of an infinite dimensional algebraic group but the interactions between these two structures are not yet clear in this paper we study the length of an element defined using the amalgamated structure with respect to the algebraic structure if the ground field is of characteristic zero we prove that the length is a lower semicontinuous function on the group