testing for monotonicity of a regression mean by calibrating for linear functions a new approach to testing for monotonicity of a regression mean not requiring computation of a curve estimator or a bandwidth is suggested it is based on the notion of running gradients over short intervals although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip excess mass approach for testing modality hypotheses about densities like the latter methods the new technique does not suffer difficulties caused by almost flat parts of the target function in fact it is calibrated so as to work well for flat response curves and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders in this respect as well as in its construction the running gradients approach differs from alternative techniques based on the notion of a critical bandwidth

resolutions of mesh algebras periodicity and calabi yau dimensions a triangulated category mathcal t sigma is said to be calabi yau of dimension d if d is a serre functor we determine which stable module categories of self injective algebras of finite type are calabi yau and compute their calabi yau dimensions correcting errors in previous work we first show that the calabi yau property of mod can be detected in the minimal projective resolution of the stable auslander algebra of over its enveloping algebra we then describe the beginning of such a minimal resolution for any mesh algebra of a stable translation quiver and apply covering theory to relate these minimal resolutions to those of the generalized preprojective algebras of dynkin graphs for representation finite self injective algebras of torsion order t 1 we obtain a complete description of their stable calabi yau properties but only partial results for those algebras of torsion order t 2 we also obtain some new information about the periods of the representation finite self injective algebras of torsion order t 1 finally we describe how these questions can also be approached by realizing the stable categories of representation finite self injective algebras as orbit categories of the bounded derived categories of hereditary algebras and illustrate this technique with several explicit computations that our previous methods left unsettled

bayesian local extremum splines we consider shape restricted nonparametric regression on a closed set formula see text where it is reasonable to assume the function has no more than h local extrema interior to formula see text following a bayesian approach we develop a nonparametric prior over a novel class of local extremum splines this approach is shown to be consistent when modeling any continuously differentiable function within the class considered and is used to develop methods for testing hypotheses on the shape of the curve sampling algorithms are developed and the method is applied in simulation studies and data examples where the shape of the curve is of interest

stabilization of discrete time nonlinear uncertain systems by feedback based on ls algorithm this paper is concerned with the use of the least squares ls algorithm to design a feedback control law to stabilize a basic class of discrete time nonlinear uncertain systems the result shows that if a certain polynomial criterion is satisfied the system can be stabilized by feedback based on the ls algorithm for gaussian distributed noise and unknown parameters this result thus provides an answer to the question of what are the fundamental limitations of the discrete time adaptive nonlinear control this issue of feedback capability has been an open problem for more than ten years since it was put forward

configurations of trivial extensions of dynkin type a n for a given trivial extensionof cartan class dn we find a combinatorial algorithm giving the configuration of zdn associated to this algorithm is stated in the theorem 6 8 and illustrated in the example 6 3 in order to do that we develop an inductive embedding technique for the auslander reiten quiver of a trivial extensionof type dn this technique uses the ordinary quiver q which is the union of oriented cycles and a well known set of relationssuch thatis the quotient path algebra kq see 1 5 and 6 giving a trivial exten sion of type dn we get a trivial extensionof type dn m 1 by inserting a cycle with m vertices in one of the so called in sertion vertices of q in section 3 we describe the embedding of into this will allow us to deduce properties offrom and since q has less cycles that q we will use this embed ding to reduce the study ofto the minimal trivial extensions which were done in section 2

presentations of trivial extensions of finite dimensional algebras and a theorem of sheila brenner let be a finite dimensional algebra over an algebraically closed field such that any oriented cycle in the ordinary quiver of is zero in we describe the ordinary quiver and relations for t d the trivial extension of by its minimal injective cogenerator d and also for the repetitive algebra formula of associated with this description we give an application of a theorem of sheila brenner

stable calabi yau dimension of self injective algebras of finite type abstract we give an equivalent definition of the stable calabi yau dimension in terms of bimodule syzygies and so called stably inner automorphisms using it we complete the computation of the stable calabi yau dimensions of the self injective algebras of finite representation type which was started by k erdmann a skowronski j bialkowski and a dugas

the symmetry period and calabi yau dimension of finite dimensional mesh algebras abstract within the class of finite dimensional mesh algebras we identify those which are symmetric and those whose stable module category is calabi yau we also give in combinatorial terms explicit formulas for the period of any such algebra where is the syzygy functor and for the calabi yau frobenius and the stable calabi yau dimensions when they are defined

a characterization of selfinjective algebras of strictly canonical type abstract we prove that the class of selfinjective algebras of strictly canonical type investigated in kwiecien and skowronski 2009 27 kwiecien and skowronski 2009 28 coincides with the class of selfinjective algebras having triangular galois coverings with infinite cyclic group and the auslander reiten quiver with quasi tubes maximally saturated by simple and projective modules satisfying natural conditions

self injective algebras and the second hochschild cohomology group abstract in this paper we study the second hochschild cohomology group hh 2 of a finite dimensional algebra in particular we determine hh 2 where is a finite dimensional self injective algebra of finite representation type over an algebraically closed field k and show that this group is zero for most such we give a basis for hh 2 in the few cases where it is not zero

embedding of the vertices of the auslander reiten quiver of an iterated tilted algebra of dynkin type δ in zδ abstract let be a dynkin diagram and k an algebraically closed field let a be an iterated tilted finite dimensional k algebra of type and denote by a its repetitive algebra we approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the auslander reiten quiver a of a in the auslander reiten quiver mod a z of the stable category mod a let t be a trivial extension of finite representation type and cartan class assume that we know the vertices of z corresponding to the radicals of the indecomposable projective t modules we determine the embedding of a in z for any algebra a such that t a t

on nonparametric tests of positivity monotonicity convexity we consider the problem of estimating the distance from an unknown signal observed in a white noise model to convex cones of positive monotone convex functions we show that when the unknown function belongs to a holder class the risk of estimating the l r distance 1 r from the signal to a cone is essentially the same up to a logarithmic factor as that of estimating the signal itself the same risk bounds hold for the test of positivity monotonicity and convexity of the unknown signal we also provide an estimate for the distance to the cone of positive functions for which risk is by a logarithmic factor smaller than that of the plug in estimate

on robust stability of discrete time adaptive nonlinear control abstract we consider adaptive control of discrete time nonlinear systems with a single unknown parameter in this paper we demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4 this result further confirms the conclusion of guo on critical stability of discrete time adaptive nonlinear control ieee trans automat control 42 1997 1488 1499 which addresses unbounded noise in a stochastic setting also in our worst case approach we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4

an impossibility theorem on a class of high order discrete time nonlinear control systems a high order discrete time nonlinear system with unknown parameters and gaussian noise is studied in this paper and it is shown that under a simple algebraic condition concerning the nonlinearity of the system there does not exist any feedback controller that globally stabilizes the uncertain system this impossibility result attempts to understand the capability and limitation of feedback mechanism of a high order discrete time nonlinear system and continues a series of previous research on similar first order systems this result shows that for the high order discrete time nonlinear system studied here a polynomial corresponding to the first order principle part of the system determines the limit of the feedback mechanism

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

multiscale testing of qualitative hypotheses suppose that one observes a process y on the unit interval where dy t n1 2f t dt dw t with an unknown function parameter f given scale parameter n 1 sample size and standard brownian motion w we propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity these tests are asymptotically optimal and adaptive in a certain sense they are constructed via a new class of multiscale statistics and an extension of levy s modulus of continuity of brownian motion

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

a limit to the capability of feedback feedback is ubiquitous and is a basic concept in the area of control where it is used primarily for reducing internal or external uncertainties or both in this note we will study the capability of feedback in dealing with both internal and external uncertainties for a class of pth order nonlinear autoregressive control systems the size of the uncertainty is described by the lipschitz constant say l of the uncertain nonlinear function in consideration it is shown that if p and l satisfy a certain inequality then there exists no globally stabilizing feedback for the corresponding class of uncertain systems and thus finding a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties

on selfinjective algebras of finite representation type with maximal almost split sequences abstract we investigate the structure of finite dimensional selfinjective algebras of finite representation type over an arbitrary field having almost split sequences of modules whose middle term admits the maximal possible number of indecomposable direct summands

on compact exceptional objects in derived module categories abstract let a be a basic and connected finite dimensional algebra and d b a be the bounded derived category of finitely generated left a modules in this paper we consider lengths of tilting objects and indecomposable compact exceptional objects in d b a and prove a sufficient condition such that these lengths are bounded by the number of isomorphism classes of simple a modules moreover we show that algebras satisfying this criterion are bounded derived simple and describe an algorithm to construct a family of algebras satisfying this condition

adaptive tests of linear hypotheses by model selection we propose a new test based on model selection methods for testing that the expectation of a gaussian vector with n independent components belongs to a linear subspace of r n against a nonparametric alternative the testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative the properties of the test are nonasymptotic and we prove that the test is rate optimal up to a possible log n factor over various classes of alternatives simultaneously we also provide a simulation study in order to evaluate the procedure when the purpose is to test goodness of fit in a regression model 1 introduction we consider the regression model

simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm this paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time the nonlinear least squares nls algorithm is applied to estimate the unknown parameters and it turns out to be the standard least squares ls algorithm whenever the model is linearly parameterized based on this algorithm both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar parameter case

testing convex hypotheses on the mean of a gaussian vector application to testing qualitative hypotheses on a regression function in this paper we propose a general methodology based on multiple testing for testing that the mean of a gaussian vector in r n belongs to a convex set we show that the test achieves its nominal level and characterize a class of vectors over which the tests achieve a prescribed power in the functional regression model this general methodology is applied to test some qualitative hypotheses on the regression function for example we test that the regression function is positive increasing convex or more generally satisfies a differential inequality uniform separation rates over classes of smooth functions are established and a comparison with other results in the literature is provided a simulation study evaluates some of the procedures for testing monotonicity

multiserial and special multiserial algebras and their representations abstract in this paper we study multiserial and special multiserial algebras these algebras are a natural generalization of biserial and special biserial algebras to algebras of wild representation type we define a module to be multiserial if its radical is the sum of uniserial modules whose pairwise intersection is either 0 or a simple module we show that all finitely generated modules over a special multiserial algebra are multiserial in particular this implies that in analogy to special biserial algebras being biserial special multiserial algebras are multiserial we then show that the class of symmetric special multiserial algebras coincides with the class of brauer configuration algebras where the latter are a generalization of brauer graph algebras we end by showing that any symmetric algebra with radical cube zero is special multiserial and so in particular it is a brauer configuration algebra

a generalization of gabriel s galois covering functors and derived equivalences abstract let g be a group acting on a category c we give a definition for a functor f c c to be a g covering and three constructions of the orbit category c g which generalizes the notion of a galois covering of locally finite dimensional categories with group g whose action on c is free and locally bonded defined by gabriel here c g is defined for any category c and we do not require that the action of g is free or locally bounded we show that a g covering is a universal g invariant functor and is essentially given by the canonical functor c c g by using this we improve a covering technique for derived equivalences also we prove theorems describing the relationships between smash product construction and the orbit category construction by cibils and marcos 2006 without the assumption that the g action is free the orbit category construction by a cyclic group generated by an auto equivalence modulo natural isomorphisms e g the construction of cluster categories is justified by a notion of the colimit orbit category in addition we give a presentation of the orbit category of a category with a monoid action by a quiver with relations which enables us to calculate many examples

gluing derived equivalences together abstract the grothendieck construction of a diagram x of categories can be seen as a process to construct a single category gr x by gluing categories in the diagram together here we formulate diagrams of categories as colax functors from a small category i to the 2 category k cat of small k categories for a fixed commutative ring k in our previous paper we defined derived equivalences of those colax functors roughly speaking two colax functors x x i k cat are derived equivalent if there is a derived equivalence from x i to x i for all objects i in i satisfying some i equivariance conditions in this paper we glue the derived equivalences between x i and x i together to obtain a derived equivalence between grothendieck constructions gr x and gr x which shows that if colax functors are derived equivalent then so are their grothendieck constructions this generalizes and well formulates the fact that if two k categories with a g action for a group g are g equivariantly derived equivalent then their orbit categories are derived equivalent as an easy application we see by a unified proof that if two k algebras a and a are derived equivalent then so are the path categories a q and a q for any quiver q so are the incidence categories a s and a s for any poset s and so are the monoid algebras a g and a g for any monoid g also we will give examples of gluing of many smaller derived equivalences together to have a larger derived equivalence

d representation finite self injective algebras abstract in this paper we initiate the study of higher dimensional auslander reiten theory of self injective algebras we give a systematic construction of weakly d representation finite self injective algebras as orbit algebras of the repetitive categories of algebras of finite global dimension satisfying a certain finiteness condition for the serre functor the condition holds in particular for all fractionally calabi yau algebras of global dimension at most d this generalizes riedtmann s classical construction of representation finite self injective algebras our method is based on an adaptation of gabriel s covering theory for k linear categories to the setting of higher dimensional auslander reiten theory applications include n fold trivial extensions and classical and higher preprojective algebras which are shown to be d representation finite in many cases we also get a complete classification of all d representation finite self injective nakayama algebras for arbitrary d

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

gorenstein versions of covering techniques for linear categories and their applications abstract let c be a g category for some group g we show that a g covering functor p c c g induces g precovering of their bounded derived categories singularity categories and gorenstein defect categories then we provide a gorenstein version of gabriel s theorem using this result we investigate the number of summands in a decomposition of the middle term of almost split sequences over monomial algebras

derived equivalences for φ auslander yoneda algebras in this paper we introduce auslander yoneda algebras in a triangulated category with a parameter set in n and present a method to construct new derived equivalences between these auslander yoneda algebras not necessarily artin algebras or their quotient algebras from a given almost stable derived equivalence as consequences of our method we have 1 suppose that a and b are representation finite self injective artin algebras with ax and by additive generators for a and b respectively if a and b are derived equivalent then the auslander yoneda algebras of x and y are derived equivalent for every admissible set in particular the auslander algebras of a and b are both derived equivalent and stably equivalent 2 for a self injective

tests for monotonicity of a regression mean with guaranteed level in this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed the procedure is based on signs of differences of observations from the response variable the test is calibrated against the most difficult null hypothesis when the regression function is constant and produces an exact test in this context in general the test is conservative the power of the test is good and comparable with that of other nonparametric tests it is shown that the testing procedure has asymptotic power 1 against certain local alternatives the method is also robust against heavy tailed error distributions and even maintains good power when the errors are for example cauchy distributed a simulation study is provided to demonstrate finite sample behaviour of the testing procedure

nonparametric bayesian testing for monotonicity this paper adopts a nonparametric bayesian approach to testing whether a function is monotone two new families of tests are constructed the first uses constrained smoothing splines with a hierarchical stochastic process prior that explicitly controls the prior probability of monotonicity the second uses regression splines together with two proposals for the prior over the regression coefficients via simulation the finite sample performance of the tests is shown to improve upon existing frequentist and bayesian methods the asymptotic properties of the bayes factor for comparing monotone versus nonmonotone regression functions in a gaussian model are also studied our results significantly extend those currently available which chiefly focus on determining the dimension of a parametric linear model

fundamental limitations of discrete time adaptive nonlinear control a particular polynomial is introduced which can be used to determine under what conditions a typical class of discrete time nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback thus demonstrating the fundamental limitations of discrete time adaptive nonlinear control as a consequence it is shown that for nonlinear systems with unknown parameters and noises the systems may indeed be nonstabilizable in general whenever the usual linear growth condition is relaxed and the number of unknown parameters is large even though the corresponding noise free systems are globally stabilizable