voevodsky s mixed motives versus kontsevich s noncommutative mixed motives abstract we prove that the quotient of voevodsky s category of geometric mixed motives dm gm by the endofunctor q 1 2 embeds fully faithfully into kontsevich s category of noncommutative mixed motives kmm we show moreover that this embedding is compatible with the one between chow motives and noncommutative chow motives along the way we relate kmm with morel voevodsky s stable a 1 homotopy category recover the twisted algebraic k theory of kahn levine from kmm and extend elmendorf mandell s foundational work on multicategories to a broader setting

two component kp hierarchy and the classical boussinesq equation it has been shown that solutions to the kp equation and other equations in the kp hierarchy take a wronskian form the authors extend these ideas to two component wronskians and the hirota equations 1986 which they satisfy by a reduction procedure they show how dependence on some of the variables can be removed and look in detail at the classical boussinesq equation and its modifications and show how these equations fit into the two component kp hierarchy

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

rings modules and algebras in infinite loop space theory we give a new construction of the algebraic k theory of small permutative categories that preserves multiplicative structure and therefore allows us to give a unified treatment of rings modules and algebras in both the input and output this requires us to define multiplicative structure on the category of small permutative categories the framework we use is the concept of multicategory elsewhere also called colored operad a generalization of symmetric monoidal category that precisely captures the multiplicative structure we have present at all stages of the construction our method ends up in the hovey shipley smith category of symmetric spectra with an intermediate stop at a category of functors out of a particular wreath product

finite rank constraints on linear flows and the davey stewartson equation finite rank constraints for the right derivatives of certain automorphisms solving the heat equation imply the davey stewartson system solutions comprising wronskian and grammian determinants are found and the real reductions for the davey stewartson i and davey stewartson ii are considered

uniqueness of the multiplicative cyclotomic trace abstract making use of the theory of noncommutative motives we characterize the topological dennis trace map as the unique multiplicative natural transformation from algebraic k theory to topological hochschild homology thh and the cyclotomic trace map as the unique multiplicative lift through topological cyclic homology tc moreover we prove that the space of all multiplicative structures on algebraic k theory is contractible we also show that the algebraic k theory functor from small stable categories to spectra is lax symmetric monoidal which in particular implies that e n ring spectra give rise to e n 1 ring algebraic k theory spectra along the way we develop a multiplicative morita theory establishing a symmetric monoidal equivalence between the category of small idempotent complete stable categories and the morita localization of the category of spectral categories

a direct method for dromion solutions of the davey stewartson equations and their asymptotic properties a new direct approach to determining a class of solutions including the dromion solutions of the davey stewartson equations is presented the form of solution obtained allows a detailed asymptotic analysis of the dromion solutions and compact expression for the phase shifts and changes of amplitude as a result of interaction of the dromions to be determined a class of solutions describing dromion scattering is discussed and computer plots of the interactions of such solutions are presented

a multiplicative comparison of segal and waldhausen k theory in this paper we establish a multiplicative equivalence between two multiplicative algebraic k theory constructions elmendorf and mandell s version of segal s k theory and blumberg and mandell s version of waldhausen s s bullet construction this equivalence implies that the ring spectra algebra spectra and module spectra constructed via these two classical algebraic k theory functors are equivalent as ring algebra or module spectra respectively it also allows for comparisons of spectrally enriched categories constructed via these definitions of k theory as both the elmendorf mandell and blumberg mandell multiplicative versions of k theory encode their multiplicativity in the language of multicategories our main theorem is that there is multinatural transformation relating these two symmetric multifunctors that lifts the classical functor from segal s to waldhausen s construction along the way we provide a slight generalization of the elmendorf mandell construction to symmetric monoidal categories

on autoequivalences of the infty 1 category of infty operads we study the infty 1 category of autoequivalences of infty operads using techniques introduced by toen lurie and barwick and schommer pries we prove that this infty 1 category is a contractible infty groupoid our calculation is based on the model of complete dendroidal segal spaces introduced by cisinski and moerdijk similarly we prove that the infty 1 category of autoequivalences of non symmetric infty operads is the discrete monoidal category associated to mathbf z 2 mathbf z we also include a computation of the infty 1 category of autoequivalences of infty n categories based on rezk s theta n spaces

an almost full embedding of the category of graphs into the category of groups abstract we construct a functor f g raphs g roups which is faithful and almost full in the sense that every nontrivial group homomorphism f x f y is a composition of an inner automorphism of fy and a homomorphism of the form ff for a unique map of graphs f x y when f is composed with the eilenberg mac lane space construction k f x 1 we obtain an embedding of the category of graphs into the unpointed homotopy category which is full up to null homotopic maps we provide several applications of this construction to localizations i e idempotent functors we show that the questions 1 is every orthogonality class reflective 2 is every orthogonality class a small orthogonality class have the same answers in the category of groups as in the category of graphs in other words they depend on set theory 1 is equivalent to weak vop nka s principle and 2 to vop nka s principle additionally the second question considered in the homotopy category is also equivalent to vop nka s principle

on the asymptotic properties of estimators of models containing limited dependent variables for the tobit model with independent observations amemiya 1 has established the strong consistency and asymptotic normality of a stationary point 9 of the log likelihood the likelihood for dependent observations may be computationally intractable so the behavior of 9 in the presence of serially correlated observations is of interest under a relaxation of amemiya s assumption of independence we prove that 9 is strongly consistent and asymptotically normal and give an expression for the limiting covariance matrix

the davey stewartson equation and constrained linear flows abstract the davey stewartson system is shown to appear when finite rank constraints are imposed over the right derivatives of certain automorphisms solving the heat equation families of solutions encompassing wronskian and zakharov shabat nakamura type solutions are found for the davey stewartson system and the reduction to the davey stewartson i is discussed

localization and periodicity in unstable homotopy theory in this paper we develop a hierarchy of natural localizations of spaces called the vn periodizations for n 0 which may be used to expose and study periodic phenomena in unstable homotopy theory these vn periodizations act less radically than the corresponding homological localizations 2 and respect fibrations to a very considerable extent a major part of this paper is devoted to developing the general theory of periodizations of spaces thereby providing a foundation for the study of the vn periodization and many others some of this general theory has been developed independently by dror farjoun 13 14 and we refer the reader to his work for an alternative approach with other interesting general results during the past decade remarkable progress was made by ravenel hopkins devinatz and smith 12 16 17 33 toward a global understanding of stable periodic phenomena and we hope that the present paper will help to prepare the way for a similar understanding of unstable periodic phenomena an excellent exposition of localization and periodicity in stable homotopy theory is now available in ravenel s book 35 major features of stable homotopy are understood chromatically as manifestations of more basic periodic phenomena these phenomena belong to a hierarchy starting with those detected rationally followed by those detected in classical k theory and in the successive morava k theories most fundamentally each finite cw spectrum has an intrinsic periodicity given by a vn self map which becomes a selfequivalence after suitable localization for simplicity we describe our results in the pointed homotopy category hoo of connected cw complexes for spaces w y e hoo we call y w periodic or w local when the pointed mapping space map w y is contractible or equivalently when xt w y for t 0 as shown more generally in 3 corollary 7 2 10 or 13 there is a natural initial example x pwx of a map from x to a w periodic space pwx in hoo and we call this the w periodization or w localization of x our notation is derived from the classical example where w sn l and pwx is the n th postnikov section

higher homotopy excision and blakers massey theorems for structured ring spectra abstract working in the context of symmetric spectra we prove higher homotopy excision and higher blakers massey theorems and their duals for algebras and left modules over operads in the category of modules over a commutative ring spectrum e g structured ring spectra

the grothendieck construction for model categories the grothendieck construction is a classical correspondence between diagrams of categories and cocartesian fibrations over the indexing category in this paper we consider the analogous correspondence in the setting of model categories as a main result we establish an equivalence between suitable diagrams of model categories indexed by m and a new notion of model fibrations over m when m is a model category our construction endows the grothendieck construction with a model structure which gives a presentation of lurie s categorical grothendieck construction and enjoys several good formal properties we apply our construction to various examples yielding model structures on strict and weak group actions and on modules over algebra objects in suitable monoidal model categories

sheaves and k theory for f1 schemes this paper is devoted to the open problem in f1 geometry of developing k theory for f1 schemes we provide all necessary facts from the theory of monoid actions on pointed sets and we introduce sheaves for m0 schemes and f1 schemes in the sense of connes and consani a wide range of results hopefully lies the background for further developments of the algebraic geometry over f1 special attention is paid to two aspects particular to f1 geometry namely normal morphisms and locally projective sheaves which occur when we adopt quillen s q construction to a definition of g theory and k theory for f1 schemes a comparison with waldhausen s s construction yields the ring structure of k theory in particular we generalize deitmar s k theory of monoids and show that k specf1 realizes the stable homotopy of the spheres as a ring spectrum

the validity of a simple statistical model for estimating fluvial constituent loads an empirical study involving nutrient loads entering chesapeake bay we consider the appropriateness of rating curves and other log linear models to estimate the fluvial transport of nutrients split sample studies using data from tributaries to the chesapeake bay reveal that a minimum variance unbiased estimator mvue based on a simple log linear model provides satisfactory load estimates even in some cases where the model exhibited significant lack of fit for total nitrogen tn the average difference between the mvue estimates and the observed loads ranges from 8 to 2 at the four sites the corresponding range for total phosphorus tp is 6 to 5 none of these differences is statistically significant the observed variability of the mvue load estimates for tn and tp which ranges from 7 to 25 depending on the case is accurately predicted by statistical theory

the application of the dressing method to some integrable dimensional nonlinear equations some integrable 2 1 dimensional nonlinear equations which are the generalizations of dispersive long wave nonlinear schrodinger sinh gordon and heat equations are studied by the inverse spectral transform method the solutions with functional parameters line solitons and rational solutions of these equations are constructed via dressing method

abstract representation theory of dynkin quivers of type a abstract we study the representation theory of dynkin quivers of type a in abstract stable homotopy theories including those associated to fields rings schemes differential graded algebras and ring spectra reflection functors partial coxeter functors and serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules certain explicitly constructed spectral bimodules in fact these universal tilting modules are spectral refinements of classical tilting complexes as a consequence we obtain split epimorphisms from the spectral picard groupoid to derived picard groupoids over arbitrary fields these results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators as further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field this includes yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral serre duality result finally using abstract representation theory of linearly oriented a n quivers we construct canonical higher triangulations in stable derivators and hence a posteriori in stable model categories and stable categories

estimating contaminant loads in rivers an application of adjusted maximum likelihood to type 1 censored data 1 this paper presents an adjusted maximum likelihood estimator amle that can be used to estimate fluvial transport of contaminants like phosphorus that are subject to censoring because of analytical detection limits the amle is a generalization of the widely accepted minimum variance unbiased estimator mvue and monte carlo experiments confirm that it shares essentially all of the mvue s desirable properties including high efficiency and negligible bias in particular the amle exhibits substantially less bias than alternative censored data estimators such as the mle tobit or the mle followed by a jackknife as with the mle and the mvue the amle comes close to achieving the theoretical frechet cramer rao bounds on its variance this paper also presents a statistical framework applicable to both censored and complete data for understanding and estimating the components of uncertainty associated with load estimates this can serve to lower the cost and improve the efficiency of both traditional and real time water quality monitoring

the dirac equation and integrable systems of kp type the propagator for the 2d heat equation in an arbitrary linear space is shown to give solutions of the two component kadomtsev petviashvilii kp equations also called davey stewartson system this propagator is subject to the klein gordon equation and its right derivatives are required to be of rank one that imply that it can be expressed in terms of solutions of the dirac equation large families of solutions of the two component kadomtsev petviashvilii equations are constructed in terms of solutions of the heat and dirac equations particular attention is paid to the real reductions of the davey stewartson type recovering in this way the line solitons and the multidromion solutions moreover new solutions to the davey stewartson i are presented as massive deformations of the dromion

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

estimating constituent loads several recent articles have called attention to the problem of retransformation bias which can arise when log linear regression models are used to estimate sediment or other constituent loads in some cases the bias can lead to underestimation of constituent loads by as much as 50 and several procedures have been suggested for reducing or eliminating it however some of the procedures recommended for reducing the bias can actually increase it this paper compares the bias and variance of three procedures that can be used with log linear regression models the traditional rating curve estimator a modified rating curve method and a minimum variance unbiased estimator mvue analytical derivations of the bias and efficiency of all three estimators are presented it is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates however other conditions exist where they have substantial bias and a large mean square error these conditions commonly occur when sample sizes are small or when loads are estimated during high flow conditions the mvue however is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct since an efficient unbiased estimator is available there seems to be no reason to employ biased estimators

algebraic theories in homotopy theory it is well known in homotopy theory that given a loop space x one can always find a simplicial group g weakly equivalent to x such that the weak equivalence can be realized by maps preserving multiplication it is also known that loop spaces are not the only class of spaces for which a statement of this kind holds for example any aoo space is weakly equivalent to a simplicial monoid and every eilenberg mac lane space k g n with g an abelian group is equivalent to a simplicial abelian monoid results like this suggest that there might be some general principle comparing homotopy structures on a space to algebraic structures our aim in this paper is to show that there is in fact such a principle to make this precise we need a few definitions

a model structure for coloured operads in symmetric spectra we describe a model structure for coloured operads with values in the category of symmetric spectra with the positive model structure in which fibrations and weak equivalences are defined at the level of the underlying collections this allows us to treat r module spectra where r is a cofibrant ring spectrum as algebras over a cofibrant spectrum valued operad with r as its first term using this model structure we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures

ring completion of rig categories we o er a solution to the long standing problem of group completing within the context of rig categories also known as bimonoidal categories given a rig category r we construct a natural additive group completion r that retains the multiplicative structure hence has become a ring category if we start with a commutative rig category r also known as a symmetric bimonoidal category the additive group completion r will be a commutative ring category in an accompanying paper we show how to use this construction to prove the conjecture that the algebraic k theory of the connective topological k theory ring spectrum ku is equivalent to the algebraic k theory of the rig category v of complex vector spaces

derived representation theory of lie algebras and stable homotopy categorification of slk abstract we set up foundations of representation theory over s the sphere spectrum which is the initial ring of stable homotopy theory in particular we treat s lie algebras and their representations characters g l n s verma modules and their duals harish chandra pairs and zuckermann functors as an application we construct a khovanov s l k stable homotopy type with a large prime hypothesis which is a new link invariant using a stable homotopy analogue of the method of j sussan

homotopical localizations of module spectra we prove that stable f localizations where f is any map of spectra preserve ring spectrum structures and module spectrum structures under suitable hypotheses and we use this fact to describe all possible localizations of the integral eilenberg mac lane spectrum hz as a consequence of this study we infer that localizations of stable gems are stable gems and it also follows that there is a proper class of nonequivalent stable localizations

skew monoidal categories and skew multicategories abstract we describe a perfect correspondence between skew monoidal categories and certain generalised multicategories called skew multicategories that arise in nature

s modules and symmetric spectra we study a symmetric monoidal adjoint functor pair between the category of s modules and the category of symmetric spectra the functors induce equivalences between the respective homotopy categories of spectra module spectra and ring spectra then at approximately the same time two categories of spectra with nice smash products were discov ered elmendorf kriz mandell and may constructed the category of s modules ekmm and je smith introduced symmetric spectra hss both categories are quillen model categories and have associated notions of ring and module spectra however these two categories arise in completely dierent ways and even though the homotopy categories are equivalent it is not a priori clear if both frameworks give rise to the same homotopy theory of rings and modules both categories have their merits described in detail in the introductions of ekmm and hss and it is desirable to be able to translate results obtained in one category into conclusions valid in the other the present paper describes an easy mechanism which facilitates such comparisons below we dene a lax symmetric monoidal functor ms sp from the category of s modules to the category of symmetric spectra the functor preserves homotopy groups and has a strong symmetric monoidal left adjoint we show that the two functors induce inverse equivalences of the homotopy categories of spectra ring spectra commutative ring spectra and module spectra main theorem the functor from the category ms of s modules to the category sp of symmetric spectra passes to a symmetric monoidal equivalence of homotopy categories

the dressing method and the solutions with constant asymptotic values at infinity of ds ii equation several classes of exact solutions with constant asymptotic values at infinity of ds ii equation are constructed via the dressing method among these solutions are the solutions with functional parameters multi line solitons and breathers and pure rational solutions

the darboux system finite rank constraints and darboux transformations the exponential solutions of the darboux equations for conjugate nets is considered it is shown that rank one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the darboux system which can be understood as a vectorial darboux transformation of the exponential background the method is extended further to obtain vectorial darboux transformations of the darboux system

energy exchange of interacting coherent structures in multidimensions abstract the formalism recently developed by fokas and the author for the solution of the initial boundary value problem for the davey stewartson equation is used to study the time evolution of the multidromion solution showing in particular that interacting coherent structures in multidimensions not only exhibit a two dimensional phase shift but also change amplitude and exchange energy several examples of physically relevant boundary conditions which generate other kinds of explicit finite energy solutions are also presented

diagram spaces and symmetric spectra abstract we present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra the main motivating examples are the i spaces which are diagrams indexed by finite sets and injections and j spaces which are diagrams indexed by quillen s localization construction 1 on the category of finite sets and bijections we show that the category of i spaces provides a convenient model for the homotopy category of spaces in which every e space can be rectified to a strictly commutative monoid similarly the commutative monoids in the category of j spaces model graded e spaces using the theory of j spaces we introduce the graded units of a symmetric ring spectrum the graded units detect periodicity phenomena in stable homotopy and we show how this can be applied to the theory of topological logarithmic structures

localization of algebras over coloured operads we give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories our approach encompasses a number of previous results about preservation of structures under localizations such as loop spaces or infinite loop spaces and provides new results of the same kind for instance under suitable assumptions homotopical localizations preserve ring spectra in the strict sense not only up to homotopy modules over ring spectra and algebras over commutative ring spectra as well as maps between ring spectra module maps and algebra maps it is principally the treatment of module spectra and their maps that led us to the use of coloured operads also called enriched multicategories in this context

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

mean square error of regression based constituent transport estimates estimates of long term transport of constituents commonly are obtained by summing retransformed estimates from regressions of logarithmically transformed response variables typical explanatory variables for these regressions include functions of flow change in flow time and time of year the mean and mean square error of four estimators of long term transport at periodically measured stations are presented as a function of the observed values of the explanatory variables from the long term record and summary statistics of the regression data estimates of the mean square errors can be used in designing sampling strategies to attempt to minimize the uncertainty in the estimation of long term transport subject to a constraint on the number of samples to be taken this uncertainty is expressed in terms of the explanatory variables in the long term record the regression coefficients and standard error of the regression and the mean and covariance structure of the explanatory variables used in the regression

tilting theory via stable homotopy theory we show that certain tilting results for quivers are formal consequences of stability and as such are part of a formal calculus available in any abstract stable homotopy theory thus these results are for example valid over arbitrary ground rings for quasi coherent modules on schemes in the differential graded context in stable homotopy theory and also in the equivariant motivic or parametrized variant thereof in further work we will continue developing this calculus and obtain additional abstract tilting results here we also deduce an additional characterization of stability based on goodwillie s strongly co cartesian n cubes as applications we construct abstract auslander reiten translations and abstract serre functors for the trivalent source and verify the relative fractionally calabi yau property this is used to offer a new perspective on may s axioms for monoidal triangulated categories