spectral parameter dependent approach to quantized algebra its multiparameter deformations and their q oscillator realizations yang baxterization of faddeev reshetikhin takhtajan algebra 1989 leading to quantum ybe is considered for a class of r matrices which satisfy hecke relations the authors apply such construction of the gl n case together with its multiparameter deformations revealing the connection between frt relations and the extended trigonometric sklyanin algebra new realizations of frt algebra through q oscillator modes are presented and their potential importance in the context of quantum integrable models is discussed a multiparametrized r matrix with the inclusion of spectral parameter is constructed as a by product

unusual solutions to the yang baxter equation the complete list of non symmetric eight vertex constant solutions to the yang baxter equation is obtained and new solutions dependent on more than one variable are presented the corresponding spin hamiltonians are derived by sutherland s method 1970

base change and a problem of serre we establish a version of level lowering for mod p galois representations arising from the reductions of representations associated to hilbert modular forms in particular we show that level lowering can be easily achieved if one replaces the base field with a suitable solvable extension this is often enough for applications to proving the modularity of p adic representations

efficient construction of reversible jump markov chain monte carlo proposal distributions the major implementational problem for reversible jump markov chain monte carlo methods is that there is commonly no natural way to choose jump proposals since there is no euclidean structure in the parameter space to guide our choice we consider mechanisms for guiding the choice of proposal the first group of methods is based on an analysis of acceptance probabilities for jumps essentially these methods involve a taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to langevin algorithms the second group of methods generalizes the reversible jump algorithm by using the so called saturated space approach these allow the chain to retain some degree of memory so that when proposing to move from a smaller to a larger model information is borrowed from the last time that the reverse move was performed the main motivation for this paper is that in complex problems the probability that the markov chain moves between such spaces may be prohibitively small as the probability mass can be very thinly spread across the space therefore finding reasonable jump proposals becomes extremely important we illustrate the procedure by using several examples of reversible jump markov chain monte carlo applications including the analysis of autoregressive time series graphical gaussian modelling and mixture modelling

level raising and symmetric power functoriality ii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

semiparametric regression in capture recapture modeling capture recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time variation in survival may be explained by incorporating relevant covariates we propose nonparametric and semiparametric regression methods for estimating survival in capture recapture models a fully bayesian approach using markov chain monte carlo simulations was employed to estimate the model parameters the work is illustrated by a study of snow petrels in which survival probabilities are expressed as nonlinear functions of a climate covariate using data from a 40 year study on marked individuals nesting at petrels island terre adelie

on special zeros of p adic l functions of hilbert modular forms let e be a modular elliptic curve over a totally real number field f we prove the weak exceptional zero conjecture which links a higher derivative of the p adic l function attached to e to certain p adic periods attached to the corresponding hilbert modular form at the places above p where e has split multiplicative reduction under some mild restrictions on p and the conductor of e we deduce the exceptional zero conjecture in the strong form i e where the automorphic p adic periods are replaced by the mathcal l invariants of e defined in terms of tate periods from a special case proved earlier by mok crucial for our method is a new construction of the p adic l function of e in terms of local data

coloured frt algebra and its yang baxterization leading to integrable models with non additive r matrices a colour representation of faddeev reshetikhin takhtajan frt algebra which in contrast to the standard case is related to the coloured braid group representation with generic values of q is presented explicit realizations of l or matrices occurring in this coloured variant of frt algebra are also obtained for the uq gl 2 quantized algebra though these realizations are found to depend manifestly on the colour parameters the underlying quantum group structure and associated co product are interestingly free from such dependence this allows us to perform the yang baxterization of the coloured frt algebra successfully which leads to the construction of an ancestor law operator associated with a new non additive type quantum r matrix through different realizations of this lax operator a new class of quantum integrable models representing colour generalizations of the well known models such as the lattice sine gordon model the ablowitz ladik model lattice and the derivative nonlinear schrodinger model etc is generated

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

transcendence of hecke operators in the big hecke algebra we prove a transcendence result of hecke operator t l over the ring generated by diamond operators over in a non cm component of the cyclotomic ordinary big p adic hecke algebra and we discuss its conjectural implication of a modulo p version to the vanishing of the cyclotomic invariant 2014

estimating migration rates using tag recovery data tag recovery data are used to estimate migration rates among a set of strata the model formulation is a simple matrix extension of the formulation of a tag recovery experiment discussed by brownie et al 1985 statistical inference from band recovery data a handbook 2nd edition washington d c u s department of the interior estimation is more difficult because of the convolution of parameters between release and recovery and this convolution may cause estimates of the survival migration parameters to have low precision derived parameters of emigration immigration harvest derivation and overall net survival are also estimated the models are applied to estimate the migration of pacific herring among spawning grounds off the west coast of canada if animals can be re released after being recaptured the model corresponds in its migration survival components to that of arnason 1972 researches in popiulation ecology 13 97 113 this correspondence is developed leading to more efficient estimators of these parameters

on the modularity of 2 adic potentially semi stable deformation rings using p adic local langlands correspondence for text gl 2 mathbb q 2 and an ordinary r mathbb t theorem we prove that the support of patched modules for quaternionic forms meet every irreducible component of the potentially semi stable deformation ring this gives a new proof of the breuil mezard conjecture for 2 dimensional representations of the absolute galois group of mathbb q 2 which is new in the case overline r a twist of an extension of the trivial character by itself as a consequence a local restriction in the proof of fontaine mazur conjecture in pask nas algebra number theory 10 6 1301 1358 2016 is removed

tate cycles on some quaternionic shimura varieties mod p let f be a totally real field in which a prime number p 2 is inert we continue the study of the generalized goren oort strata on quaternionic shimura varieties over finite extensions of fp we prove that when the dimension of the quaternionic shimura variety is even the tate conjecture for the special fiber of the quaternionic shimura variety holds for the cuspidal isotypical component as long as the two unramified satake parameters at p are not differed by a root of unity

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

closed form likelihoods for arnason schwarz models we provide a general framework for the computationally efficient analysis both bayesian and classical of integrated multi site recovery recapture models in the presence of individual level covariates by extending the basic arnason schwarz models and deriving closed form likelihood expressions together with corresponding sufficient statistics

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

solutions of the nonadditive ybe by spectral parameter factorization and re yang baxterization r matrix solutions for the nonadditive yang baxter equation are obtained in arbitrary dimension using a factorization ansatz in spectral parameters a symmetry transformation determined for the particle conserving r matrix is used to formulate a re yang baxterization scheme with multicomponent spectral parameters extending the notion of conventional yang baxterization the possible scope for such a transformation which has a striking resemblance to reshetikhin s deformation of r matrices but extended now to include spectral parameters is discussed

the failure distribution in percolation models of breakdown the probability of finding a largest defect cluster of size n in a percolation network is calculated analytically using a new distribution function scaling equation from this result and the stress voltage enhancement at the tip of the most critical defect in the network the probability of failure in percolation models of breakdown is calculated for defect fractions less than the percolation point this distribution is found to be of the form exponential of an exponential numerical simulations on the two dimensional random fuse network confirm the new distribution function and convincingly distinguish between it and the weibull 1951 form most often used in the fitting of breakdown data

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

autoregressive models for capture recapture data a bayesian approach in this article we incorporate an autoregressive time series framework into models for animal survival using capture recapture data researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next this may not be realistic for some populations using a gibbs sampling approach we can estimate covariate coefficients and autoregressive parameters for survival models the procedure is illustrated with a waterfowl band recovery dataset for northern pintails anas acuta the analysis shows that the second lag autoregressive coefficient is significantly less than 0 suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases software to implement the methodology is available at no charge on the internet

modularity of 2 adic barsotti tate representations we prove a modularity lifting theorem for two dimensional 2 adic potentially barsotti tate representations this proves hypothesis h of khare wintenberger and completes the proof of serre s conjecture the main new ingredient is a classification of connected finite flat group schemes over rings of integers of finite extensions of 2

yang baxterization of braid group representation associated with the seven dimensional representation of g2 the explicit expression of a solution that relates to the seven dimensional representation of the lie algebra g2 of the quantum yang baxter equation qybe is obtained by applying the yang baxterization procedure to the braid group representation bgr the result is consistent with an earlier one derived by a different method

on the representations of glq n using the heisenberg weyl relations using the representations of the heisenberg weyl relations the authors develop a systematic scheme for constructing finite and infinite dimensional representations of the elements of the quantum groups glq n where the deformation parameter q is a primitive root of unity explicit results for the examples glq 2 glq 3 and glq 4 are discussed

algebraic cycles on a product of two hilbert modular surfaces in this paper we prove the tate conjecture for a product of two hilbert modular surfaces for non cm submotives

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

on serre s conjecture for 2 dimensional mod p representations of gal q q we prove the existence in many cases of minimally ramified p adic lifts of 2 dimensional continuous odd absolutely irreducible mod p representations of the absolute galois group of q it is predicted by serre s conjecture that such representations arise from newforms of optimal level and weight

level raising and symmetric power functoriality iii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

consistent multiparameter quantisation of gl n the author describes a manifold of quantum group structures on the vector space of the universal enveloping algebra of gl n and on its dual the space of polynomials in n2 variables the dimension of the manifold is n2 n 2 2

semi markov arnason schwarz models we consider multi state capture recapture recovery data where observed individuals are recorded in a set of possible discrete states traditionally the arnason schwarz model has been fitted to such data where the state process is modeled as a first order markov chain though second order models have also been proposed and fitted to data however low order markov models may not accurately represent the underlying biology for example specifying a time independent first order markov process involves the assumption that the dwell time in each state i e the duration of a stay in a given state has a geometric distribution and hence that the modal dwell time is one specifying time dependent or higher order processes provides additional flexibility but at the expense of a potentially significant number of additional model parameters we extend the arnason schwarz model by specifying a semi markov model for the state process where the dwell time distribution is specified more generally using for example a shifted poisson or negative binomial distribution a state expansion technique is applied in order to represent the resulting semi markov arnason schwarz model in terms of a simpler and computationally tractable hidden markov model semi markov arnason schwarz models come with only a very modest increase in the number of parameters yet permit a significantly more flexible state process model selection can be performed using standard procedures and in particular via the use of information criteria the semi markov approach allows for important biological inference to be drawn on the underlying state process for example on the times spent in the different states the feasibility of the approach is demonstrated in a simulation study before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis

a study of representations of the algebra of functions on the quantum group glq n a q analogue of the root system is constructed for this algebra which is similar to the root system of classical lie algebras it is then used to construct in detail a class of representations of the algebra of functions on the quantum group glq n and a q boson realization of the generators of glq n is given i also construct infinite dimensional hilbert space representations of this algebra the main result of this paper is stated in proposition 8

on the exchange matrix for wznw model the connection between the exchange algebra in thesu 2 wess zumino novikov witten model and the quantum groupsu 2 is discussed it is shown that on the quasiclassical level this connection has the simple interpretation in terms of the lie poisson action ofsu 2 on the chiral components of the fields in the wznw model

universal r matrix of reductive lie algebras and quantum integrable systems from its colour representation the universal r matrix intertwining between the coproduct structures related to the universal deformations of reductive lie algebras has been found in an explicit form using twisting a possible colour representation of this r matrix and its application to the integrable systems are shown using the example of a deformed gl n algebra

yang baxterization of braid group representations for a given braid group representation bgr a process of the yang baxterization is formulated to generate solutions of the yang baxter equation ybe when a bgr admits the birman wenzl bw algebraic structure this process can be explicitly passed through and two types of trigonometric solutions of ybe are generated from such a bgr these two solutions have the essential difference to each other and both of them preserve the crossing symmetry property if the given bgr has by taking certain reduction on the bw algebra the rational solution is also generated a practical condition to judge whether a bgr satisfies the bw algebra is given from which one finds that not only the familiar bgrs of 5 7 9 but also some new ones obtained recently in 12 have the bw structure thus they can be explicitly yang baxterized to solutions of the ybe

bayesian model discrimination for multiple strata capture recapture data summary extending the work of dupuis 1995 we motivate a range of biologically plausible models for multiple site capture recapture and show how the original gibbs sampling algorithm of dupuis can be extended to obtain posterior model probabilities using reversible jump markov chain monte carlo this model selection procedure improves upon previous analyses in two distinct ways first bayesian model averaging provides a robust parameter estimation technique which properly incorporates model uncertainty in the resulting intervals secondly by discriminating among perhaps millions of competing models we are able to discern fine structure within the data and thereby answer questions of primary biological importance we demonstrate how reversible jump markov chain monte carlo methods provide the only viable method for exploring model spaces of this size we examine the lizard data discussed in dupuis 1995 and show that most of the posterior mass is placed upon models not previously considered for these data we discuss model discrimination and model averaging and focus upon the increased scientific understanding of the data obtained via the bayesian model comparison procedure

quaternionic manin symbols brandt matrices and hilbert modular forms in this paper we propose a generalization of the algorithm we developed previously along the way we also develop a theory of quaternionic m symbols whose definition bears some resemblance to the classical m symbols except for their combinatorial nature the theory gives a more efficient way to compute hilbert modular forms over totally real number fields especially quadratic fields and we have illustrated it with several examples namely we have computed all the newforms of prime levels of norm less than 100 over the quadratic fields q 29 and q 37 and whose fourier coefficients are rational or are defined over a quadratic field

on the critical values of l functions of base change for hilbert modular forms in this paper we generalize some results obtained by shimura yoshida and the author on critical values of l functions of l adic representations attached to hilbert modular forms twisted by nite order characters to the critical values of l functions of arbitrary base change to totally real number elds of l adic representations attached to hilbert modular forms twisted by some nite dimensional representations 2010 mathematics subject classication 11f41 11f80 11r42 11r80

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

on the bayesian analysis of population size summary we consider the problem of estimating the total size of a population from a series of incomplete census data we observe that inference is typically highly sensitive to the choice of model and we demonstrate how bayesian model averaging techniques easily overcome this problem we combine and extend the work of madigan york 1997 and dellaportas forster 1999 using reversible jump markov chain monte carlo simulation to calculate posterior model probabilities which can then be used to estimate modelaveraged statistics of interest we provide a detailed description of the simulation procedures involved and consider a wide variety of modelling issues such as the range of models considered their parameterisation both prior choice and sensitivity and computational efficiency we consider a detailed example concerning adolescent injuries in pennsylvania on the basis of medical school and survey data in the context of this example we discuss the relationship between posterior model probabilities and the associated information criteria values for model selection we also discuss cost efficiency issues with particular reference to inclusion and exclusion of sources on the grounds of cost we consider a decision theoretic approach which balances the cost and accuracy of different combinations of data sources to guide future decisions on data collection

relating the approaches to quantised algebras and quantum groups this paper constructs two representations of the quantum groupu q g by exploiting its quotient structure and the quantum double construction here the quantum group is taken as the dual to the quantised algebrau q g a one parameter deformation of the universal enveloping algebra of the lie algebra g as in drinfel d 6 and jimbo 10 from the two representations the hopf structure of the quantised algebrau q g is reexpressed in a matrix format this is the very structure given by faddeev et al 7 in their approach to defining quantum groups and quantised algebras via the quantisation of the function space of the associated lie group to g

moduli of finite flat group schemes and modularity we prove that under some mild conditions a two dimensional p adic galois representation which is residually modular and potentially barsotti tate at p is modular this provides a more conceptual way of establishing the shimura taniyama weil conjecture especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3 the main ingredient is a new technique for analyzing flat deformation rings it involves resolving them by spaces which parametrize finite flat group scheme models of galois representations introduction