on the quantification and visualization of transient periodic instabilities in pulsatile flows turbulent like flows without cycle to cycle variations are more frequently being reported in studies of cardiovascular flows the associated stimuli might be of mechanobiological relevance but how to quantify them objectively is not obvious classical reynolds decomposition where the flow is separated into mean and fluctuating velocity components is not applicable as the phase average is zero we therefore expanded on established techniques and present the idea analogous to reynolds decomposition to decompose a flow with transient instabilities into low versus high frequency components respectively to discriminate flow instabilities from the underlying cardiac pulsatility transient wall shear stress and velocity signals derived from computational fluid dynamic simulations were transferred to the frequency domain a high pass filter was applied to subtract the 99 most energy containing frequencies which gave a cut off frequency of 25hz we introduce here the spectral power index and compute the fluctuating kinetic energy based on the high pass filtered velocity components both being frequency based operators the efficacy was evaluated in an aneurysm model for multiple flow rates demonstrating transition to turbulent like flows the frequency based operators were found to better correlate with the qualitatively observed flow instabilities compared to conventional descriptors like time averaged wall shear stress or oscillatory shear index we demonstrate how the high frequencies beyond the physiological range could be analyzed and or transferred back to the time domain for quantification and visualization purposes we have introduced general frequency based operators easily extendable to other cardiovascular territories based on a posteriori heuristic filtering that allows for separation isolation and quantification of cycle invariant turbulent like flows

solutions of the boundary yang baxter equation for arbitrary spin we use boundary quantum group symmetry to obtain recursion formulae which determine nondiagonal solutions of the boundary yang baxter equation reflection equation of the xxz type for any spin j

integrable xyz spin chain with boundaries we consider a general class of boundary terms of the open xyz spin 1 2 chain compatible with integrability we have obtained the general elliptic solution of a k matrix obeying the boundary yang baxter equation using the r matrix of the eight vertex model and derived the associated integrable spin chain hamiltonian

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

sov approach for integrable quantum models associated with general representations on spin 1 2 chains of the 8 vertex reflection algebra the analysis of the transfer matrices associated with the most general representations of the 8 vertex reflection algebra on spin 1 2 chains is here implemented by introducing a quantum separation of variables sov method which generalizes to these integrable quantum models the method first introduced by sklyanin for representations reproducing in their homogeneous limits the open xyz spin 1 2 quantum chains with the most general integrable boundary conditions we explicitly construct representations of the 8 vertex reflection algebras for which the transfer matrix spectral problem is separated then in these sov representations we get the complete characterization of the transfer matrix spectrum eigenvalues and eigenstates and its non degeneracy moreover we present the first fundamental step toward the characterization of the dynamics of these models by deriving determinant formulae for the matrix elements of the identity on separated states which particularly apply to transfer matrix eigenstates a comparison of our analysis of the 8 vertex reflection algebra with that of niccoli g 2012 j stat mech p10025 faldella s et al 2014 j stat mech p01011 for the 6 vertex leads to an interesting remark in that there is a profound similarity in both the characterization of the spectral problems and the scalar products which exists for these two different realizations of the reflection algebra once they are described by the sov method as will be shown in a future publication this remarkable similarity will be the basis of a simultaneous determination of the form factors of local operators of integrable quantum models associated with general reflection algebra representations of both 8 vertex and 6 vertex type

the general solutions to the reflection equation of the izergin korepin model we obtain the general solutions to the reflection equation of the izergin korepin model the general solutions have two free parameters and will reduce to the non trivial diagonal solutions when both free parameters vanish it will also reduce to the solutions with upper lower triangular structures when one of the parameters vanishes moreover the hamiltonian with boundary terms for the system is obtained

algebraic bethe ansatz solutions for the sl 2 1 2 and osp 2 1 models with boundary terms this work is concerned with the formulation of the graded quantum inverse scattering method for a class of lattice models with reflecting boundary conditions the sl 2 1 2 and osp 2 1 models are considered with their diagonal reflections in bfb grading this allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the bethe ansatz equations

hecke algebraic approach to the reflection equation for spin chains we use the structural similarity of certain coxeter artin systems to the yang baxter and reflection equations to convert representations of these systems into new solutions of the reflection equation we construct certain bethe ansatz states for these solutions using a parametrization suggested by abstract representation theory

algebraic bethe ansatz for the six vertex model with upper triangular k matrices we consider a formulation of the algebraic bethe ansatz for the six vertex model with non diagonal open boundaries specifically we study the case where both left and right k matrices have an upper triangular form we show that the main difficulty entailed by those forms of the k matrices is the construction of the excited states however it is possible to treat this problem with the aid of an auxiliary transfer matrix and by means of a generalized creation operator

the quantum symmetric xxz chain at delta 1 2 alternating sign matrices and plane partitions we consider the ground state wavefunction of the quantum symmetric antiferromagnetic xxz chain with open and twisted boundary conditions at along with the ground state wavefunction of the corresponding o n loop model at n 1 based on exact results for finite size systems sums involving the wavefunction components and in some cases the largest component itself are conjectured to be directly related to the total number of alternating sign matrices and plane partitions in certain symmetry classes

contracted and expanded integrable structures we propose a generic framework to obtain certain types of contracted and centrally extended algebras this is based on the existence of quadratic algebras reflection algebras and twisted yangians naturally arising in the context of boundary integrable models a quite old misconception regarding the expansion of the e2 algebra into sl2 is resolved using the representation theory of the aforementioned quadratic algebras we also obtain centrally extended algebras associated with rational and trigonometric q deformed r matrices that are solutions of the yang baxter equation

classical and quantum integrable systems with boundaries we study two dimensional classically integrable field theory with independent boundary conditions at each end and obtain three possible generating functions for integrals of motion when this model is an ultralocal one classically integrable boundary conditions can be found when solving boundary k equations in the quantum case we also find that the unitarity condition of the quantum r matrix is sufficient to construct commutative quantities with boundaries and its reflection equations are obtained

density matrix elements and entanglement entropy for the spin 1 2 xxz chain at δ 1 2 we have analytically obtained all the density matrix elements up to six lattice sites for the spin 1 2 heisenberg xxz chain at 1 2 we use the multiple integral formula of the correlation function for the massless xxz chain derived by jimbo and miwa as for the spin spin correlation functions we have newly obtained the fourth and fifth neighbour transverse correlation functions we have calculated all the eigenvalues of the density matrix and analyse the eigenvalue distribution using these results the exact values of the entanglement entropy for the reduced density matrix up to six lattice sites have been obtained we observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory

the importance of being odd in this letter i mainly consider a finite xxz spin chain with periodic boundary conditions and an odd number of sites this system is described by the hamiltonian hxxz j 1n jx j 1x jy j 1y jz j 1z as it turns out the ground state energy is proportional to the number of sites e 3n 2 for a special value of the asymmetry parameter 1 2 the trigonometric polynomial q u the zeros of which are parameters of the ground state bethe eigenvector is explicitly constructed this polynomial of degree n n 1 2 satisfies the baxter t q equation using the second independent solution of this equation that corresponds to the same eigenvalue of the transfer matrix it is possible to find a derivative of the ground state energy w r t the asymmetry parameter this derivative is closely connected with the correlation function jz j 1z 1 2 3 2n2 this correlation function is related to the average number of spin strings for the ground state nstring n 1 n i would like to stress that all the above simple formulae are not applicable to the case of an even number of sites which is usually considered

string correlation functions of the spin 1 2 heisenberg xxz chain we calculate certain string correlation functions originally introduced as order parameters in integer spin chains for the spin 1 2 xxz heisenberg chain at zero temperature and in the thermodynamic limit for small distances we obtain exact results from bethe ansatz and exact diagonalization whereas in the large distance limit field theoretical arguments yield an asymptotic algebraic decay we also make contact with two point spin correlation functions in the asymptotic limit

reduce and boost recovering arbitrary sets of jointly sparse vectors the rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements under appropriate conditions on the measurement matrix the vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern in this paper we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set instead we prove that the entire infinite set of sparse vectors can be recovered by solving a single reduced size finite dimensional problem corresponding to recovery of a finite set of sparse vectors we then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements our approach is exact for both countable and uncountable sets as it does not rely on discretization or heuristic techniques to efficiently find the single sparse vector produced by the last reduction step we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector numerical experiments on random data demonstrate that when applied to infinite sets our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate in the finite model our boosting algorithm has fast run time and much higher recovery rate than known popular methods

relation between diameter and flow in major branches of the arch of the aorta in the analysis of arterial branching the classical cube law has provided a working model for the relation between the diameter of a blood vessel and the flow which the vessel carries on a long term basis the law has shown good agreement with biological data but questions remain regarding its applicability to all levels of the arterial tree the present study tests the hypothesis that the cube law may not be valid in the first few generations of the arterial tree where vessel capacitance and gross anatomy may play important roles biological data have shown some support for this hypothesis in the past but the heterogeneity characteristic of past data has not allowed a conclusive test so far we present new data which have been obtained from the same location on the arterial tree and in sufficient number to make this test possible for the first time also while past tests have been based primarily on correlation of the measured data with an assumed power law we show here that this can be misleading the present data allow a simpler test which does not involve correlation and which leads to more direct conclusions for the vessels surveyed the results show unequivocally that the relation between diameter and flow is governed by a square law rather than the classical cube law coupled with past findings this suggests that the square law may apply at the first few levels of the arterial tree while the cube law continues from there to perhaps the precapillary levels

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

random matrix theory and entanglement in quantum spin chains we compute the entropy of entanglement in the ground states of a general class of quantum spin chain hamiltonians those that are related to quadratic forms of fermi operators between the first n spins and the rest of the system in the limit of infinite total chain length we show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given hamiltonian and those characterizing the haar measure of the associated group these averages are either toeplitz determinants or determinants of combinations of toeplitz and hankel matrices recent generalizations of the fisher hartwig conjecture are used to compute the leading order asymptotics of the entropy as n this is shown to grow logarithmically with n the constant of proportionality is determined explicitly as is the next constant term in the asymptotic expansion the logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal field theoretic calculations in these calculations the constant of proportionality was determined in terms of the central charge of the virasoro algebra our results therefore lead to an explicit formula for this charge we also show that the entropy is related to solutions of ordinary differential equations of painleve type in some cases these solutions can be evaluated to all orders using recurrence relations

errors in power law estimations of inflow rates for intracranial aneurysm cfd patient specific inflow rates are rarely available for computational fluid dynamics cfd studies of intracranial aneurysms instead inflow rates are often estimated from parent artery diameters via power laws i e q dn reflecting adaptation of conduit arteries to demanded flow the present study aimed to validate the accuracy of these power laws internal carotid artery ica flow rates were measured from 25 ica aneurysm patients via 2d phase contrast mri ica diameters derived from 3d segmentation of rotational angiograms were used to estimate inflow rates via power laws from the aneurysm cfd literature assuming the same inlet wall shear stress wss n 3 velocity n 2 or flow rate n 0 for all cases to illustrate the potential impact of errors in flow rate estimates pulsatile cfd was carried out for four cases having large errors for at least one power law flow rates estimated by n 3 and n 0 power laws had significant p 0 01 mean biases of 22 to 32 respectively but with individual errors ranging from 78 to 120 the n 2 power law had no significant bias but had non negligible individual errors of 58 to 71 cfd showed similarly large errors for time averaged sac wss however these were reduced after normalizing by parent artery wss high frequency wss fluctuations evident in 2 4 aneurysms were also sensitive to inflow rate errors care should therefore be exercised in the interpretation of aneurysm cfd studies that rely on power law estimates of inflow rates especially if absolute vs normalized wss or wss instabilities are of interest

fusion and analytical bethe ansatz for thea 1 1 open spin chain we generalize the fusion procedure for the a 1 1 open spin chain 2 and we show that the transfer matrix satisfies a crossing property we use these results to solve the a 1 1 open spin chain with uq su symmetry by means of the analytical bethe ansatz method our results coincide with the known ones obtained via the nested bethe ansatz

asymptotics of toeplitz hankel and toeplitz hankel determinants with fisher hartwig singularities we study the asymptotics in n for n dimensional toeplitz determinants whose symbols possess fisher hartwig singularities on a smooth background we prove the general nondegenerate asymptotic behavior as conjectured by basor and tracy we also obtain asymptotics of hankel determinants on a nite interval as well as determinants of toeplitz hankel type our analysis is based on a study of the related system of orthogonal polynomials on the unit circle using the riemann hilbert approach

a semismooth newton method with multidimensional filter globalization for l_1 optimization due to their property of enhancing the sparsity of solutions l 1 regularized optimization problems have developed into a highly dynamic research area with a wide range of applications we present a class of methods for l 1 regularized optimization problems that are based on a combination of semismooth newton steps a filter globalization and shrinkage thresholding steps a multidimensional filter framework is used to control the acceptance and to evaluate the quality of the semismooth newton steps if the current newton iterate is rejected a shrinkage thresholding based step with quasi armijo stepsize rule is used instead global convergence and transition to local q superlinear convergence for both convex and nonconvex objective functions are established we present numerical results and comparisons with several state of the art methods that show the efficiency and competitiveness of the proposed method

spin chains and combinatorics in this paper we continue the investigation of finite xxz spin chains with periodic boundary conditions and odd number of sites initiated in our previous article stroganov yu g 2001 j phys a math gen 34 l179 85 as it turned out for a special value of the asymmetry parameter 1 2 the hamiltonian of the system has an eigenvalue which is exactly proportional to the number of sites e 3n 2 using mathematica we have found explicitly the corresponding eigenvectors for n 17 the obtained results support the conjecture our paper that this special eigenvalue corresponds to the ground state vector we make a lot of conjectures concerning the correlations of the model many remarkable relations between the wavefunction components are noted it turns out for example that the ratio of the largest component to the least one is equal to the number of the alternating sign matrices

boundary emptiness formation probabilities in the six vertex model at mathbf delta frac mathbf 1 mathbf 2 we define a new family of overlaps c n m for the xxz hamiltonian on a periodic chain of length n these are equal to the linear sums of the groundstate components in the canonical basis wherein m consecutive spins are fixed to the state we define the boundary emptiness formation probabilities as the ratios c n m c n 0 of these overlaps in the associated six vertex model they correspond to correlation functions on a semi infinite cylinder of perimeter n at the combinatorial point we obtain closed form expressions in terms of simple products of ratios of integers

the fisher hartwig conjecture and toeplitz eigenvalues abstract the conjecture of fisher and hartwig published in 1968 describes the asymptotic expansion of toeplitz determinants with singular generating functions for more than twenty years progress was made in extending the validity of the conjecture but recent computer experiments led to counterexamples that show the limits of the original conjecture and pointed the way to a revised conjecture this paper describes the history of the problem several numerical examples and the revised conjecture

completeness of the bethe ansatz solution of the open xxz chain with nondiagonal boundary terms a bethe ansatz solution of the open spin xxz quantum spin chain with nondiagonal boundary terms has recently been proposed using a numerical procedure developed by mccoy et al we find significant evidence that this solution can yield the complete set of eigenvalues for generic values of the bulk and boundary parameters satisfying one linear relation moreover our results suggest that this solution is practical for investigating the ground state of this model in the thermodynamic limit

free fermion branches in some quantum spin models extensive numerical analysis of the eigenspectra of the suq n invariant perk schultz hamiltonian shows some simple regularities for a significant part of the eigenspectrum inspired by those results we have found two sets of solutions of the associated nested bethe ansatz equations the first set is obtained at a special value of the anisotropy q exp i n 1 n and describes in particular the ground state and nearby excitations as a sum of free fermion quasienergies the second set of solutions provides the energies in the sectors whose number ni of particles of distinct species i 0 n 1 are less than or equal to unity except for one of the species for this last set we obtain the eigenspectra of a free fermion model for arbitrary values of the anisotropy

ruijsenaars macdonald type difference operators from belavin model with open boundary conditions antisymmetric fusions of the belavin model with integrable open boundary conditions are studied the centre of the corresponding operator algebra the sklyanin determinant is constructed we prove that the transfer matrices of the fusion hierarchies mutually commute utilizing the factorized l operators this commuting family is expressed as mutually commuting difference operators acting on a function space this gives ruijsenaars macdonald type commuting difference operators which describe the conservation laws of an integrable system

the open xxx spin chain in the sov framework scalar product of separate states in our previous paper kitanine et al 2017 j phys a math theor 50 224001 we have obtained for the xxx spin 1 2 heisenberg open chain new determinant representations for the scalar products of separate states in the quantum separation of variables sov framework in this article we perform a similar study in a more complicated case the xxz open spin 1 2 chain with the most general integrable boundary terms we first revisit the sov solution of this model using a matrix version of the vertex irf gauge transformation so as to reduce one of the boundary k matrices to a diagonal form as usual within the sov approach the scalar products of separate states are computed in terms of dressed vandermonde determinants having an intricate dependency on the inhomogeneity parameters we show that these determinants can be transformed into different ones in which the homogeneous limit can be taken straightforwardly these representations generalize in a non trivial manner to the trigonometric case the expressions found previously in the rational case we also show that generically all scalar products can be expressed in a form which is similar to although more cumbersome than the well known slavnov determinant representation for the scalar products of the bethe states of the periodic chain considering a special choice of the boundary parameters relevant in the thermodynamic limit to describe the half infinite chain with a general boundary we particularize these representations to the case of one of the two states being an eigenstate we obtain simplified formulas that should be of direct use to compute the form factors and correlation functions of this model

broken translation invariance in quasifree fermionic correlations out of equilibrium abstract using the c algebraic scattering approach to study quasifree fermionic systems out of equilibrium in quantum statistical mechanics we construct the nonequilibrium steady state in the isotropic xy chain whose translation invariance has been broken by a local magnetization and analyze the asymptotic behavior of the expectation value for a class of spatial correlation observables in this state the effect of the breaking of translation invariance is twofold mathematically the finite rank perturbation not only regularizes the scalar symbol of the invertible toeplitz operator generating the leading order exponential decay but also gives rise to an additional trace class hankel operator in the correlation determinant physically in its decay rate the nonequilibrium steady state exhibits a left mover right mover structure affected by the scattering at the impurity

fixed point continuation for ell_1 minimization methodology and convergence we present a framework for solving the large scale ell 1 regularized convex minimization problem min x 1 mu f x our approach is based on two powerful algorithmic ideas operator splitting and continuation operator splitting results in a fixed point algorithm for any given scalar mu continuation refers to approximately following the path traced by the optimal value of x as mu increases in this paper we study the structure of optimal solution sets prove finite convergence for important quantities and establish q linear convergence rates for the fixed point algorithm applied to problems with f x convex but not necessarily strictly convex the continuation framework motivated by our convergence results is demonstrated to facilitate the construction of practical algorithms

quantum spin chain toeplitz determinants and the fisher hartwig conjecture we consider the one dimensional quantum spin chain which is called the xx model xx0 model or isotropic xy model in a transverse magnetic field we are mainly interested in the entropy of a block of lneighboring spins at zero temperature and of an infinite system we represent the entropy in terms of a toeplitz determinant and calculate the asymptotic analytically we derive the first two terms of the asymptotic decomposition interestingly these two terms of decomposition clearly show a length scale related to the field h

counting free fermions on a line a fisher hartwig asymptotic expansion for the toeplitz determinant in the double scaling limit we derive an asymptotic expansion for a wiener hopf determinant arising in the problem of counting one dimensional free fermions on a line segment at zero temperature this expansion is an extension of the result in the theory of toeplitz and wiener hopf determinants known as the generalized fisher hartwig conjecture the coefficients of this expansion are conjectured to obey certain periodicity relations which renders the expansion explicitly periodic in the counting parameter we present two methods to calculate these coefficients and verify the periodicity relations order by order the matrix riemann hilbert problem and the painleve v equation we show that the expansion coefficients are polynomials in the counting parameter and list explicitly first several coefficients

boundary scattering symmetric spaces and the principal chiral model on the half line we investigate integrable boundary conditions bcs for the principal chiral model on the half line and rational solutions of the boundary yang baxter equation bybe in each case we find a connection with type i riemannian globally symmetric spaces g h there is a class of integrable bcs in which the boundary field is restricted to lie in a coset of h these bcs are parametrized by g h g h there are rational solutions of the bybe in the defining representations of all classical g parametrized by g h and using these we propose boundary s matrices for the principal chiral model parametrized by g h g h which correspond to our boundary conditions

higher spin polynomial solutions of quantum knizhnik zamolodchikov equation we provide explicit formulae for highest weight to highest weight correlation functions of perfect vertex operators of u q widehat mathfrak sl 2 in arbitrary integer level l they are given in terms of certain macdonald polynomials we apply this construction to the computation of the ground state of higher spin vertex models spin chains spin l 2 xxz or loop models in the root of unity case q e i pi ell 2

emptiness formation probability of the xxz spin heisenberg chain at δ using a multiple integral representation for the correlation functions we compute the emptiness formation probability of the xxz spin heisenberg chain at anisotropy we prove that it is expressed in terms of the number of alternating sign matrices

bethe ansatz solution of the open xxz chain with nondiagonal boundary terms we consider the integrable open xx quantum spin chain with non diagonal boundary terms we derive an exact inversion identity by which we obtain the eigenvalues of the transfer matrix and the bethe ansatz equations for generic values of the boundary parameters the bethe ansatz solution is formulated in terms of the jacobian elliptic functions

boundary k matrices for the six vertex and the n 2n 1 an 1 vertex models boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices k or theta for the six vertex model the general solution depending on four arbitrary parameters is found for the an 1 models all diagonal solutions are found the associated integrable magnetic hamiltonians are explicitly derived

constructing test instances for basis pursuit denoising the number of available algorithms for the so called basis pursuit denoising problem or the related lasso problem is large and keeps growing similarly the number of experiments to evaluate and compare these algorithms on different instances is growing in this correspondence we present a method to produce instances with exact solutions that is based on a simple observation related to the so called source condition from sparse regularization

toeplitz determinants with one fisher hartwig singularity letcbe a function defined on the unit circle with fourier coefficients cn n the fisher hartwig conjecture describes the asymptotic behaviour of the determinants of then ntoeplitz matricesdn c det ci j n 1i j 0for a certain class of functionsc in this paper we prove this conjecture in the case of functions with one singularity more precisely we consider functions of the formc ei b ei t ei 1 u ei 1 heret ei exp i 0 2 is a function with a jump discontinuity u ei 2 2 cos is a function which may have a zero a pole or a discontinuity of oscillating type andbis a sufficiently smooth nonvanishing function with winding number equal to zero the only restriction we impose on the parameters is that 2 is required not to be a negative integer in the case where re 1 2 i e where the corresponding functioncis not integrable we identifycin an appropriate way with a distribution

quantum kz equation with q 1 and correlation functions of the xxz model in the gapless regime an integral solution to the quantum knizhnik zamolodchikov qkz equation with q 1 is presented upon specialization it leads to a conjectural formula for correlation functions of the xxz model in the gapless regime the validity of this conjecture is verified in special cases including the nearest neighbour correlator with an arbitrary coupling constant and general correlators in the xxx and xy limits

third neighbour and other four point correlation functions of spin 1 2 xxz chain the correlation functions of the spin 1 2 xxz chain in the ground state were expressed in the form of multiple integrals for 1 1 and 1 in particular adjacent four point correlation functions were given as certain four dimensional integrals we show that these integrals can be reduced to polynomials with respect to specific one dimensional integrals the results give the polynomial representation of the third neighbour correlation functions

form factors and complete spectrum of xxx antiperiodic higher spin chains by quantum separation of variables the antiperiodic transfer matrices associated to higher spin representations of the rational 6 vertex yang baxter algebra are analyzed by generalizing the approach introduced recently in the framework of sklyanin s quantum separation of variables sov for cyclic representations spin 1 2 highest weight representations and also for spin 1 2 representations of the 6 vertex reflection algebra such sov approach allow us to derive exactly results which represent complicate tasks for more traditional methods based on bethe ansatz and baxter q operator in particular we both prove the completeness of the sov characterization of the transfer matrix spectrum and its simplicity then the derived characterization of local operators by sklyanin s quantum separate variables and the expression of the scalar products of separate states by determinant formulae allow us to compute the form factors of the local spin operators by one determinant formulae similar to those of the scalar products

an antiperiodic dynamical six vertex model i complete spectrum by sov matrix elements of the identity on separate states and connections to the periodic eight vertex model the spin 1 2 highest weight representations of the dynamical six vertex and the standard eight vertex yang baxter algebra on a finite chain are considered in this paper in particular the integrable quantum models associated with the corresponding transfer matrices under antiperiodic boundary conditions for the dynamical six vertex case and periodic boundary conditions for the eightvertexcaseareanalyzedhere fortheantiperiodicdynamicalsix vertextransfer matrix defined on chains with an odd number of sites we adapt sklyanin s quantum separation of variable sov method and explicitly construct the sov representations from the original space of the representations in this way we provide the complete characterization of the eigenvalues and the eigenstates proving also the simplicity of its spectrum moreover we characterize the matrix elements of the identity on separated states of this model by determinant formulae the matrices entering these determinants have elements given by sums over the sov spectrum of the product of the coefficients of the separate states this sov analysis is done without any need to be reduced to the case of the so called elliptic roots of unit and the results derived here define the required setup to extend to the dynamical six vertex model the approach recently developed by the author and collaborators to compute the form factors of the local operators in the sov framework for the periodic eight vertex transfer matrix we prove that its eigenvalues have to satisfy a fixed system of equations in the case of a chain with an odd number of sites this system of equations is the same entering in the sov characterization of the antiperiodic dynamical six vertex transfer matrix spectrum this implies that the set of the periodic eight vertex eigenvalues is contained in the set of the antiperiodic dynamical six vertex eigenvalues a criterion is introduced to find simultaneous eigenvalues of these two transfer matrices and associate with any of such eigenvalues one nonzero eigenstate of the periodic eight vertex transfer matrix by using the sov results moreover a preliminary discussion

quantum fluctuations of one dimensional free fermions and fisher hartwig formula for toeplitz determinants we revisit the problem of finding the probability distribution of a fermionic number of one dimensional spinless free fermions on a segment of a given length the generating function for this probability distribution can be expressed as a determinant of a toeplitz matrix we use the recently proven generalized fisher hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment unlike the method of bosonization the fisher hartwig formula correctly takes into account the discreteness of charge furthermore we numerically check the precision of the generalized fisher hartwig formula find that it has a higher precision than rigorously proven so far and conjecture the form of the next order correction to the existing formula

a new correlator in quantum spin chains we propose a new correlator in one dimensional quantum spin chains the s emptiness formation probability s efp this is a generalization of the emptiness formation probability efp which is the probability that the first n spins of the chain are all aligned downwards in the s efp we let the spins in question be separated by s sites the usual efp corresponds to the special case when s 1 taking s 1 allows us to quantify non local correlations we express the s efp for the anisotropic xy model in a transverse magnetic field a system with both critical and non critical regimes in terms of a toeplitz determinant for the isotropic xy model we find that the magnetic field induces an interesting length scale

diagonally and antidiagonally symmetric alternating sign matrices of odd order we study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices dasasms of fixed odd order by introducing a case of the six vertex model whose configurations are in bijection with such matrices the model involves a grid graph on a triangle with bulk and boundary weights which satisfy the yang baxter and reflection equations we obtain a general expression for the partition function of this model as a sum of two determinantal terms and show that at a certain point each of these terms reduces to a schur function we are then able to prove a conjecture of robbins from the mid 1980 s that the total number of 2n 1 x 2n 1 dasasms is prod i 0 n 3i n i and a conjecture of stroganov from 2008 that the ratio between the numbers of 2n 1 x 2n 1 dasasms with central entry 1 and 1 is n n 1 among the several product formulae for the enumeration of symmetric alternating sign matrices which were conjectured in the 1980 s that for odd order dasasms is the last to have been proved

large distance asymptotic behavior of the emptiness formation probability of the xxz spin 1 2 heisenberg chain using its multiple integral representation we compute the large distance asymptotic behaviour of the emptiness formation probability of the xxz spin 1 2 heisenberg chain in the massless regime

emergence of a singularity for toeplitz determinants and painleve v we obtain asymptotic expansions for toeplitz determinants corresponding to a family of symbols depending on a parameter t for t positive the symbols are regular so that the determinants obey szeg s strong limit theorem if t 0 the symbol possesses a fisher hartwig singularity letting t 0 we analyze the emergence of a fisher hartwig singularity and a transition between the two different types of asymptotic behavior for toeplitz determinants this transition is described by a special painleve v transcendent a particular case of our result complements the classical description of wu mccoy tracy and barouch of the behavior of a 2 spin correlation function for a large distance between spins in the two dimensional ising model as the phase transition occurs

the effect of inlet waveforms on computational hemodynamics of patient specific intracranial aneurysms due to the lack of patient specific inlet flow waveform measurements most computational fluid dynamics cfd simulations of intracranial aneurysms usually employ waveforms that are not patient specific as inlet boundary conditions for the computational model the current study examined how this assumption affects the predicted hemodynamics in patient specific aneurysm geometries we examined wall shear stress wss and oscillatory shear index osi the two most widely studied hemodynamic quantities that have been shown to predict aneurysm rupture as well as maximal wss mwss energy loss el and pressure loss coefficient plc sixteen pulsatile cfd simulations were carried out on four typical saccular aneurysms using 4 different waveforms and an identical inflow rate as inlet boundary conditions our results demonstrated that under the same mean inflow rate different waveforms produced almost identical wss distributions and wss magnitudes similar osi distributions but drastically different osi magnitudes the osi magnitude is correlated with the pulsatility index of the waveform furthermore there is a linear relationship between aneurysm averaged osi values calculated from one waveform and those calculated from another waveform in addition different waveforms produced similar mwss el and plc in each aneurysm in conclusion inlet waveform has minimal effects on wss osi distribution mwss el and plc and a strong effect on osi magnitude but aneurysm averaged osi from different waveforms has a strong linear correlation with each other across different aneurysms indicating that for the same aneurysm cohort different waveforms can consistently stratify rank osi of aneurysms

boundary k matrices for the xyz xxz and xxx spin chains the general solutions for the factorization equations of the reflection matrices k or theta for the eight vertex and six vertex models xyz xxz and xxx chains are found the associated integrable magnetic hamiltonians are derived explicitly finding families depending on several continuous as well as discrete parameters

the fisher hartwig conjecture and generalizations abstract we discuss the status of the fisher hartwig conjecture concerning the asymptotic expansion of a class of toeplitz determinants with singular generating functions a counterexample is given for a nonrational generating function and we formulate a generalized fisher hartwig conjecture

the wavefunctions for the free fermion part of the spectrum of the suq n quantum spin models we conjecture that the free fermion part of the eigenspectrum observed recently for the suq n perk schultz spin chain hamiltonian in a finite lattice with q exp i n 1 n is a consequence of the existence of a special simple eigenvalue for the transfer matrix of the auxiliary inhomogeneous suq n 1 vertex model which appears in the nested bethe ansatz approach we prove that this conjecture is valid for the case of the suq 3 spin chain with periodic boundary condition in this case we obtain a formula for the components of the eigenvector of the auxiliary inhomogeneous 6 vertex model q exp 2i 3 which permits us to find one by one all components of this eigenvector and consequently to find the eigenvectors of the free fermion part of the eigenspectrum of the suq 3 spin chain similarly as in the known case of the suq 2 case at q exp i2 3 our numerical and analytical studies induce some conjectures for special rates of correlation functions

asymptotics of toeplitz determinants and the emptiness formation probability for the xy spin chain we study an asymptotic behaviour of a special correlator known as the emptiness formation probability efp for the one dimensional anisotropic xy spin 1 2 chain in a transverse magnetic field this correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models for the xy spin chain the correlator can be expressed as the determinant of a toeplitz matrix and its asymptotical behaviours for n throughout the phase diagram are obtained using known theorems and conjectures on toeplitz determinants we find that the decay is exponential everywhere in the phase diagram of the xy model except on the critical lines i e where the spectrum is gapless in these cases a power law prefactor with a universal exponent arises in addition to an exponential or gaussian decay the latter gaussian behaviour holds on the critical line corresponding to the isotropic xy model while at the critical value of the magnetic field the efp decays exponentially at small anisotropy one has a crossover from the gaussian to the exponential behaviour we study this crossover using the bosonization approach