minimising the largest mean first passage time of a markov chain the influence of directed graphs abstract for a markov chain described by an irreducible stochastic matrix a of order n the mean first passage time m i j measures the expected time for the markov chain to reach state j for the first time given that the system begins in state i thus quantifying the short term behaviour of the chain in this article a lower bound for the maximum mean first passage time is found in terms of the stationary distribution vector of a and some matrices for which equality is attained are produced the main objective of this article is to characterise the directed graphs for which any stochastic matrix a respecting this directed graph attains equality in this lower bound producing a class of markov chains with optimal short term behaviour

sensitivity analysis of discrete markov chains via matrix calculus abstract markov chains are often used as mathematical models of natural phenomena with transition probabilities defined in terms of parameters that are of interest in the scientific question at hand sensitivity analysis is an important way to quantify the effects of changes in these parameters on the behavior of the chain many properties of markov chains can be written as simple matrix expressions and hence matrix calculus is a powerful approach to sensitivity analysis using matrix calculus we derive the sensitivity and elasticity of a variety of properties of absorbing and ergodic finite state chains for absorbing chains we present the sensitivities of the moments of the number of visits to each transient state the moments of the time to absorption the mean number of states visited before absorption the quasistationary distribution and the probabilities of absorption in each of several absorbing states for ergodic chains we present the sensitivity of the stationary distribution the mean first passage time matrix the fundamental matrix and the kemeny constant we include two examples of application of the results to demographic and ecological problems

markov chain sensitivity measured by mean first passage times abstract the purpose of this article is to present results concerning the sensitivity of the stationary probabilities for an n state time homogeneous irreducible markov chain in terms of the mean first passage times in the chain

non isotopic symplectic tori in the same homology class for any pair of integers n 1 and q 2 we construct an infinite family of mutually non isotopic symplectic tori representing the homology class q f of an elliptic surface e n where f is the homology class of the fiber we also show how such families can be non isotopically and symplectically embedded into a more general class of symplectic 4 manifolds

the filter monad and its applications abstract the aim of this paper is to study the filter monad and its applications in convergence spaces and probabilistic uniform spaces firstly strong l topologies are characterized by means of the construction of filter monad secondly a lax extension of filter monad to the category of binary relations is presented and some representations of convergence spaces by the lax algebras with respect to filter monad are obtained it is shown that the reflexive and unitary lax algebra of filter monad exactly is the pretopological convergence space and the reflexive and transitive lax algebra exactly is the topological and pretopological convergence space finally the separated completion monad in probabilistic uniform spaces is introduced and it proves that a probabilistic uniform space is hausdorff separated complete space if and only if it is an algebra with respect to the separated completion filter monad

new perturbation bounds for denumerable markov chains this paper is devoted to perturbation analysis of denumerable markov chains bounds are provided for the deviation between the stationary distribution of the perturbed and nominal chain where the bounds are given by the weighted supremum norm in addition bounds for the perturbed stationary probabilities are established furthermore bounds on the norm of the asymptotic decomposition of the perturbed stationary distribution are provided where the bounds are expressed in terms of the norm of the ergodicity coefficient or the norm of a special residual matrix refinements of our bounds for doeblin markov chains are considered as well our results are illustrated with a number of examples

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

kemeny s function for markov chains and markov renewal processes abstract extensions of kemeny s constant as derived for irreducible finite markov chains in discrete time to markov renewal processes and markov chains in continuous time are discussed three alternative kemeny s functions and their variants are considered typically they lead to a constant if and only if the mean holding times between the states in the markov renewal process are constant however one particular variant that arises under expected time to hitting of a state chosen according the continuous time stationary distribution leads to a constant analogous to the discrete time markov chain result specifically if the state space s is finite the sum j s of each mean first passage time m i j omitting the mean return time m j j when i j weighted by the stationary probability j associated with the continuous time semi markov process is a constant independent of i for any markov renewal process expressions for the kemeny s functions and the relevant constants are derived for markov renewal processes and special cases involving continuous time markov chains and birth death processes

time operator of markov chains and mixing times applications to financial data abstract we extend the notion of time operator from kolmogorov dynamical systems and bernoulli processes to markov processes the general methodology is presented and illustrated in the simple case of binary processes we present a method to compute the eigenfunctions of the time operator internal ages are related to other characteristic times of markov chains namely the kemeny time the convergence rate and goodman s intrinsic time we clarified the concept of mixing time by providing analytic formulas for two state markov chains explicit formulas for mixing times are presented for any two state regular markov chain the mixing time of a markov chain is determined also by the time operator of the markov chain within its age computation we illustrate these results in terms of two realistic examples a markov chain from us gnp data and a markov chain from dow jones closing prices we propose moreover a representation for the kemeny constant in terms of internal ages

completeness in probabilistic quasi uniform spaces abstract in this paper we give a kind of cauchy completeness in probabilistic quasi uniform space by using pair filters and prove that this kind of cauchy completeness is equivalent to the completeness of induced probabilistic uniform space introduced by hohle we also give a characterization of cauchy completeness by lawvere completeness then we study the completion of probabilistic quasi uniform space and show that each t 0 separated probabilistic quasi uniform space has a t 0 cauchy completion finally in probabilistic quasi metric space we study the relationship between the completeness of induced quasi uniform space and the completeness of probabilistic quasi metric space

transition matrices for well conditioned markov chains abstract let t r n n be an irreducible stochastic matrix with stationary distribution vector set a i t and define the quantity 3 t 1 2 max j 1 n j a j 1 where aj j 1 n are the n 1 n 1 principal submatrices of a obtained by deleting the jth row and column of a results of cho and meyer and of kirkland show that 3 provides a sensitive measure of the conditioning of under perturbation of t moreover it is known that 3 t n 1 2 n in this paper we investigate the class of irreducible stochastic matrices t of order n such that 3 t n 1 2 n for such matrices correspond to markov chains with desirable conditioning properties we identify some restrictions on the zero nonzero patterns of such matrices and construct several infinite classes of matrices for which 3 is as small as possible

categorical foundations of topology with applications to quantaloid enriched topological spaces based on ordered monads this paper uncovers the categorical basis of topology in terms of a categorical formulation of neighborhood axioms here dense subobjects lower separation axioms and regularity receive a purely categorical representation in the case of appropriate submonads of the double presheaf monad this theory is applied to quantaloid enriched topological spaces which form a common framework for many valued topology as well as for non commutative topology as an illumination of this situation two examples are given the first one is chosen from probability theory and has the following characteristics weak convergence of smooth probability measures is topological the hausdorff separation axiom is valid dirac measures form a dense subset the second example is related to operator theory and explains the topologization of spectra of non commutative c algebras

fuzzy topological spaces with conical neighborhood systems abstract for a commutative integral and meet continuous quantale q a cns space is defined to be a q topological space such that the q neighborhood system of each point is a conical q filter these spaces reduce to fuzzy t locality spaces in the case that the quantale is the unit interval endowed with a left continuous t norm t and reduce to probabilistic q topological spaces in the case that q is an mv algebra for a continuous quantale q a necessary and sufficient condition is obtained for the category of cns spaces to be simultaneously reflective and coreflective in the category of stratified q topological spaces this result provides an interesting example of the interaction between properties of the quantale q and that of q topological spaces

seiberg witten invariants orbifolds and circle actions the main result of this paper is a formula for calculating the seiberg witten invariants of 4 manifolds with fixed point free circle actions this is done by showing under suitable conditions the existence of a diffeomorphism between the moduli space of the 4 manifold and the moduli space of the quotient 3 orbifold two corollaries include the fact that b 1 4 manifolds with fixed point free circle actions are simple type and a new proof of the equality sw y 3 s 1 sw y 3 an infinite number of 4 manifolds with b 1 whose seiberg witten invariants are still diffeomorphism invariants is constructed and studied

generalized inverses of markovian kernels in terms of properties of the markov chain abstract all one condition generalized inverses of the markovian kernel i p where p is the transition matrix of a finite irreducible markov chain can be uniquely specified in terms of the stationary probabilities and the mean first passage times of the underlying markov chain special sub families include the group inverse of i p kemeny and snell s fundamental matrix of the markov chain and the moore penrose g inverse the elements of some sub families of the generalized inverses can also be re expressed involving the second moments of the recurrence time variables some applications to kemeny s constant and perturbations of markov chains are also considered

coupling and mixing times in a markov chain the derivation of the expected time to coupling in a markov chain and its relation to the expected time to mixing as introduced by the author in mixing times with applications to perturbed markov chains linear algebra appl 417 108 123 2006 are explored the two state cases and three state cases are examined in detail

clustering behaviour in markov chains with eigenvalues close to one abstract finite discrete time homogeneous markov chains are frequently used as a simple mathematical model of real world dynamical systems in many such applications an analysis of clustering behaviour in the states of the system is desirable and it is well known that the eigendecomposition of the transition matrix a of the markov chain can provide such insight clustering methods based on the sign pattern in the second eigenvector of a are frequently used when a has dominant eigenvalues that are real in this paper we present a method to include an analysis for complex eigenvalues of a which are close to 1 since a real spectrum is not guaranteed in most applications this is a valuable result in the area of spectral clustering in markov chains

diagonal conditions and continuous extension theorem abstract in this paper we obtain a generalization of kowalsky diagonal condition and that of fischer diagonal condition respectively namely kowalsky diagonal condition and fischer diagonal condition we show that our fischer diagonal condition assures a complete mv algebra valued convergence space proposed in this paper is strong l topological and kowalsky diagonal condition assures a principle or pretopological complete mv algebra valued convergence space is strong l topological also as applications we give a dual form of our fischer diagonal condition and obtain a concept of regular convergence space in addition we present an extension theorem for continuous maps from a dense subspace to a regular convergence space to show that our diagonal conditions works indeed

some stochastic properties of semi magic and magic markov chains abstract gustafson and styan gustafson and styan superstochastic matrices and magic markov chains linear algebra appl 430 2009 2705 2715 examined the mathematical properties of superstochastic matrices the transition matrices of magic markov chains formed from scaled magic squares this paper explores the main stochastic properties of such chains as well as semi magic chains with doubly stochastic transition matrices stationary distribution generalized inverses of markovian kernels mean first passage times variances of the first passage times and expected times to mixing are considered some general results are developed some observations from the chains generated by matlab are discussed some conjectures are presented and some special cases involving three and four states are explored in detail

on regularly perturbed fundamental matrices in this note we characterize regular perturbations of finite state markov chains in terms of continuity properties of its fundamental matrix a perturbation turns out to be regular if and only if the fundamental matrix can be approximated by the discounted deviation from stationarity for small perturbation parameters we also give bounds to asses the quality of the approximation

symplectic rational blowdowns we prove that the rational blowdown a surgery on smooth 4 manifolds introduced by fintushel and stern can be performed in the symplectic category as a consequence interesting families of smooth 4 manifolds including the exotic k3 surfaces of gompf and mrowka admit symplectic structures a basic problem in symplectic topology is to understand what smooth manifolds admit a symplectic structure a closed non degenerate 2 form in this paper we focus on this question in dimension 4 currently the primary methods for constructing smooth irreducible 4 manifolds in such a way that one can distinguish them by donaldson or seiberg witten invariants are surgery constructions that use complex manifolds as building blocks these surgery methods are smooth logarithmic transforms rational blowdowns and connect sums along surfaces it is interesting to see when these surgeries can be performed in the symplectic category in this paper we prove that performing a rational blowdown of a symplectic manifold along symplectic surfaces yields a symplectic manifold this result establishes that certain exotic 4 manifolds including the exotic k3 surfaces of gompf and mrowka 9 are symplectic in any even dimension two symplectic manifolds can be summed along codimension 2 symplectic submanifolds to yield a symplectic manifold we refer to this symplectic operation which was proposed by gromov 11 as the symplectic sum gompf 8 used the symplectic sum to construct a plethora of interesting symplectic manifolds including the first examples of simply connected symplectic 4 manifolds that are not homotopic to any complex surface and some exotic k3 surfaces more recently fintushel and stern 6 have used the connect sum along smoothly embedded tori to produce a rich class of exotic 4 manifolds some homeomorphic to a k3 surface many of which cannot admit a symplectic structure the author is grateful for the support of an nsf post doctoral fellowship dsm9627749

nonisomorphic lefschetz fibrations on knot surgery 4 manifolds in this article we construct an infinite family of simply connected minimal symplectic 4 manifolds each of which admits at least two nonisomorphic lefschetz fibration structures with the same generic fiber we obtain such examples by performing knot surgery on an elliptic surface e n using a special type of 2 bridge knots

kemeny s constant for countable markov chains abstract in this paper we aim to investigate kemeny s constant for discrete time or continuous time irreducible and positive recurrent markov chains on a countable state space we show that kemeny s constant is infinite for a discrete time markov chain on an infinitely countable state space which confirms a conjecture in page 1031 of 3 moreover it is shown that the study on kemeny s constant for a continuous time markov chain with a bounded generator can be converted to that for a discrete time markov chain through the uniformization technique it is different and challenging to analyze kemeny s constant for a chain with unbounded generator finally a upward skip free process is considered and some discussions for kemeny s constant are given

proximity in group inverses of m matrices and inverses of diagonally dominant m matrices in this paper we connect generalize and broaden properties of matrices related to i the triangular inequality for mean first passage times in finite homogeneous ergodic markov chains ii the triangle inequality for proximities in laplacian matrices of undirected weighted graphs and iii the metzler property of the column entrywise diagonal dominance of inverses of diagonally dominant m matrices

preordered sets valued in a gl monoid let m l be a gl monoid an m valued preordered set is an l subset endowed with a reflexive and m transitive l relation it is essentially a category enriched in a quantaloid generated by m this paper presents a study of m valued preordered sets with emphasis on symmetrization and the cauchy completion the main result states that symmetrization and the cauchy completion of m valued preordered sets commute up to a natural isomorphism

generalized inverses and their application to applied probability problems the main aim of this paper is to examine the applicability of generalized inverses to a wide variety of problems in applied probability where a markov chain is present either directly or indirectly through some form of imbedding by characterizing all generalized inverses of i p where p is the transition matrix of a finite irreducible discrete time markov chain we are able to obtain general procedures for finding stationary distributions moments of the first passage time distributions and asymp totic forms for the moments of the occupation time random variables it is shown that all known explicit methods for examining these problems can be expressed in this generalized inverse framework more generally in the context of a markov renewal process setting the aforementioned problems are also examined using generalized inverses of i p as a special case markov chains in continuous time are considered and we show that the generalized inverse technique can be applied directly to the infinitesimal generator of the process instead of to i p where p is the transition matrix of the discrete time jump markov chain

fibred links from closed braids it is proven that every fibred link in the 3 sphere s3 with k components can be obtained as the preimage of the braid axis for a d sheeted simple branched cover over s3 branched along a suitable closed closed braid with d max k 3 more generally it is shown that every open book decomposition of a closed oriented 3 manifold arises in a similar way a major step in the proof involves showing that given a compact surface with boundary expressed as a d fold simple branched covering of the 2 disk d 3 every homeomorphism of the surface fixing the boundary is isotopic to a lift of a homeomorphism of the disk finally this perspective on fibred links is applied to interpret the conjecture due to j harer that all fibred links arise from the trivial knot by a sequence of so called hopf plumbings in terms of markov moves on braids this is a rather long detailed and readable paper that can be recommended as an introduction to many of the ideas discussed the work actually dates from 1984

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

uniform environments as a general framework for metrics and uniformities this paper puts theories of classical uniformity probabilistic uniformity hutton uniformity classical metric probabilistic metric and hutton metric into one framework by introducing the concept of uniform environment which is a functor from the category of sets to the opposite category of involutive unital quantales and involutive closed unital maps subject to certain conditions the results show that uniform environments and their transformations provide a nice framework to study relationships between various notions of uniformity in the literature

on the fastest finite markov processes consider a finite irreducible markov chain with invariant probability define its inverse communication speed as the expectation to go from x to y when x y are sampled independently according to in the discrete time setting and when is the uniform distribution litvak and ejov have shown that the permutation matrices associated to hamiltonian cycles are the fastest markov chains here we prove a that the above optimality is with respect to all processes compatible with a fixed graph of permitted transitions assuming that it does contain a hamiltonian cycle not only the markov chains and b that this result admits a natural extension in both discrete and continuous time when is close to the fastest markov chains processes are those moving successively on the points of a hamiltonian cycle with transition probabilities jump rates dictated by nevertheless the claim is no longer true when is significantly different from

lattice valued convergence associated with cns spaces abstract in this paper in the context of meet continuous quantale we present a notion of conical topological lattice valued convergence space which provides the theory of lattice valued convergence associated with such conical neighborhood spaces

stationary distributions and mean first passage times of perturbed markov chains stationary distributions of perturbed finite irreducible discrete time markov chains are intimately connected with the behaviour of associated mean first passage times this interconnection is explored through the use of generalized matrix inverses some interesting qualitative results regarding the nature of the relative and absolute changes to the stationary probabilities are obtained together with some improved bounds ams classification 15a51 60j10 60j20 65f20 65f35

l proximities and totally bounded pointwise l uniformities in this paper we shall develop the study of connections between l quasi proximities in the sense of katsaras liu artico moresco and pointwise l quasi uniformities in the sense of shi we shall prove that there exists a one to one correspondence between l quasi proximity spaces and totally bounded pointwise l quasi uniform spaces

an enriched category approach to many valued topology in this paper we discuss a basic question in fuzzy set theory what is a many valued topology on a set x an answer is presented by interpreting the axioms two logical formulas for classical topological spaces in the fuzzy setting making use of the intrinsic fuzzy partial order on the fuzzy power set of x as preparation a systematic investigation of fuzzy partial orders is presented from the viewpoint of enriched category theory

lattice valued spaces completions abstract the concept of a convergence space has recently been introduced and studied these spaces are related to the top level space of a lattice valued convergence space in order to consider completions cauchy spaces are defined and investigated in the present work each cauchy space possesses a completion and moreover each topological cauchy space has a topological completion completions of uniform limit spaces are also introduced

fastest expected time to mixing for a markov chain on a directed graph for an irreducible stochastic matrix t the kemeny constant k t measures the expected time to mixing of the markov chain corresponding to t given a strongly connected directed graph d we consider the set d of stochastic matrices whose directed graph is subordinate to d and compute the minimum value of k taken over the set d the matrices attaining that minimum are also characterised thus yielding a description of the transition matrices in d that minimise the expected time to mixing we prove that k t is bounded from above as t ranges over the irreducible members of d if and only if d is an intercyclic directed graph and in the case that d is intercyclic we find the maximum value of k on the set d throughout our results are established using a mix of analytic and combinatorial techniques

parametric forms for generalized inverses of markovian kernels and their applications parametric forms for multicondition generalized inverses of i p where p is the transition matrix of a finite irreducible discrete time markov chain are derived these are utilized in techniques for obtaining moments of first passage time distributions

markov chains and optimality of the hamiltonian cycle we consider the hamiltonian cycle problem hcp embedded in a controlled markov decision process in this setting hcp reduces to an optimization problem on a set of markov chains corresponding to a given graph we prove that hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices in case of doubly stochastic matrices with symmetric linear perturbation we show that hamiltonian cycles minimize a diagonal element of a fundamental matrix for all admissible values of the perturbation parameter in contrast to the previous work on this topic our arguments are primarily based on probabilistic rather than algebraic methods

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

small lefschetz fibrations and exotic 4 manifolds we explicitly construct genus 2 lefschetz fibrations whose total spaces are minimal symplectic 4 manifolds homeomorphic to complex rational surfaces mathbb cp 2 p overline mathbb cp 2 for p 7 8 9 and to 3 mathbb cp 2 q overline mathbb cp 2 for q 12 ldots 19 complementarily we prove that there are no minimal genus 2 lefschetz fibrations whose total spaces are homeomorphic to any other simply connected 4 manifold with b le 3 with one possible exception when b 3 meanwhile we produce positive dehn twist factorizations for several new genus 2 lefschetz fibrations with small number of critical points including the smallest possible example which follow from a reverse engineering procedure we introduce for this setting we also derive exotic minimal symplectic 4 manifolds in the homeomorphism classes of mathbb cp 2 4 overline mathbb cp 2 and 3 mathbb cp 2 6 overline mathbb cp 2 from small lefschetz fibrations over surfaces of higher genera

comparison of perturbation bounds for the stationary distribution of a markov chain abstract the purpose of this paper is to review and compare the existing perturbation bounds for the stationary distribution of a finite irreducible homogeneous markov chain

on fuzzy uniformities induced by a fuzzy metric space abstract different types of fuzzy uniformities have been introduced in the literature standing out the notions due to hutton hohle and lowen the main purpose of this paper is to study several methods to endow a fuzzy metric space x m in the sense of george and veeramani with a probabilistic uniformity and with a hutton 0 1 quasi uniformity we will show the functorial behavior of these constructions as well as its relation with respect to lowen s functors and katsaras s functors which establish a relationship between the categories of probabilistic uniformities and hutton 0 1 quasi uniformities with the category of classical uniformities respectively furthermore we also study the fuzzy topologies associated with these fuzzy uniformities

mixing times with applications to perturbed markov chains abstract a measure of the mixing time or time to stationarity in a finite irreducible discrete time markov chain is considered the statistic i j 1 m m ij j where j is the stationary distribution and mij is the mean first passage time from state i to state j of the markov chain is shown to be independent of the initial state i so that i for all i is minimal in the case of a periodic chain yet can be arbitrarily large in a variety of situations an application considering the effects perturbations of the transition probabilities have on the stationary distributions of markov chains leads to a new bound involving for the 1 norm of the difference between the stationary probability vectors of the original and the perturbed chain when is large the stationary distribution of the markov chain is very sensitive to perturbations of the transition probabilities

hurwitz type bound knot surgery and smooth mathbb s 1 four manifolds in this paper we prove several related results concerning smooth mathbb z p or mathbb s 1 actions on 4 manifolds we show that there exists an infinite sequence of smooth 4 manifolds x n n ge 2 which have the same integral homology and intersection form and the same seiberg witten invariant such that each x n supports no smooth mathbb s 1 actions but admits a smooth mathbb z n action in order to construct such manifolds we devise a method for annihilating smooth mathbb s 1 actions on 4 manifolds using fintushel stern knot surgery and apply it to the kodaira thurston manifold in an equivariant setting finally the method for annihilating smooth mathbb s 1 actions relies on a new obstruction we derived in this paper for existence of smooth mathbb s 1 actions on a 4 manifold the fundamental group of a smooth mathbb s 1 four manifold with nonzero seiberg witten invariant must have infinite center we also include a discussion on various analogous or related results in the literature including locally linear actions or smooth actions in dimensions other than four

effect of function perturbation on the steady state distribution of genetic regulatory networks optimal structural intervention the dynamics of a rule based gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions in the case of boolean networks bns and more generally probabilistic boolean networks pbns there has been a significant amount of investigation into the effect of perturbing gene states in particular the design of intervention strategies based on finite or infinite horizon control polices this paper considers the less investigated issue of function perturbations a single function perturbation affects network dynamics and alters the long run distribution whereas any individual gene perturbation has only transient effects and does not change the long run distribution we derive analytic results for changes in the steady state distributions of pbns resulting from modifications to the underlying regulatory rules and apply the derived results to find optimal structural interventions to avoid undesirable states the results are applied to a wnt5a network and a mammalian cell cycle related network respectively to achieve more favorable steady state distributions and reduce the risk of getting into aberrant phenotypes

the computation of key properties of markov chains via perturbations abstract computational procedures for the stationary probability distribution the group inverse of the markovian kernel and the mean first passage times of a finite irreducible markov chain are developed using perturbations the derivation of these expressions involves the solution of systems of linear equations and structurally inevitably the inverses of matrices by using a perturbation technique starting from a simple base where no such derivations are formally required we update a sequence of matrices formed by linking the solution procedures via generalised matrix inverses and utilising matrix and vector multiplications four different algorithms are given some modifications are discussed and numerical comparisons are made using a test example the derivations are based upon the ideas outlined by hunter 14

online regret bounds for markov decision processes with deterministic transitions we consider an upper confidence bound algorithm for learning in markov decision processes with deterministic transitions for this algorithm we derive upper bounds on the online regret with respect to an e optimal policy that are logarithmic in the number of steps taken we also present a corresponding lower bound as an application multi armed bandits with switching cost are considered

fuzzy uniform spaces in this paper we introduce the notion of fuzzy uniform spaces in section 2 we give some basic results and show how a fuzzy topology is derived from a fuzzy uniformity in sections 3 and 4 we prove that the notions which are introduced are good extensions and we prove that the category of uniform spaces is nicely injected in the category of fuzzy uniform spaces finally in section 5 we prove some basic results

the geography of spin symplectic 4 manifolds in this paper we construct a family of simply connected spin non complex symplectic 4 manifolds which cover all but finitely many allowed lattice points chi mathbf c lying in the region 0 leq mathbf c leq 8 76 chi furthermore as a corollary we prove that there exist infinitely many exotic smooth structures on 2n 1 s 2 times s 2 for all n large enough

characterizations of generalized inverses associated with markovian kernels abstract a systematic investigation of the various multicondition generalized inverses of i p where p is the transition matrix of a finite irreducible discrete time markov chain is presented the characterizations are based upon the result that i p tu is nonsingular if and only if t and u are chosen so that t 0 where is the stationary probability vector of p and u e 0 where e is the vector of ones partitioned forms for the g inverses are also presented based on a full rank factorization of i p special well known cases such as the group inverses and the moore penrose inverse are given

variances of first passage times in a markov chain with applications to mixing times jm m 1 as a measure of the mixing time or time to stationarity in a finite irreducible discrete time markov chain with stationary distribution pj and mij as the mean first passage time from state i to state j of the markov chain this was shown to be independent of the initial state i with i for all i minimal in the case of a periodic chain yet can be arbitrarily large in a variety of situations in this paper we explore the variance of the mixing time v i starting in state i the v i are shown to depend on i and an exploration of recommended starting states given knowledge of the transition probabilities is considered as a preamble a study of the computation of second moments of the mixing times m ij 2 and the variance of the first passage times in a discrete time markov chain is carried out leading to some new results