title: Support varieties for quantum groups

abstract:
  For any module $M$ over small quantum group one defines the support variety
using construction from the theory of restricted Lie algebras. It is a closed
conical subset of nilpotent cone of the corresponding Lie algebra. If module
$M$ is a module over the quantum group $U_{\xi}$ with divided powers then its
support variety is invariant under the action of the corresponding algebraic
group. In this case we relate codimension $2a$ of the support variety of $M$ in
nilpotent cone and dimension of $M$. Namely, we prove that $\dim M$ is `almost'
divisible by $l^a$. Further, we give an a priori estimate for support variety
of a module in a given linkage class. We compute the support varieties for Weyl
modules. Also we compute the support varieties for tilting modules over quantum
$SL_n$ and verify in this case Humphreys' Conjecture which relates support
varieties of tilting modules with Lusztig's bijection between nilpotent orbits
and two-sided cells in the affine Weyl group.


title:
Skew Young diagram method in spectral decomposition of integrable
  lattice models II: Higher levels

abstract:
  The spectral decomposition of the path space of the vertex model associated
to the level $l$ representation of the quantized affine algebra
$U_q(\hat{sl}_n)$ is studied. The spectrum and its degeneracy are parametrized
by skew Young diagrams and what we call nonmovable tableaux on them,
respectively. As a result we obtain the characters for the degeneracy of the
spectrum in terms of an alternating sum of skew Schur functions. Also studied
are new combinatorial descriptions (spectral decomposition) of the Kostka
numbers and the Kostka--Foulkes polynomials. As an application we give a new
proof of Nakayashiki--Yamada's theorem about the branching functions of the
level $l$ basic representation $l\Lambda_k$ of $\hat{sl}_n$ and a
generalization of the theorem.


title:
The nondynamical r-matrix structure for the elliptic $A_{n-1}$
  Calogero-Moser model

abstract:
  In this paper, we construct a new Lax operator for the elliptic $A_{n-1}$
Calogero-Moser model with general $n(2\leq n$) from the classical dynamical
twisting,in which the corresponding r-matrix is purely numeric (nondynamical
one). The nondynamical r-matrix structure of this Lax operator is obtained,
which is elliptic $Z_n$-symmetric r-matrix.


title: Coloured Hopf algebras and their duals

abstract:
  Coloured Hopf algebras, related to the coloured Yang-Baxter equation, are
reviewed, as well as their duals. The special case of coloured quantum
universal enveloping algebras provides a coloured extension of Drinfeld and
Jimbo formalism. The universal $\cal T$-matrix is then generalized to the
coloured context, and shown to lead to an algebraic formulation of the coloured
RTT-relations, previously proposed by Basu-Mallick as part of a coloured
extension of Faddeev, Reshetikhin, and Takhtajan approach to quantum groups and
quantum algebras.


title:
Duals of coloured quantum universal enveloping algebras and coloured
  universal $\cal T$-matrices

abstract:
  We extend the notion of dually conjugate Hopf (super)algebras to the coloured
Hopf (super)algebras ${\cal H}^c$ that we recently introduced. We show that if
the standard Hopf (super)algebras ${\cal H}_q$ that are the building blocks of
${\cal H}^c$ have Hopf duals ${\cal H}_q^*$, then the latter may be used to
construct coloured Hopf duals ${\cal H}^{c*}$, endowed with coloured algebra
and antipode maps, but with a standard coalgebraic structure. Next, we review
the case where the ${\cal H}_q$'s are quantum universal enveloping algebras of
Lie (super)algebras $U_q(g)$, so that the corresponding ${\cal H}_q^*$'s are
quantum (super)groups $G_q$. We extend the Fronsdal and Galindo universal
${\cal T}$-matrix formalism to the coloured pairs $(U^c(g), G^c)$ by defining
coloured universal ${\cal T}$-matrices. We then show that together with the
coloured universal $\cal R$-matrices previously introduced, the latter provide
an algebraic formulation of the coloured RTT-relations, proposed by
Basu-Mallick. This establishes a link between the coloured extensions of
Drinfeld-Jimbo and Faddeev-Reshetikhin-Takhtajan pictures of quantum groups and
quantum algebras. Finally, we illustrate the construction of coloured pairs by
giving some explicit results for the two-parameter deformations of
$\bigl(U(gl(2)), Gl(2)\bigr)$, and $\bigl(U(gl(1/1)), Gl(1/1)\bigr)$.


title: Fourier Knots

abstract:
  This paper introduces the concept of a Fourier knot. A Fourier knot is a knot
that is represented by a parametrized curve in three dimensional space such
that the coordinate functions are finite Fourier series in the parameter. The
previously studied Lissajous knots constitute a case of Fourier knots with
single frequencies in each coordinate direction. Not all knots are Lissajous.
In fact the trefoil knot and the figure eight knot are the first examples of
non- Lissajous knots. This paper gives robust and simple Fourier
representations for these and other examples. This new version of the paper
contains a crucial reference to the beautiful work of Aaron Trautwein on
Harmonic Knots. See <http://www.carthage.edu/~trautwn>. See also
<http://math.uic.edu/~kauffman/>.


title:
A spin network generalization of the Jones Polynomial and Vassiliev
  invariants

abstract:
  We apply the ideas of Alvarez and Labastida to the invariant of spin networks
defined by Witten and Martin based on Chern-Simons theory. We show that it is
possible to define ambient invariants of spin networks that (for the case of
SU(2)) can be considered as extensions to spin networks of the Jones
polynomial. Expansions of the coefficients of the polynomial yield primitive
Vassiliev invariants. The resulting invariants are candidates for solutions of
the Wheeler--DeWitt equations in the spin network representation of quantum
gravity.


title: Adams operators and knot decorations

abstract:
  We use an explicit isomorphism from the representation ring of the quantum
group U_q(sl(N)) to the Homfly skein of the annulus, to determine an element of
the skein which is the image of the mth Adams operator, \psi_m, on the
fundamental representation, c_1. This element is a linear combination of m very
simple m-string braids. Using this skein element, we show that the Vassiliev
invariant of degree n in the power series expansion of the U_q(sl(N)) quantum
invariant of a knot coloured by \psi_m(c_1) is the canonical Vassiliev
invariant with weight system W_n\psi_m^{(n)} where W_n is the weight system for
the Vassiliev invariant of degree n in the expansion of the quantum invariant
of the knot coloured by c_1 and \psi_m^{(n)} is the Adams operator on n-chord
diagrams defined by Bar-Natan.


title:
Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS
  Representations, the WKB Expansion, and Applications

abstract:
  This paper is part II of a series of papers on the deformation quantization
on the cotangent bundle of an arbitrary manifold $Q$. For certain homogeneous
star products of Weyl ordered type (which we have obtained from a Fedosov type
procedure in part I, see q-alg/9707030) we construct differential operator
representations via the formal GNS construction (see q-alg/9607019). The
positive linear functional is integration over $Q$ with respect to some fixed
density and is shown to yield a reasonable version of the Schr\"odinger
representation where a Weyl ordering prescription is incorporated. Furthermore
we discuss simple examples like free particle Hamiltonians (defined by a
Riemannian metric on $Q$) and the implementation of certain diffeomorphisms of
$Q$ to unitary transformations in the GNS (pre-)Hilbert space and of time
reversal maps (involutive anti-symplectic diffeomorphisms of $T^*Q$) to
anti-unitary transformations. We show that the fixed-point set of any
involutive time reversal map is either empty or a Lagrangean submanifold.
Moreover, we compare our approach to concepts using integral formulas of
generalized Moyal-Weyl type. Furthermore we show that the usual WKB expansion
with respect to a projectable Lagrangean submanifold can be formulated by a GNS
construction. Finally we prove that any homogeneous star product on any
cotangent bundle is strongly closed, i. e. the integral over $T^*Q$ w.r.t. the
symplectic volume vanishes on star-commutators. An alternative Fedosov type
deduction of the star product of standard ordered type using a deformation of
the algebra of symmetric contravariant tensor fields is given.


title: Screening Currents in Affine Current Algebra

abstract:
  In this paper screening currents of the second kind are considered. They are
constructed in any affine current algebra for directions corresponding to
simple roots with multiplicity one in a decomposition of the highest root on a
set of simple roots. These expressions are precisely of the form previously
conjectured to be valid for all directions in general affine current algebras.
However, by working out explicitly the screening currents in the case of SO(5)
based on the Lie algebra B_2, it is demonstrated that much more complicated
structures appear in the general case. In the distinguished representation of
affine OSp(2|2) current superalgebra, the screening current of the second kind
in the bosonic direction is also provided.


title:
A one-dimensional many-body integrable model from $Z_n$ Belavin model
  with open boundary conditions

abstract:
  We use factorized $L$ operator to construct an integrable model with open
boundary conditions. By taking trigonometic limit($\tau \to \sqrt{-1}\infty$)
and scaling limit($\omega \to 0$), we get a Hamiltonian of a classical
integrable system. It shows that this integrable system is similar to those
found by Calogero et al.


title: A skein theoretic proof of the hook formula for quantum dimension

abstract:
  We give a skein theoretic proof the Reshetikhin hook length formula for
quantum dimension for the quantum group U_q(sl(N)).


title: Poincar\'e Series of Quantum Spaces Associated to Hecke Operators

abstract:
  We study the Poincar\'e series of the quantum spaces associated to a Hecke
operator, i.e., a Yang-Baxter operator satisfying the equation $(x+1)(x-q)=0$.
The Poincar\'e series of the corresponding matrix bialgebra is also considered.
Using an old result on Poly\'a frequency sequence, we show that the Poincar\'e
series of quantum spaces are always rational functions having negative roots
and positive poles. In particular, we show that the rank of an even Hecke
operator should be rational functions having negative roots and positive poles.
In particular, we show that the rank of an even Hecke operator should be
greater than the dimension of the vector space it is acting on.


title:
The consistent reduction of the differential calculus on the quantum
  group $GL_{q}(2,C)$ to the differential calculi on its subgroups and
  $\sigma$-models on the quantum group manifolds $SL_{q}(2,R)$,
  $SL_{q}(2,R)/U_{h}(1)$, $C{q}(2|0)$ and infinitesimal transformations

abstract:
  Explicit construction of the second order left differential calculi on the
quantum group and its subgroups are obtained with the property of the natural
reduction: the differential calculus on the quantum group $GL_q(2,C)$ has to
contain the 3-dimensional differential calculi on the quantum subgroup
$SL_q(2,C)$, the differential calculi on the Borel subgroups $B_{L}^{(2)}(C)$,
$B_{U}^{(2)}(C)$ of the lower and of the upper triangular matrices, on the
quantum subgroups $U_{q}(2)$, $SU_{q}(2)$, $Sp_{q}(2,C)$, $Sp_{q}(2)$,
$T_{q}(2,C)$, $B_{L}(C)$, $B_{U}(C)$, $U_{q}(1)$, $Z_{-}^{(2)}(C)$,
$Z_{+}^{(2)}(C)$ and on the their real forms. The classical limit ($q\to 1$) of
the left differential calculus is the nondeformed differential calculus. The
differential calculi on the Borel subgroups $B_{L}(C)$, $B_{U}(C)$ of the
$SL_{q}(2,C)$ coincide with two solutions of Wess-Zumino differential calculus
on the quantum plane $C_q(2|0)$.
  The spontaneous breaking symmetry in the WZNW model with $SL_{q}(2,R)$
quantum group symmetry over two-dimensional nondeformed Minkovski space and in
the $\sigma$-models with ${SL_{q}(2,R)/U_{p}(1)}$, $C_{q}(2|0)$ quantum group
symmetry is considered. The Lagrangian formalism over the quantum group
manifolds is discussed. The variational calculus on the $SL_{q}(2,R)$ group
manifold is obtained. The classical solution of $C_{q}(2|0)$ {$\sigma$}-model
is obtained.


title: Finite-dimensional irreducible representations of twisted Yangians

abstract:
  We study quantized enveloping algebras called twisted Yangians. They are
analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D
series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with
respect to the coproduct in Y(gl(N)). We give a complete description of their
finite-dimensional irreducible representations. Every such representation is
highest weight and we give necessary and sufficient conditions for an
irreducible highest weight representation to be finite-dimensional. The result
is analogous to Drinfeld's theorem for the ordinary Yangians. Its detailed
proof for the A series is also reproduced. For the simplest twisted Yangians we
construct an explicit realization for each finite-dimensional irreducible
representation in tensor products of representations of the corresponding Lie
algebras.


title: Exotic Differential Operators on Complex Minimal Nilpotent Orbits

abstract:
  Let O be the minimal nilpotent adjoint orbit in a classical complex
semisimple Lie algebra g. O is a smooth quasi-affine variety stable under the
Euler dilation action $C^*$ on g. The algebra of differential operators on O is
D(O)=D(Cl(O)) where the closure Cl(O) is a singular cone in g. See \cite{jos}
and \cite{bkHam} for some results on the geometry and quantization of O.
  We construct an explicit subspace $A_{-1}\subset D(O)$ of commuting
differential operators which are Euler homogeneous of degree -1. The space
$A_{-1}$ is finite-dimensional, g-stable and carries the adjoint
representation. $A_{-1}$ consists of (for $g \neq sp(2n,C)$) non-obvious order
4 differential operators obtained by quantizing symbols we obtained previously.
These operators are "exotic" in that there is (apparently) no geometric or
algebraic theory which explains them. The algebra generated by $A_{-1}$ is a
maximal commutative subalgebra A of D(X). We find a G-equivariant algebra
isomorphism R(O) to A, $f\mapsto D_f$, such that the formula $(f|g)=({constant
term of}D_{\bar{g}} f)$ defines a positive-definite Hermitian inner product on
R(O).
  We will use these operators $D_f$ to quantize O in a subsequent paper.


title: FRT Quantization Theory for the Nonsemisimple Cayley-Klein Groups

abstract:
  The quantization theory of the simple Lie groups and algebras was developed
by Faddeev-Reshetikhin-Takhtadjan (FRT). In group theory there is a remarkable
set of groups, namely the motion groups of n-dimensional spaces of constant
curvature or the orthogonal Cayley-Klein (CK) groups. In some sense the CK
groups are in the nearest neighborhood with the simple ones. The well known
groups of physical interest such as Euclidean E(n), Poincare P(n), Galileian
G(n) and other nonsemisimple groups are in the set of CK groups.
  But many standart algebraical costructions are not suitable for the
nonsemisimple groups and algebras, in particular Killing form is degenerate,
Cartan matrix do not exist. Nevertheless it is possible to describe and to
quantize all CK groups and algebras, as it was made for the simple ones.
  The principal proposal is to consider CK groups as the groups over an
associative algebra $D$ with nilpotent commutative generators and the
corresponding quantum CK groups as the algebra of noncommutative functions over
$D$.


title: On some Hochschild cohomology classes of fusion algebras

abstract:
  The obstructions for an arbitrary fusion algebra to be a fusion algebra of
some semisimple monoidal category are constructed. Those obstructions lie in
groups which are closely related to the Hochschild cohomology of fusion
algebras with coefficients in the K-theory of the ground (algebraically closed)
field.


title: Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra

abstract:
  We construct the vector space dual to the space of right-invariant
differential forms construct from a first order differential calculus on
inhomogeneous quantum group. We show that this vector space is equipped with a
structure of a Hopf algebra which closes on a noncommutative Lie algebra
satisfying a Jacobi identity.


title: Yang-Baxter systems, solutions and applications

abstract:
  Two types of Yang-Baxter systems play roles in the theoretical physics --
constant and colour dependent. The constant systems are used mainly for
construction of special Hopf algebra while the colour or spectral dependent for
construction of quantum integrable models. Examples of both types together with
their particular solutions are presented. The complete solution is known only
for the constant system related to the quantized braided groups in the
dimension two. The strategy for solution of the system related to quantum
doubles is suggested and partial results are presented.


title: Factorizable sheaves and quantum groups

abstract:
  The category $\cal{C}$ (studied by Andersen-Jantzen-Soergel) of
representations of a Lusztig's small quantum group at a root of unity, together
with its modular structure, is defined geometrically, using configuration
spaces.


title: On solutions of the KZ and qKZ equations at level zero

abstract:
  We discuss relations between different formulae for solutions of the
Knizhnik-Zamolodchikov differential and the quantum Knizhnik-Zamolodchikov
difference equations at level 0 and associated with rational solutions of the
Yang-Baxter equation.


title: Spiders for rank 2 Lie algebras

abstract:
  A spider is an axiomatization of the representation theory of a group,
quantum group, Lie algebra, or other group or group-like object. We define
certain combinatorial spiders by generators and relations that are isomorphic
to the representation theories of the three rank two simple Lie algebras,
namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider
for A1. Among other things, they yield bases for invariant spaces which are
probably related to Lusztig's canonical bases, and they are useful for
computing quantities such as generalized 6j-symbols and quantum link
invariants.


title: On Irreducibility of Tensor Products of Yangian Modules

abstract:
  We study the tensor product $V$ of any number of "elementary" irreducible
modules over the Yangian of the general linear Lie algebra. An elementary
module is determined by a skew Young diagram and by a complex parameter, and
contains a vector called singular. We give sufficient conditions for cyclicity
in $V$ of the tensor product of these singular vectors. By using this result,
we give an irreducibility criterion for $V$ when each of the skew Young
diagrams determining the tensor factors has rectangular shape.


title: Five Lectures on Soliton Equations

abstract:
  This is a self-contained review of a new approach to soliton equations of KdV
type developed by the author together with B. Feigin and B. Enriquez.


title: Twist Deformation of the rank one Lie Superalgebra

abstract:
  The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie
superalgebra $osp(1|2)$. The twist element is the same as for the $sl(2)$ Lie
algebra due to the embedding of the $sl(2)$ into the superalgebra $osp(1|2)$.
The R-matrix has the direct sum structure in the irreducible representations of
$osp(1|2)$. The dual quantum group is defined using the FRT-formalism. It
includes the Jordanian quantum group $SL_\xi(2)$ as subalgebra and Grassmann
generators as well.


title:
Cohomology of the Lie algebras of differential operators: lifting
  formulas

abstract:
  We construct the explicit formula for the (2n+1)-cocycle of the Lie algebra
of (pseudo)differential operators on a n-dimensional space. We prove that this
formula in fact defines a cocycle for n=1 and n=2.


title:
Noncommutative analogues of q-special polynomials and q-integral on a
  quantum sphere

abstract:
  The q-Legendre polynomials can be treated as some special "functions in the
quantum double cosets $U(1)\setminus SU_q(2)/U(1)$". They form a family
(depending on a parameter $q$) of polynomials in one variable. We get their
further generalization by introducing a two parameter family of polynomials. If
the former family arises from an algebra which is in a sense "q-commutative",
the latter one is related to its noncommutative counterpart. We introduce also
a two parameter deformation of the invariant integral on a sphere.


title:
q_R-conformal symmetries in 2D nonlocal quantum field theory,
  categorical representation theory, and Virasoro algebra

abstract:
  The paper is devoted to the symmetry aspects of 2D nonlocal field theory,
which is the simplest deformation of the conformally invariant quantum field
theory with one free bosonic field. The inverse problem of representation
theory is solved for $q_R$-conformal symmetries, which are infinite dimensional
hidden symmetries of the field theory. There is developed a mathematical
formalism based on the abstract categorical representation theory and
sufficient for applications of symmetry methods to the investigation of
processes of synthesis, decay and interaction of quasiparticles in the models
of 2D nonlocal quantum field theory.


title: A proof of Feigin's conjecture

abstract:
  The paper is devoted to the proof of the following conjecture due to B.
Feigin. Let $\frak u_\ell$ be the small quantum group a the primitive $\ell$-th
root of unity. Then it is known that the usual $Ext$ algebra of the trivial
$\frak u_\ell$-module is isomorphic to the algebra of regular functions on the
nilpotent variety $\cal N$ in the corresponding simple Lie algebra $\frak g$
(see [GK]). Consider semiinfinite cohomology of the trivial $\frak
u_\ell$-module introduced in [Ar1], [Ar2]. It was shown in [Ar2] that the $Ext$
algebra of the trivial $\frak u_\ell$-module acts naturally on semiinfinite
cohomology. Moreover semiinfinite cohomology space of the trivial
$\frak_\ell$-module is equipped with a natural $\frak g$-module structure. B.
Feigin conjectured that the described $\frak g$-module and $F(\cal N)$-module
structures coincide with the ones on the space of local cohomology of the
structure sheaf on $\cal N$ with support in the standard positive nilpotent
subalgebra $\frak n^+\subset\cal N\subset \frak g$. We give a detailed proof of
the conjecture. Moreover we generalize the statement and describe semiinfinite
cohomology of contragradient Weyl modules in terms of local cohomology of
certain coherent sheaves on the nilpotent cone and on its desingularization
$T^*(G/B)$. To do this we construct a certain specialization of the quantum BGG
resolution of the simple module $L(\lambda)$ defined for generic values of the
quantizing parameter into the root of unity called the quasi-BGG complex. The
complex conists of direct sums of quasi-Verma modules and provides
conjecturally a resolution of the Weyl module $W(\lambda)$.


title:
On Super RS algebra and Drinfeld Realization of Quantum Affine
  Superalgebras

abstract:
  We describe the realization of the super Reshetikhin-Semenov-Tian-Shansky
(RS) algebra in quantum affine superalgebras, thus generalizing the approach of
Frenkel-Reshetikhin to the supersymmetric (and twisted) case. The algebraic
homomorphism between the super RS algebra and the Drinfeld current realization
of quantum affine superalgebras is established by using the Gauss decomposition
technique of Ding-Frenkel. As an application, we obtain Drinfeld realization of
quantum affine superalgebra $U_q[osp(1|2)^{(1)}]$ and its degeneration --
central extended super Yangian double $DY_\hbar[osp(1|2)^{(1)}]$.


title: Perfect Crystals of $U_q(G_2^{(1)})$

abstract:
  The notion of perfect crystals was introduced in "Perfect Crystal and Vertex
Models", (Internat. J. Modern Phys. A7(1992)449-484) by S-J. Kang et al. In
this paper, we give a series of perfect crystals of $U_q(G_2^{(1)})$.


title: Dual Affine Quantum Groups

abstract:
  Let $\hat{\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its
Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\hat{\mathfrak{h}}$ be
the dual Lie bialgebra. By dualizing the quantum double construction - via
formal Hopf algebras - we construct a new quantum group
$U_q(\hat{\mathfrak{h}})$, dual of $U_q(\hat{\mathfrak{g}})$. Studying its
restricted and unrestricted integer forms and their specializations at roots of
1 (in particular, their classical limits), we prove that
$U_q(\hat{\mathfrak{h}})$ yields quantizations of $\hat{\mathfrak{h}}$ and
$\hat{G}^\infty$ (the formal group attached to $\hat{\mathfrak{g}}$), and we
construct new quantum Frobenius morphisms. The whole picture extends to the
untwisted affine case the results known for quantum groups of finite type.


title:
Commutation relations of vertex operators related with the spin
  representation of $U_q(D_n^{(1)})$

abstract:
  We calculate commutation relations of vertex operators for the spin
representation of $U_q(D_n^{(1)})$ by using recursive formulae of R-matrices.
In quantum symmetry approach, we obtain the energy and momentum spectrum of the
quantum spin chain model related with the spin representation from these
commutation relations.


title: Classification of Low Dimensional Lie Super-Bialgebras

abstract:
  A thorough analysis of Lie super-bialgebra structures on Lie super-algebras
osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic
computations and a subsequent identification of equivalent structures is
applied. In all the cases Poisson-Lie brackets on supergroups are found.
Possibility of quantizing them in order to obtain quantum groups is discussed.
It turns out to be straightforward for all but one structures for super-E(2)
group.


title: Dynamical systems related to the Cremmer-Gervais R-matrix

abstract:
  The generalized Cremmer-Gervais R-matrix being a twist of the standard
R-matrix of $SL_q(3)$, depends on two extra parameters. Properties of this
R-matrix are discussed and two dynamical systems, the quantum group covariant
$q$-oscillator and an integrable spin chain with a non-hermitian Hamiltonian,
are constructed.


title: Unification of parastatistics defined as triple operator algebras

abstract:
  We unify parastatistics, defined as triple operator algebras represented on
Fock space, in a simple way using the transition number operators. We express
them as a normal ordered expansion of creation and annihilation operators. We
discuss several examples of parastatistics, particularly Okubo's and Palev's
parastatistics connected to many-body Wigner quantum systems. We relate them to
the notion of extended Haldane statistics.


title: Generalized Temperley-Lieb algebras and decorated tangles

abstract:
  We give presentations, by means of diagrammatic generators and relations, of
the analogues of the Temperley-Lieb algebras associated as Hecke algebra
quotients to Coxeter graphs of type B and $D$. This generalizes Kauffman's
diagram calculus for the Temperley-Lieb algebra.


title: Cellular algebras arising from Hecke algebras of type H_n

abstract:
  We study a finite-dimensional quotient of the Hecke algebra of type $H_n$ for
general $n$, using a calculus of diagrams. This provides a basis of monomials
in a certain set of generators. Using this, we prove a conjecture of C.K. Fan
about the semisimplicity of the quotient algebra. We also discuss the cellular
structure of the algebra, with certain restrictions on the ground ring.


title:
Classification of eight-vertex solutions of the colored Yang-Baxter
  equation

abstract:
  In this paper all eight-vertex type solutions of the colored Yang-Baxter
equation dependent on spectral as well as color parameter are given. It is
proved that they are composed of three groups of basic solutions, three groups
of their degenerate forms and two groups of trivial solutions up to five
solution transformations. Moreover, all non-trivial solutions can be classified
into two types called Baxter and Free-Fermion type.


title: Capelli Identities for Classical Lie Algebras

abstract:
  We extend the Capelli identities (1890) from the Lie algebra $gl_N$ to the
other two classical Lie algebras $so_N$ and $sp_N$. We employ the theory of
reductive dual pairs due to Howe. Our technique comes from the representation
theory of Yangians.


title: Screening Current Representation of Quantum Superalgebras

abstract:
  In this letter a screening current or contour representation is given of
certain quantum superalgebras. The Gomez-Sierra construction of quantum groups
in conformal field theory is generalized to cover superalgebras and illustrated
using recent results on screening currents in affine current superalgebra.


title: On modules associated to coalgebra Galois extensions

abstract:
  For a given entwining structure $(A,C)_\psi$ involving an algebra $A$, a
coalgebra $C$, and an entwining map $\psi: C\otimes A\to A\otimes C$, a
category $\M_A^C(\psi)$ of right $(A,C)_\psi$-modules is defined and its
structure analysed. In particular, the notion of a measuring of $(A,C)_\psi$ to
$(\tA,\tC)_\tpsi$ is introduced, and certain functors between $\M_A^C(\psi)$
and $\M_\tA^\tC(\tpsi)$ induced by such a measuring are defined. It is shown
that these functors are inverse equivalences iff they are exact (or one of them
faithfully exact) and the measuring satisfies a certain Galois-type condition.
Next, left modules $E$ and right modules $\bar{E}$ associated to a $C$-Galois
extension $A$ of $B$ are defined. These can be thought of as objects dual to
fibre bundles with coalgebra $C$ in the place of a structure group, and a fibre
$V$. Cross-sections of such associated modules are defined as module maps $E\to
B$ or $\bar{E}\to B$. It is shown that they can be identified with suitably
equivariant maps from the fibre to $A$. Also, it is shown that a $C$-Galois
extension is cleft if and only if $A=B\tens C$ as left $B$-modules and right
$C$-comodules. The relationship between the modules $E$ and $\bar{E}$ is
studied in the case when $V$ is finite-dimensional and in the case when the
canonical entwining map is bijective.


title: Past the Highest-Weight, and What You Can Find There

abstract:
  The properties of highest-weight representations of the N=2 superconformal
algebra in two dimensions can be considerably simplified when re-expressed in
terms of relaxed ^sl(2) representations. This applies to the appearance of
submodules and hence, of singular vectors, and to the structure of the
embedding diagrams and the BGG-type resolution. I also discuss the realization
of these representations in the bosonic string, where the generalized DDK
prescription amounts to the requirement that the representations have a charged
singular vector, and the role of the fermionic screening operator.


title: The quantum Euler class and the quantum cohomology of the Grassmannians

abstract:
  The Poincare duality of classical cohomology and the extension of this
duality to quantum cohomology endows these rings with the structure of a
Frobenius algebra. Any such algebra possesses a canonical ``characteristic
element;'' in the classical case this is the Euler class, and in the quantum
case this is a deformation of the classical Euler class which we call the
``quantum Euler class.'' We prove that the characteristic element of a
Frobenius algebra A is a unit if and only if A is semisimple, and then apply
this result to the cases of the quantum cohomology of the finite complex
Grassmannians, and to the quantum cohomology of hypersurfaces. In addition we
show that, in the case of the Grassmannians, the [quantum] Euler class equals,
as [quantum] cohomology element and up to sign, the determinant of the Hessian
of the [quantum] Landau-Ginzbug potential.


title:
Hecke algebraic properties of dynamical R-matrices. Application to
  related quantum matrix algebras

abstract:
  The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines
an R-matrix R(p), where $p$ stands for a set of mutually commuting variables. A
family of SL(n)-type solutions of this equation provides a new realization of
the Hecke algebra. We define quantum antisymmetrizers, introduce the notion of
quantum determinant and compute the inverse quantum matrix for matrix algebras
of the type R(p) a_1 a_2 = a_1 a_2 R. It is pointed out that such a quantum
matrix algebra arises in the operator realization of the chiral zero modes of
the WZNW model.


title: Coherence Constraints for Operads, Categories and Algebras

abstract:
  Coherence phenomena appear in two different situations. In the context of
category theory the term `coherence constraints' refers to a set of diagrams
whose commutativity implies the commutativity of a larger class of diagrams. In
the context of algebra coherence constrains are a minimal set of generators for
the second syzygy, that is, a set of equations which generate the full set of
identities among the defining relations of an algebraic theory.
  A typical example of the first type is Mac Lane's coherence theorem for
monoidal categories, an example of the second type is the result of Drinfel'd
saying that the pentagon identity for the `associator' of a quasi-Hopf algebra
implies the validity of a set of identities with higher instances of this
associator.
  We show that both types of coherence are governed by a homological invariant
of the operad for the underlying algebraic structure. We call this invariant
the (space of) coherence constraints. In many cases these constraints can be
explicitly described, thus giving rise to various coherence results, both
classical and new.


title: Two-parameter deformation of loop algebras and superalgebras

abstract:
  We discuss two-parameter deformations of an universal enveloping algebra
$U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a
finite-dimensional complex simple Lie algebra (or superalgebra). These
deformations are Hopf algebras. One deformation called Drinfeldian is a
quantization of $U(g[u])$ in the direction of a classical r-matrix which is a
sum of the simplest rational and trigonometric r-matrices. Another deformation
(discussed only for the case $g=sl_{2}$) is a twisting of the usual Yangian
$Y_{\eta}(sl_{2})$.


title: Quasi-Hopf twistors for elliptic quantum groups

abstract:
  The Yang-Baxter equation admits two classes of elliptic solutions, the vertex
type and the face type. On the basis of these solutions, two types of elliptic
quantum groups have been introduced (Foda et al., Felder). Fronsdal made a
penetrating observation that both of them are quasi-Hopf algebras, obtained by
twisting the standard quantum affine algebra U_q(g). In this paper we present
an explicit formula for the twistors in the form of an infinite product of the
universal R matrix of U_q(g). We also prove the shifted cocycle condition for
the twistors, thereby completing Fronsdal's findings.
  This construction entails that, for generic values of the deformation
parameters, representation theory for U_q(g) carries over to the elliptic
algebras, including such objects as evaluation modules, highest weight modules
and vertex operators. In particular, we confirm the conjectures of Foda et al.
concerning the elliptic algebra A_{q,p}(^sl_2).


title: An Ariki-Koike like extension of the Birman-Murakami-Wenzl Algebra

abstract:
  We introduce an Ariki-Koike like extension of the Birman-Murakami-Wenzl
Algebra and show it to be semi-simple. This algebra supports a faithful Markov
trace that gives rise to link invariants of closures of Coxeter type B braids.


title: Actions of Tensor Categories and Cylinder Braids

abstract:
  Categorial actions of braided tensor categories are defined and shown to be
the right framework for a discussion of the categorial structure related to the
group of braids in the cylinder. A Kauffman polynomial of links in the solid
torus is constructed.


title: The Potts Model with a Reflecting Boundary

abstract:
  A Potts model with a reflecting boundary is introduced and it is shown that
its partition function can be expressed as a Markov trace on the Temperley-Lieb
Algebra of Coxeter type B.


title: Some Properties of Finite-Dimensional Semisimple Hopf Algebras

abstract:
  Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf
algebra over an algebraically closed field k of characteristic 0, then H is of
Frobenius type (i.e. if V is an irreducible representation of H then dimV
divides dimH). It was proved by Montgomery and Witherspoon that the conjecture
is true for H of dimension p^n, p prime, and by Nichols and Richmond that if H
has a 2-dimensional representation then dimH is even. In this paper we first
prove that if V is an irreducible representation of D(H), the Drinfeld double
of any finite-dimensional semisimple Hopf algebra H over k, then dimV divides
dimH (not just dimD(H)=(dimH)^2). In doing this we use the theory of modular
tensor categories (in particular Verlinde formula). We then use this statement
to prove that Kaplansky's conjecture is true for finite-dimensional semisimple
quasitriangular Hopf algebras over k. As a result we prove easily the result of
Zhu that Kaplansky's conjecture on prime dimensional Hopf algebras over k is
true, by passing to their Drinfeld doubles. Second, we use a theorem of Deligne
on characterization of tannakian categories to prove that triangular semisimple
Hopf algebras over k are equivalent to group algebras as quasi-Hopf algebras.


title: Nonstandard solutions of the Yang-Baxter equation

abstract:
  Explicit solutions of the quantum Yang-Baxter equation are given
corresponding to the non-unitary solutions of the classical Yang-Baxter
equation for sl(5).


title: A solution of the quantum Knizhnik Zamolodchikov equation of type $C_n$

abstract:
  We construct a solution of Cherednik's quantum Knizhnik Zamolodchikov
equation associated with the root system of type $C_n$. This solution is given
in terms of a restriction of a $q$-Jordan-Pochhammer integral. As its
applicaton, we give an explicit expression of a special case of the Macdonald
polynomial of the $C_n$ type. Finally we explain the connection with the
representation of the Hecke algebra.


title: The Cremmer-Gervais solution of the Yang-Baxter equation

abstract:
  A direct proof is given of the fact that the Cremmer-Gervais R-matrices
satisfy the Yang-Baxter equation.


title: Universal Solutions of Quantum Dynamical Yang-Baxter Equations

abstract:
  We construct a universal trigonometric solution of the Gervais-Neveu-Felder
equation in the case of finite dimensional simple Lie algebras and finite
dimensional contragredient simple Lie superalgebras.


title: Braid group approach to the derivation of universal \v{R} matrices

abstract:
  A new method for deriving universal \v{R} matrices from braid group
representation is discussed. In this case, universal \v{R} operators can be
defined and expressed in terms of products of braid group generators. The
advantage of this method is that matrix elements of \v{R} are rank independent,
and leaves multiplicity problem concerning coproducts of the corresponding
quantum groups untouched. As examples, \v{R} matrix elements of $[1]\times
  [1]$, $[2]\times [2]$, $[1^{2}]\times [1^{2}]$, and $[21]\times [21]$ with
multiplicity two for $A_{n}$, and $[1]\times [1]$ for $B_{n}$,
  $C_{n}$, and $D_{n}$ type quantum groups, which are related to Hecke algebra
and Birman-Wenzl algebra, respectively, are derived by using this method.


title: Genus-zero modular functors and intertwining operator algebras

abstract:
  In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the
notion of intertwining operator algebra, a nonmeromorphic generalization of the
notion of vertex operator algebra involving monodromies. The problem of
constructing intertwining operator algebras from representations of suitable
vertex operator algebras were solved implicitly earlier in [H3]
(q-alg/9505019). In the present paper, we generalize the geometric and operadic
formulation of the notion of vertex operator algebra given in [H1], [H2], [HL1]
(hep-th/9301009), [HL2] and [H6] to the notion of intertwining operator
algebra. We show that the category of intertwining operator algebras of central
charge c is isomorphic to the category of algebras over rational genus-zero
modular functors (certain analytic partial operads) of central charge c
satisfying certain generalized meromorphicity. This result is one main step in
the construction of genus-zero conformal field theories from representations of
vertex operator algebras announced in [H5] (q-alg/9512024). One byproduct of
the proof of the present isomorphism theorem is a geometric construction of
(framed) braid group representations from intertwining operator algebras and
thus from representations of suitable vertex operator algebras.


title: Double Lie algebras and Manin triples

abstract:
  The construction of Lie bialgebra from double Lie algebra is presented. It is
used to relate some types of cobracket on inhomogenous so(p,q) algebras with
double Lie algebra structures on so(p+1,q) or so(p,q+1). Also it is shown that
the cobracket corresponding to kappa-deformation gives rise to complete
Poisson-Lie Euclidean groups and non-complete Poincare groups.


title:
Affine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for
  Projective Representations of the Symmetric Group

abstract:
  We study a $q$-deformation for the semi-direct product of the symmetric group
$S_n$ with the Clifford algebra on $n$ anticommuting generators. We obtain a
$q$-version of the projective analogue for the classical Young symmetrizer
found by the second author [Adv. Math. 127(1997), 190-257]. Our main tool is an
analogue of the Hecke algebra of complex valued functions on the group $GL_{n}$
over a $p$-adic field relative to the Iwahori subgroup.


title: Tensor product representations of the quantum double of a compact group

abstract:
  We consider the quantum double D(G) of a compact group G, following an
earlier paper. We use the explicit comultiplication on D(G) in order to build
tensor products of irreducible *-representations. Then we study their behaviour
under the action of the R-matrix, and their decomposition into irreducible
*-representations. The example of D(SU(2)) is treated in detail, with explicit
formulas for direct integral decomposition (`Clebsch-Gordan series') and
Clebsch-Gordan coefficients. We point out possible physical applications.


title:
Deformed Harmonic Oscillator Algebras defined by their Bargmann
  representations

abstract:
  Deformed Harmonic Oscillator Algebras are generated by four operators, two
mutually adjoint $a$ and $a^\dagger$, and two self-adjoint $N$ and the unity
$1$ such as:
  $[a,N] = a, [a^\dagger, N]= -a^\dagger, a^\dagger a = \psi(N)$ and
$aa^\dagger =\psi(N+1)$.
  The Bargmann Hilbert space is defined as a space of functions, holomorphic in
a ring of the complex plane, equipped with a scalar product involving a true
integral. In a Bargmann representation, the operators of a Deformed Harmonic
Oscillator Algebra act on a Bargmann Hilbert space and the creation (or the
annihilation operator) is the multiplication by $z$.
  We discuss the conditions of existence of Deformed Harmonic Oscillator
Algebras assumed to admit a given Bargmann representation.


title: Theory of linear G-difference equations

abstract:
  We introduce the notion of difference equation defined on a structured set.
The symmetry group of the structure determines the set of difference operators.
All main notions in the theory of difference equations are introduced as
invariants of the symmetry group. Linear equations are modules over the skew
group algebra, solutions are morphisms relating a given equation to other
equations,symmetries of an equation are module endomorphisms and conserved
structures are invariants in the tensor algebra of the given equation. We show
that the equations and their solutions can be described through representations
of the isotropy group of the symmetry group of the underluing set. We relate
our notion of difference equations and solutions to systems of classical
difference equations and their solutions and show that our notions include
these as a special case.


title: Finite type invariants, the mapping class group and blinks

abstract:
  The goal of the present paper is to find higher genus surgery formulae for
the set of finite-type invariants of homology spheres, and to develop a
companion theory of finite-type invariants to be applied, in a subsequent
publication, to the study of subgroups of the mapping class group. The main
result is to show that six filtrations on the vector space generated by
oriented homology spheres (three coming from surgery on special classes of
links and three coming from subgroups of the mapping class group) are equal. En
route we introduce the notion of blink (a special case of a link) and of a new
subgroup of the mapping class group.


title: Web bases for sl(3) are not dual canonical

abstract:
  We compare two natural bases for the invariant space of a tensor product of
irreducible representations of A_2, or sl(3). One basis is the web basis,
defined from a skein theory called the combinatorial A_2 spider. The other
basis is the dual canonical basis, the dual of the basis defined by Lusztig and
Kashiwara. For sl(2) or A_1, the web bases have been discovered many times and
were recently shown to be dual canonical by Frenkel and Khovanov.
  We prove that for sl(3), the two bases eventually diverge even though they
agree in many small cases. The first disagreement comes in the invariant space
Inv((V^+ tensor V^+ tensor V^- tensor V^-)^{tensor 3}), where V^+ and V^- are
the two 3-dimensional representations of sl(3). If the tensor factors are
listed in the indicated order, only 511 of the 512 invariant basis vectors
coincide.


title: Non-involutory Hopf algebras and 3-manifold invariants

abstract:
  We present a definition of an invariant #(M,H), defined for every
finite-dimensional Hopf algebra (or Hopf superalgebra or Hopf object) H and for
every closed, framed 3-manifold M. When H is a quantized universal enveloping
algebra, #(M,H) is closely related to well-known quantum link invariants such
as the HOMFLY polynomial, but it is not a topological quantum field theory.


title: Detecting knot invertibility

abstract:
  We discuss the consequences of the possibility that Vassiliev invariants do
not detect knot invertibility as well as the fact that quantum Lie group
invariants are known not to do so. On the other hand, finite group invariants,
such as the set of homomorphisms from the knot group to M_11, can detect knot
invertibility. For many natural classes of knot invariants, including Vassiliev
invariants and quantum Lie group invariants, we can conclude that the
invariants either distinguish all oriented knots, or there exist prime,
unoriented knots which they do not distinguish.


title:
On hypergeometric functions connected with quantum cohomology of flag
  spaces

abstract: Givental's recursion relations for the flag varieties $G/B$ are established.


title: Centralizer construction for twisted Yangians

abstract:
  For each of the classical Lie algebras $g(n)=o(2n+1), sp(2n), o(2n)$ of type
B, C, D we consider the centralizer of the subalgebra $g(n-m)$ in the universal
enveloping algebra $U(g(n))$. We show that the $n$th centralizer algebra can be
naturally projected onto the $(n-1)$th one, so that one can form the projective
limit of the centralizer algebras as $n\to\infty$ with $m$ fixed. The main
result of the paper is a precise description of this limit (or stable)
centralizer algebra, denoted by $A_m$. We explicitly construct an algebra
isomorphism $A_m=Z\otimes Y_m$, where $Z$ is a commutative algebra and $Y_m$ is
the so-called twisted Yangian associated to the rank $m$ classical Lie algebra
of type B, C, or D. The algebra $Z$ may be viewed as the algebra of virtual
Laplace operators; it is isomorphic to the algebra of polynomials with
countably many indeterminates. The twisted Yangian $Y_m$ (and hence the algebra
$A_m$) can be described in terms of a system of generators with quadratic and
linear defining relations which are conveniently presented in R-matrix form
involving the so-called reflection equation. This extends the earlier work on
the type A case by the second author.


title: On Cherednik-Macdonald-Mehta identities

abstract:
  In this note we give a short proof of Cherednik's generalization of
Macdonald-Mehta identities for the root system $A_{n-1}$ using the
representation theory of quantum groups. These identities, suggested and proved
by Cherednik, give an explicit formula for the integral of a product of
Macdonald polynomials with respect to a ``difference analogue of the Gaussian
measure''.


title: A characterization of interpolation Macdonald polynomials

abstract:
  In this elementary paper we prove that the extra vanishing property
characterizes the BC interpolation Macdonald polynomials inside a very general
class of multivariate interpolation polynomials. It follows that they are the
only polynomials in this class that admit a tableaux sum formula or a
q-integral representation.


title: Skew divided difference operators and Schubert polynomials

abstract:
  We study an action of the skew divided difference operators on the Schubert
polynomials and give an explicit formula for structural constants for the
Schubert polynomials in terms of certain weighted paths in the Bruhat order on
the symmetric group. We also prove that, under certain assumptions, the skew
divided difference operators transform Schubert polynomials into polynomials
with positive integer coefficients.


title:
Eigenfunctions of Macdonald's $q$-difference operator for the root
  system of type $C_n$

abstract:
  We construct an integral representation of eigenfunctions for Macdonald's
$q$-difference operator associated with the root system of type $C_n .$ It is
given in terms of a restriction of a $q$-Jordan-Pochhammer integral. Choosing a
suitable cycle of the integral, we obtain an integral representation of a
special case of the Macdonald polynomial for the root system of type $C_n .$


title: The $q$-Fourier transform of $q$-distributions

abstract:
  We consider functions on the lattice generated by the integer powers of $q^2$
for $0<q<1$ and construct the $q$-analog of Fourier transform based on the
Jackson integral in the space of distributions on the lattice.


title:
Solutions of the qKZB Equation in Tensor Products of finite dimensional
  modules over the elliptic quantum group $E_{\tau,\eta}sl_2$

abstract:
  We consider the quantized Knizhnik-Zamolodchikov-Bernard difference equation
(qKZB) with step $p$ and values in a tensor product of finite dimensional
evaluation modules over the elliptic quantum group $E_{\tau,\eta}(sl_2)$, the
equation defined in terms of elliptic dynamical R-matrices. We solve the
equation in terms of multidimensional q-hypergeometric integrals and describe
its monodromy properties. We identify the space of solutions of the qKZ
equation with the space of functions with values in the tensor product of the
corresponding modules over the elliptic quantum group $E_{p,\eta}(sl_2)$.


title: Yangian Algebras and Classical Riemann Problems

abstract:
  We investigate different Hopf algebras associated to Yang's solution of
quantum Yang-Baxter equation. It is shown that for the precise definition of
the algebra one needs the commutation relations for the deformed algebra of
formal currents and the specialization of the Riemann problem for the currents.
Two different Riemann problems are considered. They lead to the central
extended Yangian double associated with ${sl}_2$ and to the degeneration of
scaling limit of elliptic affine algebra. Unless the defining relations for the
generating functions of the both algebras coincide their properties and the
theory of infinite-dimensional representations are quite different. We discuss
also the Riemann problem for twisted algebras and for scaled elliptic algebra.


title: Monotone Systems with Inputs and Outputs

abstract:
  Monotone systems constitute one of the most important classes of dynamical
systems used in mathematical biology modeling. The objective of this paper is
to extend the notion of monotonicity to systems with inputs and outputs, a
necessary first step in trying to understand interconnections, especially
including feedback loops, built up out of monotone components. Basic
definitions and theorems are provided, as well as an application of a theorem
regarding negative feedback loops to the study of a model of one of the cell's
most important subsystems (MAPK cascades) .


title: Multi-Stability in Monotone Input/Output Systems

abstract:
  This paper studies the emergence of multi-stability and hysteresis in those
systems that arise, under positive feedback, starting from monotone systems
with well-defined steady-state responses. Such feedback configurations appear
routinely in several fields of application, and especially in biology.
Characterizations of global stability behavior are stated in terms of easily
checkable graphical conditions. An example of a signaling cascade under
positive feedback is presented.


title: Adaptation and regulation with signal detection implies internal model

abstract:
  This note provides a theorem showing, under suitable technical assumptions,
that if a system S adapts to a class of external signals U, in the sense of
egulation against disturbances or tracking signals in U, then S must ecessarily
contain a subsystem which is capable of generating all the signals in U. It is
not assumed that regulation is robust, nor is there a prior requirement for the
system to be partitioned into separate plant and controller components.
Instead, one assumes that a ``signal detection'' property holds. The result was
motivated by questions of adaptation in bacterial chemotaxis, but the general
mathematical principle is of wide applicability.


title: Mobility of Taxol in Microtubule Bundles

abstract:
  Mobility of taxol inside microtubules was investigated using fluorescence
recovery after photobleaching (FRAP) on flow-aligned bundles. Bundles were made
of microtubules with either GMPCPP or GTP at the exchangeable site on the
tubulin dimer. Recovery times were sensitive to bundle thickness and packing,
indicating that taxol molecules are able to move laterally through the bundle.
The density of open binding sites along a microtubule was varied by controlling
the concentration of taxol in solution for GMPCPP samples. With > 63% sites
occupied, recovery times were independent of taxol concentration and,
therefore, inversely proportional to the microscopic dissociation rate,
k_{off}. It was found that 10*k_{off} (GMPCPP) ~ k_{off} (GTP), consistent
with, but not fully accounting for, the difference in equilibrium constants for
taxol on GMPCPP and GTP microtubules. With < 63% sites occupied, recovery times
decreased as ~ [Tax]^{-1/5} for both types of microtubules. We conclude that
the diffusion of taxol along the microtubule interior is hindered by rebinding
events when open sites are within ~7 nm of each other.


title:
On the 20 canonical amino acids by a cooperative vector-addition
  principle based on the quasi-28-gon symmetry of the genetic code

abstract:
  Upon the covalent-bonding hybrid of the nitrogen atoms taken as a measure for
the structural regularity in nucleobases, it can be identified that the
internal relation within the 20 amino acids follows a cooperative
vector-in-space addition principle based on the spherical and rotational
symmetry of a quasi-28-gon (quasi-icosikaioctagon), with two evolutionary axes.


title:
Probabilistic estimation of microarray data reliability and underlying
  gene expression

abstract:
  Background: The availability of high throughput methods for measurement of
mRNA concentrations makes the reliability of conclusions drawn from the data
and global quality control of samples and hybridization important issues. We
address these issues by an information theoretic approach, applied to
discretized expression values in replicated gene expression data.
  Results: Our approach yields a quantitative measure of two important
parameter classes: First, the probability $P(\sigma | S)$ that a gene is in the
biological state $\sigma$ in a certain variety, given its observed expression
$S$ in the samples of that variety. Second, sample specific error probabilities
which serve as consistency indicators of the measured samples of each variety.
The method and its limitations are tested on gene expression data for
developing murine B-cells and a $t$-test is used as reference. On a set of
known genes it performs better than the $t$-test despite the crude
discretization into only two expression levels. The consistency indicators,
i.e. the error probabilities, correlate well with variations in the biological
material and thus prove efficient.
  Conclusions: The proposed method is effective in determining differential
gene expression and sample reliability in replicated microarray data. Already
at two discrete expression levels in each sample, it gives a good explanation
of the data and is comparable to standard techniques.


title: The Inter-Strand Modes of the DNA as a Probe into MW-Radiation

abstract:
  We consider the regime in which the bands of the torsional acoustic (TA) and
the hydrogen-bond-stretch (HBS) modes of the DNA interpenetrate each other.
Within the framework of a model that accommodates the structure of the double
helix, we find the three-wave interaction between the TA- and the HBS-modes,
and show that microwave radiation could bring about torsional vibrations that
could serve as a pump mode for maintaining the HBS-one. Rayleigh's threshold
condition for the parametric resonance provides an estimate for the power
density of the mw-field necessary for generating the HBS-mode.


title:
The bi-pyramidal nature, the Lucas series in the genetic code and their
  relation to aminoacyl-tRNA synthetases

abstract:
  New analyses of the organization of the genetic code system together with
their relation to the two classes of aminoacyl-tRNA synthetases are reported in
this work. A closer inspection revealed how the enzymes and the 20 amino acids
of the genetic code are intertwined on a polyhedron model. Complimentarily and
cooperative symmetry between class I and class II aminoacyl-tRNA synthetases
displayed by a 28-gon model are discussed, and we found that the two previously
suggested evolutionary axes of the genetic code overlap the three two-fold
symmetry axes within the two classes of aminoacyl-tRNA synthetases. Moreover,
it is identified that the amino-acid side-chain carbon-atom numbers (1, 3, 4
and 7) in the overwhelming majority of the amino acids recognized by each of
the two classes of aminoacyl-tRNA synthetases meet a mathematical relationship,
the Lucas series.

categories: q-bio.BM math.MG math.OC q-bio.GN q-bio.PE


title:
Quantum noise, entanglement and chaos in the quantum field theory of
  mind/brain states

abstract:
  We review the dissipative quantum model of brain and present recent
developments related with the r\^ole of entanglement, quantum noise and chaos
in the model.


title: Force steps during viral DNA packaging ?

abstract:
  Biophysicists and structural biologists increasingly acknowledge the role
played by the mechanical properties of macromolecules as a critical element in
many biological processes. This change has been brought about, in part, by the
advent of single molecule biophysics techniques that have made it possible to
exert piconewton forces on key macromolecules and observe their deformations at
nanometer length scales, as well as to observe the mechanical action of
macromolecules such as molecular motors. This has opened up immense
possibilities for a new generation of mechanical investigations that will
respond to such measurements in an attempt to develop a coherent theory for the
mechanical behavior of macromolecules under conditions where thermal and
chemical effects are on an equal footing with deterministic forces. This paper
presents an application of the principles of mechanics to the problem of DNA
packaging, one of the key events in the life cycle of bacterial viruses with
special reference to the nature of the internal forces that are built up during
the DNA packaging process.


title: Discovery and analysis of biochemical subnetwork hierarchies

abstract:
  The representation of a biochemical network as a graph is the coarsest level
of description in cellular biochemistry. By studying the network structure one
can draw conclusions on the large scale organisation of the biochemical
processes. We describe methods how one can extract hierarchies of subnetworks,
how these can be interpreted and further deconstructed to find autonomous
subnetworks. The large-scale organisation we find is characterised by a tightly
connected core surrounded by increasingly loosely connected substrates.


title: On the structure of proten-protein interaction networks

abstract:
  We present a simple model for the underlying structure of protein-protein
pairwise interaction graphs that is based on the way in which proteins attach
to each other in experiments such as yeast two-hybrid assays. We show that data
on the interactions of human proteins lend support to this model. The frequency
of the number of connections per protein under this model does not follow a
power law, in contrast to the reported behaviour of data from large scale yeast
two-hybrid screens of yeast protein-protein interactions. Sampling sub-graphs
from the underlying graphs generated with our model, in a way analogous to the
sampling performed in large scale yeast two-hybrid searches, gives degree
distributions that differ subtly from the power law and that fit the observed
data better than the power law itself. Our results show that the observation of
approximate power law behaviour in a sampled sub-graph does not imply that the
underlying graph follows a power law.


title:
Robust gene regulation: Deterministic dynamics from asynchronous
  networks with delay

abstract:
  We compare asynchronous vs. synchronous update of discrete dynamical networks
and find that a simple time delay in the nodes may induce a reproducible
deterministic dynamics even in the case of asynchronous update in random order.
In particular we observe that the dynamics under synchronous parallel update
can be reproduced accurately under random asynchronous serial update for a
large class of networks. This mechanism points at a possible general principle
of how computation in gene regulation networks can be kept in a
quasi-deterministic ``clockwork mode'' in spite of the absence of a central
clock. A delay similar to the one occurring in gene regulation causes
synchronization in the model. Stability under asynchronous dynamics disfavors
topologies containing loops, comparing well with the observed strong
suppression of loops in biological regulatory networks.


title: The naturally designed spherical symmetry in the genetic code

abstract:
  In the present work, 16 genetic code doublets and their cognate amino acids
in the genetic code are fitted into a polyhedron model. Based on the structural
regularity in nucleobases, and by using a series of common-sense topological
approaches to rearranging the Hamiltonian-type graph of the codon map, it is
identified that the degeneracy of codons and the internal relation of the 20
amino acids within the genetic code are in agreement with the spherical and
polyhedral symmetry of a quasi-28-gon, i.e., icosikaioctagon. Hence, a
quasi-central, quasi-polyhedral and rotational symmetry within the genetic code
is described. Accordingly, the rotational symmetry of the numerical
distribution of side-chain carbon atoms of the 20 amino acids and the
side-chain skeleton atoms (carbon, nitrogen, oxygen and sulfur) of the 20 amino
acids are presented in the framework of this quasi-28-gon model. Two
evolutionary axes within the 20 standard amino acids are suggested.


title: A Quasispecies on a Moving Oasis

abstract:
  A population evolving in an inhomogeneous environment will adapt differently
to different regions. We study the conditions under which such a population can
maintain adaptations to a particular region when that region is not stationary,
but can move. In particular, we study a quasispecies living near a favorable
patch ("oasis") in the middle of a large "desert." The population has two
genetic states, one of which which conveys a relative advantage while in the
oasis at the cost of a disadvantage in the desert. We consider the population
dynamics when the oasis is moving, or equivalently some form of "wind" is
blowing the population away from the oasis. We find that the ratio of the two
types of individuals exhibits sharp transitions at particular oasis velocities.
We calculate an extinction velocity, and a switching velocity above which the
dominance switches from the oasis-adapted genotype to the desert-adapted one.
This switching velocity is analagous to the quasispecies mutational error
threshold. Above this velocity, the population cannot maintain adaptations to
the properties of the oasis.


title:
Probing subtle fluorescence dynamics in cellular proteins by streak
  camera based Fluorescence Lifetime Imaging Microscopy

abstract:
  We report the cell biological applications of a recently developed
multiphoton fluorescence lifetime imaging microscopy system using a streak
camera (StreakFLIM). The system was calibrated with standard fluorophore
specimens and was shown to have high accuracy and reproducibility. We
demonstrate the applicability of this instrument in living cells for measuring
the effects of protein targeting and point mutations in the protein sequence
which are not obtainable in conventional intensity based fluorescence
microscopy methods. We discuss the relevance of such time resolved information
in quantitative energy transfer microscopy and in measurement of the parameters
characterizing intracellular physiology.


title: Differential hydrophobicity drives self-assembly in Huntington's disease

abstract:
  Identifying the driving forces and the mechanism of association of
huntingtin-exon1, a close marker for the progress of Huntington's disease, is
an important prerequisite towards finding potential drug targets, and
ultimately a cure. We introduce here a modelling framework based on a key
analogy of the physico-chemical properties of the exon1 fragment to block
copolymers. We use a systematic mesoscale methodology, based on Dissipative
Particle Dynamics, which is capable of overcoming kinetic barriers, thus
capturing the dynamics of significantly larger systems over longer times than
considered before. Our results reveal that the relative hydrophobicity of the
poly-glutamine block as compared to the rest of the (proline-based) exon1
fragment, ignored to date, constitutes a major factor in the initiation of the
self-assembly process. We find that the assembly is governed by both the
concentration of exon1 and the length of the poly-glutamine stretch, with a low
length threshold for association even at the lowest volume fractions we
considered. Moreover, this self-association occurs irrespective of whether the
glutamine stretch is in random coil or hairpin configuration, leading to
spherical or cylindrical assemblies, respectively. We discuss the implications
of these results for reinterpretation of existing research within this context,
including that the routes towards aggregation of exon1 may be distinct to those
of the widely studied homopolymeric poly-glutamine peptides.


title:
Coherence resonance in models of an excitable neuron with both fast and
  slow dynamics

abstract:
  We demonstrate the existence of noise-induced periodicity (coherence
resonance) in both a discrete-time model and a continuous-time model of an
excitable neuron. In particular, we show that the effects of noise added to the
fast and slow dynamics of the models are dramatically different. A
Fokker-Planck analysis gives a quantitative explanation of the effects.


title:
Scaling in Counter Expressed Gene Networks Constructed from Gene
  Expression Data

abstract:
  We study counter expressed gene networks constructed from gene-expression
data obtained from many types of cancers. The networks are synthesized by
connecting vertices belonging to each others' list of K-farthest-neighbors,
with K being an a priori selected non-negative integer. In the range of K
corresponding to minimum homogeneity, the degree distribution of the networks
shows scaling. Clustering in these networks is smaller than that in equivalent
random graphs and remains zero till significantly large K. Their small
diameter, however, implies small-world behavior which is corroborated by their
eigenspectrum. We discuss implications of these findings in several contexts.


title: Human housekeeping genes are compact

abstract:
  We identify a set of 575 human genes that are expressed in all conditions
tested in a publicly available database of microarray results. Based on this
common occurrence, the set is expected to be rich in "housekeeping" genes,
showing constitutive expression in all tissues. We compare selected aspects of
their genomic structure with a set of background genes. We find that the
introns, untranslated regions and coding sequences of the housekeeping genes
are shorter, indicating a selection for compactness in these genes.


title:
Development of a Multiphoton Fluorescence Lifetime Imaging Microscopy
  (FLIM) system using a Streak Camera

abstract:
  We report the development and detailed calibration of a multiphoton
fluorescence lifetime imaging system (FLIM) using a streak camera. The present
system is versatile with high spatial (0.2 micron) and temporal (50 psec)
resolution and allows rapid data acquisition and reliable and reproducible
lifetime determinations. The system was calibrated with standard fluorescent
dyes and the lifetime values obtained were in very good agreement with values
reported in literature for these dyes. We also demonstrate the applicability of
the system to FLIM studies in cellular specimens including stained pollen
grains and fibroblast cells expressing green fluorescent protein. The lifetime
values obtained matched well with those reported earlier by other groups for
these same specimens. Potential applications of the present system include the
measurement of intracellular physiology and Fluorescence Resonance Energy
Transfer (FRET) imaging which are discussed in the context of live cell
imaging.


title:
Quantitative Imaging of Protein-Protein Interactions by Multiphoton
  Fluorescence Lifetime Imaging Microscopy using a Streak camera

abstract:
  Fluorescence Lifetime Imaging Microscopy (FLIM) using multiphoton excitation
techniques is now finding an important place in quantitative imaging of
protein-protein interactions and intracellular physiology. We review here the
recent developments in multiphoton FLIM methods and also present a description
of a novel multiphoton FLIM system using a streak camera that was developed in
our laboratory. We provide an example of a typical application of the system in
which we measure the fluorescence resonance energy transfer between a
donor/acceptor pair of fluorescent proteins within a cellular specimen.


title: Idl Signal Processing Library 1.0

abstract:
  We make available a library of documented IDL .pro files as well as a
shareable object library that allows IDL to call routines from LAPACK. The
routines are for use in the spectral analysis of time series data. The primary
focus of these routines are David Thomson's multitaper methods but a whole
range of functions will be made available in future revisions of the
submission. At present routines are provided to carry out the following
operations: calculate prolate spheroidal sequences and eigenvalues, project
time-series into frequency bands, calculate spectral estimates with or without
moving windows, and calculate the cross-coherence between two time series as a
function of frequency as well as the coherence between frequencies for a single
time series.


title:
Synchronization and oscillatory dynamics in heterogeneous mutually
  inhibited neurons

abstract:
  We study some mechanisms responsible for synchronous oscillations and loss of
synchrony at physiologically relevant frequencies (10-200 Hz) in a network of
heterogeneous inhibitory neurons. We focus on the factors that determine the
level of synchrony and frequency of the network response, as well as the
effects of mild heterogeneity on network dynamics. With mild heterogeneity,
synchrony is never perfect and is relatively fragile. In addition, the effects
of inhibition are more complex in mildly heterogeneous networks than in
homogeneous ones. In the former, synchrony is broken in two distinct ways,
depending on the ratio of the synaptic decay time to the period of repetitive
action potentials ($\tau_s/T$), where $T$ can be determined either from the
network or from a single, self-inhibiting neuron. With $\tau_s/T > 2$,
corresponding to large applied current, small synaptic strength or large
synaptic decay time, the effects of inhibition are largely tonic and
heterogeneous neurons spike relatively independently. With $\tau_s/T < 1$,
synchrony breaks when faster cells begin to suppress their less excitable
neighbors; cells that fire remain nearly synchronous. We show numerically that
the behavior of mildly heterogeneous networks can be related to the behavior of
single, self-inhibiting cells, which can be studied analytically.


title: Frequency control in synchronized networks of inhibitory neurons

abstract:
  We analyze the control of frequency for a synchronized inhibitory neuronal
network. The analysis is done for a reduced membrane model with a
biophysically-based synaptic influence. We argue that such a reduced model can
quantitatively capture the frequency behavior of a larger class of neuronal
models. We show that in different parameter regimes, the network frequency
depends in different ways on the intrinsic and synaptic time constants. Only in
one portion of the parameter space, called `phasic', is the network period
proportional to the synaptic decay time. These results are discussed in
connection with previous work of the authors, which showed that for mildly
heterogeneous networks, the synchrony breaks down, but coherence is preserved
much more for systems in the phasic regime than in the other regimes. These
results imply that for mildly heterogeneous networks, the existence of a
coherent rhythm implies a linear dependence of the network period on synaptic
decay time, and a much weaker dependence on the drive to the cells. We give
experimental evidence for this conclusion.


title: Coding Strategies in Monkey V1 and Inferior Temporal Cortices

abstract:
  We would like to know whether the statistics of neuronal responses vary
across cortical areas. We examined stimulus-elicited spike count response
distributions in V1 and IT cortices of awake monkeys. In both areas the
distribution of spike counts for each stimulus was well-described by a
Gaussian, with the log of the variance in the spike count linearly related to
the log of the mean spike count. Two significant differences in response
characteristics were found: both the range of spike counts and the slope of the
log(variance) vs. log(mean) regression were larger in V1 than in IT. However,
neurons in the two areas transmitted approximately the same amount of
information about the stimuli, and had about the same channel capacity (the
maximum possible transmitted information given noise in the responses). These
results suggest that neurons in V1 use more variable signals over a larger
dynamic range than neurons in IT, which use less variable signals over a
smaller dynamic range. The two coding strategies are approximately as effective
in transmitting information.


title: Measuring the dynamics of neural responses in primary auditory cortex

abstract:
  We review recent developments in the measurement of the dynamics of the
response properties of auditory cortical neurons to broadband sounds, which is
closely related to the perception of timbre. The emphasis is on a method that
characterizes the spectro-temporal properties of single neurons to dynamic,
broadband sounds, akin to the drifting gratings used in vision. The method
treats the spectral and temporal aspects of the response on an equal footing.


title: Analysis of Dynamic Brain Imaging Data

abstract:
  Modern imaging techniques for probing brain function, including functional
Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging,
and magnetoencephalography, generate large data sets with complex content. In
this paper we develop appropriate techniques of analysis and visualization of
such imaging data, in order to separate the signal from the noise, as well as
to characterize the signal. The techniques developed fall into the general
category of multivariate time series analysis, and in particular we extensively
use the multitaper framework of spectral analysis. We develop specific
protocols for the analysis of fMRI, optical imaging and MEG data, and
illustrate the techniques by applications to real data sets generated by these
imaging modalities. In general, the analysis protocols involve two distinct
stages: `noise' characterization and suppression, and `signal' characterization
and visualization. An important general conclusion of our study is the utility
of a frequency-based representation, with short, moving analysis windows to
account for non-stationarity in the data. Of particular note are (a) the
development of a decomposition technique (`space-frequency singular value
decomposition') that is shown to be a useful means of characterizing the image
data, and (b) the development of an algorithm, based on multitaper methods, for
the removal of approximately periodic physiological artifacts arising from
cardiac and respiratory sources.


title: Bayesian Inference Applied to the Electromagnetic Inverse Problem

abstract:
  We present a new approach to the electromagnetic inverse problem that
explicitly addresses the ambiguity associated with its ill-posed character.
Rather than calculating a single ``best'' solution according to some criterion,
our approach produces a large number of likely solutions that both fit the data
and any prior information that is used. While the range of the different likely
results is representative of the ambiguity in the inverse problem even with
prior information present, features that are common across a large number of
the different solutions can be identified and are associated with a high degree
of probability. This approach is implemented and quantified within the
formalism of Bayesian inference which combines prior information with that from
measurement in a common framework using a single measure. To demonstrate this
approach, a general neural activation model is constructed that includes a
variable number of extended regions of activation and can incorporate a great
deal of prior information on neural current such as information on location,
orientation, strength and spatial smoothness. Taken together, this activation
model and the Bayesian inferential approach yield estimates of the probability
distributions for the number, location, and extent of active regions. Both
simulated MEG data and data from a visual evoked response experiment are used
to demonstrate the capabilities of this approach.


title: Synaptic Transmission: An Information-Theoretic Perspective

abstract:
  Here we analyze synaptic transmission from an information-theoretic
perspective. We derive closed-form expressions for the lower-bounds on the
capacity of a simple model of a cortical synapse under two explicit coding
paradigms. Under the ``signal estimation'' paradigm, we assume the signal to be
encoded in the mean firing rate of a Poisson neuron. The performance of an
optimal linear estimator of the signal then provides a lower bound on the
capacity for signal estimation. Under the ``signal detection'' paradigm, the
presence or absence of the signal has to be detected. Performance of the
optimal spike detector allows us to compute a lower bound on the capacity for
signal detection. We find that single synapses (for empirically measured
parameter values) transmit information poorly but significant improvement can
be achieved with a small amount of redundancy.


title:
Metric-space analysis of spike trains: theory, algorithms, and
  application

abstract:
  We present the mathematical basis of a new approach to the analysis of
temporal coding. The foundation of the approach is the construction of several
families of novel distances (metrics) between neuronal impulse trains. In
contrast to most previous approaches to the analysis of temporal coding, the
present approach does not attempt to embed impulse trains in a vector space,
and does not assume a Euclidean notion of distance. Rather, the proposed
metrics formalize physiologically-based hypotheses for what aspects of the
firing pattern might be stimulus-dependent, and make essential use of the point
process nature of neural discharges. We show that these families of metrics
endow the space of impulse trains with related but inequivalent topological
structures. We show how these metrics can be used to determine whether a set of
observed responses have stimulus-dependent temporal structure without a
vector-space embedding. We show how multidimensional scaling can be used to
assess the similarity of these metrics to Euclidean distances. For two of these
families of metrics (one based on spike times and one based on spike
intervals), we present highly efficient computational algorithms for
calculating the distances. We illustrate these ideas by application to
artificial datasets and to recordings from auditory and visual cortex.


title:
The power ratio and the interval map: spiking models and extracellular
  data

abstract:
  We describe a new, computationally simple method for analyzing the dynamics
of neuronal spike trains driven by external stimuli. The goal of our method is
to test the predictions of simple spike-generating models against
extracellularly recorded neuronal responses. Through a new statistic called the
power ratio, we distinguish between two broad classes of responses: (1)
responses that can be completely characterized by a variable firing rate, (for
example, modulated Poisson and gamma spike trains); and (2) responses for which
firing rate variations alone are not sufficient to characterize response
dynamics (for example, leaky integrate-and-fire spike trains as well as Poisson
spike trains with long absolute refractory periods). We show that the responses
of many visual neurons in the cat retinal ganglion, cat lateral geniculate
nucleus, and macaque primary visual cortex fall into the second class, which
implies that the pattern of spike times can carry significant information about
visual stimuli. Our results also suggest that spike trains of X-type retinal
ganglion cells, in particular, are very similar to spike trains generated by a
leaky integrate-and-fire model with additive, stimulus-independent noise that
could represent background synaptic activity.


title: Sensory Coding with Dynamically Competitive Networks

abstract:
  Studies of insect olfactory processing indicate that odors are represented by
rich spatio-temporal patterns of neural activity. These patterns are very
difficult to predict a priori, yet they are stimulus specific and reliable upon
repeated stimulation with the same input. We formulate here a theoretical
framework in which we can interpret these experimental results. We propose a
paradigm of ``dynamic competition'' in which inputs (odors) are represented by
internally competing neural assemblies. Each pattern is the result of dynamical
motion within the network and does not involve a ``winner'' among competing
possibilities. The model produces spatio-temporal patterns with strong
resemblance to those observed experimentally and possesses many of the general
features one desires for pattern classifiers: large information capacity,
reliability, specific responses to specific inputs, and reduced sensitivity to
initial conditions or influence of noise. This form of neural processing may
thus describe the organizational principles of neural information processing in
sensory systems and go well beyond the observations on insect olfactory
processing which motivated its development.


title:
Temporal structure in neuronal activity during working memory in Macaque
  parietal cortex

abstract:
  A number of cortical structures are reported to have elevated single unit
firing rates sustained throughout the memory period of a working memory task.
How the nervous system forms and maintains these memories is unknown but
reverberating neuronal network activity is thought to be important. We studied
the temporal structure of single unit (SU) activity and simultaneously recorded
local field potential (LFP) activity from area LIP in the inferior parietal
lobe of two awake macaques during a memory-saccade task. Using multitaper
techniques for spectral analysis, which play an important role in obtaining the
present results, we find elevations in spectral power in a 50--90 Hz (gamma)
frequency band during the memory period in both SU and LFP activity. The
activity is tuned to the direction of the saccade providing evidence for
temporal structure that codes for movement plans during working memory. We also
find SU and LFP activity are coherent during the memory period in the 50--90 Hz
gamma band and no consistent relation is present during simple fixation.
Finally, we find organized LFP activity in a 15--25 Hz frequency band that may
be related to movement execution and preparatory aspects of the task. Neuronal
activity could be used to control a neural prosthesis but SU activity can be
hard to isolate with cortical implants. As the LFP is easier to acquire than SU
activity, our finding of rich temporal structure in LFP activity related to
movement planning and execution may accelerate the development of this medical
application.


title:
Comorbidity and Anticomorbidity: Autocognitive developmental disorders
  of structured psychosocial stress

abstract:
  We examine interacting cognitive modules of human biology which, in the
asymptotic limit of long sequences of responses, define the output of an
appropriate 'dual' information source. Applying a 'necessary condition'
communication theory formalism roughly similar to that of Dretske, but focused
entirely on long sequences of signals, we examine the regularities apparent in
comorbid psychiatric and chronic physical disorders using an extension of
recent perspectives on autoimmune disease. We find that structured psychosocial
stress can literally write a distorted image of itself onto child development,
resulting in a life course trajectory to characteristic forms of comorbid
mind/body dysfunction affecting both dominant and subordinate populations
within a pathogenic social hierarchy.


title:
Deriving the respiratory sinus arrhythmia from the heartbeat time series
  using Empirical Mode Decomposition

abstract:
  Heart rate variability (HRV) is a well-known phenomenon whose characteristics
are of great clinical relevance in pathophysiologic investigations. In
particular, respiration is a powerful modulator of HRV contributing to the
oscillations at highest frequency. Like almost all natural phenomena, HRV is
the result of many nonlinearly interacting processes; therefore any linear
analysis has the potential risk of underestimating, or even missing, a great
amount of information content. Recently the technique of Empirical Mode
Decomposition (EMD) has been proposed as a new tool for the analysis of
nonlinear and nonstationary data. We applied EMD analysis to decompose the
heartbeat intervals series, derived from one electrocardiographic (ECG) signal
of 13 subjects, into their components in order to identify the modes associated
with breathing. After each decomposition the mode showing the highest frequency
and the corresponding respiratory signal were Hilbert transformed and the
instantaneous phases extracted were then compared. The results obtained
indicate a synchronization of order 1:1 between the two series proving the
existence of phase and frequency coupling between the component associated with
breathing and the respiratory signal itself in all subjects.


title:
Plant defense multigene families: I. Divergence of Fusarium
  solani-induced expression in Pisum and Lathyrus

abstract:
  The defense response in plants challenged with pathogens is characterized by
the activation of a diverse set of genes. Many of the same genes are induced in
the defense responses of a wide range of plant species. How plant defense gene
families evolve may therefore provide an important clue to our understanding of
how disease resistance evolves. Because studies usually focus on a single host
species, little data are available regarding changes in defense gene expression
patterns as species diverge. The expression of defense-induced genes PR10,
chitinase and chalcone synthase was assayed in four pea species (Pisum sativum,
P. humile, P. elatius and P. fulvum) and two Lathyrus species (L. sativus and
L. tingitanus) which exhibited a range of infection phenotypes with Fusarium
solani . In P. sativum, resistance was accompanied by a strong induction of
defense genes at 8 hr. post-inoculation. Weaker induction was seen in
susceptible interactions in wild species. Divergence in the timing of PR10
expression was most striking between P. sativum and its closest realtive, P.
humile. Two members of this multigene family, designated PR10.1 and PR10.2, are
strongly-expressed in response to Fusarium, while the PR10.3 gene is more
weakly expressed, among Pisum species. The rapidity with which PR10 expression
evolves raises the question, is divergence of defense gene expression a part of
the phenotypic diversity underlying plant/pathogen coevolution?


title: Complexity and hierarchical game of life

abstract:
  Hierarchical structure is an essential part of complexity, important notion
relevant for a wide range of applications ranging from biological population
dynamics through robotics to social sciences. In this paper we propose a simple
cellular-automata tool for study of hierarchical population dynamics.


title: Structured psychosocial stress and therapeutic failure

abstract:
  Generalized language-of-thought arguments appropriate to interacting
cognitive modules permit exploration of how disease states interact with
medical treatment. The interpenetrating feedback between treatment and response
to it creates a kind of idiotypic hall-of-mirrors generating a synergistic
pattern of efficacy, treatment failure, adverse reactions, and patient
noncompliance which, from a Rate Distortion perspective, embodies a distorted
image of externally-imposed structured psychosocial stress. For the US,
accelerating spatial and social diffusion of such stress enmeshes both dominant
and subordinate populations in a linked system which will express itself, not
only in an increasingly unhealthy society, but in the diffusion of therapeutic
failure, including, but not limited to, drug-based treatments.


title: Dynamics of Fixation of Advantageous Mutations

abstract:
  We investigate the process of fixation of advantageous mutations in an
asexual population. We assume that the effect of each beneficial mutation is
exponentially distributed with mean value $\omega_{med}=1/\beta$. The model
also considers that the effect of each new deleterious mutation reduces the
fitness of the organism independent on the previous number of mutations. We use
the branching process formulation and also extensive simulations to study the
model. The agreement between the analytical predictions and the simulational
data is quite satisfactory. Surprisingly, we observe that the dependence of the
probability of fixation $P_{fix}$ on the parameter $\omega_{med}$ is precisely
described by a power-law relation, $P_{fix} \sim \omega_{med}^{\gamma}$. The
exponent $\gamma$ is an increase function of the rate of deleterious mutations
$U$, whereas the probability $P_{fix}$ is a decreasing function of $U$. The
mean value $\omega_{fix}$ of the beneficial mutations which reach ultimate
fixation depends on $U$ and $\omega_{med}$. The ratio
$\omega_{fix}/\omega_{med}$ increases as we consider higher values of mutation
value $U$ in the region of intermediate to large values of $\omega_{med}$,
whereas for low $\omega_{med}$ we observe the opposite behavior.


title:
Response kinetics of tethered bacteria to stepwise changes in nutrient
  concentration

abstract:
  We examined the changes in swimming behaviour of the bacterium Rhodobacter
sphaeroides in response to stepwise changes in a nutrient (propionate),
following the prestimulus motion, the initial response and the adaptation to
the sustained concentration of the chemical. This was carried out by tethering
motile cells by their flagella to glass slides and following the rotational
behaviour of their cell bodies in response to the nutrient change. Computerised
motion analysis was used to analyse the behaviour. Distributions of run and
stop times were obtained from rotation data for tethered cells. Exponential and
Weibull fits for these distributions, and variability in individual responses
are discussed. In terms of parameters derived from the run and stop time
distributions, we compare the responses to stepwise changes in the nutrient
concentration and the long-term behaviour of 84 cells under twelve propionate
concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for
the random walk approximation to bacterial swimming and compare them with the
observed R. sphaeroides motile behaviour.


title: The long reach of DNA sequence heterogeneity in diffusive processes

abstract:
  Many biological processes involve one dimensional diffusion over a correlated
inhomogeneous energy landscape with a correlation length $\xi_c$. Typical
examples are specific protein target location on DNA, nucleosome repositioning,
or DNA translocation through a nanopore, in all cases with $\xi_c\approx$ 10
nm. We investigate such transport processes by the mean first passage time
(MFPT) formalism, and find diffusion times which exhibit strong sample to
sample fluctuations. For a a displacement $N$, the average MFPT is diffusive,
while its standard deviation over the ensemble of energy profiles scales as
$N^{3/2}$ with a large prefactor. Fluctuations are thus dominant for
displacements smaller than a characteristic $N_c \gg \xi_c$: typical values are
much less than the mean, and governed by an anomalous diffusion rule. Potential
biological consequences of such random walks, composed of rapid scans in the
vicinity of favorable energy valleys and occasional jumps to further valleys,
is discussed.

categories: q-bio.BM cond-mat.dis-nn cond-mat.soft physics.bio-ph


title: Resilience reconsidered: Case histories from disease ecology

abstract:
  We expand the current understanding of ecological resilience to include the
nested hierarchy of cognitive submodules that particularly, if not uniquely,
delineates human ecosystems. These modules, ranging from the immune system to
the local social network, are embedded in a cultural milieu which, to take the
perspective of the evolutionary anthropologist Robert Boyd, ''is as much a part
of human biology as the enamel on our teeth''. We begin by extending recent
treatments of cognitive process as associated with characteristic information
sources to a certain class of ecosystems through a generalization of
coarse-graining. In the spirit of the Large Deviations Program, we then import
renormalization formalism via the Asymptotic Equipartition Theorem to obtain
punctuated response to parameters of increasing habitat degradation. A Legendre
transform of an appropriate joint information permits analysis away from
critical points, and generates the expected quasi-stability in a highly natural
manner. We interweave the discussion with applications to the public health
impacts of the massive deurbanization and deindustrialization presently
afflicting the United States.


title: The Yeast Cell-Cycle Network Is Robustly Designed

abstract:
  The interactions between proteins, DNA, and RNA in living cells constitute
molecular networks that govern various cellular functions. To investigate the
global dynamical properties and stabilities of such networks, we studied the
cell-cycle regulatory network of the budding yeast. With the use of a simple
dynamical model, it was demonstrated that the cell-cycle network is extremely
stable and robust for its function. The biological stationary state--the G1
state--is a global attractor of the dynamics. The biological pathway--the
cell-cycle sequence of protein states--is a globally attracting trajectory of
the dynamics. These properties are largely preserved with respect to small
perturbations to the network. These results suggest that cellular regulatory
networks are robustly designed for their functions.


title:
Complex Independent Component Analysis of Frequency-Domain
  Electroencephalographic Data

abstract:
  Independent component analysis (ICA) has proven useful for modeling brain and
electroencephalographic (EEG) data. Here, we present a new, generalized method
to better capture the dynamics of brain signals than previous ICA algorithms.
We regard EEG sources as eliciting spatio-temporal activity patterns,
corresponding to, e.g., trajectories of activation propagating across cortex.
This leads to a model of convolutive signal superposition, in contrast with the
commonly used instantaneous mixing model. In the frequency-domain, convolutive
mixing is equivalent to multiplicative mixing of complex signal sources within
distinct spectral bands. We decompose the recorded spectral-domain signals into
independent components by a complex infomax ICA algorithm. First results from a
visual attention EEG experiment exhibit (1) sources of spatio-temporal dynamics
in the data, (2) links to subject behavior, (3) sources with a limited spectral
extent, and (4) a higher degree of independence compared to sources derived by
standard ICA.