We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate elements. Moreov
er, we present several results concerning embeddings into such groups. As another application of these techniques, we prove that every countable group $C$ can be realized as a group of outer automorphisms of a group $N$, where $N$ is a finitely generated group having Kazhdans property (T) and containing exactly two conjugacy classes.
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper,
we study the number of positive steady states of a general multisite phosphorylation-dephosphorylation cycle, and how the number of positive steady states varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (in particular, this implies that for n=2, including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.
The pure spinor formulation of the ten-dimensional superstring leads to manifestly supersymmetric loop amplitudes, expressed as integrals in pure spinor superspace. This paper explores different methods to evaluate these integrals and then uses them
to calculate the kinematic factors of the one-loop and two-loop massless four-point amplitudes involving two and four Ramond states.
In this paper, we introduce the on-line Viterbi algorithm for decoding hidden Markov models (HMMs) in much smaller than linear space. Our analysis on two-state HMMs suggests that the expected maximum memory used to decode sequence of length $n$ with
$m$-state HMM can be as low as $Theta(mlog n)$, without a significant slow-down compared to the classical Viterbi algorithm. Classical Viterbi algorithm requires $O(mn)$ space, which is impractical for analysis of long DNA sequences (such as complete human genome chromosomes) and for continuous data streams. We also experimentally demonstrate the performance of the on-line Viterbi algorithm on a simple HMM for gene finding on both simulated and real DNA sequences.
Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya in quiescence during 1991 and 2001 are presented. Spin-modulated radial velocities consistent with an outer disc origin were detected for the first time in an IP. The spin
pulsation was modulated with velocities near ~500-600 km/s. These velocities are consistent with those of material circulating at the outer edge of the accretion disc, suggesting corotation of the accretion curtain with material near the Roche lobe radius. Furthermore, spin Doppler tomograms have revealed evidence of the accretion curtain emission extending from velocities of ~500 km/s to ~1000 km/s. These findings have confirmed the theoretical model predictions of King & Wynn (1999), Belle et al. (2002) and Norton et al. (2004) for EX Hya, which predict large accretion curtains that extend to a distance close to the Roche lobe radius in this system. Evidence for overflow stream of material falling onto the magnetosphere was observed, confirming the result of Belle et al. (2005) that disc overflow in EX Hya is present during quiescence as well as outburst. It appears that the hbeta and hgamma spin radial velocities originated from the rotation of the funnel at the outer disc edge, while those of halpha were produced due to the flow of material along the field lines far from the white dwarf (narrow component) and close to the white dwarf (broad-base component), in agreement with the accretion curtain model.
As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in th
e range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.
In a quantum mechanical model, Diosi, Feldmann and Kosloff arrived at a conjecture stating that the limit of the entropy of certain mixtures is the relative entropy as system size goes to infinity. The conjecture is proven in this paper for density m
atrices. The first proof is analytic and uses the quantum law of large numbers. The second one clarifies the relation to channel capacity per unit cost for classical-quantum channels. Both proofs lead to generalization of the conjecture.
We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form [ L_{e_i}L_{f_j} = sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}] where $u= (u_{i,j,k,l})$ is an $n
m times nm$ unitary matrix. These algebras, which generalise the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to isometric isomorphism in terms of the matrix $u$.
We employ granular hydrodynamics to investigate a paradigmatic problem of clustering of particles in a freely cooling dilute granular gas. We consider large-scale hydrodynamic motions where the viscosity and heat conduction can be neglected, and one
arrives at the equations of ideal gas dynamics with an additional term describing bulk energy losses due to inelastic collisions. We employ Lagrangian coordinates and derive a broad family of exact non-stationary analytical solutions that depend only on one spatial coordinate. These solutions exhibit a new type of singularity, where the gas density blows up in a finite time when starting from smooth initial conditions. The density blowups signal formation of close-packed clusters of particles. As the density blow-up time $t_c$ is approached, the maximum density exhibits a power law $sim (t_c-t)^{-2}$. The velocity gradient blows up as $sim - (t_c-t)^{-1}$ while the velocity itself remains continuous and develops a cusp (rather than a shock discontinuity) at the singularity. The gas temperature vanishes at the singularity, and the singularity follows the isobaric scenario: the gas pressure remains finite and approximately uniform in space and constant in time close to the singularity. An additional exact solution shows that the density blowup, of the same type, may coexist with an ordinary shock, at which the hydrodynamic fields are discontinuous but finite. We confirm stability of the exact solutions with respect to small one-dimensional perturbations by solving the ideal hydrodynamic equations numerically. Furthermore, numerical solutions show that the local features of the density blowup hold universally, independently of details of the initial and boundary conditions.
