Evolution of the Stellar-to-Dark Matter relation: separating star-forming and passive galaxies from z = 1 to 0

We use measurements of the stellar mass function, galaxy clustering, and galaxy-galaxy lensing within the COSMOS survey to constrain the stellar-to-halo mass relation (SHMR) of star forming and quiescent galaxies over the redshift range z = [0.2, 1.0]. For massive galaxies, M * gsim 1010.6 M ☉, our results indicate that star-forming galaxies grow proportionately as fast as their dark matter halos while quiescent galaxies are outpaced by dark matter growth. At lower masses, there is minimal difference in the SHMRs, implying that the majority low-mass quiescent galaxies have only recently been quenched of their star formation. Our analysis also affords a breakdown of all COSMOS galaxies into the relative numbers of central and satellite galaxies for both populations. At z = 1, satellite galaxies dominate the red sequence below the knee in the stellar mass function. But the number of quiescent satellites exhibits minimal redshift evolution; all evolution in the red sequence is due to low-mass central galaxies being quenched of their star formation. At M * ~ 1010 M ☉, the fraction of central galaxies on the red sequence increases by a factor of 10 over our redshift baseline, while the fraction of quenched satellite galaxies at that mass is constant with redshift. We define a "migration rate" to the red sequence as the time derivative of the passive galaxy abundances. We find that the migration rate of central galaxies to the red sequence increases by nearly an order of magnitude from z = 1 to z = 0. These results imply that the efficiency of quenching star formation for centrals is increasing with cosmic time, while the mechanisms that quench the star formation of satellite galaxies in groups and clusters is losing efficiency

On the Computation of the Linear Complexity and the k-Error Linear Complexity of Binary Sequences with Period a Power of Two

The linear Games-Chan algorithm for computing the linear complexity c(s) of a binary sequence s of period ℓ = 2n requires the knowledge of the full sequence, while the quadratic Berlekamp-Massey algorithm only requires knowledge of 2c(s) terms. We show that we can modify the Games-Chan algorithm so that it computes the complexity in linear time knowing only 2c(s) terms. The algorithms of Stamp-Martin and Lauder-Paterson can also be modified, without loss of efficiency, to compute analogues of the k-error linear complexity for finite binary sequences viewed as initial segments of infinite sequences with period a power of two. We also develop an algorithm which, given a constant c and an infinite binary sequence s with period ℓ = 2n, computes the minimum number k of errors (and the associated error sequence) needed over a period of s for bringing the linear complexity of s below c. The algorithm has a time and space bit complexity of O(ℓ). We apply our algorithm to decoding and encoding binary repeated-root cyclic codes of length ℓ in linear, O(ℓ), time and space. A previous decoding algorithm proposed by Lauder and Paterson has O(ℓ(logℓ)2) complexity

Singular open book structures from real mappings

We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus \Sing \psi \subset \psi^{-1}(0), for which the Milnor fibration exists and yields an open book structure with singular binding.Comment: more remark

How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

Non-Equilibrium Statistical Physics of Currents in Queuing Networks

We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition rates between nodes. For such systems, we ask the question ``What is the most likely way for large currents to accumulate over time in a network ?'', where time is large compared to the system correlation time scale. We identify two interesting regimes. In the first regime, in which the accumulation of currents over time exceeds the expected value by a small to moderate amount (moderate large deviation), we find that the large-deviation distribution of currents is universal (independent of the interaction details), and there is no long-time and averaged over time accumulation of particles (condensation) at any nodes. In the second regime, in which the accumulation of currents over time exceeds the expected value by a large amount (severe large deviation), we find that the large-deviation current distribution is sensitive to interaction details, and there is a long-time accumulation of particles (condensation) at some nodes. The transition between the two regimes can be described as a dynamical second order phase transition. We illustrate these ideas using the simple, yet non-trivial, example of a single node with feedback.Comment: 26 pages, 5 figure