Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Optimizing information flow in small genetic networks. II: Feed forward interactions

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkacik et al, Phys Rev E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems

Care Coordination as Imagined, Care Coordination as Done: Findings from a Cross-national Mental Health Systems Study

Introduction Care coordination is intended to ensure needs are met and integrated services are provided. Formalised processes for the coordination of mental health care arrived in the UK with the introduction of the care programme approach in the early 1990s. Since then the care coordinator role has become a central one within mental health systems. Theory and methods This paper contrasts care coordination as work that is imagined with care coordination as work that is done. This is achieved via a critical review of policy followed by a qualitative analysis of interviews, focusing on day-to-day work, conducted with 28 care coordinators employed in four NHS organisations in England and two in Wales. Findings Care coordination is imagined as a vehicle for the provision of collaborative, recovery-focused, care. Those who practise care coordination are concerned with the quality of their relationships with service users and the tailoring of services, but limits exist to collaboration and open discussion. Care coordinators describe doing necessary work connecting people and the system of care. However, this work also brings significant administrative demands, is subject to performance management which distorts its primary purpose, and in a context of scarce resources promotes generic professional roles. Conclusion Care coordination must be done. However, it is not consistently being done in the way policymakers imagine, and in the real world of work can be done differently

Atomic and molecular interstellar absorption lines toward the high galactic latitude stars HD~141569 and HD~157841 at ultra-high resolution

We present ultra-high resolution (0.32 km/s) spectra obtained with the 3.9m Anglo-Australian Telescope (AAT) and Ultra-High-Resolution Facility (UHRF), of interstellar NaI D1, D2, Ca II K, K I and CH absorption toward two high galactic latitude stars HD141569 and HD157841. We have compared our data with 21-cm observations obtained from the Leiden/Dwingeloo HI survey. We derive the velocity structure, column densities of the clouds represented by the various components and identify the clouds with ISM structures seen in the region at other wavelengths. We further derive abundances, linear depletions and H2 fractional abundances for these clouds, wherever possible. Toward HD141569, we detect two components in our UHRF spectra : a weak, broad component at - 15 km/s, seen only in CaII K absorption and another component at 0 km/s, seen in NaI D1, D2, Ca II K, KI and CH absorption. In the case of the HD157841 sightline, a total of 6 components are seen on our UHRF spectra in NaI D1, D2 Ca II K, K I and CH absorption. 2 of these 6 components are seen only in a single species.Comment: 16 pages, Latex, 4 figures, ps files Astrophysical Journal (in press

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Entropy and information in neural spike trains: Progress on the sampling problem

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where other techniques fail. This opens new possibilities for the information theoretic analysis of experiments, and may be of general interest as an example of learning from limited data.Comment: 7 pages, 4 figures; referee suggested changes, accepted versio

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure