4,754 research outputs found
Statistical Signatures of Structural Organization: The case of long memory in renewal processes
Identifying and quantifying memory are often critical steps in developing a
mechanistic understanding of stochastic processes. These are particularly
challenging and necessary when exploring processes that exhibit long-range
correlations. The most common signatures employed rely on second-order temporal
statistics and lead, for example, to identifying long memory in processes with
power-law autocorrelation function and Hurst exponent greater than .
However, most stochastic processes hide their memory in higher-order temporal
correlations. Information measures---specifically, divergences in the mutual
information between a process' past and future (excess entropy) and minimal
predictive memory stored in a process' causal states (statistical
complexity)---provide a different way to identify long memory in processes with
higher-order temporal correlations. However, there are no ergodic stationary
processes with infinite excess entropy for which information measures have been
compared to autocorrelation functions and Hurst exponents. Here, we show that
fractal renewal processes---those with interevent distribution tails ---exhibit long memory via a phase transition at .
Excess entropy diverges only there and statistical complexity diverges there
and for all . When these processes do have power-law
autocorrelation function and Hurst exponent greater than , they do not
have divergent excess entropy. This analysis breaks the intuitive association
between these different quantifications of memory. We hope that the methods
used here, based on causal states, provide some guide as to how to construct
and analyze other long memory processes.Comment: 13 pages, 2 figures, 3 appendixes;
http://csc.ucdavis.edu/~cmg/compmech/pubs/lrmrp.ht
Statistical properties of the spectrum the extended Bose-Hubbard model
Motivated by the role that spectral properties play for the dynamical
evolution of a quantum many-body system, we investigate the level spacing
statistic of the extended Bose-Hubbard model. In particular, we focus on the
distribution of the ratio of adjacent level spacings, useful at large
interaction, to distinguish between chaotic and non-chaotic regimes. After
revisiting the bare Bose-Hubbard model, we study the effect of two different
perturbations: next-nearest neighbor hopping and nearest-neighbor interaction.
The system size dependence is investigated together with the effect of the
proximity to integrable points or lines. Lastly, we discuss the consequences of
a cutoff in the number of onsite bosons onto the level statistics.Comment: 18 pages, 15 figure
Decoding the urban grid: or why cities are neither trees nor perfect grids
In a previous paper (Figueiredo and Amorim, 2005), we introduced the continuity
lines, a compressed description that encapsulates topological and geometrical
properties of urban grids. In this paper, we applied this technique to a large
database of maps that included cities of 22 countries. We explore how this
representation encodes into networks universal features of urban grids and, at the
same time, retrieves differences that reflect classes of cities. Then, we propose an
emergent taxonomy for urban grids
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Single Molecule Conformational Memory Extraction: P5ab RNA Hairpin
Extracting kinetic models from single
molecule data is an important
route to mechanistic insight in biophysics, chemistry, and biology.
Data collected from force spectroscopy can probe discrete hops of
a single molecule between different conformational states. Model extraction
from such data is a challenging inverse problem because single molecule
data are noisy and rich in structure. Standard modeling methods normally
assume (i) a prespecified number of discrete states and (ii) that
transitions between states are Markovian. The data set is then fit
to this predetermined model to find a handful of rates describing
the transitions between states. We show that it is unnecessary to
assume either (i) or (ii) and focus our analysis on the zipping/unzipping
transitions of an RNA hairpin. The key is in starting with a very
broad class of non-Markov models in order to let the data guide us
toward the best model from this very broad class. Our method suggests
that there exists a folding intermediate for the P5ab RNA hairpin
whose zipping/unzipping is monitored by force spectroscopy experiments.
This intermediate would not have been resolved if a Markov model had
been assumed from the onset. We compare the merits of our method with
those of others
Dynamics on the Way to Forming Glass: Bubbles in Space-time
We review a theoretical perspective of the dynamics of glass forming liquids
and the glass transition. It is a perspective we have developed with our
collaborators during this decade. It is based upon the structure of trajectory
space. This structure emerges from spatial correlations of dynamics that appear
in disordered systems as they approach non-ergodic or jammed states. It is
characterized in terms of dynamical heterogeneity, facilitation and excitation
lines. These features are associated with a newly discovered class of
non-equilibrium phase transitions. Equilibrium properties have little if
anything to do with it. The broken symmetries of these transitions are obscure
or absent in spatial structures, but they are vivid in space-time (i.e.,
trajectory space). In our view, the glass transition is an example of this
class of transitions. The basic ideas and principles we review were originally
developed through the analysis of idealized and abstract models. Nevertheless,
the central ideas are easily illustrated with reference to molecular dynamics
of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che
Single-cell landscape in mammary epithelium reveals bipotent-like cells associated with breast cancer risk and outcome
Adult stem-cells may serve as the cell-of-origin for cancer, yet their unbiased identification in
single cell RNA sequencing data is challenging due to the high dropout rate. In the case of
breast, the existence of a bipotent stem-like state is also controversial. Here we apply a
marker-free algorithm to scRNA-Seq data from the human mammary epithelium, revealing a
high-potency cell-state enriched for an independent mammary stem-cell expression module.
We validate this stem-like state in independent scRNA-Seq data. Our algorithm further
predicts that the stem-like state is bipotent, a prediction we are able to validate using FACS
sorted bulk expression data. The bipotent stem-like state correlates with clinical outcome in
basal breast cancer and is characterized by overexpression of YBX1 and ENO1, two modulators of basal breast cancer risk. This study illustrates the power of a marker-free computational framework to identify a novel bipotent stem-like state in the mammary epithelium
- …