6,528 research outputs found
Crawling the Cosmic Network: Exploring the Morphology of Structure in the Galaxy Distribution
Although coherent large-scale structures such as filaments and walls are
apparent to the eye in galaxy redshift surveys, they have so far proven
difficult to characterize with computer algorithms. This paper presents a
procedure that uses the eigenvalues and eigenvectors of the Hessian matrix of
the galaxy density field to characterize the morphology of large-scale
structure. By analysing the smoothed density field and its Hessian matrix, we
can determine the types of structure - walls, filaments, or clumps - that
dominate the large-scale distribution of galaxies as a function of scale. We
have run the algorithm on mock galaxy distributions in a LCDM cosmological
N-body simulation and the observed galaxy distributions in the Sloan Digital
Sky Survey. The morphology of structure is similar between the two catalogues,
both being filament-dominated on 10-20 h^{-1} Mpc smoothing scales and
clump-dominated on 5 h^{-1} Mpc scales. There is evidence for walls in both
distributions, but walls are not the dominant structures on scales smaller than
~25 h^{-1} Mpc. Analysis of the simulation suggests that, on a given comoving
smoothing scale, structures evolve with time from walls to filaments to clumps,
where those found on smaller smoothing scales are further in this progression
at a given time.Comment: 37 pages, 14 figures. Accepted to MNRAS
A morphospace of functional configuration to assess configural breadth based on brain functional networks
The best approach to quantify human brain functional reconfigurations in
response to varying cognitive demands remains an unresolved topic in network
neuroscience. We propose that such functional reconfigurations may be
categorized into three different types: i) Network Configural Breadth, ii)
Task-to-Task transitional reconfiguration, and iii) Within-Task
reconfiguration. In order to quantify these reconfigurations, we propose a
mesoscopic framework focused on functional networks (FNs) or communities. To do
so, we introduce a 2D network morphospace that relies on two novel mesoscopic
metrics, Trapping Efficiency (TE) and Exit Entropy (EE), which capture topology
and integration of information within and between a reference set of FNs. In
this study, we use this framework to quantify the Network Configural Breadth
across different tasks. We show that the metrics defining this morphospace can
differentiate FNs, cognitive tasks and subjects. We also show that network
configural breadth significantly predicts behavioral measures, such as episodic
memory, verbal episodic memory, fluid intelligence and general intelligence. In
essence, we put forth a framework to explore the cognitive space in a
comprehensive manner, for each individual separately, and at different levels
of granularity. This tool that can also quantify the FN reconfigurations that
result from the brain switching between mental states.Comment: main article: 24 pages, 8 figures, 2 tables. supporting information:
11 pages, 5 figure
When Can You Fold a Map?
We explore the following problem: given a collection of creases on a piece of
paper, each assigned a folding direction of mountain or valley, is there a flat
folding by a sequence of simple folds? There are several models of simple
folds; the simplest one-layer simple fold rotates a portion of paper about a
crease in the paper by +-180 degrees. We first consider the analogous questions
in one dimension lower -- bending a segment into a flat object -- which lead to
interesting problems on strings. We develop efficient algorithms for the
recognition of simply foldable 1D crease patterns, and reconstruction of a
sequence of simple folds. Indeed, we prove that a 1D crease pattern is
flat-foldable by any means precisely if it is by a sequence of one-layer simple
folds.
Next we explore simple foldability in two dimensions, and find a surprising
contrast: ``map'' folding and variants are polynomial, but slight
generalizations are NP-complete. Specifically, we develop a linear-time
algorithm for deciding foldability of an orthogonal crease pattern on a
rectangular piece of paper, and prove that it is (weakly) NP-complete to decide
foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper,
(2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a
square piece of paper, and (3) crease patterns without a mountain/valley
assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks
to referees, including formal definitions of simple folds, more figures,
table summarizing results, new open problems, and additional reference
Symmetry Protected Topological phases of Quantum Matter
We describe recent progress in our understanding of the interplay between
interactions, symmetry, and topology in states of quantum matter. We focus on a
minimal generalization of the celebrated topological band insulators to
interacting many particle systems, known as Symmetry Protected Topological
(SPT) phases. In common with the topological band insulators these states have
a bulk gap and no exotic excitations but have non-trivial surface states that
are protected by symmetry. We describe the various possible such phases and
their properties in three dimensional systems with realistic symmetries. We
develop many key ideas of the theory of these states using simple examples. The
emphasis is on physical rather than mathematical properties. We survey insights
obtained from the study of SPT phases for a number of other theoretical
problems.Comment: Invited Review for Annual Reviews of Condensed Matter Physic
- …