Development of modularity in the neural activity of children's brains

We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might be achieved for more modular neural activity, and modularity might likely increase as children develop. The value of modularity calculated from fMRI data is observed to increase during childhood development and peak in young adulthood. Head motion is deconvolved from the fMRI data, and it is shown that the dependence of modularity on age is independent of the magnitude of head motion. A model is presented to illustrate how modularity can provide greater cognitive performance at short times, i.e.\ task switching. A fitness function is extracted from the model. Quasispecies theory is used to predict how the average modularity evolves with age, illustrating the increase of modularity during development from children to adults that arises from selection for rapid cognitive function in young adults. Experiments exploring the effect of modularity on cognitive performance are suggested. Modularity may be a potential biomarker for injury, rehabilitation, or disease.Comment: 29 pages, 11 figure

Modularity Enhances the Rate of Evolution in a Rugged Fitness Landscape

Biological systems are modular, and this modularity affects the evolution of biological systems over time and in different environments. We here develop a theory for the dynamics of evolution in a rugged, modular fitness landscape. We show analytically how horizontal gene transfer couples to the modularity in the system and leads to more rapid rates of evolution at short times. The model, in general, analytically demonstrates a selective pressure for the prevalence of modularity in biology. We use this model to show how the evolution of the influenza virus is affected by the modularity of the proteins that are recognized by the human immune system. Approximately 25\% of the observed rate of fitness increase of the virus could be ascribed to a modular viral landscape.Comment: 45 pages; 7 figure

Hierarchy of Gene Expression Data is Predictive of Future Breast Cancer Outcome

We calculate measures of hierarchy in gene and tissue networks of breast cancer patients. We find that the likelihood of metastasis in the future is correlated with increased values of network hierarchy for expression networks of cancer-associated genes, due to correlated expression of cancer-specific pathways. Conversely, future metastasis and quick relapse times are negatively correlated with values of network hierarchy in the expression network of all genes, due to dedifferentiation of gene pathways and circuits. These results suggest that hierarchy of gene expression may be useful as an additional biomarker for breast cancer prognosis.Comment: 14 pages, 5 figure

Field Theoretic Approach to Long Range Reactions

We analyze bimolecular reactions that proceed by a long-ranged reactive interaction, using a field theoretic approach that takes into account fluctuations. We consider both the one-species, $A+A \to \emptyset$ reaction and the two-species, $A+B \to \emptyset$ reaction. We consider both mobile and immobile reactants, both in the presence and in the absence of adsorption.Comment: 9 pages. 4 figures. Uses svjour macros. To appear in Europ. Phys. J.

Higher-Rank Numerical Ranges and Compression Problems

We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems.Comment: 14 pages, 3 figures, to appear in Linear Algebra and its Application

An assessment of multibody simulation tools for articulated spacecraft

A survey of multibody simulation codes was conducted in the spring of 1988, to obtain an assessment of the state of the art in multibody simulation codes from the users of the codes. This survey covers the most often used articulated multibody simulation codes in the spacecraft and robotics community. There was no attempt to perform a complete survey of all available multibody codes in all disciplines. Furthermore, this is not an exhaustive evaluation of even robotics and spacecraft multibody simulation codes, as the survey was designed to capture feedback on issues most important to the users of simulation codes. We must keep in mind that the information received was limited and the technical background of the respondents varied greatly. Therefore, only the most often cited observations from the questionnaire are reported here. In this survey, it was found that no one code had both many users (reports) and no limitations. The first section is a report on multibody code applications. Following applications is a discussion of execution time, which is the most troublesome issue for flexible multibody codes. The representation of component flexible bodies, which affects both simulation setup time as well as execution time, is presented next. Following component data preparation, two sections address the accessibility or usability of a code, evaluated by considering its user interface design and examining the overall simulation integrated environment. A summary of user efforts at code verification is reported, before a tabular summary of the questionnaire responses. Finally, some conclusions are drawn

An exact effective two-qubit gate in a chain of three spins

We show that an effective two-qubit gate can be obtained from the free evolution of three spins in a chain with nearest neighbor XY coupling, without local manipulations. This gate acts on the two remote spins and leaves the mediating spin unchanged. It can be used to perfectly transfer an arbitrary quantum state from the first spin to the last spin or to simultaneously communicate one classical bit in each direction. One ebit can be generated in half of the time for state transfer. For longer spin chains, we present methods to create or transfer entanglement between the two end spins in half of the time required for quantum state transfer, given tunable coupling strength and local magnetic field. We also examine imperfect state transfer through a homogeneous XY chain.Comment: RevTeX4, 7 pages, 4 figue

Galaxy pairs as a probe for mergers at z ~ 2

In this work I investigate the redshift evolution of pair fraction of a sample of 196 massive galaxies from z = 0 to 3, selected from the COSMOS field. We find that on average a massive galaxy undergoes ~ 1.1 \pm 0.5 major merger since z = 3. I will review the current limitations of using the pair fraction as a probe for quantifying the impact of mergers on galaxy evolution. This work is based on the paper Man et al. (2011).Comment: 4 pages; to appear on the Conference Proceedings for "Galaxy Mergers in an Evolving Universe", held in Hualien, Taiwan (October 2011