Von Neumann Regular Cellular Automata

For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element $\tau \in \text{CA}(G;A)$ is von Neumann regular (or simply regular) if there exists $\sigma \in \text{CA}(G;A)$ such that $\tau \circ \sigma \circ \tau = \tau$ and $\sigma \circ \tau \circ \sigma = \sigma$, where $\circ$ is the composition of functions. Such an element $\sigma$ is called a generalised inverse of $\tau$. The monoid $\text{CA}(G;A)$ itself is regular if all its elements are regular. We establish that $\text{CA}(G;A)$ is regular if and only if $\vert G \vert = 1$ or $\vert A \vert = 1$, and we characterise all regular elements in $\text{CA}(G;A)$ when $G$ and $A$ are both finite. Furthermore, we study regular linear CA when $A= V$ is a vector space over a field $\mathbb{F}$; in particular, we show that every regular linear CA is invertible when $G$ is torsion-free elementary amenable (e.g. when $G=\mathbb{Z}^d, \ d \in \mathbb{N}$) and $V=\mathbb{F}$, and that every linear CA is regular when $V$ is finite-dimensional and $G$ is locally finite with $\text{Char}(\mathbb{F}) \nmid o(g)$ for all $g \in G$.Comment: 10 pages. Theorem 5 corrected from previous versions, in A. Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer, 201

smarce1 mutants have a defective endocardium and an increased expression of cardiac transcription factors in zebrafish

Animal science

TRALI: Party of One; Real-Time Hemovigilance Demonstrates Multiple Event-Free Transfusions

Mechele Adrian pictured.https://openworks.mdanderson.org/aprn-week-23/1019/thumbnail.jp

On finite monoids of cellular automata.

For any group G and set A, a cellular automaton over G and A is a transformation τ:AG→AGτ:AG→AG defined via a finite neighbourhood S⊆GS⊆G (called a memory set of ττ) and a local function μ:AS→Aμ:AS→A. In this paper, we assume that G and A are both finite and study various algebraic properties of the finite monoid CA(G,A)CA(G,A) consisting of all cellular automata over G and A. Let ICA(G;A)ICA(G;A) be the group of invertible cellular automata over G and A. In the first part, using information on the conjugacy classes of subgroups of G, we give a detailed description of the structure of ICA(G;A)ICA(G;A) in terms of direct and wreath products. In the second part, we study generating sets of CA(G;A)CA(G;A). In particular, we prove that CA(G,A)CA(G,A) cannot be generated by cellular automata with small memory set, and, when G is finite abelian, we determine the minimal size of a set V⊆CA(G;A)V⊆CA(G;A) such that CA(G;A)=⟨ICA(G;A)∪V⟩CA(G;A)=⟨ICA(G;A)∪V⟩

Bonding, Moment Formation, and Magnetic Interactions in Ca14MnBi11 and Ba14MnBi11

The ``14-1-11'' phase compounds based on magnetic Mn ions and typified by Ca14MnBi11 and Ba14MnBi11 show unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local orbital based method within the local spin density approximation to study the electronic structure, we find a gap between a bonding valence band complex and an antibonding conduction band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the MnBi4 tetrahedral unit and partially compensates the high spin d^5 Mn moment, leaving a net spin near 4 \mu_B that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating `jungle gym' networks of spin 4/2 MnBi4^{9-} units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. Ca14MnBi11 is calculated to be ferromagnetic as observed, while for Ba14MnBi11 (which is antiferromagnetic) the ferro- and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic.Comment: 17 pages, containing 10 postscript figures and 5 tables. Two additional figures (Fig.8 and 11 of the paper) are provided in JPG format in separate files. Submitted to Phys. Rev. B on September 20th 200

Functional Network Development During the First Year: Relative Sequence and Socioeconomic Correlations

The first postnatal year is characterized by the most dramatic functional network development of the human lifespan. Yet, the relative sequence of the maturation of different networks and the impact of socioeconomic status (SES) on their development during this critical period remains poorly characterized. Leveraging a large, normally developing infant sample with multiple longitudinal resting-state functional magnetic resonance imaging scans during the first year (N = 65, scanned every 3 months), we aimed to delineate the relative maturation sequence of 9 key brain functional networks and examine their SES correlations. Our results revealed a maturation sequence from primary sensorimotor/auditory to visual to attention/default-mode, and finally to executive control networks. Network-specific critical growth periods were also identified. Finally, marginally significant positive SES–brain correlations were observed at 6 months of age for both the sensorimotor and default-mode networks, indicating interesting SES effects on functional brain maturation. To the best of our knowledge, this is the first study delineating detailed longitudinal growth trajectories of all major functional networks during the first year of life and their SES correlations. Insights from this study not only improve our understanding of early brain development, but may also inform the critical periods for SES expression during infancy

Anosognosia in Amnestic Mild Cognitive Impairment is Related to Diminished Hippocampal Volume Comparable to Alzheimer's Disease Dementia:Preliminary MRI Findings

Although the presence of anosognosia in amnestic mild cognitive impairment (aMCI) may be predictive of conversion to Alzheimer’s disease (AD), little is known about its neural correlates in AD and aMCI. Four different groups were compared using volumetric and diffusion magnetic resonance imaging metrics in regions of interest (hippocampus and cingulum cortex gray matter, cingulum bundle white matter): aMCI subjects with anosognosia (n = 6), aMCI subjects without anosognosia (n = 12), AD subjects with anosognosia (n = 6), and AD subjects without anosognosia (n = 9). aMCI subjects with anosognosia displayed a significantly lower gray matter density (GMD) in the bilateral hippocampus than aMCI subjects without anosognosia, which was accounted for by bilateral hippocampal differences. Furthermore, we identified that the mean hippocampal gray matter density of aMCI subjects with anosognosia was not statistically different than that of AD subjects. The groups of aMCI and AD subjects with anosognosia also displayed a lower GMD in the bilateral cingulum cortex compared to subjects without anosognosia, but these differences were not statistically significant. No statistically significant differences were found in the fractional anisotropy or mean diffusivity of the hippocampus or cingulum between subjects with and without anosognosia in aMCI or AD groups. While these findings are derived from a small population of subjects and are in need of replication, they suggest that anosognosia in aMCI might be a useful clinical marker to suspect brain changes associated with AD neuropathology

Cosmic acceleration from asymmetric branes

We consider a single 3-brane sitting in between two different five dimensional spacetimes. On each side of the brane, the bulk is a solution to Gauss-Bonnet gravity, although the bare cosmological constant, funda mental Planck scale, and Gauss-Bonnet coupling can differ. This asymmetry leads to weighted junction conditions across the brane and interesting brane cosmology. We focus on two special cases: a generalized Randall-Sundrum model without any Gauss-Bonnet terms, and a stringy model, without any bare cosmological constants, and positive Gauss-Bonnet coupling. Even though we assume there is no vacuum energy on the brane, we find late time de Sitter cosmologies can occur. Remarkably, in certain parameter regions, this acceleration is preceded by a period of matter/radiation domination, with $H^2 \propto \rho$, all the way back to nucleosynthesis.Comment: Version appearing in CQ