Automata on the plane vs particles and collisions

AbstractIn this note, colorings of the plane by finite sequential machines are compared to previously introduced notions of ultimately periodic tilings of the plane. Finite automata with no counter characterize exactly biperiodic tilings. Finite automata with one counter characterize exactly particles — periodic colorings that are ultimately periodic in every direction. Finite automata with two counters and aperiodic colorings characterize exactly collisions — ultimately periodic tilings of the plane

Aperiodic tilings and entropy

In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected

On Factor Universality in Symbolic Spaces

The study of factoring relations between subshifts or cellular automata is central in symbolic dynamics. Besides, a notion of intrinsic universality for cellular automata based on an operation of rescaling is receiving more and more attention in the literature. In this paper, we propose to study the factoring relation up to rescalings, and ask for the existence of universal objects for that simulation relation. In classical simulations of a system S by a system T, the simulation takes place on a specific subset of configurations of T depending on S (this is the case for intrinsic universality). Our setting, however, asks for every configurations of T to have a meaningful interpretation in S. Despite this strong requirement, we show that there exists a cellular automaton able to simulate any other in a large class containing arbitrarily complex ones. We also consider the case of subshifts and, using arguments from recursion theory, we give negative results about the existence of universal objects in some classes

An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $\Theta(n)$ such tilings exist.Comment: In proceedings of ISAAC 201

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

The Ubiquitin Ligase Ubr2, a Recognition E3 Component of the N-End Rule Pathway, Stabilizes Tex19.1 during Spermatogenesis

Ubiquitin E3 ligases target their substrates for ubiquitination, leading to proteasome-mediated degradation or altered biochemical properties. The ubiquitin ligase Ubr2, a recognition E3 component of the N-end rule proteolytic pathway, recognizes proteins with N-terminal destabilizing residues and plays an important role in spermatogenesis. Tex19.1 (also known as Tex19) has been previously identified as a germ cell-specific protein in mouse testis. Here we report that Tex19.1 forms a stable protein complex with Ubr2 in mouse testes. The binding of Tex19.1 to Ubr2 is independent of the second position cysteine of Tex19.1, a putative target for arginylation by the N-end rule pathway R-transferase. The Tex19.1-null mouse mutant phenocopies the Ubr2-deficient mutant in three aspects: heterogeneity of spermatogenic defects, meiotic chromosomal asynapsis, and embryonic lethality preferentially affecting females. In Ubr2-deficient germ cells, Tex19.1 is transcribed, but Tex19.1 protein is absent. Our results suggest that the binding of Ubr2 to Tex19.1 metabolically stabilizes Tex19.1 during spermatogenesis, revealing a new function for Ubr2 outside the conventional N-end rule pathway

A Small RNA Controls Expression of the Chitinase ChiA in Listeria monocytogenes

In recent years, more than 60 small RNAs (sRNAs) have been identified in the gram-positive human pathogen Listeria monocytogenes, but their putative roles and mechanisms of action remain largely unknown. The sRNA LhrA was recently shown to be a post-transcriptional regulator of a single gene, lmo0850, which encodes a small protein of unknown function. LhrA controls the translation and degradation of the lmo0850 mRNA by an antisense mechanism, and it depends on the RNA chaperone Hfq for efficient binding to its target. In the present study, we sought to gain more insight into the functional role of LhrA in L. monocytogenes. To this end, we determined the effects of LhrA on global-wide gene expression. We observed that nearly 300 genes in L. monocytogenes are either positively or negatively affected by LhrA. Among these genes, we identified lmo0302 and chiA as direct targets of LhrA, thus establishing LhrA as a multiple target regulator. Lmo0302 encodes a hypothetical protein with no known function, whereas chiA encodes one of two chitinases present in L. monocytogenes. We show here that LhrA acts as a post-transcriptional regulator of lmo0302 and chiA by interfering with ribosome recruitment, and we provide evidence that both LhrA and Hfq act to down-regulate the expression of lmo0302 and chiA. Furthermore, in vitro binding experiments show that Hfq stimulates the base pairing of LhrA to chiA mRNA. Finally, we demonstrate that LhrA has a negative effect on the chitinolytic activity of L. monocytogenes. In marked contrast to this, we found that Hfq has a stimulating effect on the chitinolytic activity, suggesting that Hfq plays multiple roles in the complex regulatory pathways controlling the chitinases of L. monocytogenes

A Novel Mouse Synaptonemal Complex Protein Is Essential for Loading of Central Element Proteins, Recombination, and Fertility

The synaptonemal complex (SC) is a proteinaceous, meiosis-specific structure that is highly conserved in evolution. During meiosis, the SC mediates synapsis of homologous chromosomes. It is essential for proper recombination and segregation of homologous chromosomes, and therefore for genome haploidization. Mutations in human SC genes can cause infertility. In order to gain a better understanding of the process of SC assembly in a model system that would be relevant for humans, we are investigating meiosis in mice. Here, we report on a newly identified component of the murine SC, which we named SYCE3. SYCE3 is strongly conserved among mammals and localizes to the central element (CE) of the SC. By generating a Syce3 knockout mouse, we found that SYCE3 is required for fertility in both sexes. Loss of SYCE3 blocks synapsis initiation and results in meiotic arrest. In the absence of SYCE3, initiation of meiotic recombination appears to be normal, but its progression is severely impaired resulting in complete absence of MLH1 foci, which are presumed markers of crossovers in wild-type meiocytes. In the process of SC assembly, SYCE3 is required downstream of transverse filament protein SYCP1, but upstream of the other previously described CE–specific proteins. We conclude that SYCE3 enables chromosome loading of the other CE–specific proteins, which in turn would promote synapsis between homologous chromosomes

Facilitate Insight by Non-Invasive Brain Stimulation

Our experiences can blind us. Once we have learned to solve problems by one method, we often have difficulties in generating solutions involving a different kind of insight. Yet there is evidence that people with brain lesions are sometimes more resistant to this so-called mental set effect. This inspired us to investigate whether the mental set effect can be reduced by non-invasive brain stimulation. 60 healthy right-handed participants were asked to take an insight problem solving task while receiving transcranial direct current stimulation (tDCS) to the anterior temporal lobes (ATL). Only 20% of participants solved an insight problem with sham stimulation (control), whereas 3 times as many participants did so (p = 0.011) with cathodal stimulation (decreased excitability) of the left ATL together with anodal stimulation (increased excitability) of the right ATL. We found hemispheric differences in that a stimulation montage involving the opposite polarities did not facilitate performance. Our findings are consistent with the theory that inhibition to the left ATL can lead to a cognitive style that is less influenced by mental templates and that the right ATL may be associated with insight or novel meaning. Further studies including neurophysiological imaging are needed to elucidate the specific mechanisms leading to the enhancement