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Deterministic progenitor behavior and unitary production of neurons in the neocortex
No full textRadial glial progenitors (RGPs) are responsible for producing nearly all neocortical neurons. To gain insight into the patterns of RGP division and neuron production, we quantitatively analyzed excitatory neuron genesis in the mouse neocortex using Mosaic Analysis with Double Markers, which provides single-cell resolution of progenitor division patterns and potential in vivo. We found that RGPs progress through a coherent program in which their proliferative potential diminishes in a predictable manner. Upon entry into the neurogenic phase, individual RGPs produce ∼8–9 neurons distributed in both deep and superficial layers, indicating a unitary output in neuronal production. Removal of OTX1, a transcription factor transiently expressed in RGPs, results in both deep- and superficial-layer neuron loss and a reduction in neuronal unit size. Moreover, ∼1/6 of neurogenic RGPs proceed to produce glia. These results suggest that progenitor behavior and histogenesis in the mammalian neocortex conform to a remarkably orderly and deterministic program
Eliminating Tverberg points, I. An analogue of the Whitney trick
Get PDFMotivated by topological Tverberg-type problems, we consider multiple (double, triple, and higher multiplicity) self-intersection points of maps from finite simplicial complexes (compact polyhedra) into Rd, and study conditions under which such multiple points can be eliminated. The most classical case is that of embeddings (i.e., maps without double points) of a k-dimensional complex K into R2k. For this problem, the work of van Kampen, Shapiro, and Wu provides an efficiently testable necessary condition for embeddability (namely, vanishing of the van Kampen obstruction). For k ≥ 3, the condition is also sufficient, and yields a polynomial-time algorithm for deciding embeddability: One starts with an arbitrary map f: K → R2k, which generically has finitely many double points; if k ≥ 3 and if the obstruction vanishes then one can successively remove these double points by local modifications of the map f. One of the main tools is the famous Whitney trick that permits eliminating pairs of double points of opposite intersection sign. We are interested in generalizing this approach to intersection points of higher multiplicity. We call a point y ∈ Rd an r-fold Tverberg point of a map f: Kk → Rd if y lies in the intersection f(σ1)∩…∩ f(σr) of the images of r pairwise disjoint simplices of K. The analogue of (non-)embeddability that we study is the problem Tverberg r k→d: Given a k-dimensional complex K, does it satisfy a Tverberg-type theorem with parameters r and d, i.e., does every map f:Kk → Rd have an r-fold Tverberg point? Here, we show that for fixed r, k and d of the form d = rm and k = (r−1)m, m ≥ 3, there is a polynomial-time algorithm for deciding this (based on the vanishing of a cohomological obstruction, as in the case of embeddings). Our main tool is an r-fold analogue of the Whitney trick: Given r pairwise disjoint simplices of K such that the intersection of their images contains two r-fold Tverberg points y+ and y− of opposite intersection sign, we can eliminate y+ and y− by a local isotopy of f. In a subsequent paper, we plan to develop this further and present a generalization of the classical Haefliger--Weber Theorem (which yields a necessary and sufficient condition for embeddability of k-complexes into R, for a wider range of dimensions) to intersection points of higher multiplicity
Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications
Get PDFWe consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty
Playful Math – An Introduction to Mathematical Games
Get PDFIt is difficult to give a precise definition for the concept of a mathematical game. Instead, we list some features, which apply for most games (in particular for those we introduce in the next section). Usually there are two players (or teams) playing against each other. Complete information. This roughly means that in every turn, each of the players can make a perfectly logical decision based on the history of the game. The game has no gambling part; the outcome does not depend on luck, but purely on the strategy of the players. The rules are simple to understand, and usually there are only a few of them. The ultimate goal is not winning, but understanding the structure of the game.If a game always comes to an end in finitely many turns, one of the players always has a winning strategy.
All the games we present are of this type
The fitness costs of adaptation via phenotypic plasticity and maternal effects
No full textSummary: Phenotypes are often environmentally dependent, which requires organisms to track environmental change. The challenge for organisms is to construct phenotypes using the most accurate environmental cue. Here, we use a quantitative genetic model of adaptation by additive genetic variance, within- and transgenerational plasticity via linear reaction norms and indirect genetic effects respectively. We show how the relative influence on the eventual phenotype of these components depends on the predictability of environmental change (fast or slow, sinusoidal or stochastic) and the developmental lag Ï„ between when the environment is perceived and when selection acts. We then decompose expected mean fitness into three components (variance load, adaptation and fluctuation load) to study the fitness costs of within- and transgenerational plasticity. A strongly negative maternal effect coefficient m minimizes the variance load, but a strongly positive m minimises the fluctuation load. The adaptation term is maximized closer to zero, with positive or negative m preferred under different environmental scenarios. Phenotypic plasticity is higher when Ï„ is shorter and when the environment changes frequently between seasonal extremes. Expected mean population fitness is highest away from highest observed levels of phenotypic plasticity. Within- and transgenerational plasticity act in concert to deliver well-adapted phenotypes, which emphasizes the need to study both simultaneously when investigating phenotypic evolution
Mutational studies on resurrected ancestral proteins reveal conservation of site-specific amino acid preferences throughout evolutionary history
No full textLocal protein interactions ("molecular context" effects) dictate amino acid replacements and can be described in terms of site-specific, energetic preferences for any different amino acid. It has been recently debated whether these preferences remain approximately constant during evolution or whether, due to coevolution of sites, they change strongly. Such research highlights an unresolved and fundamental issue with far-reaching implications for phylogenetic analysis and molecular evolution modeling. Here, we take advantage of the recent availability of phenotypically supported laboratory resurrections of Precambrian thioredoxins and β-lactamases to experimentally address the change of site-specific amino acid preferences over long geological timescales. Extensive mutational analyses support the notion that evolutionary adjustment to a new amino acid may occur, but to a large extent this is insufficient to erase the primitive preference for amino acid replacements. Generally, site-specific amino acid preferences appear to remain conserved throughout evolutionary history despite local sequence divergence. We show such preference conservation to be readily understandable in molecular terms and we provide crystallographic evidence for an intriguing structural-switch mechanism: Energetic preference for an ancestral amino acid in a modern protein can be linked to reorganization upon mutation to the ancestral local structure around the mutated site. Finally, we point out that site-specific preference conservation naturally leads to one plausible evolutionary explanation for the existence of intragenic global suppressor mutations
Boolean modelling reveals new regulatory connections between transcription factors orchestrating the development of the ventral spinal cord
No full textWe have assembled a network of cell-fate determining transcription factors that play a key role in the specification of the ventral neuronal subtypes of the spinal cord on the basis of published transcriptional interactions. Asynchronous Boolean modelling of the network was used to compare simulation results with reported experimental observations. Such comparison highlighted the need to include additional regulatory connections in order to obtain the fixed point attractors of the model associated with the five known progenitor cell types located in the ventral spinal cord. The revised gene regulatory network reproduced previously observed cell state switches between progenitor cells observed in knock-out animal models or in experiments where the transcription factors were overexpressed. Furthermore the network predicted the inhibition of Irx3 by Nkx2.2 and this prediction was tested experimentally. Our results provide evidence for the existence of an as yet undescribed inhibitory connection which could potentially have significance beyond the ventral spinal cord. The work presented in this paper demonstrates the strength of Boolean modelling for identifying gene regulatory networks
Functional and bioinformatics analysis of two Campylobacter jejuni homologs of the thiol-disulfide oxidoreductase, DsbA
No full textBackground: Bacterial Dsb enzymes are involved in the oxidative folding of many proteins, through the formation of disulfide bonds between their cysteine residues. The Dsb protein network has been well characterized in cells of the model microorganism Escherichia coli. To gain insight into the functioning of the Dsb system in epsilon-Proteobacteria, where it plays an important role in the colonization process, we studied two homologs of the main Escherichia coli Dsb oxidase (EcDsbA) that are present in the cells of the enteric pathogen Campylobacter jejuni, the most frequently reported bacterial cause of human enteritis in the world. Methods and Results: Phylogenetic analysis suggests the horizontal transfer of the epsilon-Proteobacterial DsbAs from a common ancestor to gamma-Proteobacteria, which then gave rise to the DsbL lineage. Phenotype and enzymatic assays suggest that the two C. jejuni DsbAs play different roles in bacterial cells and have divergent substrate spectra. CjDsbA1 is essential for the motility and autoagglutination phenotypes, while CjDsbA2 has no impact on those processes. CjDsbA1 plays a critical role in the oxidative folding that ensures the activity of alkaline phosphatase CjPhoX, whereas CjDsbA2 is crucial for the activity of arylsulfotransferase CjAstA, encoded within the dsbA2-dsbB-astA operon. Conclusions: Our results show that CjDsbA1 is the primary thiol-oxidoreductase affecting life processes associated with bacterial spread and host colonization, as well as ensuring the oxidative folding of particular protein substrates. In contrast, CjDsbA2 activity does not affect the same processes and so far its oxidative folding activity has been demonstrated for one substrate, arylsulfotransferase CjAstA. The results suggest the cooperation between CjDsbA2 and CjDsbB. In the case of the CjDsbA1, this cooperation is not exclusive and there is probably another protein to be identified in C. jejuni cells that acts to re-oxidize CjDsbA1. Altogether the data presented here constitute the considerable insight to the Epsilonproteobacterial Dsb systems, which have been poorly understood so far
Topology-preserving watermarking of vector graphics
No full textWatermarking techniques for vector graphics dislocate vertices in order to embed imperceptible, yet detectable, statistical features into the input data. The embedding process may result in a change of the topology of the input data, e.g., by introducing self-intersections, which is undesirable or even disastrous for many applications. In this paper we present a watermarking framework for two-dimensional vector graphics that employs conventional watermarking techniques but still provides the guarantee that the topology of the input data is preserved. The geometric part of this framework computes so-called maximum perturbation regions (MPR) of vertices. We propose two efficient algorithms to compute MPRs based on Voronoi diagrams and constrained triangulations. Furthermore, we present two algorithms to conditionally correct the watermarked data in order to increase the watermark embedding capacity and still guarantee topological correctness. While we focus on the watermarking of input formed by straight-line segments, one of our approaches can also be extended to circular arcs. We conclude the paper by demonstrating and analyzing the applicability of our framework in conjunction with two well-known watermarking techniques
The persistent homology of a self-map
No full textConsidering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility