A counterexample to parabolic dichotomies in holomorphic iteration

We give an example of a parabolic holomorphic self-map $f$ of the unit ball $\mathbb B^2\subset \mathbb C^2$ whose canonical Kobayashi hyperbolic semi-model is given by an elliptic automorphism of the disc $\mathbb D\subset \mathbb C$, which can be chosen to be different from the identity. As a consequence, in contrast to the one dimensional case, this provides a first example of a holomorphic self-map of the unit ball which has points with zero hyperbolic step and points with nonzero hyperbolic step, solving an open question and showing that parabolic dynamics in the ball $\\mathbb B^2$ is radically different from parabolic dynamics in the disc. The example is obtained via a geometric method, embedding the ball $\mathbb B^2$ as a domain $\Omega$ in the bidisc $\\mathbb D\times \mathbb{H}$ that is forward invariant and absorbing for the map $(z,w)\mapsto (e^{i\theta}z,w+1)$, where $\mathbb H\subset \mathbb C$ denotes the right half-plane. We also show that a complete Kobayashi hyperbolic domain $\Omega$ with such properties cannot be Gromov hyperbolic w.r.t. the Kobayashi distance (hence, it cannot be biholomorphic to $\\mathbb B^2$) if an additional quantitative geometric condition is satisfied

Knowledge Graph Completion via Complex Tensor Factorization

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs—labeled directed graphs—and predicting missing relationships—labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices—thus all possible relation/adjacency matrices—are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ3/(4πσ)2 seconds where µ is the mean period of an oscillator in seconds and σ2 its variance in seconds2. We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed

Tuning chelation by the surfactant-like peptide A6H using predetermined pH values

We examine the self-assembly of a peptide A6H comprising a hexa-alanine sequence A6 with a histidine (H) “head group”, which chelates Zn2+ cations. We study the self assembly of A6H and binding of Zn2+ ions in ZnCl2 solutions, under acidic and neutral conditions. A6H self-assembles into nanotapes held together by a β-sheet structure in acidic aqueous solutions. By dissolving A6H in acidic ZnCl2 solutions, the carbonyl oxygen atoms in A6H chelate the Zn2+ ions and allow for β-sheet formation at lower concentrations, consequently reducing the onset concentration for nanotape formation. A6H mixed with water or ZnCl2 solutions under neutral conditions produces short sheets or pseudocrystalline tapes, respectively. The imidazole ring of A6H chelates Zn2+ ions in neutral solutions. The internal structure of nanosheets and pseudocrystalline sheets in neutral solutions is similar to the internal structure of A6H nanotapes in acidic solutions. Our results show that it is possible to induce dramatic changes in the self-assembly and chelation sites of A6H by changing the pH of the solution. However, it is likely that the amphiphilic nature of A6H determines the internal structure of the self-assembled aggregates independent from changes in chelation

Odor supported place cell model and goal navigation in rodents

Experiments with rodents demonstrate that visual cues play an important role in the control of hippocampal place cells and spatial navigation. Nevertheless, rats may also rely on auditory, olfactory and somatosensory stimuli for orientation. It is also known that rats can track odors or self-generated scent marks to find a food source. Here we model odor supported place cells by using a simple feed-forward network and analyze the impact of olfactory cues on place cell formation and spatial navigation. The obtained place cells are used to solve a goal navigation task by a novel mechanism based on self-marking by odor patches combined with a Q-learning algorithm. We also analyze the impact of place cell remapping on goal directed behavior when switching between two environments. We emphasize the importance of olfactory cues in place cell formation and show that the utility of environmental and self-generated olfactory cues, together with a mixed navigation strategy, improves goal directed navigation

Viral capsids: Mechanical characteristics, genome packaging and delivery mechanisms

The main functions of viral capsids are to protect, transport and deliver their genome. The mechanical properties of capsids are supposed to be adapted to these tasks. Bacteriophage capsids also need to withstand the high pressures the DNA is exerting onto it as a result of the DNA packaging and its consequent confinement within the capsid. It is proposed that this pressure helps driving the genome into the host, but other mechanisms also seem to play an important role in ejection. DNA packaging and ejection strategies are obviously dependent on the mechanical properties of the capsid. This review focuses on the mechanical properties of viral capsids in general and the elucidation of the biophysical aspects of genome packaging mechanisms and genome delivery processes of double-stranded DNA bacteriophages in particular

Conformation and self-association of peptide amphiphiles based on the KTTKS collagen sequence

Studying peptide amphiphiles (PAs), we investigate the influence of alkyl chain length on the aggregation behavior of the collagen-derived peptide KTTKS with applications ranging from antiwrinkle cosmetic creams to potential uses in regenerative medicine. We have studied synthetic peptides amphiphiles C14− KTTKS (myristoyl Lys-Thr-Thr-Lys-Ser) and C18−KTTKS(stearoyl-Lys-Thr Thr-Lys-Ser) to investigate in detail their physicochemical properties. It is presumed that the hydrophobic chain in these self-assembling peptide amphiphiles enhances peptide permeation across the skin compared to KTTKS alone. Subsequently Cn−KTTKS should act as a prodrug and release the peptide by enzymatic cleavage. Our results should be useful in the further development of molecules with collagen-stimulating activity