Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development

Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during colonial development. One method of modeling is the continuous, or coupled reaction-diffusion approach, in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields. In the context of branching growth, this idea has been pursued by a number of groups. We present an additional model which includes a lubrication fluid excreted by the bacteria. We also add fields of chemotactic agents to the other models. We then present a critique of this whole enterprise with focus on the models' potential for revealing new biological features.Comment: 1 latex file, 40 gif/jpeg files (compressed into tar-gzip). Physica A, in pres

Modeling branching and chiral colonial patterning of lubricating bacteria

In nature, microorganisms must often cope with hostile environmental conditions. To do so they have developed sophisticated cooperative behavior and intricate communication capabilities, such as: direct cell-cell physical interactions via extra-membrane polymers, collective production of extracellular "wetting" fluid for movement on hard surfaces, long range chemical signaling such as quorum sensing and chemotactic (bias of movement according to gradient of chemical agent) signaling, collective activation and deactivation of genes and even exchange of genetic material. Utilizing these capabilities, the colonies develop complex spatio-temporal patterns in response to adverse growth conditions. We present a wealth of branching and chiral patterns formed during colonial development of lubricating bacteria (bacteria which produce a wetting layer of fluid for their movement). Invoking ideas from pattern formation in non-living systems and using ``generic'' modeling we are able to reveal novel survival strategies which account for the salient features of the evolved patterns. Using the models, we demonstrate how communication leads to self-organization via cooperative behavior of the cells. In this regard, pattern formation in microorganisms can be viewed as the result of the exchange of information between the micro-level (the individual cells) and the macro-level (the colony). We mainly review known results, but include a new model of chiral growth, which enables us to study the effect of chemotactic signaling on the chiral growth. We also introduce a measure for weak chirality and use this measure to compare the results of model simulations with experimental observations.Comment: 50 pages, 24 images in 44 GIF/JPEG files, Proceedings of IMA workshop: Pattern Formation and Morphogenesis (1998

A Minimal Set of Koopman Eigenfunctions -- Analysis and Numerics

This work provides the analytic answer to the question of how many Koopman eigenfunctions are necessary to generate the whole spectrum of the Koopman operator, this set is termed as a \emph{minimal set}. For an $N$ dimensional dynamical system, the cardinality of a minimal set is $N$. In addition, a numeric method is presented to find such a minimal set. The concept of time mappings, functions from the state space to the time axis, is the cornerstone of this work. It yields a convenient representation that splits the dynamic into $N$ independent systems. From them, a minimal set emerges which reveals governing and conservation laws. Thus, equivalency between a minimal set, flowbox representation, and conservation laws is made precise. In the numeric part, the curse of dimensionality in samples is discussed in the context of system recovery. The suggested method yields the most reduced representation from samples justifying the term \emph{minimal set}

Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime

We have demonstrated a recoil-free spectroscopy on the ${}^1S_0-{}^3P_1$ transition of strontium atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the ${}^1S_0$ and ${}^3P_1(m_J=0)$ states, we determined the {\it magic wavelength} where the Stark shifts for both states coincide. The Lamb-Dicke confinement provided by this Stark-free optical lattice enabled the measurement of the atomic spectrum free from Doppler as well as recoil shifts.Comment: 5pages, 4figure

BASiS: Batch Aligned Spectral Embedding Space

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely instrumental to design deep network building blocks with spectral graph characteristics. For instance, such a network allows the design of optimal graphs for certain tasks or obtaining a canonical orthogonal low-dimensional embedding of the data. Recent attempts to solve this problem were based on minimizing Rayleigh-quotient type losses. We propose a different approach of directly learning the eigensapce. A severe problem of the direct approach, applied in batch-learning, is the inconsistent mapping of features to eigenspace coordinates in different batches. We analyze the degrees of freedom of learning this task using batches and propose a stable alignment mechanism that can work both with batch changes and with graph-metric changes. We show that our learnt spectral embedding is better in terms of NMI, ACC, Grassman distance, orthogonality and classification accuracy, compared to SOTA. In addition, the learning is more stable.Comment: 14 pages, 10 figure

Spiking Optical Patterns and Synchronization

We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between the two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks