UNSEG: unsupervised segmentation of cells and their nuclei in complex tissue samples.

Multiplexed imaging technologies have made it possible to interrogate complex tumor microenvironments at sub-cellular resolution within their native spatial context. However, proper quantification of this complexity requires the ability to easily and accurately segment cells into their sub-cellular compartments. Within the supervised learning paradigm, deep learning based segmentation methods demonstrating human level performance have emerged. Here we present an unsupervised segmentation (UNSEG) method that achieves deep learning level performance without requiring any training data. UNSEG leverages a Bayesian-like framework and the specificity of nucleus and cell membrane markers to construct an a posteriori probability estimate of each pixel belonging to the nucleus, cell membrane, or background. It uses this estimate to segment each cell into its nuclear and cell-membrane compartments. We show that UNSEG is more internally consistent and better at generalizing to the complexity of tissue samples than current deep learning methods. This allows UNSEG to unambiguously identify the cytoplasmic compartment of a cell, which we employ to demonstrate its use in an example biological scenario. Within the UNSEG framework, we also introduce a new perturbed watershed algorithm capable of stably and accurately segmenting a cell nuclei cluster into individual cell nuclei. Perturbed watershed can also be used as a standalone algorithm that researchers can incorporate within their supervised or unsupervised learning approaches to replace classical watershed. Finally, as part of developing UNSEG, we have generated a high-quality annotated gastrointestinal tissue dataset, which we anticipate will be useful for the broader research community. Segmentation, despite its long antecedents, remains a challenging problem, particularly in the context of tissue samples. UNSEG, an easy-to-use algorithm, provides an unsupervised approach to overcome this bottleneck, and as we discuss, can help improve deep learning based segmentation methods by providing a bridge between unsupervised and supervised learning paradigms.

Logic gates on stationary dissipative solitons.

Stable dissipative solitons are perfect carries of optical information due to remarkable stability of their waveforms that allows the signal transmission with extremely dense soliton packing without losing the encoded information. Apart from unaffected passing of solitons through a communication network, controllable transformations of soliton waveforms are needed to perform all-optical information processing. In this paper we employ the basic model of dissipative optical solitons in the form of the complex Ginzburg-Landau equation with a potential term to study the interactions between two stationary dissipative solitons under the control influences and use those interactions to implement various logic gates. In particular, we demonstrate not, and, nand, or, nor, xor, and xnor gates, where the plain (fundamental soliton) and composite pulses are used to represent the low and high logic levels.

Induced waveform transitions of dissipative solitons.

The effect of an externally applied force upon the dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a potential term with an explicit coordinate dependence. The potential accounts for the external force manipulations and consists of three symmetrically arranged potential wells whose depth varies along the longitudinal coordinate. It is found out that under an influence of such potential a transition between different soliton waveforms coexisting under the same physical conditions can be achieved. A low-dimensional phase-space analysis is applied in order to demonstrate that by only changing the potential profile, transitions between different soliton waveforms can be performed in a controllable way. In particular, it is shown that by means of a selected potential, stationary dissipative soliton can be transformed into another stationary soliton as well as into periodic, quasi-periodic, and chaotic spatiotemporal dissipative structures.

Control of dissipative solitons in a magneto-optic planar waveguide.

We propose a mechanism to control propagation of a group of stable dissipative solitons in a nonlinear magneto-optic planar waveguide. The control is realized by means of a spatially inhomogeneous external magnetic field, which is induced by a set of direct conducting wires placed on the top of the guiding layer. The wires are extended in the direction of soliton propagation, and carry electric currents with particular piecewise constant profiles. In order to describe the soliton evolution the one-dimensional cubic-quintic complex Ginzburg-Landau equation has been adapted by tailoring an additional linear term, which is responsible for the magneto-optic effect.

Cascade replication of dissipative solitons.

We report a new effect of a cascade replication of dissipative solitons from a single one. It is discussed in the framework of a common model based on the one-dimensional cubic-quintic complex Ginzburg-Landau equation in which an additional linear term is introduced to account the perturbation from a particular potential of externally applied force. The effect is demonstrated on the light beams propagating through a planar waveguide. The waveguide consists of a nonlinear layer able to guide dissipative solitons and a magneto-optic substrate. In the waveguide an externally applied force is considered to be an inhomogeneous magnetic field which is induced by modulated electric currents flowing along a set of conducting wires adjusted on the top of the waveguide.