Domination Coloring of Graphs

A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the complexity of the k-domination coloring problem by proving its NP-completeness for arbitrary graphs. We give basic results and properties of χdd(G), including the bounds and characterization results, and further research χdd(G) of some special classes of graphs, such as the split graphs, the generalized Petersen graphs, corona products, and edge corona products. Several results on graphs with χdd(G)=χ(G) are presented. Moreover, an application of domination colorings in social networks is proposed.

A Linear-Time Algorithm for 4-Coloring Some Classes of Planar Graphs

Every graph G=(V, E) considered in this paper consists of a finite set V of vertices and a finite set E of edges, together with an incidence function that associates each edge e ∈ E of G with an unordered pair of vertices of G which are called the ends of the edge e. A graph is said to be a planar graph if it can be drawn in the plane so that its edges intersect only at their ends. A proper k-vertex-coloring of a graph G=(V, E) is a mapping c : V⟶S (S is a set of k colors) such that no two adjacent vertices are assigned the same colors. The famous Four Color Theorem states that a planar graph has a proper vertex-coloring with four colors. However, the current known proof for the Four Color Theorem is computer assisted. In addition, the correctness of the proof is still lengthy and complicated. In 2010, a simple O(n²) time algorithm was provided to 4-color a 3-colorable planar graph. In this paper, we give an improved linear-time algorithm to either output a proper 4-coloring of G or conclude that G is not 3-colorable when an arbitrary planar graph G is given. Using this algorithm, we can get the proper 4-colorings of 3-colorable planar graphs, planar graphs with maximum degree at most five, and claw-free planar graphs.

Deriving Visual Cues from Deep Learning to Achieve Subpixel Cell Segmentation in Adaptive Optics Retinal Images

Direct visualization of photoreceptor cells, specialized neurons in the eye that sense light, can be achieved using adaptive optics (AO) retinal imaging. Evaluating photoreceptor cell morphology in retinal diseases is important for monitoring the onset and progression of blindness, but segmentation of these cells is a critical first step. Most segmentation approaches focus on cell region extraction, without directly considering cell boundary localization. This makes it difficult to track cells that have ambiguous boundaries, which result from low image contrast, anisotropic cell regions, or densely-packed cells whose boundaries appear to touch each other. These are all characteristics of the AO images that we consider here. To address these challenges, we develop an AOSeg-Net method that uses a multi-channel U-Net to predict the spatial probabilities of the cell boundary and obtain cell centroid and region distribution information as a means for facilitating cell segmentation. Five-color theorem guarantees the separation of any touching cells. Finally, a region-based level set algorithm that combines all of these visual cues is used to achieve subpixel cell segmentation. Five-fold cross-validation on 428 high resolution retinal images from 23 human subjects showed that AOSegNet substantially outperformed the only other existing approach with Dice coefficients [%] of 84.7 and 78.4, respectively, and average symmetric contour distances [μm] of 0.59 and 0.80, respectively.

Machine behaviour

Machines powered by artificial intelligence increasingly mediate our social, cultural, economic and political interactions. Understanding the behaviour of artificial intelligence systems is essential to our ability to control their actions, reap their benefits and minimize their harms. Here we argue that this necessitates a broad scientific research agenda to study machine behaviour that incorporates and expands upon the discipline of computer science and includes insights from across the sciences. We first outline a set of questions that are fundamental to this emerging field and then explore the technical, legal and institutional constraints on the study of machine behaviour.

A Joint Routing and Channel Assignment Scheme for Hybrid Wireless-Optical Broadband-Access Networks

In this paper, we investigate mechanisms for improving the quality of communications in wireless-optical broadband access networks (WOBAN), which present a promising solution to meet the growing needs for capacity of access networks. This is achieved by using multiple gateways and multi-channel operation along with a routing protocol that effectively reduces the effect of radio interference. We present a joint route and channel assignment scheme with the objective of maximizing the end-to-end probability of success and minimizing the end-to-end delay for all active upstream traffic in the WOBAN. Performance evaluations of the proposed scheme are presented using ns-2 simulations, which show that the proposed scheme improves the network throughput up to three times and reduces the traffic delay by six times in presence of 12 channels and four network interface cards (NICs), compared to a single channel scenario.

Solving Constraint-Satisfaction Problems with Distributed Neocortical-Like Neuronal Networks

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of the CSP's planar four-color graph coloring, maximum independent set, and sudoku on this substrate and provide mathematical proofs that guarantee these graph coloring problems will convergence to a solution. The network is composed of nonsaturating linear threshold neurons. Their lack of right saturation allows the overall network to explore the problem space driven through the unstable dynamics generated by recurrent excitation. The direction of exploration is steered by the constraint neurons. While many problems can be solved using only linear inhibitory constraints, network performance on hard problems benefits significantly when these negative constraints are implemented by nonlinear multiplicative inhibition. Overall, our results demonstrate the importance of instability rather than stability in network computation and offer insight into the computational role of dual inhibitory mechanisms in neural circuits.

Generic Decentralized Control for Lattice-Based Self-Reconfigurable Robots

Previous work on self-reconfiguring modular robots has concentrated primarily on designing hardware and developing reconfiguration algorithms tied to specific hardware systems. In this paper, we introduce a generic model for lattice-based self-reconfigurable robots and present several generic locomotion algorithms that use this model. The algorithms presented here are inspired by cellular automata, using geometric rules to control module actions. The actuation model used is a general one, assuming only that modules can generally move over the surface of a group of modules. These algorithms can then be instantiated onto a variety of particular systems. Correctness proofs of many of the rule sets are also given for the generic geometry; this analysis can carry over to the instantiated algorithms to provide different systems with correct locomotion algorithms. We also present techniques for automated analysis that can be used for algorithms that are too complex to be easily analyzed by hand.

Coloring [Formula: see text]-Embeddable [Formula: see text]-Uniform Hypergraphs

This paper extends the scenario of the Four Color Theorem in the following way. Let [Formula: see text] be the set of all [Formula: see text]-uniform hypergraphs that can be (linearly) embedded into [Formula: see text]. We investigate lower and upper bounds on the maximum (weak) chromatic number of hypergraphs in [Formula: see text]. For example, we can prove that for [Formula: see text] there are hypergraphs in [Formula: see text] on [Formula: see text] vertices whose chromatic number is [Formula: see text], whereas the chromatic number for [Formula: see text]-vertex hypergraphs in [Formula: see text] is bounded by [Formula: see text] for [Formula: see text].

Chapter 17: bioimage informatics for systems pharmacology

Recent advances in automated high-resolution fluorescence microscopy and robotic handling have made the systematic and cost effective study of diverse morphological changes within a large population of cells possible under a variety of perturbations, e.g., drugs, compounds, metal catalysts, RNA interference (RNAi). Cell population-based studies deviate from conventional microscopy studies on a few cells, and could provide stronger statistical power for drawing experimental observations and conclusions. However, it is challenging to manually extract and quantify phenotypic changes from the large amounts of complex image data generated. Thus, bioimage informatics approaches are needed to rapidly and objectively quantify and analyze the image data. This paper provides an overview of the bioimage informatics challenges and approaches in image-based studies for drug and target discovery. The concepts and capabilities of image-based screening are first illustrated by a few practical examples investigating different kinds of phenotypic changes caEditorsused by drugs, compounds, or RNAi. The bioimage analysis approaches, including object detection, segmentation, and tracking, are then described. Subsequently, the quantitative features, phenotype identification, and multidimensional profile analysis for profiling the effects of drugs and targets are summarized. Moreover, a number of publicly available software packages for bioimage informatics are listed for further reference. It is expected that this review will help readers, including those without bioimage informatics expertise, understand the capabilities, approaches, and tools of bioimage informatics and apply them to advance their own studies.

Solving hard computational problems efficiently: asymptotic parametric complexity 3-coloring algorithm

Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular biology, e.g., genome sequencing; global alignment of multiple genomes; identifying siblings or discovery of dysregulated pathways. In almost all of these problems, there is the need for proving a hypothesis about certain property of an object that can be present if and only if it adopts some particular admissible structure (an NP-certificate) or be absent (no admissible structure), however, none of the standard approaches can discard the hypothesis when no solution can be found, since none can provide a proof that there is no admissible structure. This article presents an algorithm that introduces a novel type of solution method to "efficiently" solve the graph 3-coloring problem; an NP-complete problem. The proposed method provides certificates (proofs) in both cases: present or absent, so it is possible to accept or reject the hypothesis on the basis of a rigorous proof. It provides exact solutions and is polynomial-time (i.e., efficient) however parametric. The only requirement is sufficient computational power, which is controlled by the parameter α∈N. Nevertheless, here it is proved that the probability of requiring a value of α>k to obtain a solution for a random graph decreases exponentially: P(α>k)≤2(-(k+1)), making tractable almost all problem instances. Thorough experimental analyses were performed. The algorithm was tested on random graphs, planar graphs and 4-regular planar graphs. The obtained experimental results are in accordance with the theoretical expected results.

Cell population tracking and lineage construction with spatiotemporal context

Automated visual-tracking of cell populations in vitro using time-lapse phase contrast microscopy enables quantitative, systematic, and high-throughput measurements of cell behaviors. These measurements include the spatiotemporal quantification of cell migration, mitosis, apoptosis, and the reconstruction of cell lineages. The combination of low signal-to-noise ratio of phase contrast microscopy images, high and varying densities of the cell cultures, topological complexities of cell shapes, and wide range of cell behaviors poses many challenges to existing tracking techniques. This paper presents a fully automated multi-target tracking system that can efficiently cope with these challenges while simultaneously tracking and analyzing thousands of cells observed using time-lapse phase contrast microscopy. The system combines bottom-up and top-down image analysis by integrating multiple collaborative modules, which exploit a fast geometric active contour tracker in conjunction with adaptive interacting multiple models (IMM) motion filtering and spatiotemporal trajectory optimization. The system, which was tested using a variety of cell populations, achieved tracking accuracy in the range of 86.9-92.5%.

A 1.375-approximation algorithm for sorting by transpositions

Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a 10-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper, we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: we improve the lower bound for the transposition diameter of the symmetric group and determine the exact transposition diameter of simple permutations.

Cell segmentation using coupled level sets and graph-vertex coloring

Current level-set based approaches for segmenting a large number of objects are computationally expensive since they require a unique level set per object (the N-level set paradigm), or [log2N] level sets when using a multiphase interface tracking formulation. Incorporating energy-based coupling constraints to control the topological interactions between level sets further increases the computational cost to O(N2). We propose a new approach, with dramatic computational savings, that requires only four, or fewer, level sets for an arbitrary number of similar objects (like cells) using the Delaunay graph to capture spatial relationships. Even more significantly, the coupling constraints (energy-based and topological) are incorporated using just constant O(1) complexity. The explicit topological coupling constraint, based on predicting contour collisions between adjacent level sets, is developed to further prevent false merging or absorption of neighboring cells, and also reduce fragmentation during level set evolution. The proposed four-color level set algorithm is used to efficiently and accurately segment hundreds of individual epithelial cells within a moving monolayer sheet from time-lapse images of in vitro wound healing without any false merging of cells.

The challenge of computer mathematics

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.

Expansions: a study in the unity of science

This article attempts to establish some of the general laws relating to spatial aspects of general systems theory, i.e., how forces, impulses, and ideas (matter, energy, and information) spread, diversify, and compete with one another, and how the earlier history of observed structures can be traced by backtracking. Principles that have long been accepted for nonliving and low-level living systems are recognized in the activities of individual human beings, groups, and supranational systems.