Transition Graph Research Articles

Set Invariance and Optimal Set Stabilization of Boolean Control Networks: A Graphical Approach

This article investigates set invariance and optimal set stabilization of Boolean control networks (BCNs) from a novel graph-theoretical perspective. First, we establish the relationship between the control invariant sets and the strongly connected components of the state transition graph (STG), and propose a new algorithm to compute the largest control invariant subset. Second, both set stabilizability and time-optimal set stabilization via state feedback are characterized by a breadth-first tree of the STG. Though the prior two problems have been attempted by existing algebraic methods, the primary advantage of our alternative graphical approach is the enhanced computational efficiency. Third, we consider for the first time, the optimal set stabilization problem with general cost criteria, not limited to time optimality. A state feedback controller is constructed for general optimal set stabilization using a shortest-path tree of the STG. Finally, it is straightforward to extend the proposed approach to handle various constraints as well as other types of logical networks by slightly modifying the STG. Two biological networks are used to test the performance of our approach. Results show that in accordance with time complexity analysis, our algorithms can dramatically reduce the running time for the first two problems compared with existing work, and effectively solve the general optimal set stabilization problem.

Where to go? Predicting next location in IoT environment

Next location prediction has aroused great interests in the era of internet of things (IoT). With the ubiquitous deployment of sensor devices, e.g., GPS and Wi-Fi, IoT environment offers new opportunities for proactively analyzing human mobility patterns and predicting user’s future visit in low cost, no matter outdoor and indoor. In this paper, we consider the problem of next location prediction in IoT environment via a session-based manner. We suggest that user’s future intention in each session can be better inferred for more accurate prediction if patterns hidden inside both trajectory and signal strength sequences collected from IoT devices can be jointly modeled, which however existing state-of-the-art methods have rarely addressed. To this end, we propose a trajectory and sIgnal sequence (TSIS) model, where the trajectory transition regularities and signal temporal dynamics are jointly embedded in a neural network based model. Specifically, we employ gated recurrent unit (GRU) for capturing the temporal dynamics in the multivariate signal strength sequence. Moreover, we adapt gated graph neural networks (gated GNNs) on location transition graphs to explicitly model the transition patterns of trajectories. Finally, both the low-dimensional representations learned from trajectory and signal sequence are jointly optimized to construct a session embedding, which is further employed to predict the next location. Extensive experiments on two real-world Wi-Fi based mobility datasets demonstrate that TSIS is effective and robust for next location prediction compared with other competitive baselines.

Companions and an Essential Motion of a Reaction System

For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.

LncMirNet: Predicting LncRNA-miRNA Interaction Based on Deep Learning of Ribonucleic Acid Sequences.

Long non-coding RNA (LncRNA) and microRNA (miRNA) are both non-coding RNAs that play significant regulatory roles in many life processes. There is cumulating evidence showing that the interaction patterns between lncRNAs and miRNAs are highly related to cancer development, gene regulation, cellular metabolic process, etc. Contemporaneously, with the rapid development of RNA sequence technology, numerous novel lncRNAs and miRNAs have been found, which might help to explore novel regulated patterns. However, the increasing unknown interactions between lncRNAs and miRNAs may hinder finding the novel regulated pattern, and wet experiments to identify the potential interaction are costly and time-consuming. Furthermore, few computational tools are available for predicting lncRNA–miRNA interaction based on a sequential level. In this paper, we propose a hybrid sequence feature-based model, LncMirNet (lncRNA–miRNA interactions network), to predict lncRNA–miRNA interactions via deep convolutional neural networks (CNN). First, four categories of sequence-based features are introduced to encode lncRNA/miRNA sequences including k-mer (k = 1, 2, 3, 4), composition transition distribution (CTD), doc2vec, and graph embedding features. Then, to fit the CNN learning pattern, a histogram-dd method is incorporated to fuse multiple types of features into a matrix. Finally, LncMirNet attained excellent performance in comparison with six other state-of-the-art methods on a real dataset collected from lncRNASNP2 via five-fold cross validation. LncMirNet increased accuracy and area under curve (AUC) by more than 3%, respectively, over that of the other tools, and improved the Matthews correlation coefficient (MCC) by more than 6%. These results show that LncMirNet can obtain high confidence in predicting potential interactions between lncRNAs and miRNAs.

A low-power asynchronous hardware implementation of a novel SVM classifier, with an application in a speech recognition system

Machine Learning (ML) has been applied in so many areas in reason of its robustness, usability, and reliability, mainly in hardware implementation. One of its well-known algorithms is the Support Vector Machine (SVM), the simplest to be applied in hardware because of its mathematical modeling. In this study, we propose the implementation in hardware of SVM multi-class classifiers within the asynchronous paradigm (i.e., without clock signal application) in a 4-stage pipeline architecture. With the purpose to evaluate the proposed architecture behavior, we used a Field Programmable Gate Array (FPGA) device to prototype the circuit. The proposed asynchronous SVM classifier is applied in a Speech Recognition system of 30 classes where a hybrid training algorithm was processed in the Matlab software, known as PSO-SVM training algorithm. Therefore, the training phase was processed in software in reason of its computational load. For the SVM classification phase, we propose, for the first time to the best of our knowledge, an asynchronous pipeline architecture of four stages with Multiply-Accumulator (MAC) unit application and three different control circuits described from Extended Burst-Mode (XBM) and State Transition Graph (STG) specifications, leading to energy-efficient design. In order to validate the SVM recognition results in the speech recognition application, the tests are from 60 speeches and 20 speakers, so it is a diversified and reliable data set of tests. The main goal here was to design a machine learning hardware implementation in a low power application and, through that, to prove that the asynchronous paradigm reduced power. As a result, we obtained a reduced power consumption of 5.72 mW, a fast average response time which was 0.61μs and the most area-efficient circuit (1315 LUTs); the accuracy in recognition success rate was another preoccupation, and it was very successful, 98% of success. Besides, we present comparisons with an asynchronous version of the same SVM datapath and with different synchronous architectures from literature to prove that our novelty is better in power consumption and area size. For hardware applications where low power and high performance are the sought features, the presented architecture revealed the best position when compared to similar works from the recent technical literature for pattern recognition systems.

Absorption in Time-Varying Markov Chains: Graph-Based Conditions

We investigate absorption, i.e., almost sure convergence to an absorbing state, in time-varying (non-homogeneous) discrete-time Markov chains with finite state space. We consider systems that can switch among a finite set of transition matrices, which we call the modes. Our analysis is focused on two properties: 1) almost sure convergence to an absorbing state under any switching, and 2) almost sure convergence to a desired set of absorbing states via a proper switching policy. We derive necessary and sufficient conditions based on the structures of the transition graphs of modes. More specifically, we show that a switching policy that ensures almost sure convergence to a desired set of absorbing states from any initial state exists if and only if those absorbing states are reachable from any state on the union of simplified transition graphs. We then show three sufficient conditions for absorption under arbitrary switching. While the first two conditions depend on the acyclicity (weak acyclicity) of the union (intersection) of simplified transition graphs, the third condition is based on the distances of each state to the absorbing states in all the modes. These graph theoretic conditions can verify the stability and stabilizability of absorbing states based only on the feasibility of transitions in each mode.

Facilitation in reaction systems

Reaction systems is a formal model of computation which originated as a model of interactions between biochemical reactions in the living cell. These interactions are based on two mechanisms, facilitation and inhibition, and this is well reflected in the formulation of reaction systems. In this paper, we investigate the facilitation aspect of reaction systems, where the products of a reaction may facilitate other reactions by providing some of their reactants. This aspect is formalized through positive dependency graphs which depict explicitly such facilitating interactions. The focus of the paper is on demonstrating how structural properties of reaction systems defined through the properties of their positive dependency graphs influence the behavioural properties of (suitable subclasses of) reaction systems, which, as usual, are defined through their transition graphs.

Autonomous Cognitive Model and Analysis for Survivable System

The research on autonomous recognition mechanism for survivability has vigorously been growing up. A method of autonomous cognitive model and quantitative analysis for survivable system was proposed based on cognitive computing technology. Firstly, a cognitive model for survivable system with cross-layer perception ability was established, a self-feedback evolution mode of cognitive unit based on monitor-decide-execute loop structure was improved, and a self-configuration of cognitive unit is realized. Then, combined with the cognitive state transition graph, the analysis of cognitive performance for survivable systems based on dynamic cognitive behavioral changes was constructed. Finally, the cognitive processes of survivable system were described by using formal modeling. Simulation validated the influence degree of test parameters on system survivability from two perspectives of the probability of intrusion detection systems vulnerability and attacks detected. Results show that enhancing the rate of monitoring actions change and the rate of performing actions change obviously improved the cognitive performance of survivable system.

Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics.

Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor and suggested a Langevin formulation with noise coefficient matrix such that SS. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this article, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 28 noise coefficient matrix . We show that (1) the corresponding 14D system of ordinary differential equations is consistent with the classical 4D representation of the HH system; (2) the 14D representation leads to a noise coefficient matrix that can be obtained cheaply on each time step, without requiring a matrix decomposition; (3) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, as well as trajectories of several existing Langevin models; (4) our 14D representation (and those equivalent to it) gives the most accurate interspike interval distribution, not only with respect to moments but under both the and metric-space norms; and (5) the 14D representation gives an approximation to exact Markov chain simulations that are as fast and as efficient as all equivalent models. Our approach goes beyond existing models, in that it supports a stochastic shielding decomposition that dramatically simplifies with minimal loss of accuracy under both voltage- and current-clamp conditions.

Calculation of the reliability of frame systems under seismic impact and survivability assessment during the formation of plastic hinges in the nodes

Aim . The research aims to develop mathematical models for evaluating the reliability of two-story frame systems under the seismic impact, covering all possible ways of transition to the mechanism state due to the formation of plastic hinges in the frame nodes. Methods . The study is based on the application of the theory of Markov random processes in continuous time and their discrete states to describe the transition of a system into a different state. Such states include faults resulting from the formation of plastic hinges in the frame nodes. Results . Possible schemes of forming plastic hinges in two types of statically indeterminate frames under horizontal seismic impact are described: in the frame of a 2-story industrial building with a large-span upper floor and with the support of the roof truss on the heads of columns and a two-story two-span frame of a simple regular structure with rigid nodes. Possible states are noted and transition graphs are compiled, which are typical for the frames under consideration in the case of rigid disks of floor slabs during seismic impact, represented as a stationary random process. By representing the transition of systems to the states under consideration caused by the formation of plastic hinges in one or another sequence under seismic action in the form of a Markov random process in continuous time and discrete states, systems of first-order differential equations describing these transitions are obtained. Having solved them by applying the Laplace transform, analytical expressions for estimating the probabilities of finding frame systems in the states under consideration and expressions for estimating the probabilities of failure-free operation of these systems are obtained. Conclusion . By constructing transition graphs covering all possible states of frame systems during the formation of plastic hinges in nodes under seismic action and describing the process of frame transitions from one state to another by a Markov random process in continuous time and discrete states, analytical expressions for evaluating the probabilities of these system states, as well as their reliability and survivability under seismic action, can be obtained.

Preservice Science Teachers\u2019 Strategies in Scientific Reasoning: the Case of Modeling

The development of scientific reasoning competencies is a key goal of science education. To better understand the complex construct of scientific reasoning, which includes modeling as one style of reasoning, thorough investigations of the underlying processes are needed. Therefore, in this study, a typology of preservice science teachers’ modeling strategies was developed. Thirty-two preservice science teachers were videotaped while engaging in the modeling task of investigating a black box. Following a qualitative content analysis, sequences of modeling activities were identified. By transforming these sequences of modeling activities into state transition graphs, six types of modeling strategies were derived, differing in the homogeneity and complexity of their modeling processes. The preservice science teachers engaged in activities of (1) exploration only; (2a) exploration and development with a focus on development; (2b) exploration and development with a focus on exploration; (2c) exploration and development, balanced; (3a) exploration, development, and drawing predictions from a model once; or (3b) exploration, development, and repeatedly drawing predictions from a model. Finally, this typology is discussed regarding the process of its development and its potential to inform and guide further research as well as the development of interventions aiming to foster competencies in scientific modeling.

Infinite-Horizon Optimal Control of Switched Boolean Control Networks With Average Cost: An Efficient Graph-Theoretical Approach.

This study investigates the infinite-horizon optimal control (IHOC) problem for switched Boolean control networks with an average cost criterion. A primary challenge of this problem is the prohibitively high computational cost when dealing with large-scale networks. We attempt to develop a more efficient approach from a novel graph-theoretical perspective. First, a weighted directed graph structure called the optimal state transition graph (OSTG) is established, whose edges encode the optimal action for each admissible state transition between states reachable from a given initial state subject to various constraints. Then, we reduce the IHOC problem into a minimum-mean cycle (MMC) problem in the OSTG. Finally, we develop an algorithm that can quickly find a particular MMC by resorting to Karp's algorithm in the graph theory and construct an optimal switching control law based on state feedback. The time complexity analysis shows that our algorithm, albeit still running in exponential time, can outperform all the existing methods in terms of time efficiency. A 16-state-3-input signaling network in leukemia is used as a benchmark to test its effectiveness. Results show that the proposed graph-theoretical approach is much more computationally efficient and can reduce the running time dramatically: it runs hundreds or even thousands of times faster than the existing methods. The Python implementation of the algorithm is available at https://github.com/ShuhuaGao/sbcn_mmc.

State transition graph of the Preisach model and the role of return-point memory.

The Preisach model has been useful as a null model for understanding memory formation in periodically driven disordered systems. In amorphous solids, for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by Mungan etal. [Phys. Rev. Lett. 123, 178002 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.178002], the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between soft spots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying soft-spot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return-point memory in organizing thegraphinto a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion ofthisgraph is actually not governed by the values of the switching fields that describe the hysteretic behavior of the individual elements but by a coarser parameter, a permutation ρ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states |R| constituting the main hysteresis loop and its nested subloops. We find that |R| is equal to the number of increasing subsequences contained in the permutation ρ.

Intrinsic coupling between twinning plasticity and transformation plasticity in metastable β Ti-alloys: A symmetry and pathway analysis

In addition to conventional dislocation plasticity, mechanical twinning and structural phase transformations are another two important plasticity carriers. Although both are symmetry-breaking processes and theories to treat each of them individually have been well-established, the intrinsic coupling between the two has not been investigated. Here we employ a phase transition graph approach to analyze systematically deformation modes arising from the interplay between mechanical twinning and phase transformations. Using metastable β Ti-alloys as an example, we show that mechanical twinning and phase transformations are intrinsically coupled in the symmetry-breaking processes, which results in multiple interconnected transformation and non-transformation deformation pathways and characteristic twinning modes. This work not only reveals the physical origin of unique twinning modes (e.g., {332}, {5 8 11} and {3 9 10} twins) and extended core structures of twin boundaries (e.g., nested twins) observed in experiments, but also provides a new insight into the enhanced plasticity of metastable β Ti-alloys through coupled twinning and transformation pathway engineering.

Integer linear programming formulations of the filter partitioning minimization problem

Combinatorial filters, which take the form of labelled transition graphs, are a general representation for filtering and inference tasks in robotics. They are of particular interest in contexts where the objective is to minimize the computational resources needed to execute the filter. One specific problem is called the filter minimization (FM) problem, in which the goal is to find, for a given original filter, a state-minimal filter equivalent to the original filter. We consider a special case of FM, called the filter partitioning minimization (FPM) problem, in which the reduced filter must partition the state space of the original filter. This problem has been proven to be NP-hard. This paper considers the practical problem of solving FPM in spite of these hardness results. In contrast to the best known algorithm for this problem, a heuristic approach based on graph coloring proposed by O’Kane and Shell, we show how to convert an FPM instance to an instance of the well-known integer linear programming (ILP) problem. We present three distinct formulations of this reduction. Though ILP is itself a challenging problem, reducing FPM to ILP has the advantage that the ILP problem has been studied in great detail, and highly-optimized solvers are readily available. We describe experiments comparing this approach to the heuristic algorithm of O’Kane and Shell. The results show that the proposed ILP technique performs better in computing exact solutions as the filter sizes grow, and that the ILP approach obtains higher-quality feasible solutions, in contexts where time limitations prohibit the computation of exact solutions.

Exact solving and sensitivity analysis of stochastic continuous time Boolean models

BackgroundSolutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models.ResultsWe show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation’s kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights.ConclusionUp to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model’s timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

Transitions between human functional brain networks reveal complex, cost-efficient and behaviorally-relevant temporal paths

Resting-state functional MRI activity is organized as a complex network. However, this coordinated brain activity changes with time, raising questions about its evolving temporal arrangement. Does the brain visit different configurations through time in a random or ordered way? Advances in this area depend on developing novel paradigms that would allow us to shed light on these issues. We here propose to study the temporal changes in the functional connectome by looking at transition graphs of network activity. Nodes of these graphs correspond to brief whole-brain connectivity patterns (or meta-states), and directed links to the temporal transition between consecutive meta-states. We applied this method to two datasets of healthy subjects (160 subjects and a replication sample of 54), and found that transition networks had several non-trivial properties, such as a heavy-tailed degree distribution, high clustering, and a modular organization. This organization was implemented at a low biological cost with a high cost-efficiency of the dynamics. Furthermore, characteristics of the subjects’ transition graphs, including global efficiency, local efficiency and their transition cost, were correlated with cognition and motor functioning. All these results were replicated in both datasets. We conclude that time-varying functional connectivity patterns of the brain in health progress in time in a highly organized and complex order, which is related to behavior.

Transition operations over plane trees

The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and planar straight-line graphs. For the latter, several variants have been studied (e.g., edge slides and edge rotations). In a transition graph on the set T(S) of noncrossing straight-line spanning trees on a finite point set S in the plane, two spanning trees are connected by an edge if one can be transformed into the other by such an operation. We study bounds on the diameter of these graphs, and consider the various operations on point sets in both general position and convex position. In addition, we address variants of the problem where operations may be performed simultaneously or the edges are labeled. We prove new lower and upper bounds for the diameters of the corresponding transition graphs and pose open problems.

О специальных свойствах некоторых квазиметрик

В статье рассмотрены свойства квазиметрики среднего времени первого прохода - обобщенной метрической структуры, тесно связанной с эргодическими однородными цепями Маркова.Во введении представлена история вопроса, дан обзор основных идей и результатов работы.В первом разделе собраны основные понятия теориицепей Маркова - последовательностей случайных событий с конечным или счетным числом исходов, характеризующихся тем, что, говоря нестрого, при фиксированномнастоящем будущее независимо от прошлого. Точнее, математическая модель некоторого случайного процесса представляет собой марковскую цепь, если распределение вероятностей параметров процесса в следующий момент времени зависиттолько от параметров процесса в предыдущий момент.Во втором разделе собраны базовые определения, необходимые для рассмотрения роли графовых моделейв представлении и исследовании эргодических однородных цепей Маркова.Марковская цепь может быть изображена в виде ориентированного взвешенного графа переходов, вершины которого соответствуют состояниям цепи, а дуги - переходам между ними.Процесс будет эргодическим, если построенный взвешенный орграф является слабо связным, и наибольший общий делитель длин всех его циклов равен единице.С другой стороны, любой связный граф может служить базой для построения модели простейшей цепи Маркова: если вершина $i$ имеетстепень $k$, то все выходящие из нее ребра превращаются в дуги с весами $\frac{1}{k}$.%Основное место занимают понятия, связанные с теорией остовного леса сходящихся деревьев ориентированного %графа, соответствующего матрице перехода однородной эргодической цепи Маркова.В третьем разделе дано определение среднего времени первого прохода для однородной эргодической цепи Маркова. Представлены несколько способов построения соответствующей матрицы $M$. Подробно проанализирован алгоритм нахождения среднего времени первого прохода с помощью использования сходящихся деревьев ориентированного графа, связанного с матрицей перехода эргодической однородной цепи Маркова. Описана родственная рекуррентная процедура.В четвертом разделе матрица среднего времени первого прохода рассмотрена как {\it квазиметрика } $m$среднего времени первого прохода на множестве вершин $V=\{1, 2, ..., n\}$ ориентированного графа, соответствующего матрице перехода эргодической однородной цепи Маркова: $m(i,j)$ - ожидаемое количество шагов (дуг) для случайного блуждания на орграфе $\Gamma$, начинающегося с $i$, для достижения $j$ в первый раз. Эта квазиметрика обладает рядом важных теоретических и прикладных свойств.В частности, квазиметрика среднего времени первого прохода для простого случайного блуждания по связному невзвешенному графу $G$, в котором из любой вершины графа существует равная вероятность перемещения в любую соседнюю вершину,является взвешиваемой квазиметрикой, т.е. существует весовая функция $w: V\rightarrow\mathbb{R}_{\ge 0}$,%$w=(w_1, w_2,\ldots, w_n)$,такая, что для всех $i,j\in V$ имеет место сотношение %& Было бы здорово найти для $m_i$ наглядную интерпретацию.$m(i,j)+w_i=m(j,i)+w_j.$Менее изучены, но не менее интересны связи квазиметрики среднего времени первого прохода с другими метрическими структурами на графах, в частности, с $\alpha$-метрикой леса и ее вариациями.Наконец, в пятом разделе рассмотрены примеры построения и исследования квазиметрики среднего времени первого прохода. Помимо иллюстрации ''графовой`` процедуры построения матрицы $M$, представлены рекуррентные алгоритмы исследования и проанализированы получающиеся при этом обобщенные метрические структуры.

Search Tree Pruning for Progressive Neural Architecture Search (Student Abstract)

Our neural architecture search algorithm progressively searches a tree of neural network architectures. Child nodes are created by inserting new layers determined by a transition graph into a parent network up to a maximum depth and pruned when performance is worse than its parent. This increases efficiency but makes the algorithm greedy. Simpler networks are successfully found before more complex ones that can achieve benchmark performance similar to other top-performing networks.