Global dynamics of a Lotka–Volterra competition patch model*

The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.

The Connection Matrix analysis of a Prey-Predator system with a Strong Allee effect and multiple interior equilibria

We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.

A brain structural connectivity biomarker for diagnosis of autism spectrum disorder in early childhood

Objective: Autism spectrum disorder (ASD) is associated with altered brain development, but it is unclear which specific structural changes may serve as potential diagnostic markers. This study aimed to identify and model brain-wide differences in structural connectivity using MRI diffusion tensor imaging (DTI) in young ASD and typically developing (TD) children (3.5-6 years old). Methods: Ninety-three ASD and 26 TD children were included in a discovery dataset and 12 ASD and 9 TD children from different sites included as independent validation datasets. Brain-wide (294 regions) structural connectivity was measured using DTI (fractional anisotropy, FA) under sedation together with symptom severity and behavioral and cognitive development. A connection matrix was constructed for each child for comparisons between ASD and TD groups. Pattern classification was performed and the resulting model tested on two independent datasets. Results: Thirty-three structural connections showed increased FA in ASD compared to TD children and associated with both symptom severity and general cognitive development. The majority (29/33) involved the frontal lobe and comprised five different networks with functional relevance to default mode, motor control, social recognition, language and reward. Overall, classification accuracy is very high in the discovery dataset 96.77%, and 91.67% and 88.89% in the two independent validation datasets. Conclusions: Identified structural connectivity differences primarily involving the frontal cortex can very accurately distinguish individual ASD from TD children and may therefore represent a robust early brain biomarker.

EVALUATION OF IMPROVEMENT OPPORTUNITIES FOR THE COLLABORATION OF DESIGN AND SIMULATION - AN INDUSTRIAL MULTI-METHOD STUDY

As mechanical simulations play an increasingly role in engineering projects, an appropriate integration of simulations into design-oriented product development processes is essential for efficient collaboration. To identify and overcome barriers between design and simulation departments, the BRIDGES approach was elaborated for barrier reduction in design engineering and simulation. This paper shows the industrial evaluation of the approach using a multi-method study of an online survey and focus group workshops. The experts' assessments were statistically analysed to build a connection matrix of barriers and recommendations. 59 participants from multiple industries with practical experience in the field contributed to the online survey, while 24 experts could be acquired for the focus group workshops. As a result of the workshops, both the data-based and the workshop-based part of the BRIDGES approach were assessed as beneficial to raise the efficiency of collaboration and practically applicable. This provides an empirically secured connection of barriers and suitable recommendations, allowing companies to identify and overcome collaboration barriers between design and simulation.

Inverse Problem for Ising Connection Matrix with Long-Range Interaction

In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

STOCHASTIC PSEUDOSPIN NEURAL NETWORK WITH TRIDIAGONAL SYNAPTIC CONNECTIONS

Context. To reduce the computational resource time in the problems of diagnosing and recognizing distorted images based on a fully connected stochastic pseudospin neural network, it becomes necessary to thin out synaptic connections between neurons, which is solved using the method of diagonalizing the matrix of synaptic connections without losing interaction between all neurons in the network. Objective. To create an architecture of a stochastic pseudo-spin neural network with diagonal synaptic connections without loosing the interaction between all the neurons in the layer to reduce its learning time. Method. The paper uses the Hausholder method, the method of compressing input images based on the diagonalization of the matrix of synaptic connections and the computer mathematics system MATLAB for converting a fully connected neural network into a tridiagonal form with hidden synaptic connections between all neurons. Results. We developed a model of a stochastic neural network architecture with sparse renormalized synaptic connections that take into account deleted synaptic connections. Based on the transformation of the synaptic connection matrix of a fully connected neural network into a Hessenberg matrix with tridiagonal synaptic connections, we proposed a renormalized local Hebb rule. Using the computer mathematics system “WolframMathematica 11.3”, we calculated, as a function of the number of neurons N, the relative tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network. Conclusions. We found that with an increase in the number of neurons, the tuning time of synaptic connections (per iteration) in a stochastic pseudospin neural network with a tridiagonal connection Matrix, relative to the tuning time of synaptic connections (per iteration) in a fully connected synaptic neural network, decreases according to a hyperbolic law. Depending on the direction of pseudospin neurons, we proposed a classification of a renormalized neural network with a ferromagnetic structure, an antiferromagnetic structure, and a dipole glass.

On the intersection between data quality and dynamical modelling of large-scale fMRI signals

Large-scale dynamics of the brain are routinely modelled us- ing systems of nonlinear dynamical equations that describe the evolution of population-level activity, with distinct neural pop- ulations often coupled according to an empirically measured structural connection matrix. This modelling approach has been used to generate insights into the neural underpinnings of spontaneous brain dynamics, as recorded with techniques such as resting state functional MRI (fMRI). In fMRI, researchers have many degrees of freedom in the way that they can pro- cess the data and recent evidence indicates that the choice of pre-processing steps can have a major effect on empirical esti- mates of functional connectivity. However, the potential influ- ence of such variations on modelling results are seldom consid- ered. Here we show, using three popular whole-brain dynam- ical models, that different choices during fMRI preprocessing can dramatically affect model fits and interpretations of find- ings. Critically, we show that the ability of these models to ac- curately capture patterns in fMRI dynamics is mostly driven by the degree to which they fit global signals rather than inter- esting sources of coordinated neural dynamics. We show that widespread deflections can arise from simple global synchroni- sation. We introduce a simple two-parameter model that cap- tures these fluctuations and which performs just as well as more complex, multi-parameter biophysical models. From our com- bined analyses of data and simulations, we describe benchmarks to evaluate model fit and validity. Although most models are not resilient to denoising, we show that relaxing the approxima- tion of homogeneous neural populations by more explicitly modelling inter-regional effective connectivity can improve model accuracy at the expense of increased model complexity. Our results suggest that many complex biophysical models may be fitting relatively trivial properties of the data, and underscore a need for tighter integration between data quality assurance and model development.

GateRL: Automated Circuit Design Framework of CMOS Logic Gates Using Reinforcement Learning

This paper proposes a GateRL that is an automated circuit design framework of CMOS logic gates based on reinforcement learning. Because there are constraints in the connection of circuit elements, the action masking scheme is employed. It also reduces the size of the action space leading to the improvement on the learning speed. The GateRL consists of an agent for the action and an environment for state, mask, and reward. State and reward are generated from a connection matrix that describes the current circuit configuration, and the mask is obtained from a masking matrix based on constraints and current connection matrix. The action is given rise to by the deep Q-network of 4 fully connected network layers in the agent. In particular, separate replay buffers are devised for success transitions and failure transitions to expedite the training process. The proposed network is trained with 2 inputs, 1 output, 2 NMOS transistors, and 2 PMOS transistors to design all the target logic gates, such as buffer, inverter, AND, OR, NAND, and NOR. Consequently, the GateRL outputs one-transistor buffer, two-transistor inverter, two-transistor AND, two-transistor OR, three-transistor NAND, and three-transistor NOR. The operations of these resultant logics are verified by the SPICE simulation.

THE OPTIMIZATION OF PLACING ELECTRONIC COMPONENTS BY A MODIFIED ALTERNATING-VARIABLE DESCENT METHOD

The problem of optimal placement of elements of electrical and electronic circuits is considered. The minimum weighted connection length is selected as the criterion. A computational method is proposed that is a modification of the coordinate descent method and one of the variants of the General approach based on pair permutations. The scheme is defined by the connection matrix. We consider a fixed set of element positions and a distance matrix based on an orthogonal metric. This problem is a variant of the General mathematical model, called the quadratic assignment problem. Geometric restriction of the problem – no more than one element can be placed in one cell. It is stated that approaches based on paired and similar permutations are economical, and the method of the penalty function leads to” ditching ” and is ineffective. A modified coordinate descent method is described, which is a variant of the pair permutation method, in which pairs are selected based on the coordinate descent method. In the proposed version of the coordinate descent method, two coordinates are changed simultaneously at one stage of calculations (and not one, as in the usual optimization method). one of the coordinates is used for the usual trial step, and the other is used for correction, returning to the acceptable area. Next, the value of the target function is calculated at the found point and compared with the previously reached value. If the value has improved, the found point becomes the new starting point. Otherwise, a step is made on a different coordinate with simultaneous correction of the vector of item position numbers (return to the allowed area). The experience of using the modified method in solving the problem of placing EVA elements has shown its significant advantages in comparison with other known methods, for example, the genetic algorithm, as well as the method of penalty functions. An example of calculations using the proposed method is considered. The connection matrix was set analytically. First, the initial approximation was searched by the Monte Carlo method (10,000 iterations), after which the local optimum was calculated using a modified method of coordinate descent in the permutation space without repetitions (a limit of 100 iterations was set). The initial value of the coordinate step is equal to the size of the permutation, then at each iteration it was reduced by 1 to the minimum possible value of 1. The advantage of this method is that there is no penalty function. The search is performed automatically in the permutation space without repetitions. Computational experiments have shown high computational qualities of the proposed method.