Discrete Steps Research Articles

Persistence of hubs in growing random networks

We consider models of evolving networks $$\left\{ {\mathcal {G}}_n:n\ge 0\right\} $$ modulated by two parameters: an attachment function $$f:{\mathbb {N}}_0 \rightarrow {\mathbb {R}}_+$$ and a (possibly random) attachment sequence $$\left\{ m_i:i\ge 1\right\} $$ . Starting with a single vertex, at each discrete step $$i\ge 1$$ a new vertex $$v_i$$ enters the system with $$m_i\ge 1$$ edges which it sequentially connects to a pre-existing vertex $$v\in {\mathcal {G}}_{i-1}$$ with probability proportional to $$f(\text{ degree }(v))$$ . We consider the problem of emergence of persistent hubs: existence of a finite (a.s.) time $$n^*$$ such that for all $$n\ge n^*$$ the identity of the maximal degree vertex (or in general the K largest degree vertices for $$K\ge 1$$ ) does not change. We obtain general conditions on f and $$\left\{ m_i:i\ge 1\right\} $$ under which a persistent hub emerges, and also those under which a persistent hub fails to emerge. In the case of lack of persistence, for the specific case of trees ( $$m_i\equiv 1$$ for all i), we derive asymptotics for the maximal degree and the index of the maximal deg ree vertex (time at which the vertex with current maximal degree entered the system) to understand the movement of the maximal degree vertex as the network evolves. A key role in the analysis is played by an inverse rate weighted martingale constructed from a continuous time embedding of the discrete time model. Asymptotics for this martingale, including concentration inequalities and moderate deviations form the technical foundations for the main results.

DIGITAL IMAGE REDUCTION FOR EFFICIENT COMPUTATION TOPOLOGICAL CHANGES IN THE ROCK MATRIX

The article describes the application of the digital image reduction algorithm to speed up the calculation of persistent diagrams that describe changes in the topology of the pore space of the rock matrix during the dissolution process. The dependence of the efficiency of the reduction algorithm on the properties of the rock sample and the value of the discrete time step is shown.

Faster heuristics for graph burning.

Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes that have to be given information so that the network is covered in least number of steps. Graph burning problem is NP-Hard for which two approximation algorithms and a few heuristics have been proposed in the literature. In this work, we propose three heuristics, namely, Backbone Based Greedy Heuristic (BBGH), Improved Cutting Corners Heuristic (ICCH), and Component Based Recursive Heuristic (CBRH). These are mainly based on Eigenvector centrality measure. BBGH finds a backbone of the network and picks vertex to be burned greedily from the vertices of the backbone. ICCH is a shortest path based heuristic and picks vertex to burn greedily from best central nodes. The burning number problem on disconnected graphs is harder than on the connected graphs. For example, burning number problem is easy on a path where as it is NP-Hard on disjoint paths. In practice, large networks are generally disconnected and moreover even if the input graph is connected, during the burning process the graph among the unburned vertices may be disconnected. For disconnected graphs, ordering the components is crucial. Our CBRH works well on disconnected graphs as it prioritizes the components. All the heuristics have been implemented and tested on several bench-mark networks including large networks of size more than 50K nodes. The experimentation also includes comparison to the approximation algorithms. The advantages of our algorithms are that they are much simpler to implement and also several orders faster than the heuristics proposed in the literature.

Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation

A new approach for calculating Laguerre expansion coefficients is proposed. In solving applied problems, initial data may be specified as time series with a constant discretization step. In this case, the use of quadratures of high-order accuracy is limited due to their instability. In order to overcome these difficulties, this paper considers an approach in which algorithms are proposed to calculate integral Laguerre transform by solving a one-dimensional transport equation. In contrast to the direct calculation of improper integrals of rapidly oscillating functions, these procedures make it possible to calculate the expansion coefficients of a Laguerre series expansion with better stability, higher accuracy, and less computational burden. The numerical experiments have shown that the methods are economical in terms of operation count, stable, and have reasonable accuracy in practical calculations.

ESO-MAPF: Bridging Discrete Planning and Continuous Execution in Multi-Agent Pathfinding

We present ESO-MAPF, a research and educational platform for experimenting with multi-agent path finding (MAPF). ESO-MAPF focuses on demonstrating the planning-acting chain in the MAPF domain. MAPF is the task of finding collision free paths for agents from their starting positions to given individual goals. The standard MAPF uses the abstraction where agents move in an undirected graph via traversing its edges in discrete steps. The discrete abstraction simplifies the planning phase however resulting discrete plans often need to be executed in the real continuous environment. ESO-MAPF shows how to bridge discrete planning and the acting phase in which the resulting plans are executed on physical robots. We simulate centralized plans on a group of OZOBOT Evo robots using their reflex functionalities and outputs on the surface of the screen that serves as the environment. Various problems arising along the planning-acting chain are illustrated to emphasize the educational point of view.

Optimization of the DRESOR method for application in a medium with large scattering albedo

The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method, one of the most effective methods to solve the radiation intensity problem with high directional resolution in radiation transfer analysis, suffers performance degradation as the medium scattering albedo becomes large. A scheme is put forward to subdivide the discrete energy beam step length, and take its infinitesimal limit to calculate the scattering/reflection fraction (DRESOR value) with high efficiency and precision. The preliminary simulation results show that when the scattering albedo is greater than 0.5, the optimized DRESOR method can greatly reduce the calculation time and improve the calculation accuracy.

The role of a distant typhoon in extending a high PM2.5 episode over Northeast Asia

In Northeast Asia, high-pressure systems typically initiate high PM2.5 episodes. However, the role of low-pressure systems, including typhoons, in high PM2.5 episodes is not well understood. In this study, we attempted to explain the evolution of the high PM2.5 episode event that was initiated by a migratory high-pressure system and the extension of the event in the presence of low-pressure systems. To achieve this aim, we conducted a multilateral analysis of a high PM2.5 episode that occurred in October 2015 in Northeast Asia using surface observation data, satellite measurements, weather maps, trajectory analyses, and three-dimensional air quality simulations. The analysis results revealed the discrete steps of the event. First, air pollutants over inland China were transported to Northern China by an anticyclone in the region. Then, in Northern China, elevated PM2.5 concentrations were observed in the following 2–3 days due to local emissions under the enhanced stagnant conditions in addition to the transported air pollution from inland China. Subsequently, under the influence of a slow-moving migratory high-pressure system in China, South Korea (a downwind area of China) experienced a high (>50 μg/m3) PM2.5 episode due to the transboundary transport of PM2.5 and local emissions. Usually, high PM2.5 episodes in South Korea under similar meteorological conditions last up to five days. However, during this period, the synoptic displacement of the high-/low pressure systems at 35°–38° latitudes in the region caused an extended (e.g., four or more days) of air pollutant residence time in Northeast Asia. Further, Typhoon Champi located in the northern Pacific (about 500 km south of Japan) interfered with the eastward movement of the high-pressure system located in the downwind area, which resulted in poor ventilation conditions for PM2.5 and its precursors. Thus, we determined that Typhoon Champi played a crucial role in maintaining PM2.5 concentrations over 50 μg/m3 for nine days or longer. We also noted that the aforementioned steps also occurred for another extended PM2.5 episode under the influence of a distant low-pressure system in the past. The findings of this study warrant further investigation of the relationship between extended PM2.5 episodes in Northeast Asia and distant typhoons.

An efficient analytical based technique to numerical calculation of extended earth return impedance and admittance of overhead lines

This paper describes an efficient numerical integration technique for the extended overhead line earth return impedance and admittance formula. In-appropriate handling of the infinite integral in the formula can lead to erroneous calculated earth-return parameters at extreme frequencies, and a significant increase in computational effort. In this paper, an efficient technique based on an analytical approach is introduced to enforce proper discretization of the extended transmission line equations. Firstly, the line equations are analyzed, and a common cause of improper discretization is identified. Then the equations are further broken down numerically, based on which a procedure to suitably select a discretization interval and step is developed. Validation was conducted by calculating the earth return parameters of overhead-line cases using the proposed method and equal distance discretization. The proposed technique shows accurate results while using fewer discretization points than equal distance discretization.

Catalyst material comprising nanoparticles

This paper describes an efficient numerical integration technique for the extended overhead line earth return impedance and admittance formula. In-appropriate handling of the infinite integral in the formula can lead to erroneous calculated earth-return parameters at extreme frequencies, and a significant increase in computational effort. In this paper, an efficient technique based on an analytical approach is introduced to enforce proper discretization of the extended transmission line equations. Firstly, the line equations are analyzed, and a common cause of improper discretization is identified. Then the equations are further broken down numerically, based on which a procedure to suitably select a discretization interval and step is developed. Validation was conducted by calculating the earth return parameters of overhead-line cases using the proposed method and equal distance discretization. The proposed technique shows accurate results while using fewer discretization points than equal distance discretization.

Numerical analysis of a bi-modal covid-19 SITR model

This study presents a structure preserving nonstandard finite difference scheme to analyze a susceptible-infected-treatment-recovered (SITR) dynamical model of coronavirus 2019 (covid-19) with bimodal virus transmission in susceptible population. The underlying model incorporates the possible treatment measures as the emerging scenario of covid-19 vaccines. Keeping in view the fact that the real time data for covid-19 is updated at discrete time steps, we propose a new structure preserving numerical scheme for the proposed model. The proposed numerical scheme produces realistic solutions of the complex bi-modal SITR nonlinear model, converges unconditionally to steady states and reflects dynamical consistency with continuous sense of the model. The analysis of the model reveals that the model remains stable at the steady state points. The basic reproduction number Rcovid falls less than 1 when treatment rate is increased and disease will die out. On the other hand, it predicts that human population may face devastating effects of pandemic if the treatment measures are not strictly implemented.

Invariability of EEG error-related potentials during continuous feedback protocols elicited by erroneous actions at predicted or unpredicted states

Objective. When humans perceive an erroneous action, an EEG error-related potential (ErrP) is elicited as a neural response. ErrPs have been largely investigated in discrete feedback protocols, where actions are executed at discrete steps, to enable seamless brain-computer interaction. However, there are only a few studies that investigate ErrPs in continuous feedback protocols. The objective of the present study is to better understand the differences between two types of ErrPs elicited during continuous feedback protocols, where errors may occur either at predicted or unpredicted states. We hypothesize that ErrPs of the unpredicted state is associated with longer latency as it requires higher cognitive workload to evaluate actions compared to the predicted states. Approach. Participants monitored the trajectory of an autonomous cursor that occasionally made erroneous actions on its way to the target in two conditions, namely, predicted or unpredicted states. After characterizing the ErrP waveform elicited by erroneous actions in the two conditions, we performed single-trial decoding of ErrPs in both synchronous (i.e. time-locked to the onset of the erroneous action) and asynchronous manner. Furthermore, we explored the possibility to transfer decoders built with data of one of the conditions to the other condition. Main results. As hypothesized, erroneous actions at unpredicted states gave rise to ErrPs with higher latency than erroneous actions at predicted states, a correlate of higher cognitive effort in the former condition. Moreover, ErrP decoders trained in a given condition successfully transferred to the other condition with a slight loss of classification performance. This was the case for synchronous as well as asynchronous ErrP decoding, showing the invariability of ErrPs across conditions. Significance. These results advance the characterization of ErrPs during continuous feedback protocols, enlarging the potential use of ErrPs during natural operation of brain-controlled devices as it is not necessary to have different decoders for each kind of erroneous conditions.

Long noncoding RNAs in cancer metastasis.

Metastasis is a major contributor to cancer-associated deaths. It is characterized by a multistep process that occurs through the acquisition of molecular and phenotypic changes enabling cancer cells from a primary tumour to disseminate and colonize at distant organ sites. Over the past decade, the discovery and characterization of long noncoding RNAs (lncRNAs) have revealed the diversity of their regulatory roles, including key contributions throughout the metastatic cascade. Here, we review how lncRNAs promote metastasis by functioning in discrete pro-metastatic steps including the epithelial-mesenchymal transition, invasion and migration and organotrophic colonization, and by influencing the metastatic tumour microenvironment, often by interacting within ribonucleoprotein complexes or directly with other nucleic acid entities. We discuss well-characterized lncRNAs with in vivo phenotypes and highlight mechanistic commonalities such as convergence with the TGFβ-ZEB1/ZEB2 axis or the nuclear factor-κB pathway, in addition to lncRNAs with controversial mechanisms and the influence of methodologies on mechanistic interpretation. Furthermore, some lncRNAs can help identify tumours with increased metastatic risk and spur novel therapeutic strategies, with several lncRNAs having shown potential as novel targets for antisense oligonucleotide therapy in animal models. In addition to well-characterized examples of lncRNAs functioning in metastasis, we discuss controversies and ongoing challenges in lncRNA biology. Finally, we present areas for future study for this rapidly evolving field.

Internal model control design based on approximation of linear discrete dynamical systems

In this paper, a new direct discrete approximation based internal model control design is proposed to the linear discrete dynamical systems. The approximation method is used to determine an accurate and stable reduced-order model for the considered original higher-order discrete-time system. The method involves an enhanced Differential Evolution algorithm to ascertain the stable denominator polynomial coefficients, and the preferable reduced numerator polynomial coefficients are evaluated by using the improved discrete multi-point Padé approximation approach. The method deploys on discrete step integral square error minimization between the original dynamical system and the approximated model, together with retaining their discrete impulse response energy values. The approximated model has been considered an internal (predictive) model and proceeds with an optimal internal model controller design to improve the discrete dynamical system behaviour according to the reference input/the set point. The controller's best performance is attained by tuning the single filter parameter ′λ′ by minimizing the integral square error between the reference input and the actual output of the dynamical system using the enhanced differential evolution algorithm. The acceptability and applicability of the proposed process reduction-based controller design have been validated on a single-input single-output supersonic jet engine inlet dynamical model. The controller robust study is conducted by inserting 10% disruption uncertainty in the system dynamical model poles and zeros. The method has also been extended to the discrete multi-input multi-output dynamical model of the single machine infinite bus power system to develop an optimal internal model control-based power system stabilizer. The simulation results showing better reference input tracking, comparison of performance indices, and also highlight the efficacy of the proposed controller design.

Scalable mmWave Non-Volatile Phase Change GeTe-Based Compact Monolithically Integrated Wideband Digital Switched Attenuator

This article reports a scalable millimeter-wave (mmWave) non-volatile switched attenuator based on phase change material (PCM) germanium telluride (GeTe). The proposed attenuator is designed using four fixed attenuation bits. The PCM GeTe-based T-type switches and two single-pole ${n}$ -throw (SP ${n}\text{T}$ ) switches are monolithically integrated with four passive bridged-T resistor networks to provide a wide attenuation range. Utilizing a T-type switch as a routing core provide scalability with low loss and offers a reduced number of switches in various signal routing paths. It also offers signal routing functionality if there is a switch failure in the T-type unit-cell. The nonvolatile PCM GeTe-based switches do not consume any static dc power. The integrated planar resistors are fabricated precisely on-wafer, and capacitive coupling is added to get wideband operation with a flat response at high frequencies. The fully integrated device is fabricated in-house using a custom eight-layer microfabrication process. The Ka -band attenuator is designed at 30 GHz center frequency with 8 GHz bandwidth. The proposed circuit is highly miniaturized, with a device core size of 0.3 mm2 only. The switched attenuator exhibits a measured attenuation from 3.9 to 28 dB at the center frequency in nine discrete steps.

Activation of Lyn kinase and translocation of its PKCδ target regulate phosphorylation in the IL-4-induced alternate pathway for BCR signaling

Abstract B cell signaling for activation via the BCR occurs as an isolated event only in vitro; in real life, BCR signaling takes place within a complex milieu that involves interactions with agents that trigger additional receptors. Chief among these agents is IL-4. We have shown that BCR signaling is reprogrammed by IL-4 receptor engagement, and that this reprogramming involves creation of a new, signalosome-independent, Lyn-dependent alternate signaling pathway out of pre-existing, otherwise noninteracting, elements. A unique aspect of alternate pathway BCR signaling is PKCδ phosphorylation. In dissecting this pathway, we unexpectedly found that IL-4 alone induces phosphorylation and activation of Lyn, and that Lyn immunoprecipitated from IL-4-treated B cells capably phosphorylates PKCδ in a cell-free system, although PKCδ phosphorylation does not occur in the absence of BCR triggering in vivo. This raised the question of why IL-4 alone failed to produce PKCδ phosphorylation. We considered the possibility that Lyn and PKCδ may be spatially separated. As expected, Lyn is located primarily in the membrane fraction, whereas PKCδ is located mainly in the cytosol fraction. However, when anti-Ig follows IL-4 treatment, PKCδ is found in the membrane fraction and phosphorylated. This translocation of PKCδ to the membrane fraction is not affected by loss of Lyn, although PKCδ is not phosphorylated without Lyn. Thus, PKCδ phosphorylation through the alternate pathway appears to consist of several discrete steps: 1.IL-4 induces Lyn phosphorylation and activation; 2. IL-4 produces a change such that PKCδ is translocated from the cytosol to the membrane after BCR engagement; 3. Activated Lyn in the membrane phosphorylates PKCδ in the membrane.

A fresh look at the dynamics of a flexible body application to substructuring for flexible multibody dynamics

AbstractThe general formulation of the dynamics of an elastic body undergoing arbitrary motion is revisited with emphasis on the orthogonality between rigid body motion and elastic deformation on the one hand, and on the appropriate definition of the relative velocities induced by elastic deformation on the other hand. A mixed displacement–velocity approach is adopted, thus allowing a local frame definition of velocities which results in simplification of the discretization and solution steps. The proposed formulation is applied to model reduction starting from a set of free‐free elastic modes and attachment modes. The Herting–Martinez component mode synthesis method is used to replace the modal intensities by a body‐frame nodal set of elastic degrees of freedom. A body‐to‐global frame transformation is then applied to the system equations in incremental form to avoid the use of Lagrange multipliers for expressing node‐to‐node connections. Examples are presented to assess the methodology proposed and its numerical implementation.

Optimizing the cellular automata finite element model for additive manufacturing to simulate large microstructures

This study proposes an implementation of the cellular automata finite element (CAFE) model in order to optimize its performance for simulating the solidification of additively manufactured (AM) materials. The translating melt pool in AM leads to a highly localized region of activity at any given time. The time scale associated with the evolving temperature field is much larger than the time scale associated with grain solidification. A separation of temporal scales is proposed such that solidification analysis is treated independently as sub-cycles within each discrete time step of the scanning laser. At each laser time step, all of the domain is idle except a small portion, which is the region where the material is undercooled but has yet to be solidified. This region is identified, and a second partition of the computational resources is established such that the solidification computations are evenly balanced. Numerical studies demonstrate that the proposed implementation achieves dramatic improvement in parallel scalability than previously reported and thus advances the state-of-the-art of CAFE modeling for AM in terms of computational efficiency. This improved computational performance is necessary to simulate the large 3D polycrystalline microstructures required to evaluate texture and grain morphology, and two of such simulations are presented. The model is validated for laser powder bed fusion 316L stainless steel, where the polycrystalline grain morphology and crystallographic texture of the simulated microstructure closely match experimental characterization data. A second simulation is performed for a different scan pattern in order to highlight and evaluate its effect on microstructural features.

Thermoresponsive glycopolymer vesicles: in situ observation of morphological changes and triggered cargo release

Thermoresponsive polymer vesicles are promising drug-delivery carriers because of their ability to release cargo in a controlled manner. However, the process of thermoresponsive vesicle disassembly has attracted only limited attention to date, and the details remain elusive. Herein, we report using small-angle X-ray scattering and confocal laser scanning microscopy for in situ observation of the disassembly process during the cooling of thermoresponsive maltopentaose-b-poly(propylene oxide) polymer vesicle solutions. Notably, vesicle collapse mainly involves three discrete steps, not a concerted process. We also demonstrate that protein-loaded vesicles can be triggered to release their cargo upon cooling and that released protein retains its enzymatic activity. This study can thus provide a basis for generating guidelines for using thermoresponsive polymer vesicles in the triggered release of cargo and facilitating the development of new thermoresponsive materials based on poly(propylene oxide). The real-time structural changes of thermoresponsive polymer vesicles upon cooling were investigated by small-angle X-ray scattering and confocal laser scanning microscopy. The disassembly process of the vesicles consists of multiple steps: 1) pore formation, 2) opening and shrinkage of the membrane, and 3) dissolving in the solvent. We also demonstrated that the vesicles can be used as compartments for the controlled release of proteins. This study provides the basis for the mechanism of the disassembly process of thermoresponsive vesicles and a guideline for their use as controlled-release medical devices.

Single-Phase Symmetric-Bipolar-Type High-Frequency Isolated Buck-Boost AC–AC Converter With Continuous Input and Output Currents

A single-phase symmetric-bipolar-type high-frequency isolated buck-boost ac–ac (SBT-HFI-BBAC) converter is proposed. The converter is composed of two full-bridge inverter modules, input/output <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filters, and a high-frequency transformer (HFT) with series capacitors. It can provide identical noninverting and inverting buck-boost output voltages with symmetric-bipolar voltage gains of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \pm D/({1 - D})$</tex-math></inline-formula> . The frequency of the output voltage can also be adjusted in discrete steps, similar to single-phase matrix converters (MCs). It supplies continuous input and output currents and works well with nonunity power factor loads. The magnetizing current of the HFT has no line frequency component due to the presence of the series blocking capacitors. Moreover, due to the absence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</i> switches, the converter has a simple commutation process, unlike conventional ac-ac/MCs. Two switching strategies are proposed; Strategy-I with fewer high-frequency switches and Strategy-II with reduced switch currents, providing more flexibility in switch power loss optimization. The proposed SBT-HFI-BBAC converter is well suited for application as a dynamic voltage restorer, compensating a wide range of grid voltage sags and swells, without the need for a low-frequency voltage injection transformer. Its step-changed frequency operation can also find use in various applications, such as high-gain ac–dc converters, traction systems, etc. A comprehensive description of circuit operation is presented along with component design guidelines and appropriate comparisons. Experimental verification results are provided using a 400-W laboratory test circuit.

State-space based discretize-then-differentiate adjoint sensitivity method for transient responses of non-viscously damped systems

In this paper, a new design sensitivity analysis (DSA) method for transient responses of non-viscously damped systems is developed. The damping force of the non-viscously damped systems depends on the past history of motion and is represented by convolution integrals over suitable kernel functions. The equations of motion are first transformed into a state-space formulation and the time-history analysis of the responses relies on a modified precise integration method (MPIM). The residual equation in each discrete time step is achieved by a recurrence formula of the MPIM. The sensitivities of the transient responses are calculated with an adjoint variable method (AVM). In particular, a discretize-then-differentiate approach is adopted for the DSA. The accuracy, consistency, implementation effort and computational complexity are discussed. Two numerical examples are illustrated to show the performances of the proposed method compared with other two methods. The results indicate that, when calculating the sensitivities of the transient responses for non-viscously damped systems based on the MPIM, the order of differentiation and discretization has no obvious effect on the consistency. The proposed state-space based discretize-then-differentiate AVM is more efficient than other two methods.