Initial Region Research Articles

The Evolutionary Dynamics of Soft-Max Policy Gradient in Multi-Agent Settings

Policy gradient is one of the most famous algorithms in reinforcement learning. This paper studies the mean dynamics of the soft-max policy gradient algorithm and its properties in multi-agent settings by resorting to evolutionary game theory and dynamical system tools. Unlike most multi-agent reinforcement learning algorithms, whose mean dynamics are a slight variant of the replicator dynamics not affecting the properties of the original dynamics, the soft-max policy gradient dynamics presents a structure significantly different from that of the replicator. In particular, we show that the soft-max policy gradient dynamics in a given game are equivalent to the replicator dynamics in an auxiliary game obtained by a non-convex transformation of the payoffs of the original game. Such a structure gives the dynamics several non-standard properties. The first property we study concerns the convergence to the best response. In particular, while the continuous-time mean dynamics always converge to the best response, the crucial question concerns the convergence speed. Precisely, we show that the space of initializations can be split into two complementary sets such that the trajectories initialized from points of the first set (said good initialization region) directly move to the best response. In contrast, those initialized from points of the second set (said bad initialization region) move first to a series of sub-optimal strategies and then to the best response. Interestingly, in multi-agent adversarial machine learning environments, we show that an adversary can exploit this property to make any current strategy of the learning agent using the soft-max policy gradient fall inside a bad initialization region, thus slowing its learning process and exploiting that policy. When the soft-max policy gradient dynamics is studied in multi-population games, modeling the learning dynamics in self-play, we show that the dynamics preserve the volume of the set of initial points. This property proves that the dynamics cannot converge when the only equilibrium of the game is fully mixed, as the volume of the set of initial points would need to shrink. We also give empirical evidence that the volume expands over time, suggesting that the dynamics in games with fully-mixed equilibrium is chaotic.

A Preliminary Assessment of Land Restoration Progress in the Great Green Wall Initiative Region Using Satellite Remote Sensing Measurements

A Preliminary Assessment of Land Restoration Progress in the Great Green Wall Initiative Region Using Satellite Remote Sensing Measurements

Effect of Precipitation-Free Zone on Fatigue Properties in Al-7.02Mg-1.98Zn Alloys: Crystal Plasticity Finite Element Analysis.

Age-strengthened aluminum alloys, as important lightweight structural materials, have significantly lower fatigue properties compared to non-age-strengthened aluminum alloys. In this study, the polycrystalline models containing precipitation-free zones (PFZ) were constructed by secondary development of the traditional polycrystalline model by modifying the mesh file. Polycrystalline finite element simulations of peak age-treated Al-7.02Mg-1.98Zn alloys were carried out with this model. The results demonstrate that the PFZ's presence markedly reduces the alloy's yield strength and a substantial stress concentration occurs adjacent to the PFZ, generating significant compressive stresses at the PFZ. Under cyclic loading, the maximum strain energy dissipation in the model containing the PFZ far exceeds that observed in the conventional polycrystalline model, and the strain energy dissipation observed in the PFZ is significantly higher than that at other locations. This indicates that the PFZ is the main region for fatigue crack initiation. In addition, the introduction of a rotation factor to simulate the inhomogeneous rotation within the grain reveals that the additional stress concentration in the PFZ introduced by the aluminum alloy-forming process further increases the fatigue crack initiation driving force.

Analysis of underwater radiated noise from ships using distributed acoustic sensing technology

Distributed Acoustic Sensing (DAS) technology enables continuous monitoring of acoustic vibrations along fiber optic cables, providing high-resolution spatial and temporal data. This study explores the application of DAS technology for analyzing underwater radiated noise from ships. In November 2021, four days of DAS data were collected using two cables from the Ocean Observatories Initiative Regional Cabled Array, extending offshore central Oregon. Numerous ship passages occurred over these cables, with information available through the Automatic Identification System (AIS). DAS data were collected using two different interrogators on two fibers in each cable, providing an opportunity to investigate the differences in ship noise detected on different fibers within the same cable and across different DAS systems with varying configurations. Preliminary analysis of two large ships shows that their noise is clearly detected in the DAS measurements. By combining these measurements with AIS data, we can accurately locate the receiving channels on the cable. This talk will expand on these observations to perform a comparative analysis of the measurements across different fibers and interrogators. These findings demonstrate the capability of DAS technology in maritime acoustic monitoring and its potential to enhance our understanding of underwater noise pollution.

Quantifying future carbon emissions uncertainties under stochastic modeling and Monte Carlo simulation: Insights for environmental policy consideration for the Belt and Road Initiative Region

This study critically examines future carbon (CO2) emissions in the Belt & Road Initiative (BRI) region, considering factors such as energy consumption, economic growth, population growth, and population density. The objective of this study is to identify critical areas of higher emissions, which require policy intervention capable of strengthening sustainability in the BRI compact. A combined approach of stochastic modeling and Monte Carlo simulations was employed, utilizing panel data from 45 countries in the BRI region from 1990 to 2021. Results confirm that emissions are higher in all scenarios in direct proportion to electric power consumption, population growth, and Gross Domestic Product (GDP) growth. In scenarios with high emissions, a continuous and significant upward trend in CO2 emissions was observe. The medium emissions scenario exhibited a more moderated rise in emissions, suggesting a balance between economic development and environmental considerations. Critical areas for future environmental policy-making resides in electric power consumption, population growth, and GDP growth. The study strongly recommends for a shift from the current focus on road and railway infrastructure to renewable energy infrastructure, green innovations and efficient technology transfer to member countries. Without this, the BRI region is likely to face increased emissions, posing significant challenges to future sustainable development and global environmental sustainability.

Trade-offs and synergies pattern evolution of ecosystem structure-resilience-activity-services (SRAS) in the Belt and Road Initiative region

This study develops an analytical framework comprising “ecosystem pattern – trade-off and synergy process – multidimensional response mechanism – future risk management” to investigate the evolution of trade-off and synergy patterns of SRAS performance and its sustainability among BRI nations and 80 representative cities. The synergistic levels of SRAS in BRI countries declined, but will increase in the future, the increased trend of BRI cities will transfer to decline in the future. The interaction of multi-dimensional human urban activities could achieve a stronger impact on SRAS performance synergies of BRI countries and cities, and the PD-LU and PD-ED were the dominant interaction influence chains, respectively. This study was the first one to holistically reveal the evolution of trade-off and synergy patterns of SRAS performances, at both nation and city levels, in the BRI region. It also contributes new perspectives from the BRI region to the sustainable urban planning, terrestrial ecosystems conservation, and urban ecological governance programs.

Bulk synthesis and beyond: The roles of eukaryotic replicative DNA polymerases

An organism’s genomic DNA must be accurately duplicated during each cell cycle. DNA synthesis is catalysed by DNA polymerase enzymes, which extend nucleotide polymers in a 5′ to 3′ direction. This inherent directionality necessitates that one strand is synthesised forwards (leading), while the other is synthesised backwards discontinuously (lagging) to couple synthesis to the unwinding of duplex DNA. Eukaryotic cells possess many diverse polymerases that coordinate to replicate DNA, with the three main replicative polymerases being Pol α, Pol δ and Pol ε. Studies conducted in yeasts and human cells utilising mutant polymerases that incorporate molecular signatures into nascent DNA implicate Pol ε in leading strand synthesis and Pol α and Pol δ in lagging strand replication. Recent structural insights have revealed how the spatial organization of these enzymes around the core helicase facilitates their strand-specific roles. However, various challenging situations during replication require flexibility in the usage of these enzymes, such as during replication initiation or encounters with replication-blocking adducts. This review summarises the roles of the replicative polymerases in bulk DNA replication and explores their flexible and dynamic deployment to complete genome replication. We also examine how polymerase usage patterns can inform our understanding of global replication dynamics by revealing replication fork directionality to identify regions of replication initiation and termination.

Consensus control and initialization region optimization for leader‐following multi‐agent systems under time‐varying communication delay and consecutive packet dropouts

AbstractThis article is to investigate the consensus control and initialization region optimization for leader‐following multi‐agent systems with time‐varying communication delay and nonidentical consecutive packet dropouts. By combining the Bernoulli distribution model of the data loss and the Hadamard product, the control protocols affected by both communication delay and packet dropouts are utilized to formulate the consensus problem into the mean‐square stability problem of the augmented error systems. Resorting to the Lyapunov function methodology and a structure separation method, a sufficient condition to ensure the consensus is built in the form of linear matrix inequality. Relying on the given Lyapunov function and set‐membership analysis, an optimization procedure is proposed to simultaneously ensure the consensus and enlarge the estimated ellipsoid of initial conditions. The validity of the provided method is illustrated through a comparative simulation.

Volumetric Image Analysis Of Pulsed Non-Thermal Plasma Produced By Microwave

We have been developing microwave pulsed mode ignition system using 2.45 GHz microwaves. This technology has shown improvements in the lean combustion limit and fuel efficiency using a real engine with propane using a microwave discharged igniter (MDI). However, the MDI’s expensive parts are a major drawback when compared to common igniters. For practicality, we shifted to a more economical flat spiral igniter to generate plasma enabling stable and sustained non-equilibrium plasma in the atmosphere. Incorporating semiconductor elements, we miniaturized the microwave generator system, enhancing compactness and increasing its efficiency. Initial plasma was generated by the partial energy from the microwaves (1 mJ) and the sustained plasma was maintained in the atmosphere by the rest of the microwave’s energy. We varied long to short-pulsed modes, changed microwave pulse widths, increasing repetition rates which affecting plasma volume and stability. Our findings highlight the significance of microwave input patterns and the transition from thermal to non-equilibrium plasma. Future discussions should focus on the ignition mechanisms of various fuels and the transition from plasma source to initialization region. Our work contributes to the understanding and practical application of non-thermal plasma in combustion systems.

Liner shipping connectivity: A dynamic link between energy trade, green exchange and inclusive growth using advanced econometric modelling

The ocean economy is crucial in facilitating green exchanges and promoting inclusive growth. Despite its significance, this domain needs more investigation, leading to diverse findings in existing literature. This study empirically examines the links between energy trade, green exchanges, and inclusive growth within the context of the ocean economy in the Belt and Road Initiative (BRI) region. Using the Liner Shipping Connectivity Index as a proxy for ocean economy and debt-for-nature swaps as a proxy for green exchanges, we employ an advanced Two-Step System of GMM econometric modelling. Data from 23 BRI member countries, sourced from WDI (World Bank), OECD Statistics, and UNCTAD Statistics, covering the period from 2004 to 2022, form the basis of our analysis. Our findings confirm a long-run dynamic relationship between the ocean economy, energy trade, green exchanges, and inclusive growth. The results indicate that the ocean economy and debt-for-nature swap financing contribute to economic growth. However, results show a weak marine structural development because the results are not highly significant. To address this, we propose comprehensive policy measures to strengthen structural development to enhance inclusive economic growth. Our study highlights the need for strategic policies that balance economic benefits with sustainability goals, leveraging technological advancements and promoting equitable growth.

2D unified atmosphere and wind simulations of O-type stars

Context. Massive and luminous O-type star (O star) atmospheres with winds have been studied primarily using one-dimensional (1D), spherically symmetric, and stationary models. However, observations and theory have suggested that O star atmospheres are highly structured, turbulent, and time-dependent. As such, when making comparisons to observations, present-day 1D modeling tools require the introduction of ad hoc quantities such as photospheric macro- and microturbulence, wind clumping, and other relevant properties. Aims. We present a series of multi-dimensional, time-dependent, radiation-hydrodynamical (RHD) simulations for O stars that encapsulate the deeper sub-surface envelope (down to T ~ 450 kK), as well as the supersonic line-driven wind outflow in one unified approach. Our overarching aim is to develop a framework that is free from the ad-hoc prescriptions that plague present-day 1D models. Here, we start with an analysis of a small set of such multi-dimensional simulations and then compare them to atmospheric structures predicted by their 1D counterparts. Methods. We performed time-dependent, two-dimensional (2D) simulations of O star atmospheres with winds using a flux-limiting RHD finite volume modelling technique. Opacities are computed using a hybrid approach combining tabulated Rosseland means with calculations (based on the Sobolev approximation) of the enhanced line opacities expected for supersonic flows. The initial conditions and comparison models were derived using similar procedures as those applied in standard 1D stationary model atmosphere with wind codes. Results. Structure starts appearing in our simulations just below the iron-opacity peak at ~200 kK. Local pockets of gas with radiative accelerations that exceed gravity then shoot up from these deep layers into the upper atmosphere, where they interact with the line-driven wind outflow initiated around or beyond the variable photosphere. This complex interplay creates large turbulent velocities in the photospheric layers of our simulations, on the order of ~30–100km s−1, with higher values for models with higher luminosity-to-mass ratios. This offers a generally good agreement with observations of large photospheric ‘macroturbulence’ in O stars. When compared to 1D models, the average structures in the 2D simulations display less envelope expansion and no sharp density-inversions, along with density and temperature profiles that are significantly less steep around the photosphere, and a strong anti-correlation between velocity and density in the supersonic wind. Although the wind initiation region is complex and highly variable in our simulations, our average mass-loss rates agree well with stationary wind models computed by means of full co-moving frame radiative transfer solutions. Conclusions. The different atmospheric structures found in 2D and 1D simulations are likely to affect the spectroscopic determination of fundamental stellar and wind parameters for O stars as well as the empirical derivation of their chemical abundance patterns. To qualitatively match the different density and temperature profiles seen in our multi-dimensional and 1D models, we need to add a modest amount of convective energy transport in the deep sub-surface layers and a large turbulent pressure around the photosphere to the 1D models.

The regulation of methylation on the Z chromosome and the identification of multiple novel Male Hyper-Methylated regions in the chicken.

DNA methylation is a key regulator of eukaryote genomes, and is of particular relevance in the regulation of gene expression on the sex chromosomes, with a key role in dosage compensation in mammalian XY systems. In the case of birds, dosage compensation is largely absent, with it being restricted to two small Male Hyper-Methylated (MHM) regions on the Z chromosome. To investigate how variation in DNA methylation is regulated on the Z chromosome we utilised a wild x domestic advanced intercross in the chicken, with both hypothalamic methylomes and transcriptomes assayed in 124 individuals. The relatively large numbers of individuals allowed us to identify additional genomic MHM regions on the Z chromosome that were significantly differentially methylated between the sexes. These regions appear to down-regulate local gene expression in males, but not remove it entirely (unlike the lncRNAs identified in the initial MHM regions). These MHM regions were further tested and the most balanced genes appear to show decreased expression in males, whilst methylation appeared to be far more correlated with gene expression in the less balanced, as compared to the most balanced genes. In addition, quantitative trait loci (QTL) that regulate variation in methylation on the Z chromosome, and those loci that regulate methylation on the autosomes that derive from the Z chromosome were mapped. Trans-effect hotspots were also identified that were based on the autosomes but affected the Z, and also one that was based on the Z chromosome but that affected both autosomal and sex chromosome DNA methylation regulation. We show that both cis and trans loci that originate from the Z chromosome never exhibit an interaction with sex, whereas trans loci originating from the autosomes but affecting the Z chromosome always display such an interaction. Our results highlight how additional MHM regions are actually present on the Z chromosome, and they appear to have smaller-scale effects on gene expression in males. Quantitative variation in methylation is also regulated both from the autosomes to the Z chromosome, and from the Z chromosome to the autosomes.

Unraveling the Dual-Stretch-Mode Impact on Tension Gauge Tethers' Mechanical Stability.

Tension gauge tethers (TGTs), short DNA segments serving as extracellular tension sensors, are instrumental in assessing the tension dynamics in mechanotransduction. These TGTs feature an initial shear-stretch region and an unzip-stretch region. Despite their utility, no theoretical model has been available to estimate their tension-dependent lifetimes [τ(f)], restricting insights from cellular mechanotransduction experiments. We have now formulated a concise expression for τ(f) of TGTs, accommodating contributions from both stretch regions. Our model uncovers a tension-dependent energy barrier shift occurring when tension surpasses a switching force of approximately 13 pN for the recently developed TGTs, greatly influencing τ(f) profiles. Experimental data from several TGTs validated our model. The calibrated expression can predict τ(f) of TGTs at 37 °C based on their sequences with minor fold changes, supporting future applications of TGTs.

Automated detection of fin whale calls recorded with distributed acoustic sensing

As the global biodiversity crisis intensifies, wildlife monitoring has become a necessity. From an oceanographic perspective, the tracking of baleen whales allows studies of their habitat use and can support call density estimates, which are indicative of ocean health. Distributed Acoustic Sensing (DAS) is a promising observational technique that measures strain rates along a spare optical fiber with a spatial resolution of tens of meters to distances of ∼100 km. Over 4-days in November 2021, a public domain DAS dataset was collected on the submarine cables of the Ocean Observatories Initiative Regional Cabled Array off the coast of central Oregon. The experiment recorded the acoustic signals from tens of thousands of fin whale calls as well as blue whale calls, ship signals and T-phases. We will describe preliminary efforts to develop automated methods to detect and localize fin whale calls using small representative examples of the DAS data. Our longer-term goal is to extend this approach to the full data set to understand the sensitivity of DAS to fin whale calls as function of cable geometry and seafloor characteristics and to study the distribution of calling fin whales in coastal waters off central Oregon. [Work supported by ONR.]

Behavioral and Neurophysiological Implications of Pathological Human Tau Expression in Serotonin Neurons.

Alzheimer's disease (AD) is a progressive degenerative disorder that results in a severe loss of brain cells and irreversible cognitive decline. Memory problems are the most recognized symptoms of AD. However, approximately 90% of patients diagnosed with AD suffer from behavioral symptoms, including mood changes and social impairment years before cognitive dysfunction. Recent evidence indicates that the dorsal raphe nucleus (DRN) is among the initial regions that show tau pathology, which is a hallmark feature of AD. The DRN harbors serotonin (5-HT) neurons, which are critically involved in mood, social, and cognitive regulation. Serotonergic impairment early in the disease process may contribute to behavioral symptoms in AD. However, the mechanisms underlying vulnerability and contribution of the 5-HT system to AD progression remain unknown. Here, we performed behavioral and electrophysiological characterizations in mice expressing a phosphorylation-prone form of human tau (hTauP301L) in 5-HT neurons. We found that pathological tau expression in 5-HT neurons induces anxiety-like behavior and alterations in stress-coping strategies in female and male mice. Female mice also exhibited social disinhibition and mild cognitive impairment in response to 5-HT neuron-specific hTauP301L expression. Behavioral alterations were accompanied by disrupted 5-HT neuron physiology in female and male hTauP301L expressing mice with exacerbated excitability disruption in females only. These data provide mechanistic insights into the brain systems and symptoms impaired early in AD progression, which is critical for disease intervention.

Low-cycle fatigue behaviour of extruded 7075 aluminium alloy bar: Competition of grain sizes and textures

The low-cycle fatigue (LCF) behaviour of a large 7075 aluminium alloy bar was investigated, and the results indicated that the microstructure at the center (0R) and surface section of the bar (R) were different in terms of grain sizes and textures. The microstructure of the 0R specimen was characterised by coarser elongated grain and higher <111> texture intensity compared to that of the R specimen. The LCF life of the 0R specimen was higher than that of the R specimen at a strain amplitude range of 0.6%–0.9%, thereby indicating the dominant effect of higher texture intensity. However, the 0R specimen sustained short LCF life at low strain amplitudes of 0.4% and 0.5%, indicating the predominant effect of grain refinement. The fracture analysis results indicated that there were wider striations for the 0R specimen at a strain amplitude of 0.4%. Interestingly, the yield strength, ultimate tensile strength and elongation of the 0R specimen were higher than that of the R specimen. The higher mechanical properties of the 0R specimen was consistent with its longer low cycle fatigue life at strain amplitude range of 0.6%–0.9%. Moreover, the features of the fracture, including fracture initiation and fast fracture regions, were also elaborated. The competition of grain sizes and texture evolutions determined the LCF life of the alloy depending on the strain amplitude range: the grain size effect gradually overshadowed that of the texture with decreasing strain in terms of fatigue life.

The Effectiveness of the Regional Regulation Formation Agency in Producing Initiative Regional Regulations

This research aims to analyze the effectiveness of the Regional Regulation Formation Agency in Producing Initiative Regional Regulations in the DPRD of North Sulawesi. This research uses the theory of Richard M. Steers with measures of effectiveness, namely goal achievement, integration and adaptation. This research used a qualitative descriptive method with 4 informants consisting of the deputy chairman of the DPRD of North Sulawesi, the chairman of BAPEMPERDA (Regional Regulation Establishment Agency), members of BAPEMPERDA, and BAPEMPERDA staff. The results of this research show that the performance of BAPEMPERDA is still not optimal, seen from the lack of effectiveness in making regional regulations, to the point that they do not reach directly to the community. Based on research findings, several things that need to be suggested to the DPRD (Regional People's Representative Council), especially BAPEMPERDA North Sulawesi, are the need for commitment from DPRD members so that a regional regulation can be effective, not only in terms of quality, but can be felt by the constituents, namely the community.

Effects of pulse repetition frequency on bubble cloud characteristics and ablation in single-cycle histotripsy

Objective. Histotripsy is a cavitation-based ultrasound ablation method in development for multiple clinical applications. This work investigates the effects of pulse repetition frequency (PRF) on bubble cloud characteristics and ablative capabilities for histotripsy using single-cycle pulsing methods. Approach. Bubble clouds produced by a 500 kHz histotripsy system at PRFs from 0.1 to 1000 Hz were visualized using high-speed optical imaging in 1% agarose tissue phantoms at peak negative pressures, p-, of 2–36 MPa. Main results. Results showed a decrease in the cavitation cloud threshold with increasing PRF, ranging from 26.7 ± 0.5 MPa at 0.1 Hz to 15.0 ± 1.9 MPa at 1000 Hz. Bubble cloud analysis showed cavitation clouds generated at low PRFs (0.1–1 Hz) were characterized by consistently dense bubble clouds (41.7 ± 2.8 bubbles mm−2 at 0.1 Hz), that closely matched regions of the focus above the histotripsy intrinsic threshold. Bubble clouds formed at higher PRFs measured lower cloud densities (23.1 ± 4.0 bubbles mm−2 at 1000 Hz), with the lowest density measured for 10 Hz (8.8 ± 4.1 bubbles mm−2). Furthermore, higher PRFs showed increased pulse-to-pulse correlation, characteristic of cavitation memory effects; however, bubble clouds still filled the entire volume of the focus due to their initial density and enhanced bubble expansion from the restimulation of residual nuclei at the higher PRFs. Histotripsy ablation assessed through lesion analysis in red blood cell (RBC) phantoms showed higher PRFs generated lesions with lower adherence to the initial focal region compared to low PRF ablations; however, no trend of decreasing ablation efficiency with PRF was observed, with similar efficiencies observed for all the PRFs tested in this study. Significance. Notably, this result is different than what has previously been shown for shock-scattering histotripsy, which has shown decreased ablation efficiencies at higher PRFs. Overall, this study demonstrates the essential effects of PRF on single-cycle histotripsy procedures that should be considered to help guide future histotripsy pulsing strategies.

Influence of the mRNA initial region on protein production: a case study using recombinant detoxified pneumolysin as a model.

Recombinant proteins are of great importance in modern society, mostly as biopharmaceutical products. However, challenging and complex processes with low production yield are major drawbacks. Normally, the optimization to overcome these obstacles is focused on bioreactor and purification processes, and the biomolecular aspects are neglected, seen as less important. In this work, we present how the 5' mRNA secondary structure region can be relevant for translation and, therefore, protein production. For this, Escherichia coli BL21(DE3) clones, producing recombinant detoxified pneumolysin (PdT) with and without the N-terminal His-tag, were cultivated in 10-L bioreactors. Another version of the pdt gene (version 2) with synonymous changes in the 5'-end nucleotide sequence was also obtained. Protein production, plasmid stability, carbon sources, and acetic acid were quantified during the cultures. Furthermore, in silico mRNA analyses were performed using TIsigner and RNAfold. The results showed that the His-tag presence at the N-terminus generated a minimum 1.5-fold increase in target protein synthesis, which was explained by the in silico mRNA analyses that returned an mRNA secondary structure easier to translate and, therefore, higher protein production than without the His-tag. The pdt gene version 2 showed lower 5' mRNA opening energy than version 1, allowing higher PdT production even without a tag. This work reveals that simple mRNA analyses during heterologous gene design and production steps can help reach high-recombinant protein titers in a shorter time than using only traditional bioprocess optimization strategies.

Defense against smart invaders with swarms of sweeping agents

The goal of this research is to devise guaranteed defense policies that allow to protect a given region from the entrance of smart mobile invaders by detecting them using a team of defending agents equipped with identical line sensors. By designing cooperative defense strategies that ensure all invaders are detected, conditions on the defenders’ speed are derived. Successful accomplishment of the defense task implies invaders with a known limit on their speed cannot slip past the defenders and enter the guarded region undetected. The desired outcome of the defense protocols is to defend the area and additionally to expand it as much as possible. Expansion becomes possible if the defenders’ speed exceeds a critical speed that is necessary to only defend the initial region. We present results on the total search time, critical speeds and maximal expansion possible for two types of novel pincer-movement defense processes, circular and spiral, for any even number of defenders. The proposed spiral process allows to detect invaders at nearly the lowest theoretically optimal speed, and if this speed is exceeded, it also allows to expand the protected region almost to the maximal area.