Repeat Step Research Articles

Visuomotor control of step descent: evidence of specialised role of the lower visual field

We often complete step downs in the absence of visual feedback of the lower-limbs, and/or of the area on the ground where we intend to land (e.g. when descending a step whilst carrying a laundry basket). Therefore, the present study examined whether information from lower visual field (lvf) provides any advantage to the control of step descent. Ten healthy subjects (age 24.4 +/- 9.4 years) completed repeated step downs over three-step heights with visual information available from either full or upper visual fields (lvf occluded), and for specific intervals relative to step initiation. Visuomotor control of step descent was assessed by determining pre-landing kinematic measures and landing mechanic variables for the initial landing period. Findings indicate that whilst there were only limited effects on pre-landing kinematic measures under lvf occlusion, individual's ability to plan/control landing mechanics was significantly different in such conditions compared to when they had access to full field vision. These changes were consistent with participants being uncertain regarding precise floor height when access to lvf was restricted, and consequently led them to adapt their landing behaviour but without fundamentally altering their stepping strategy. Compared to when vision was available throughout, the occlusion of vision (full or upper visual field) from toe-off or mid-swing onwards caused very few differences in landing behaviour. This suggests that the contribution of information from lvf to the control of landing behaviour occurs predominantly prior to or during movement initiation and that 'online' vision is used only in the latter portion of the descent phase to subtly 'fine tune' landings.

A Fast Method for Linear Waves Based on Geometrical Optics

We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the wave speed, with amplitude that is slowly changing depending on the medium coefficients, under the assumption that the medium coefficients vary slowly compared to the wavelength. Based on this we construct a method of optimal, $O(N)$ complexity, with basically the following steps: 1. decouple the wavefield into an approximately forward and an approximately backward propagating part; 2. propagate each component explicitly along the characteristics over a time step that is small compared to the medium scale but can be large compared to the wavelength; 3. apply a correction to account for the errors in the explicit propagation; repeat steps 2 and 3 over the necessary amount of time steps; and 4. reconstruct the full field by adding forward and backward propagating components again. Due to step 3 the method accurately computes the full wavefield. A variant of the method was implemented and outperformed a standard order (4,4) finite difference method by a substantial factor. The general principle is applicable also in higher dimensions, but requires efficient implementations of Fourier integral operators which are still the subject of current research.

Medium- and short-chain dehydrogenase/reductase gene and protein families

Medium- and short-chain dehydrogenase/reductase gene and protein families

Step-size Analyses of the Mitochondrial Hsp70 Import Motor Reveal the Brownian Ratchet in Operation

Newly synthesized mitochondrial precursor proteins have to become unfolded by the mitochondrial Hsp70 (mtHsp70) import motor to cross the mitochondrial membranes. To assess the mechanism of unfolding of precursor proteins by mtHsp70, we designed a system to measure step sizes of the mtHsp70 import motor, which are distances at which the motor system moves along polypeptide chains during a single turnover of ATP. We made a series of fusion proteins consisting of a mitochondrial presequence containing the first mtHsp70 binding site, a spacer sequence containing an Hsp70 avoidance segment followed by the second mtHsp70 binding site, and different folded mature domains. Analyses of the dependence of the import rates of those fusion proteins on the lengths of Hsp70 avoidance segments allowed us to estimate the step sizes, which differ for different mature domains and different lengths of the spacers. These results suggest that the mtHsp70 import motor functions at least as a molecular Brownian ratchet to unfold mitochondrial precursor proteins.

Controllable Formation of Nanoscale Patterns on TiO2 by Conductive-AFM Nanolithography

We report on the nanopatterning of double-bond-terminated silane (5-hexenyltrichlorosilane, HTCS) molecules on titania (TiO2) using conductive atomic force microscopy (AFM). The influences of tip electrostatic potential and scanning velocity, relative humidity and of the repeated application of voltage on the topographic height, width, and hydrophilic and hydrophobic contrast of the resultant patterns were investigated. Tip voltage and tip velocity ( v) were applied between -10 V <or= V tip <or= +10 V and 100 nm/s <or= v <or= 2 microm/s during the lithography step(s), respectively. Average height and Lateral Force Mode (LFM) images of patterns were obtained with different values of (-10 V <or= V tip <or= -7 V) and v (100 nm/s <or= v <or= 2 microm/s). The average height of the patterns is seen to decrease for increasing v and decreasing V tip in both a single or repeated lithography step. No patterns were observed following a single or repeated lithography step for -5 V <or= V tip <or= +10 V. This conductive lithography technique results in nanoscale physiochemical manipulations of the HTCS molecules that are manifested as controllable step heights ranging from approximately 1-15 nm possessing different chemistries on the patterned and unpatterned areas. The use of conductive-AFM nanolithography for altering and manipulating double-bond-terminated molecules on TiO2 surfaces suggests a range of applications, including selective immobilization and assembly of functionalized inorganic nanoparticles and biomolecules.

Motor step size and ATP coupling efficiency of the dsDNA translocase EcoR124I

The Type I restriction-modification enzyme EcoR124I is an archetypical helicase-based dsDNA translocase that moves unidirectionally along the 3′–5′ strand of intact duplex DNA. Using a combination of ensemble and single-molecule measurements, we provide estimates of two physicochemical constants that are fundamental to a full description of motor protein activity—the ATP coupling efficiency (the number of ATP consumed per base pair) and the step size (the number of base pairs transported per motor step). Our data indicate that EcoR124I makes small steps along the DNA of 1 bp in length with 1 ATP consumed per step, but with some uncoupling of the ATPase and translocase cycles occurring so that the average number of ATP consumed per base pair slightly exceeds unity. Our observations form a framework for understanding energy coupling in a great many other motors that translocate along dsDNA rather than ssDNA.

An experimental data set for benchmarking 1-D, transient heat and moisture transfer models of hygroscopic building materials. Part II: Experimental, numerical and analytical data

This paper presents the experimental results on spruce plywood and cellulose insulation using the transient moisture transfer (TMT) facility presented in Part I [P. Talukdar, S.O. Olutmayin, O.F. Osanyintola, C.J. Simonson, An experimental data set for benchmarking 1-D, transient heat and moisture transfer models of hygroscopic building materials-Part-I: experimental facility and property data, Int. J. Heat Mass Transfer, in press, doi:10.1016/j.ijheatmasstransfer.2007.03.026] of this paper. The temperature, relative humidity and moisture accumulation distributions within both materials are presented following different and repeated step changes in air humidity and different airflow Reynolds numbers above the materials. The experimental data are compared with numerical data, numerical sensitivity studies and analytical solutions to increase the confidence in the experimental data set.

SU-FF-T-332: Optimizing Leaf Width for Multileaf Collimator

Purpose: The multileaf collimator(MLC) has been a standard device for shaping radiation fields. However, the shaped field has stepwise boundary, and can not exactly conform to a treatment target. That means there is always under‐blocked and (or) over‐blocked areas. The total area discrepancy depends on MLC leaf width. The purpose of this study is to minimize the total area discrepancy through optimizing the width of each individual leaf under the assumption that the total number of leaves and the total width of all leaves remain the same. Method and Materials: A program was developed to realize the optimization algorithm. Its flow is like this: a). read data of target shapes; b). initialize leaf widths; c). calculate the total area discrepancy; d). randomly change leaf widths and judge whether to accept the change with simulating annealing technique; e). repeat step d till the iteration process is converged. The algorithm performance was preliminarily evaluated. 113 targets from different treatment sites were randomly selected from the patient data base of our TPS. The target width ranged from 6.8cm to 31.2cm, and had the average of 16.6cm. Results: We obtained the data for a MLC when the total number of leaf pairs was 5, 7, and 13, respectively. The data show that the optimal leaf width super‐linearly increases with the distance away from the central axis. Compared against the MLC with equal leaf width, the MLC with optimal leaf width reduced the total area discrepancy by 25.9%, 28.5%, and 31.4%, respectively. We are collecting data for MLC with more leaf pairs, and investigating the influence of number of targets on optimal leaf width. Conclusions: Optimizing leaf width significantly improves the conformity of MLC shape to target.

Purification of recombinant proteins from Escherichia coli at low expression levels by inverse transition cycling

A crucial and challenging problem in proteomics is purification, identification, and characterization of proteins, some of which are expressed at very low levels. The preferred method for purification of low abundance proteins exploits multiple affinity purification tags on a single recombinant protein e.g. tandem affinity purification (TAP) [1]. However TAP is both experimentally lengthy, involving many sequential binding, washing and elution steps and costly, requiring two different and expensive resins to recover the purified recombinant protein. Hence processing large amounts of cell lysate makes it prohibitively expensive especially for scale-up. Here we present a new and simple strategy to purify soluble recombinant proteins from E. coli at a protein concentration that approaches the limit of a single protein molecule per cell. This method utilizes the unique aggregation properties of elastin-like polypeptides (ELPs) to capture recombinant fusion proteins composed of a target protein and an ELP tag from cell lysate. ELPs are artificial, genetically encodable polypeptides composed the repeating pentapeptides sequence VPGXG, where the guest residue (X) can be any naturally occurring amino acid except Pro [2,3]. ELPs exhibit a unique reversible inverse phase transition behavior; below a critical transition temperature (Tt) ELPs are highly soluble in aqueous solution, however at temperatures even a few degrees Celsius above Tt, ELP will undergo a solubilityinsolubility phase transition, leading to aggregation of the polypeptide [4]. The Tt of an ELP is a function of a number of variables including identity and stoichiometry of the guest residue, molecular weight, ELP and salt concentration in aqueous solution [5–9]. The environmental sensitivity and reversible solubility of ELPs are retained when expressed as recombinant fusions with proteins. This feature can be exploited for non-chromatographic purification of recombinant proteins by inverse transition cycling (ITC) [10]. In ITC, an ELP fusion protein is selectively separated from other contaminating biomolecules in cell lysate by the sequential and repeated steps of aggregation, centrifugation, and resolubilization of the fusion protein [10,11]. A number of different proteins have been purified by this method using either centrifugation [11–18] or micro-filtration [19]. The direct purification of ELPs has also been extended to the capture of native proteins by ELP-tagged capture reagents [14–17]. Proteins expressed at the level of micrograms per liter of culture are difficult to purify by chromatography because of the losses associated with non-specific and irreversible adsorption of the target protein to chromatography resins as well as the relative increase in contamination from host proteins that are non-specifically adsorbed to the chromatography resin are subsequently eluted with the target protein. We demonstrate a new variant of ITC that solves

The Phylogenetically Conserved Molluscan Chitinase-like Protein 1 (Cg-Clp1), Homologue of Human HC-gp39, Stimulates Proliferation and Regulates Synthesis of Extracellular Matrix Components of Mammalian Chondrocytes

Members of chitinase-like proteins (CLPs) have attracted much attention because of their ability to promote cell proliferation in insects (imaginal disc growth factors) and mammals (YKL-40). To gain insights into the molecular processes underlying the physiological control of growth and development in Lophotrochozoa, we report here the cloning and biochemical characterization of the first Lophotrochozoan CLP from the oyster Crassostrea gigas (Cg-Clp1). Gene expression profiles monitored by real time quantitative reverse transcription-PCR in different adult tissues and during development support the involvement of this protein in the control of growth and development in C. gigas. Recombinant Cg-Clp1 demonstrates a strong affinity for chitin but no chitinolytic activity, as was described for the HC-gp39 mammalian homolog. Furthermore, transient expression of Cg-Clp1 in primary cultures of rabbit articular chondrocytes as well as the use of both purified recombinant protein and conditioned medium from Cg-Clp1-expressing rabbit articular chondrocytes established that Cg-Clp1 stimulates cell proliferation and regulates extracellular matrix component synthesis, showing for the first time a possible involvement of a CLP on type II collagen synthesis regulation. These observations together with the fact that Cg-Clp1 gene organization strongly resembles that of its mammalian homologues argue for an early evolutionary origin and a high conservation of this class of proteins at both the structural and functional levels.

An Oligonucleotide Microarray for High-Throughput Sequencing of the Mitochondrial Genome

Previously we developed an oligonucleotide sequencing microarray (MitoChip) as an array-based sequencing platform for rapid and high-throughput analysis of mitochondrial DNA. The first generation MitoChip, however, was not tiled with probes for the noncoding D-loop region, a site frequently mutated in human cancers. Here we report the development of a second-generation MitoChip (v2.0) with oligonucleotide probes to sequence the entire mitochondrial genome. In addition, the MitoChip v2.0 contains redundant tiling of sequences for 500 of the most common haplotypes including single-nucleotide changes, insertions, and deletions. Sequencing results from 14 primary head and neck tumor tissues demonstrated that the v2.0 MitoChips detected a larger number of variants than the original version. Multiple coding region variants detected only in the second generation MitoChips, but not the earlier chip version, were further confirmed with conventional sequencing. Moreover, 31 variations in noncoding region were identified using MitoChips v2.0. Replicate experiments demonstrated >99.99% reproducibility in the second generation MitoChip. In seven head and neck cancer samples with matched lymphocyte DNA, the MitoChip v2.0 detected at least one cancer-associated mitochondrial mutation in four (57%) samples. These results indicate that the second generation MitoChip is a high-throughput platform for identification of mitochondrial DNA mutations in primary tumors.

Phase-stepped gauge block interferometry using a frequency-tunable visible laser diode

Frequency changes induced by bias or temperature modulation of injection diode lasers can provide an economical and effective method of applying phase-stepping interferometry to optical metrology. However, the intrinsic frequency instability of these devices limits their use in gauge block interferometry where precise and repeatable phase steps must be maintained simultaneously on two discontinuous surfaces and over relatively long path lengths. We demonstrate a method using a visible injection diode laser, the frequency of which is locked by using a Fabry-Perot interferometer. Small changes to the length of the Fabry-Perot interferometer shift the frequency of the laser producing proportional and repeatable phase steps to the gauge block interferogram. This method has been successfully implemented with a Fizeau-type gauge block interferometer with a phase measurement resolution of 0.005 lambda. The phase data are then processed to map the surface form of gauge blocks up to 100 mm in length and to objectively assess surface shape parameters.

Crystal growth of analcime studied by AFM and atomistic simulation

A combined atomic force microscopy (AFM) and atomistic simulation approach affords a high-resolution picture of the structure and surface termination of synthetic analcime and provides insight into the atomic-scale mechanism of crystal growth. AFM measurement reveals a repeated step height of ∼0.6 nm on the {2 1 1} crystal face corresponding to the interlayer separation for the {2 1 1} rather than higher index surfaces, as is observed in, e.g., zeolite A. Analysis of the possible terminating structures for the {2 1 1} face from surface energy evaluations indicates that a unique terminating structure is favoured implying a step height of ∼0.6 nm in accord with the experimental measurement. Analysis of intermediate stages of growth using classical simulation approaches suggests that the mechanism may be mediated purely by monomeric rather than oligomeric species, which contrasts with the presumed secondary building unit mechanism for many zeolitic materials.

Rapid vasoregulatory mechanisms in exercising human skeletal muscle: dynamic response to repeated changes in contraction intensity

We tested the hypothesis that vasoregulatory mechanisms exist in humans that can rapidly adjust muscle blood flow to repeated increases and decreases in exercise intensity. Six men and seven women (age, 24.4+/-1.3 yr) performed continuous dynamic forearm handgrip contractions (1- to 2-s contraction-to-relaxation duty cycle) during repeated step increases and decreases in contraction intensity. Three step change oscillation protocols were examined: Slow (7 contractions per contraction intensityx10 steps); Fast (2 contractions per contraction intensityx15 steps); and Very Fast (1 contraction per contraction intensityx15 steps). Forearm blood flow (FBF; Doppler and echo ultrasonography), heart rate (ECG), and mean arterial pressure (arterial tonometry) were examined for the equivalent of a cardiac cycle during each relaxation phase (FBFrelax). Mean arterial pressure and heart rate did not change during repeated step changes (P=0.352 and P=0.190). For both Slow and Fast conditions, relaxation phase FBFrelax adjusted immediately and repeatedly to both increases and decreases in contraction intensity, and the magnitude and time course of FBFrelax changes were virtually identical. For the Very Fast condition, FBFrelax increased with the first contraction and thereafter slowly increased over the course of repeated contraction intensity oscillations. We conclude that vasoregulatory mechanisms exist in human skeletal muscle that are capable of rapidly and repeatedly adjusting muscle blood flow with ongoing step changes in contraction intensity. Importantly, they demonstrate symmetry in response magnitude and time course with increasing versus decreasing contraction intensity but cannot adjust to very fast exercise intensity oscillations.

Influence of initial metabolic rate on pulmonary O2 uptake on-kinetics during severe intensity exercise

We hypothesised that the fundamental (Phase II) component of pulmonary oxygen uptake (VO(2)) kinetics would be significantly slower when step transitions to severe intensity cycle exercise were initiated from elevated baseline metabolic rates, and that this would be associated with evidence for a greater activation of higher-order (i.e. type II) muscle fibres. Seven male subjects (age 22-34 years) completed repeat step transitions to a severe (S) work rate, estimated to require 100% VO(2) peak, from a baseline of: (1) 3 min of unloaded cycling (L-->S); (2) 6 min of moderate exercise (M-->S); (3) 6 min of heavy exercise (H-->S). Pulmonary gas exchange and the electromyogram (EMG) of the m. vastus lateralis were measured throughout all exercise tests. The Phase II VO(2) kinetics became progressively slower at higher baseline metabolic rates (tau was 37 +/- 6, 59 +/- 23, and 93 +/- 50 s for L-->S, M-->S, and H-->S, respectively; P < 0.05 between L-->S and H-->S). Both the integrated EMG and the mean power frequency were significantly higher immediately before the step transition to severe exercise when it was initiated from higher metabolic rates. Although indirect, these data suggest that the slower Phase II VO(2) kinetics observed at higher baseline metabolic rates was related to alterations in muscle activation and fibre recruitment patterns.

Redox and photochemical behaviour of a porphyrin monolayer on an indium-tin oxide electrode

In order to investigate photoluminescence behaviour of an ordered molecular porphyrin monolayer and its quenching properties by oxygen gas, a porphyrin with long alkyl chains, 5,10,15,20-tetrakis[4-(11-carboxylundecane-1-oxy)phenyl]porphyrin ( 4), was synthesized and adsorbed onto an indium-tin oxide (ITO) substrate by a chemical dipping method. Cyclic voltammetry was used to analyze the ITO electrode coated with 4. The peak current of the first oxidation was proportional to the sweep rate, and the surface coverage was estimated to be 2.3–2.5 × 10 −10 mol cm −2. The UV–vis spectrum of the monolayer showed a broadened Soret band, which shifted to longer wavelength. These features suggest that the porphyrin moieties of 4 are packed to form a J-type structure. The oxygen quenching ratio of the porphyrin 4 monolayer on the ITO electrode, I 0/ I 100, was estimated to be 1.25, where I 0 and I 100 are, respectively, luminescence intensity values in 100% argon and 100% oxygen. On repeated step cycling between 100% argon and 100% oxygen atmospheres, the response times of luminescence quenching were 10 s (argon to oxygen) and 23 s (oxygen to argon). These findings suggest that a monolayer of sensing dye is applicable for oxygen sensing system without deterioration of size-accuracy of models.

Gas Lift Optimization for Long-Term Reservoir Simulations

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 90506, "Gas Lift Optimization for Long-Term Reservoir Simulations," by Pengju Wang and Michael Litvak, SPE, BP plc, prepared for the 2004 SPE Annual Technical Conference and Exhibition, Houston, 26-29 September. Although various gas-lift-optimization algorithms have been proposed in the literature, few are suitable for long-term reservoir-development studies that require the gas-lift-optimization process to be highly efficient, flexible, and sufficiently powerful to handle complicated fluid flows and operational constraints. These algorithms also must converge rapidly. The gas-lift-optimization problem considered in the full-length paper is to maximize daily hydrocarbon production by selecting the optimal well-production and lift-gas rates subject to pressure and rate constraints of the surface pipeline network and amount of lift gas available. Introduction When oil fields mature, oil production often is assisted by continuous lift-gas injection and constrained by the gas- and/or liquid-handling capacities of surface facilities. The optimal allocation of production rates and lift-gas rates is subject to reservoir deliverability and surface-facility capacities and other capital-investment decisions. Compared to real-time production optimization, the optimal rate allocation in long-term reservoir-simulation studies poses unique problems. Problem The optimization problem is to maximize the daily oil production by optimally selecting the well-production and lift-gas rates subject to surface-facility pressure and rate constraints. The optimization problem is considered a well-management problem in a commercial reservoir simulator capable of simulating multiphase compositional fluid flow in reservoirs, well tubing strings, surface pipeline-network systems, and separation facilities. Integration Procedure. The following is a procedure to integrate the optimization problem into the reservoir simulator. 1. Start with the pressure and fluid com-position in reservoir gridblocks calculated in the previous Newton iteration. Use well lift-gas rates from the previous Newton iteration as the initial guesses. 2. Solve the surface pipeline-network problem; convert pressure constraints to flow-rate constraints. 3. Perform production- and lift-gas-rate allocation optimization. 4. Determine active constraints in wells and nodes. Linearize multiphase-fluid-flow equations for well tubing strings and the surface pipeline network (numerical derivatives are used). Add these equations to the linearized fluid-flow equations for reservoir gridblocks. 5. Solve the linearized system of equations established in Step 4. 6. Repeat Steps 1 through 5 until convergence. 7. Advance to the next timestep.

Multilevel electroforming for the components of a microdroplet ejector by UV LIGA technology

A microdroplet ejector actuated by the shear mode PZT actuator is proposed. It consists of three electroforming components including a vibration plate, a chamber plate and a nozzle plate. The three components are fabricated by nickel electroforming technology and assembled by aligning apparatus using epoxy adhesive. The AZ-type thick positive photoresist is used as the electroforming mould, which is patterned by UV lithography. The repeat steps including the photoresist patterning and nickel electroforming make the component form a quasi 3D (or 2.5D) multilevel microstructure. The vibration plate has the feature of two different sized bulges piled on the diaphragm. Those nozzles in the nozzle plate are formed by the nickel lateral deposition when depositing over columnar photoresist moulds.

Measuring Single Cardiac Myocyte Contractile Force via Moving a Magnetic Bead

One of the biggest problems of heart failure is the heart’s inability to effectively pump blood to meet the body’s demands, which may be caused by disease-induced alterations in contraction properties (such as contractile force and Young’s modulus). Thus, it is very important to measure contractile properties at single cardiac myocyte level that can lay the foundation for quantitatively understanding the mechanism of heart failure and understanding molecular alterations in diseased heart cells. In this article, we report a novel single cardiac myocyte contractile force measurement technique based on moving a magnetic bead. The measuring system is mainly composed of 1), a high-power inverted microscope with video output and edge detection; and 2), a moving magnetic bead based magnetic force loading module. The main measurement procedures are as follows: 1), record maximal displacement of single cardiac myocyte during contraction; 2), attach a magnetic bead on one end of the myocyte that will move with myocyte during the contraction; 3), repeat step 1 and record contraction processes under different magnitudes of magnetic force loading by adjusting the magnetic field applied on the magnetic bead; and 4), derive the myocyte contractile force base on the maximal displacement of cell contraction and magnetic loading force. The major advantages of this unique approach are: 1), measuring the force without direct connections to the cell specimen (i.e., “remote sensing”, a noninvasive/minimally invasive approach); 2), high sensitivity and large dynamic range (force measurement range: from pico Newton to micro Newton); 3), a convenient and cost-effective approach; and 4), more importantly, it can be used to study the contractile properties of heart cells under different levels of external loading forces by adjusting the magnitude of applied magnetic field, which is very important for studying disease induced alterations in contraction properties. Experimental results demonstrated the feasibility of proposed approach.

Interspecific Segregation in a Lattice Ecosystem with Intraspecific Competition

Coexistence of competing species is extremely common in nature. If competing species live separately, then they can coexist easily. In the present article, we present a lattice version of Lotka–Volterra competition model. This system contains two competing species. They can coexist, when intraspecific competition is stronger than interspecific competition. We find a self-organized isolation of microhabitat: when the densities of both species approach zero, living regions of both species are naturally and completely separated from each other. Previously, co-workers in our laboratory presented a model of habitat segregation. In this case, however, a specific interaction was assumed: the rock-paper-scissors relation was assumed among three species. In contrast, the model presented here may be applicable to many ecosystems, since we only assume competition which is very common in real systems. Our model composed of two species X and Y is defined by j! E ðrate: mjÞ ð1aÞ jþ E! 2j ðrate: rjÞ ð1bÞ jþ j! jþ E ðrate: cjÞ ð1cÞ Here j is the lattice site occupied by species j ( j 1⁄4 X, Y), and E is the empty site. The pair of reactions (1a) and (1b) are called the contact process, where (1a) and (1b) represent death and birth processes, respectively. The last reaction means the intraspecific competition. An example is the direct competition between a pair of plants; neighboring plants are competing to take sunlight or resources. The parameters mj, rj and cj respectively denote mortality, reproduction and competition rates. Besides the direct competition (1c), our model contains a tacit (indirect) competition: according to reaction (1b), any pair of individuals compete to get the empty space E. Simulations are performed by the method of lattice Lotka–Volterra model: 1) Initially, we distribute X and Y on the square lattice. 2) The lattice is updated as follows: (i) we perform two-body reactions (1b) and (1c). Choose one lattice site randomly, and then randomly specify one of four neighboring sites. Let the pair react; for example, if the pair of sites are (X, E), then E is changed into X with the rate rx. (ii) we perform one-body reactions (1a). Choose one lattice point randomly; if the site is X (or Y), it will become E by the rate mx (or my). 3) Repeat step 2) until the system reaches a stationary state. If the global interaction is allowed between any pair of lattice sites, the population dynamics of our system (1) is given by the mean-field theory (rate equation):