Paenibacillus polymyxa, is an important antibiotic normally against Gram-negative pathogens. In this study, we found that polymyxin E can kill its producer P. polymyxa, a Gram-positive bacterium, by disrupting its cell membrane. Membrane damage was clearly revealed by detecting the leakage of intracellular molecules. The observation using scanning electron microscopy also supported that polymyxin E can destroy the cell membrane and cause an extensive cell surface alteration. On the other hand, divalent cations can give protection against polymyxin E. Compared with Mg2+, Ca2+ can more effectively alleviate polymyxin E-induced damage to the cell membrane, thus remarkably increasing the P. polymyxa survival. Our findings would shed light on a not yet described bactericidal mechanism of polymyxin E against Gram-positive bacteria and more importantly the nature of limited fermentation output of polymyxin E from P. polymyxa.Polymyxin E, produced by  Paenibacillus polymyxa, a Gram-positive bacterium [Polymyxin E (colistin), a nonribosomal peptide with molecular weight of approximately 1200 Da, is biosynthesized by acterium . Since 1acterium , 5. Howeacterium –8.N-terminal fatty acyl chain and the D-Leu6-L-Leu7 segment of the colistin molecule will insert into OM. This insertion will weaken the packing of adjacent lipid A and induce the expansion of OM monolayer [The basic structure of colistin is a cyclic heptapeptide with a tripeptide side chain acylated by a fatty acid at its amino terminus , 10. Theonolayer , 13. Subonolayer , 15 and onolayer , eventuaStaphylococcus aureus, Streptococcus agalactiae, Bacillus cereus, Bacillus subtilis and Listeria monocytogenes. However, the bactericidal mechanism of colistin against Gram-positive bacteria is not very clear yet. In this study, we found that colistin can also kill its producer P. polymyxa, a Gram-positive bacterium, through disruption of its cell membrane. To our knowledge, it is the first report showing colistin can cause cell death of P. Polymyxa via inducing leakage of the intracellular molecules. We also investigated the effect of divalent cations on protection of the cell membrane. It was found that Ca2+ is more effective than Mg2+ in alleviating the colistin-induced damage. Since colistin is biosynthesized by P. polymyxa, its bactericidal activity to its producer would potentially repress its accumulation in P. polymyxa during fermentation. Therefore, our findings not only enrich our understanding of colistin’s bactericidal activity to Gram-positive bacteria, but also help to improve its fermentation output in the future.Compared to extensive studies on colistin’s antibacterial activity against Gram-negative bacteria, little is known about its bactericidal activity against Gram-positive ones. Yet, in some cases, there are studies which report that colistin can kill Gram-positive bacteria –20, suchP. polymyxa was tested at various concentrations using disk diffusion assay , demonstrating that colistin can disrupt the cell membrane and Ca2+ can keep the membrane integrity.PI (red fluorometric dye) staining was used for determination of cell membrane disruption , 24. OncP. polymyxa surface morphology was observed under SEM [P. polymyxa displays a regular smooth and plump surface. In contrast, most colistin-treated cells have irregular shapes and damaged areas on the cell surface. In the presence of both colistin and CaCl2, majority of P. polymyxa cells appear to be normal as the colistin-free cells, except that a few cells carry the damaged scarring. Our findings indicate that colistin can damage the cell surface integrity, but Ca2+ can alleviate this damage. This is in line with all our previous experiments.The alteration of nder SEM . As showEscherichia coli, Pseudomonas aeruginosa, Klebsiella pneumoniae and Acinetobacter baumannii is to kill the cells through membrane lysis by specifically targeting negatively charged LPS on Gram-negative bacteria and increasing bacterial membrane permeability. Typically, colistin at concentration of about 500 U/mL can already give bactericidal activity to many Gram-positive bacteria (data not shown). However, our study indicates that colistin at concentration only higher than 8×104 U/mL can yield inhibition zones to P. polymyxa, a Gram-positive bacterium. Therefore, the concentration of colistin against Gram-positive bacteria is hundreds of times higher than that against Gram-negative bacteria. It has been found that under colistin pressure, Gram-positive bacteria will modify their teichoic acids on the cell wall through incorporation of positively charged residues, such as D-alanine, to decrease net negative charges on the cell surface for survival [As a cyclic lipodecapeptide, colistin carries 5 free amino groups with 5 positive charges . Colistisurvival , 18. The2+ ion is one of the most major intracellular cations. The membrane-proximal Ca2+ can directly bind to phosphate groups of acidic phospholipids, and normally function to bridge and stabilize LPS on the membrane [P. aeruginosa can be inhibited by Ca2+ ion [2+ ion can alleviate colistin-induced damage to Gram-positive bacterium P. polymyxa. Colistin contains 5 positive charges and enables to replace Ca2+ on the membrane by binding to acidic phospholipids. With the decrease of LPS stability, the plasma membrane will be disrupted and the cell will be killed by colistin. The added Ca2+ ions are supposed to occupy binding sites on LPS and stabilize the plasma membrane of P. polymyxa, providing protection from colistin. Interestingly, our data in 2+ immediately following colistin, the addition of Ca2+ with 15min delay following colistin causes about one order of magnitude further drop of P. polymyxa CFU, indicating that the colistin-induced damage to P. polymyxa is probably fast and irreversible.Phospholipids are the major components in the plasma membrane and play fundamental roles in forming lipid bilayers. Acidic phospholipids are present in all cell membranes, but the plasma membrane has the highest enrichment to supply lots of negative charges. Camembrane . It has Ca2+ ion . Our datP. polymyxa. Therefore, understanding of the bactericidal mechanism of colistin against its producer would not only enrich our knowledge of colistin against Gram-positive bacteria, but also provide an important guideline for optimization of fermentation condition and improvement of colistin output from P. polymyxa in the future.Colistin is biosynthesized by P. polymyxa used in this work was supplied by Zhejiang Qianjiang Biochemical Co., Ltd., China and kept frozen at -80°C in our lab at Zhejiang University of Technology, China. Unless otherwise specified, the medium for culture of P. polymyxa was followed as beef exact 10 g/L, peptone 15 g/L, glucose 10 g/L, yeast extract 2 g/L, NaCl 3 g/L and FeSO4·7H2O 0.1 g/L. To make solid medium, agar was added to a final concentration of 20 g/L. In general, the colony of P. polymyxa was first picked up using a sterilized wire loop and streaked on agar plate for incubation at 30°C for 2 d. Then, a ring of P. polymyxa was transferred to 50 mL of medium for incubation at 30°C for 18 h with a shaking at 200 rpm.7 (colony forming unit or CFU/mL). Then, unless otherwise specified, colistin with final concentration of 1.6×105 U/mL  together with or without divalent cation (Ca2+ or Mg2+) was added into cell solution and the mixture was incubated for various times at 30°C with a shaking at 200 rpm. One unit is equal to 0.0418 μg of colistin.After cultivation, the cells were harvested by centrifugation at 4,000 g for 5 min. After washing twice with fresh medium, the cells were resuspended in fresh medium with appropriate volume to make a final cell concentration of about 10After colistin treatment with or without divalent cation, the mixture was either directly centrifuged at 4,000 g for 5 min, followed by detection of supernatant absorbances at 260 nm and 280 nm, or diluted 10 times with ultra-pure water for measurement of electrical conductivity.To evaluate the bactericidal activity, the colistin-treated mixture was centrifuged for 5 min at 4,000 g to collect the cells. After washing twice with fresh medium, the cells were resuspended in fresh medium. Then, colony forming unit (CFU/mL) was measured on fresh agar plate after gradient dilution.5 U/mL) treatment with or without 20 mM Ca2+, the cells were harvested by centrifugation at 4,000 g for 5 min. Next, 100 μL of fluorometric dye propidium iodide  solution  was used to resuspend the cells. After incubation at room temperature for 5 min, the cells were harvested by centrifugation at 4,000 g for 5 min and washed twice with sterilized ultra-pure water. Finally, the cells were resuspended in 1 mL of sterilized ultra-pure water and the fluorescence signal was recorded using a multimode reader  with excitation at 535 nm and emission at 615 nm.After colistin  for 4 h and washed three times with phosphate buffer (pH7.0). Then, the specimen was post-fixed with 1% hungry acid in phosphate buffer (pH7.0) for 1 h and washed three times in phosphate buffer (pH7.0). Subsequently, the specimen was gradually dehydrated by a series of ethanol  for 20 min per dehydration. Next, the specimen was transferred to a mixture of alcohol and isoamyl acetate (v:v = 1:1) for a 30min-incubation and then pure isoamyl acetate for another 1h-incubation. After another dehydration in Hitachi Model HCP-2 critical point dryer with liquid CO


Patients were randomly divided into group I (N = 8) and group II (N = 8). The dogs in group I were sprayed with HCA on the affected skin once a day for three weeks. The dogs in group II were treated once a day for 3 days followed by no treatment for 4 days for a total of three weeks. For the dogs in group I and group II the CADESI-03 scores before and after use of HCA showed significant reduction (P < 0.01). The postcortisol level after the use of HCA in group I showed 36.0% decrease and showed significant suppression (P < 0.01). By comparison, the use of HCA on group II did not show decrease in postcortisol levels. There was a tendency of suppression for hypothalamus—pituitary gland—adrenal gland system, but it was not serious influence. In addition, there was no influence on peripheral blood CCR4+ CD4+ lymphocytes percentage in dogs in group I after treatment with HCA.This study investigated the influence of 0.00584% hydrocortisone aceponate spray  on blood serum cortisol levels and peripheral blood CCR4 Canine atopic dermatitis is an intractable chronic skin disease, and management requires a combination of many treatments . Treatme0.00584% hydrocortisone aceponate spray  is different from a conventional steroid, due to the fact that the absence of a halogen at C6, C9, and C21 is associated with better local and systemic tolerance . Double + CD4+ lymphocytes percentage in blood both before and after use of HCA in randomized clinical study.The effectiveness of HCA for treatment of inflammation is proved in former studies –10. The All dogs were diagnosed with canine atopic dermatitis and had severe itch; they were seen at one hospital . The study was conducted from June to November, 2011, with the owners' consent.Malassezia dermatitis) were diagnosed by cytology, it was treated mainly by shampoo therapy. All dogs underwent an elimination diet using “hypoallergenic” foods  for at least 8 weeks. The diagnosis of CAD was based on compatible history and clinical signs of Favrot's criteria [The diagnosis of CAD was made by ruling out other causes of the itch. All dogs received flea control and appropriate treatment for scabies mites. If bacterial pyoderma and yeast (criteria . IntradeDermatophagoides farinae and D. pteronyssinus) and the other four showed no reactions to intradermal test and were diagnosed as having atopic like dermatitis. In group II, five dogs had positive reactions to house dust mite mix and the other three were diagnosed with atopic like dermatitis. Owners were instructed to apply to the dog two pumps of HCA spray per 100 cm2 of affected skin. HCA spray was mainly applied to axilla and inguina, not to the face. They were instructed not to spray more than 1/3 of the whole body. The clinical evaluation and blood tests were performed on day 0 and day 21. Owners of dogs in group I sprayed HCA on the affected skin once a day for three weeks. Owners of dogs in group II sprayed HCA on the affected skin . Owners were instructed to apply the spray once daily to affected skin only from 10 cm away at a dose rate of two sprays per 100 cm2 of affected skin [Sixteen dogs diagnosed with CAD were distributed into two groups randomly. In group I, four of the eight dogs had positive reactions to house dust mite mix  . The samBlood sample was collected from the jugular vein, and the peripheral blood was used for each inspection. The following inspection was performed before and after use of HCA.Cortrosyn  5 ug/kg was injected intravenously . The ser+ CD4+ T lymphocytes were detected by flow cytometry following methods previously reported [A sample of peripheral blood was collected in EDTA before and after use of HCA. The sample was saved by refrigeration and transported to a commercial laboratory . The CCR4reported , 15.t-tests and Wilcoxon signed-rank test. Statistical significance was defined as P < 0.05.Statistical analysis was performed by paired P < 0.01). In group II, the mean and SD of the total CADESI-03 score before and after the use of HCA was 393.3 ± 171.4 and 335.4 ± 157.0, respectively. A total score rate of decrease was 14.8%, and it was significantly different after use of HCA (P < 0.01). Even though, CADESI-03 scores of group I and II are different, both groups showed decrease in the score which were significantly different. It represents the efficacy of HCA on both treatment methods.In group I, the mean and SD of the total CADESI-03 score before and after the use of HCA was 294.8 ± 175.0 and 208.8 ± 138.4, respectively. A total score rate of decrease was 29.2%, and it was significantly different after use of HCA (μg/dL (standard range 1.0–7.7 μg/dL) pre-ACTH and 13.9 ± 4.3 μg/dL (standard range 1.0–18.0 μg/dL) post-ACTH, μg/dL pre-ACTH and 8.9 ± 3.6 μg/dL post-ACTH, In group I, prior to the use of HCA, the mean and SD of the cortisol levels were 3.7 ± 2.4 μg/dL pre-ACTH and 13.6 ± 3.0 μg/dL post-ACTH, In group II, the mean and SD of cortisol levels after use of HCA were 2.8 ± 1.7 P < 0.01). The post-ACTH cortisol level before use of HCA in group I and the postcortisol level after use of HCA in group II showed no significant difference (P > 0.05). From these results, limitation use of the spray might recover the postcortisol value of after use of the spray.In group I, the decrease in cortisol levels post-ACTH before and after use of HCA was 36.0% and showed significant difference .In group I, the mean and SD of CCR4ff level . The CCRAfter 21 days of HCA use, the total score of CADESI-03 decreased by 29.2% in group I and 14.8% in group II. Dogs in both groups showed significant difference after use of the spray. It represents an effectiveness of HCA which resembles a result in the report of Nutall and others , which s+ CD4+ lymphocytes percentage were measured to make up for these lacks. This study showed 36.0% decrease in postcortisol value compared with before and after use of HCA and it showed significant difference (<0.01). On the other hand, CCR4+ CD4+ lymphocytes percentage did not move and showed no effect to it. These results suggest weak suppression of the hypothalamus pituitary gland; adrenal gland axis might be caused by use of HCA. These data support the first hypothesis of Bizikova and others, which is that HCA might be absorbed from the treated skin with activity and it can be said that there was not enough degradation of HCA. However, influence was in the tolerated level, and it can be avoided by limited use of the spray. And there was little influence of the recurrence of the clinical score even if it reduce the frequency of use.One report of the use HCA described the skin atrophy as an adverse effect . In the + CD4+ lymphocytes percentage in group I.Comparing with the result of past study, use of the HCA showed little influence than other dosage routes –20. For + CD4+ lymphocytes percentage detects the migration degree of these T-cells and it can also judge the allergic strength of the live body or an immunoreactive state [+ CD4+ lymphocytes percentage before and after the use of HCA in this study. It meant that HCA shows extremely little influence to systemic immunoreaction. The Bizikova and others [+ lymphocytes. From two studies, HCA spray infiltrated very small amount systemically, but the main area of the effect is limited to the skin epidermis and restrained inflammation and the cell-mediated immunity in that part, so the influence on systemic immunoreaction might be extremely little.Because a Langerhans cell present antigen to a T-cell in the skin epidermis, these T-cells migrate the main route of the expose to the live body of the sensitization antigen of the CAD to lesion skin. In other words peripheral blood CCR4ve state , 14. Thed others  also perHCA spray is a promising next generation anti-inflammatory steroidal therapeutic drug. The use of HCA spray should be compared with other steroid ointments and sprays. It is thought that the use of HCA spray is likely to help the transition from the use of an oral steroid, helping to minimize the development of iatrogenic Cushing disease.


Atypical self-processing is an emerging theme in autism research, suggested by lower self-reference effect in memory, and atypical neural responses to visual self-representations. Most research on physical self-processing in autism uses visual stimuli. However, the self is a multimodal construct, and therefore, it is essential to test self-recognition in other sensory modalities as well. Self-recognition in the auditory modality remains relatively unexplored and has not been tested in relation to autism and related traits. This study investigates self-recognition in auditory and visual domain in the general population and tests if it is associated with autistic traits.Thirty-nine neurotypical adults participated in a two-part study. In the first session, individual participant’s voice was recorded and face was photographed and morphed respectively with voices and faces from unfamiliar identities. In the second session, participants performed a ‘self-identification’ task, classifying each morph as ‘self’ voice (or face) or an ‘other’ voice (or face). All participants also completed the Autism Spectrum Quotient (AQ). For each sensory modality, slope of the self-recognition curve was used as individual self-recognition metric. These two self-recognition metrics were tested for association between each other, and with autistic traits.t = 3.142; P < 0.01). No significant correlation was noted between self-recognition bias across sensory modalities . Higher recognition bias for self-voice was observed in individuals higher in autistic traits . No such correlation was observed between recognition bias for self-face and autistic traits .Fifty percent ‘self’ response was reached for a higher percentage of self in the auditory domain compared to the visual domain (Our data shows that recognition bias for physical self-representation is not related across sensory modalities. Further, individuals with higher autistic traits were better able to discriminate self from other voices, but this relation was not observed with self-face. A narrow self-other overlap in the auditory domain seen in individuals with high autistic traits could arise due to enhanced perceptual processing of auditory stimuli often observed in individuals with autism. The concept of ‘self’ has challenged thinkers and empiricists across disciplines, cultures, and time. A leading theoretical account of self-representation was proposed by William James . AccordiPhysical self-representation is multimodal in nature and manifests across different senses and domains. Self-face, self-voice, self-body, and self-agency can all be regarded as instances of physical self-representation. However, most studies investigating self-other processing in the physical domain have used self-face processing as a metric of self-representation -12. UndeTo address this gap in the literature, the first aim of our study was to systematically test multiple aspects of physical self-representation by measuring individual bias to both self-face and self-voice recognition. This line of enquiry tested how metrics of self-face and self-voice recognition compared across and within individuals. Self-face recognition has previously been tested by presenting self and other faces in a random order ,10,15 asThe second aim of our study was to explore individual differences in self-face and self-voice recognition and their association with autistic traits. Autistic traits are distributed continuously across the population, and individuals with autism spectrum conditions (ASC) score highly on these measures . ImportaAccordingly, we investigated how these measures of physical self-representation were mapped onto traits related to autism. However, in the absence of any directly relevant prior evidence, we did not have a hypothesis about the directionality of this relationship.Thirty-nine White Caucasian participants aged between 18 and 40 years were recruited in the study . Only White Caucasian participants were chosen since the ‘other’ faces were constant across participants and were of this ethnicity. All participants had normal or corrected to normal vision and hearing and were right handed. Participants took part in a two-part experiment (face and voice), the order of which was counter-balanced across participants. Three participants did not complete the voice part of the experiment due to technical issues. Participants also completed the Autism Spectrum Quotient (AQ) questionnaire online (18.59 ± 7.55). All participants signed a consent form giving their consent to taking part in the study. The study was approved by School of Psychology and Clinical Language Sciences Ethics Committee, University of Reading.Stimuli were individually tailored for each participant. Each participant was photographed using a digital camera  in identical conditions under artificial lighting. Four volunteers  were selected to serve as ‘unfamiliar faces’ were also photographed under the same conditions. Participants looked directly at the camera and were seated at a distance of 100 cm with a white background while holding a neutral expression. The photographs were then converted to grayscale and external features  were removed. This photograph was then mounted on an oval frame and cropped to a dimension of 350 × 500 pixels using GIMP . Two setEach face morph continuum had 21 images at 5% step sizes   and ‘l’ key for other face in one block, and the response keys were reversed in the next block (right-hand self-response) , and normalization to peak volume of 0 dB using Audacity . The preThe test run comprised of 2 blocks, each consisting of 2 sets of ‘self-unfamiliar’ voice morph continuum consisting of 22 stimuli in total, presented twice in a randomized manner. Each block had a total of 44 trials, thus making each run consists of 88 trials. Each trial consisted of a cross-hair presented for 500 ms followed by the stimuli which lasted for 1,000 ms during which participant had to log in the key-press response  was recorded, and a response curve was generated (separately for face and voice). For each modality, the percentage ‘self-response’ was normalized within participants, to account for baseline differences in self-recognition. The slope for each participant, for each modality, was calculated using a psychometric function fitted for maximum likelihood estimation for Weibull distribution. Depending on the task, the psychometric function gives a steep or shallow slope Figure . The steStatistical analyses were conducted using SPSS  and R sot-test revealed that the morph level at which self-face response reached 50% was lower (i.e. containing lower percentage of self) compared to the morph level at which 50% self-voice response was reached  . The maximum percentage labelled as self was comparable across two modalities. Furthermore, the morph level at which the shift occurs from the label of ‘self’ to ‘other’ for both modalities across all participants was calculated . This analysis included only the participants who completed both auditory and visual tasks. After analysis for outliers, there was no significant correlation between slope for self-face and self-voice recognition (τ(35) = −0.165, P = 0.204). A partial Kendall correlation coefficient was calculated controlling for gender . This analysis did not alter the results . To further elaborate on this null result, Bayes factor was computed. The Bayes factor for this correlation was 0.70, indicating barely any evidence for the hypothesis that physical self-representation across modalities are correlated [The self-other overlap was characterized using the slope of the psychometric function as described earlier. To test the overlap between self and other representation in the two sensory domains exhibited any relationship, Kendall rank correlation coefficient (two-tailed) was calculated between the slopes of self-face and self-voice recognition. The choice of the test was made as neither of the slope variables for faces and voices showed a normal distribution Auditory self-other representation and autistic traits – (voice slope and AQ scores)To evaluate individual differences in physical self-representation across sensory domains and autistic symptoms, Kendall rank correlation coefficient was calculated between the following variable pairs:τAQ(34) = 0.301, P = 0.008  = −0.020, P = 0.438). The corresponding Bayes factor value of 0.55 indicates barely any evidence for the theory that visual self-representation and autistic traits are related. The data was further analysed with gender as a covariate . This analysis revealed a very similar pattern of results to those reported above .Outliers (defined as cook's d > 4/N where N is the number of participants) were removed prior to analysis. All p-values reported are one-tailed, in light of the directional nature of the hypotheses. Auditory self-representation was found to be positively correlated to the AQ scores .To check if the pattern of response was biased by specific ‘other’ faces/voices (since two ‘other’ faces/voices were used), This study tested (a) if physical self-representation is comparable between visual and auditory modalities and (b) if autistic traits are associated with sensory modality-specific self-representation.Physical self-representation was measured as the slope for self-recognition, varying as a function of available physical self-related information. Available physical self-related information was manipulated in both visual and auditory domains by creating degrees of morphs with differing percentages of self-related information. The steepness of the slope, calculated from the self-recognition responses across the different degrees of morphs, provided a measure of stimulus range over which the participant shifts between categories. A steeper slope indicates narrower range and a reduced overlap between self and other. This metric was then compared across the modalities and with the autistic traits.We found that physical self-representation across the auditory and visual domains did not correlate with each other. In other words, individuals with a narrower self-other overlap in visual domain (or more distinct self-face representation) did not show a correspondingly narrow self-other overlap in the auditory domain. This observation suggests that physical self-representation is not unitary across sensory modalities. While common brain regions such as the inferior frontal gyrus IFG might be involved in responding to both self-face and self-voice , this reOur results further show that individuals with high autistic traits show narrower self-other overlap in the auditory domain than in the visual domain. The steeper slope in the auditory domain for individuals high in autistic trait indicates that the stimulus features allowed such individuals to shift categories (from ‘self’ to ‘other’) over a narrow range. This suggests that a narrow representation of self-voice (or a more distinct representation of self-voice) is associated with higher autistic traits. One interpretation of this result is that individuals high in autistic traits have a ‘narrower’ physical self-representation. This narrow physical self-representation can be interpreted such that any deviation from it is perceived to be an ‘other’, making it difficult to simulate others. This is particularly interesting, since flexibility of self-representation can be useful in order to put oneself in another person’s shoes . However, this relationship of high autistic traits and narrower physical self-representation was seen only for self-voice stimuli, and not for self-face stimuli. One potential mechanism through which a more distinct physical self-representation can be instantiated is through heightened attention to interoceptive cues, as has been noted by a recent study in individuals with ASC .Since the relationship of autistic traits and narrower physical self-representation is only seen for self-voice and not for self-face, an alternative explanation based on the sensory characteristics of self-face and self-voice stimuli is offered here. In contrast to faces, our familiarity with our own voices as it sounds to others is usually lower. This is because we hear our own voices through bone conduction, which sounds different from that we can hear from recorded self-voice that we hear through air conduction. Previous reports have suggested that individuals focus on the grammar, syntax, and psychological characteristics of other speakers, while they focus on the tonal qualities when hearing their own voice . The natIt should be noted that the current study sample was not balanced for gender and did not have sufficient power for the analyses to be stratified by gender. Notwithstanding this limitation, controlling for gender in a separate correlation analysis did not change the reported results. However, in view of a female advantage suggested in an early study based on polaroid photographs of self-faces , future Self-representation in the psychological domain has been investigated widely in recent behavioural and neuroimaging studies ,41. It wIn this study, we showed that recognition bias for physical self-representation across the visual and auditory domain is not a unitary or correlated phenomenon. We also showed that recognition bias for self-voice is correlated with autistic traits, such that individuals with high autistic traits show a narrow self-other overlap. Future experiments should include non-voice stimuli to test between competing interpretations suggested in this report and extend the paradigm to other cultures as well as individuals with autism spectrum conditions.


The hydrogel walkers consisting of polyanionic poly(2-acrylamido-2-methylpropanesulfonic acid-co-acrylamide) exhibit an arc looper-like shape with two “legs” for walking. The hydrogel walkers can reversibly bend and stretch via repeated “on/off” electro-triggers in electrolyte solution. Based on such bending/stretching behaviors, the hydrogel walkers can move their two “legs” to achieve one-directional walking motion on a rough surface via repeated “on/off” electro-triggering cycles. Moreover, the hydrogel walkers loaded with very heavy cargo also exhibit excellent walking motion for cargo transport. Such hydrogel systems create new opportunities for developing electro-controlled soft systems with simple design/fabrication strategies in the soft robotic field for remote manipulation and transportation.In this study, soft hydrogel walkers with electro-driven motility for cargo transport have been developed  Stimuli-responsive hydrogels with controllable volume/shape changes in response to external stimuli such as electric field124579101214151617181920212224252627Typically, electro-responsive hydrogels are made of polyelectrolyte networks that contain ionic groups. Under electric fields, the polyelectrolyte networks can achieve asymmetric swelling/shrinking volume changes as well as bending behaviors, due to the osmotic pressure difference induced by electric-field-driven ion motion. Based on the electro-induced volume/shape changes, electro-responsive hydrogels are widely used for engineering soft chemo-mechanical systems, such as artificial crawler2930co-acrylamide) (poly(AMPS-co-AAm)) networks with an arc looper-like shape. The hydrogel walkers can reversibly bend and stretch via repeated “on/off’ electrical fields in electrolyte solution to achieve one-directional walking motion on a rough surface. Furthermore, the hydrogel walkers can be used to load very heavy cargo for efficient one-directional transportation. Such hydrogel systems are promising as soft robotics for cargo transport, and also show great potential for developing remotely-controllable soft systems such as artificial muscles and actuators.In this study, we report on a facile strategy for fabricating hydrogel walkers with electro-driven motility for cargo transport. The hydrogel walkers consist of crosslinked polyanionic poly(2-acrylamido-2-methylpropanesulfonic acid-co-AAm) hydrogel walkers is shown in N,N’-methylenebisacrylamide (MBAA), and 2-oxoglutaricacid (KGA) is injected into the mould  hydrogel walkers, the AMPS acts as the electro-responsive moiety due to its strongly ionizable sulfonate group; while the AAm serves as the copolymer to improve the mechanical strength of the fragile PAMPS hydrogel. The effects of the monomer ratio on the electro-responsive property and the mechanical strength of the hydrogels are shown in ε), as compared to those with 0.6 M and 0.5 M AMPS (co-AAm) hydrogel. To investigate the crosslinkage of hydrogel walker, the distribution of sulfur element at the cross-section of hydrogel walker, which is only contained in the AMPS monomer, is studied by SEM that coupled with Energy Dispersive Spectrometer (EDS)  . Three der (EDS)  are seleer (EDS)  from theer (EDS)  indicateco-AAm) hydrogel is a polyanionic hydrogel that can bends toward the cathode in electrolyte solutions quickly and significantly. Thus, the electro-induced bending behaviors of the hydrogel walkers are investigated by immersing them between two horizontally-placed carbon electrodes in NaCl solution, with the belly side and the back side respectively facing the cathode and the anode (ε) reaching 100% as compared with the one under voltage of 10 V (ε = ~90.69%). Meanwhile, with increasing the voltage from 10 V to 25 V, the time required for the hydrogel walker to reach the equilibrium bending deformation reduces from ~32 s to ~6 s. The results indicate that the poly(AMPS-co-AAm) hydrogel walkers can achieve faster and more significant bending behaviors with increasing voltage. Therefore, we can control the bending behaviors of the hydrogel walkers by regulating the applied voltage.The poly(AMPS-he anode . As showco-AAm) hydrogel walkers under 25 V voltage for fast actuation. As shown in co-AAm) hydrogel walkers in response to electric field.The reversibility and repeatability of the bending behaviors are investigated by applying the poly(AMPS-co-AAm) hydrogel walkers with reversible and repeatable bending/stretching behaviors can achieve one-directional walking motion by applying repeated electrical triggers. To investigate such electro-induced walking behaviors, a resin plate with ratchet surface that fabricated by Stereo Lithography Apparatus is used as the rough substrate for the walking (m × n) are employed to study the effect of ratchet topography on the walking motion of the hydrogel walker. A cargo-loaded hydrogel walker, with cargo weight (mc) being 25 times that of the walker at dried state (m0), is placed on four different ratchet plates, with step sizes of 0.4 mm × 0.2 mm, 0.8 mm × 0.2 mm, 0.8 mm × 0.4 mm, and 1.2 mm × 0.2 mm for electro-induced walking  hydrogel walkers for cargo transport, cargo with different weights of 25 m0, 50 m0, 75 m0, 100 m0 and 125 m0, are respectively loaded on the hydrogel walkers for walking  hydrogel is synthesized by free radical polymerization in an assembled mould. The mould is assembled with a quartz glass plate, a Teflon plate and a Teflon spacer. In the mould, the monomers are polymerized under UV irradiation from the quartz glass side. Due to the attenuation of UV light strength along the irradiation distance, there exists a gradient distribution of crosslinkage of hydrogel networks along the spacer height. Thus, poly(AMPS-co-AAm) hydrogels with anisotropic networks can be produced, with the body slightly bending to the more densely crosslinked side in water to form hydrogel walkers with an arc-shape containing two legs. The poly(AMPS-co-AAm) hydrogel walkers possess crosslinked networks with negatively-charged sulfonic groups. When applying an electric field to the hydrogel walkers in NaCl solution, the free ions of NaCl solution can move toward the counter-electrodes. However, for the hydrogels, only the mobile counterions of the negatively-charged sulfonic groups can move toward the counter-electrodes, since the motion of the sulfonic groups is restricted by the crosslinked networks. Such ion motions can create an ionic concentration gradient within the hydrogel networks along the direction of the electric field, resulting in an osmotic pressure difference within the hydrogel walkers14co-AAm) hydrogels can be well-controlled by regulating the applied voltage. Such bending/stretching behaviors of the poly(AMPS-co-AAm) hydrogel walkers enable moving of the two legs on a rough surface to achieve one-directional walking motion under repeated "on/off" electric field. Moreover, although loading cargo suppresses the bending/stretching behaviors, hydrogel walkers that loaded with very heavy cargo still exhibit efficient walking motion for achieving cargo transportation.To create an arched hydrogel walker with two legs for walking motion, poly(AMPS-co-AAm) hydrogel walkers that enable electro-driven motion for cargo transport. The hydrogel walkers allow controllable and reversible bending/stretching behaviors via repeated "on/off" electrical fields in electrolyte solution. Based on such bending/stretching behaviors, the hydrogel walkers can move their two legs to achieve one-directional walking motion on a rough surface via repeated "on/off" electro-triggering cycles. Furthermore, the hydrogel walkers can also achieve one-directional walking motion when loaded with very heavy cargo for efficient cargo transport. The poly(AMPS-co-AAm) hydrogel walkers with simple design/fabrication strategy and excellent cargo-loaded walking behaviors are promising for developing electro-controlled soft systems in the soft robotic field for remote manipulation and transportation.In summary, we have developed a simple approach for creation of arched poly and sodium chloride (NaCl) were purchased from Chengdu Kelong Chemical Reagents. 2-oxoglutaricacid (KGA) was purchased from J&K Scientific Ltd. All chemicals were used as received without further purification. Deionized water  from a Milli-Q Plus water purification system (Millipore) was used throughout this work.2-Acrylamido-2-methylpropanesulfonic acid (AMPS) was purchased from Sigma-Aldrich. Acrylamide (AAm), co-AAm) hydrogel with thickness of ca. 0.5 mm was cut into uniform strips as the hydrogel walkers for further study. All hydrogel walkers were dyed with methylene blue for easy observation. The chemical composition of the hydrogel walker was characterized by FT-IR . The crosslinkage of the hydrogel walker was investigated by studying the distribution of sulfur element that contained only in the AMPS monomer at the cross-section of hydrogel walker using SEM  coupled with Energy Dispersive Spectrometer (EDS).The hydrogel walker was synthesized by free radical polymerization. 0.7 M AMPS, 0.3 M AAm, 0.05 M cross-linking agent MBA, and 0.008 M initiator KGA were dissolved in deionized water as monomer solution. Nitrogen gas was bubbled into the monomer solution for 15 min to remove dissolved oxygen in the system. For fabricating hydrogel walkers with looper-like shape, a quartz glass plate, a Teflon plate spacer (thickness: 0.3 mm) and a teflon plate were sequentially assembled by clamps to create a mould for hydrogel synthesis . Next, tco-AAm) hydrogel walkers in response to electric field were investigated by using hydrogel walkers with fully stretched size of 10.0 mm × 2.0 mm × 0.5 mm (length × width × thickness) as the sample. Two parallel carbon electrodes, horizontally placed 44 mm apart, were immersed in 0.01 M NaCl solution to apply the electric field. Then, the hydrogel walker was immersed in the NaCl solution and placed in the centre of the two carbon electrodes, with the belly side facing the cathode (ε) was employed to evaluate the bending behaviors, which can be calculated by the following equation:The bending behaviors of poly.where l walker  before aco-AAm) hydrogel walkers were studied by using hydrogel walkers with fully stretched size of 10.0 mm × 4.0 mm × 0.5 mm as the sample. The distance between the ends of their two legs (L0) was 8.6 mm. Meanwhile, the fully stretched size of the hydrogel in dry state was 2.6 mm × 1.0 mm × 0.1 mm. The hydrogel walker, with mass (m0) of 1.058 mg at dried state, was loaded with different weights of Teflon cargo by an adhesive (Konishi). The mass percentages of the loads compared to the dry mass of the hydrogel were 25 m0, 50 m0, 75 m0, 100 m0, and 125 m0, respectively. Then, the cargo-loaded hydrogel walker was placed onto a resin ratchet substrate fabricated by Stereo Lithography Apparatus for the walking. Considering that the loaded hydrogel walkers suffer from larger resistance against their movements, two parallel carbon electrodes, both immersed in 0.01 M NaCl solution, were vertically placed 34 mm apart to provide stronger electric intensity for powering their walking. The ratchet substrate was centrally placed between the two parallel carbon electrodes .


Given that alcohol use is highly prevalent at US colleges, we explored factors related to problem drinking behaviors  among 4098 Black and White students from two- and four-year colleges who completed an online survey. We found an interaction between race and sex such that, among Whites, females had less PDB than males . An interaction between race and school type also existed, such that White students from four-year schools had greater PDB . An interaction between race and stress suggested that Black students were more negatively affected by stress in terms of PBD . For US college students, alcohol use is highly prevalent , and driTwo commonly reported risk behavior areas coinciding with alcohol consumption and binge drinking include sexual health risk behaviors  and drivi.e., binge drinking, driving after drinking, having sexual intercourse after significant alcohol consumption) among Black and White students attending two- and four-year colleges.Problem Behavior Theory suggests that problem behaviors, defined as socially problematic, concerning, or undesirable behaviors usually with negative consequences , typicalIn Fall, 2010, 24,055 students at six Southeast colleges were recruited to complete an online survey. The survey consisted of 230 questions that assessed for a variety of health topic areas, which took approximately 20 – 25 minutes to complete. Students received an e-mail containing a link to the consent form with the alternative of option out. Those who gave consent were directed to the survey; 4849 (20.1%) completed the survey . This sti.e., other race/ethnicities were excluded from the analyses).Students’ age, sex, race/ethnicity, and type of school attended were assessed. Race/ethnicity was categorized as non-Hispanic White or Black given the focus of the current study  “In the past 30 days, on how many of those days did you drink more than 5 alcoholic drinks on one occasion?”; 2) “Did you drink alcohol or use drugs before you had sexual intercourse the last time?” ; and 3) “During the past 30 days, how many times did you drive a car or other vehicle when you had been drinking alcohol?” For the second question regarding alcohol or drugs prior to the last sexual episode, we found that 88% of students that reported marijuana use also reported frequent alcohol use in the past 30 days; thus, this limitation in the assessment is assumed to minimally impact research findings. An aggregate PDB score was then created, with a range of 0 to 5. The variable alcohol or drugs prior to last intercourse was maintained as a dichotomous variable, with 0 indicating no use prior to last intercourse and 1 indicating use. Binge drinking was recoded into a sub-score of 0 to 2, with 0 indicating no binge drinking, 1 indicating binge drinking 1 – 2 times in the past 30 days, and 2 indicating binge drinking ≥3 days in the past 30 days. Driving after drinking was recoded into a sub-score of 0 to 2, with 0 indicating no drinking and driving, 1 indicating drinking and driving once in the past 30 days, and 2 indicating drinking and driving 2 days in the past 30 days. A score of 5 indicated engaging in all three PDBs and frequently engaging in binge drinking and driving after drinking .To assess depression, we administered the Patient Health Questionnaire (PHQ-2) , which iBivariate analyses were conducted to examine differences in sociodemographic and psychosocial factors in relation to the three dichotomous PDB, using chi-squared tests for categorical variables and t-tests for continuous variables. Sociodemographic and psychosocial factors associated with the aggregate PDB score were then examined using multivariate regression, forcing the correlates of interest into the model. Interactions between race and other sociodemographic and psychosocial factors were also examined in relation to PDB. Statistical significance was set a p = 0.05 for all tests.This study’s limitations include a lack of generalizability and a low response rate (20.1%), which may suggest responder bias. Furthermore, previous research has indicated that, despite lower response rates, internet surveys yield similar statistics regarding health behaviors compared to mail and phone surveys .We aimed to determine the sociodemographic and psychosocial factors impacting problem drinking behaviors among black and white students attending two- and four-year colleges. Our research included students from two-year colleges whose nationwide population has shown a five-fold increase over the past 40 years and have been studied less frequently compared to those from four-year colleges  17]. Th. Th17]. Our study documented novel correlates of PDB, particularly related to race/ethnicity. We found that White females had lower PDB index scores compared to their male counterparts. Previous studies found similar findings such that males accounted for the majority of binge or heavy drinking  and thatResults also indicated that White students attending four-year schools had higher PDB index scores compared to Whites students attending two-year schools. This effect, however, was not demonstrated among Black students. This difference may be due to the varying social norms, cultures, and environments among two- and four- year academic institutions. Risk factors for alcohol abuse are known to be related to the presence of residence halls, fraternities and sororities, or intercollegiate athletic programs, which are all relatively absent at two-year colleges . There mIn addition, despite having lower PDB indexes, Black students were more negatively affected by higher perceived stress in terms of their PDB compared to White students. While perceived stress levels have previously been found to impact PDB  no otherThe novel findings presented in this study indicate that potential strategies to address PDB ought to consider the differences among races in relation to sex, campus environments, and reactions to stress as they impact PDB. Further examination of these interactions is warranted in other college student and young adult samples.Our results have several important implications for future prevention efforts. In addition to the observed inter- actions, our findings suggest that students who are male, attending four-year colleges, and have significant depressive symptoms are most susceptible to engaging in problem drinking behaviors. Thus, future prevention efforts may consider placing greater emphasis on this subgroup. Additionally, while our results suggest that students attending four year colleges have higher problem drinking behavior indexes, we believe that further research is needed to accurately assess the two-year college population where a knowledge gap still exists. Specifically, perceived social norms have been suggested to play a role in being a contributor to drinking among traditional four-year colleges  but has Our study results suggest there are significant interactions between ethnicity with gender, type of school, and perceived stress on problem drinking behavior. In addition, several sociodemographic and psychosocial variables were found to be significantly associated with each of the three problem drinking behavioral factors and may assist in ultimately guiding future public health research and interventions. Additionally, whereas many previous alcohol-related studies have focused on traditional four-year academic institutions, our study included students from both two- and four-year colleges. Ultimately, these findings highlight the need for race/ethnic- and gender-specific interventions that ought to consider the varying environments among two- and four-year colleges. Interventions including a component that addresses stress may also prove to be an effective strategy.


Emergency General Surgery (EGS) is a rapidly evolving but understudied branch of Acute Care Surgery. Limited information exists regarding the contribution of malnutrition to the outcome of critically ill patients who undergo EGS.We hypothesized that malnutrition would be associated with increased risk of 90 day all cause mortality following ICU admission.We performed a single center observational study of patients treated in medical and surgical ICUs in Boston. We studied 1,361 patients age ≥ 18 years, who received critical care and an EGS associated procedure between 1997 and 2011. The exposure of interest, malnutrition, was determined in patients at risk for malnutrition via a Registered Dietitian formal assessment within 48 hours of ICU admission and categorized as non-specific malnutrition, protein-energy malnutrition, or without malnutrition. Nutrition data was determined via anthropometric measurements, clinical signs of malnutrition, malnutrition risk factors, and metabolic stress. Energy and protein delivery goals were determined by the Registered Dietitian. The primary outcome was all cause 90 day mortality determined by the US Social Security Death Master File. Adjusted odds ratios were estimated by multivariable logistic regression models.P = 0.009] and in patients with protein-energy malnutrition a 3.0 fold increased odds of 90-day mortality  compared to patients without malnutrition. Further, in survivors of hospitalization  patients with protein-energy malnutrition at ICU admission have a 2.8 fold increased odds of 90-day post discharge mortality  compared to patients without malnutrition. In a subset of patients with detailed follow up nutrient intake data (n = 533), the mean (SD) percent of goal energy and protein delivered was 48.3 (31) and 44.7 (30) during the seven days following EGS.The cohort was 58% male, 74% white and had a mean age of 60.1 years. 26% of the cohort had sepsis, 14% had acute kidney injury and 33% had non-cardiac acute respiratory failure. 17% of the cohort were readmitted to the Brigham and Women’s Hospital or Massachusetts General Hospital within 30 days of discharge. 60% had non-specific malnutrition, 8% had protein-energy malnutrition, and 32% without malnutrition. The 30, 90 and 365-day mortality was 9.1 and 17.9 and 29.6%. In an logistic regression model adjusted for gender and an ICU risk prediction score , patients with non-specific malnutrition have a 1.6 fold increased odds of 90-day mortality [adjusted OR 1.56 (95%CI 1.12-2.18), In critically ill patients who undergo EGS, malnutrition at ICU admission is predictive of adverse outcomes. In survivors of hospitalization, malnutrition at ICU admission is associated with increases in mortality following discharge.


Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations. Fruit” and “Vegetable” can be combined to form a new concept “Fruit And Vegetable” , μ(B), and μ(AB) be the membership weights of an exemplar p with respect to a pair of conceptsandand their conjunctionWe say that these membership weights are classical conjunction data if there exists a Kolmogorovian probability space , P), A, EBand events E ∈ σ(Ω) such thatDefinition 1. Classical conjunction data characterizes the membership values of the conjunction of concepts that can be modeled in a classical probabilistic framework. It is therefore important to characterize the notion of classical conjunction data in terms of the membership weights.The membership weights μ(A), μ(B), and μ(AB) of an exemplar p with respect to conceptsand their conjunctionare classical conjunction data if and only ifCorollary 1. A large body of experimental evidence and a considerable amount of data analysis indicate that the membership of exemplars with respect to concept combinations does not form classical conjunction data  of the item p1 = “coffee table” with respect to the conjunction 11 = “Furniture And Household Appliances” is single overextended with respect to the membership weights μ1(A) and μ1(B) of concepts 1 = “Furniture,” and 1 = “Household Appliances,” respectively. In the second case, membership weight μ2(AB) of the item p2 = “tree house” with respect to the conjunction 22 = “Building And Dwelling” is doubly overextended with respect to the membership weigths μ2(A) and μ2(B) of the concepts 2 = “Building,” and 2 = “Dwelling,” respectively.In Supplementary Table The phenomenon of overextension has also been demonstrated not only for membership estimations, but also in typicality  corresponds to the sum of the average of μ(A) and μ(B), plus an interference term ℜ(〈A|M|B〉) bounded byWhen A|M|B〉) = 0, the membership weight is simply the average of the former membership weights. This particular case, which has been shown to provide a good first approximation to exemplars of conceptual conjunction μ(B), which is equivalent to the probability of two joint classical events that are independent. When 0 < n < 1, the state of the concept is in the superposition of the two modes of combination.In the absence of interference, i.e., when ℜ = 0.97, μ(B) = 0.31, and μ(AB) = 0.53. This case is represented by the vectorsFor the second exemplar, μ(A) = 1, μ(B) = 0.49, and μ(AB) = 0.78, and the state vectors are given byFor example, Aerts  builds aM is defined by the projection operatorIn both cases n − 1, for n = dim.The next theorem shows that Let μ(A), μ(B), and μ(AB) denote the membership of an exemplar with respect to conceptsand their conjunctionThe membership weights are compatible with a complex Hilbert space model3if and only ifwhereTheorem 1. Proof. We derive Equation (17) by applying conditions (13–16). First, if M is a zero- or three-dimensional projector, thenA〉 and |B〉 to be any two mutually orthogonal unit vectors.M is either a one- or two-dimensional projector. We apply conditions (13–16) to vectors |A〉 and |B〉 in these two cases separately, and combine the results to obtain (Equation 17).Next, we consider the cases where M is a one-dimensional projector, then without loss of generality, we can chooseIf A〉 and |B〉 as follows:AB) is given byNote that conditions (13) and (15) are satisfied by choosing the coefficients in |We then apply condition (14) to obtainF, cos(γ3)) is a convex combination of Since 1, θ2 in We setSubstituting Equations (27) and (28) in Equation (26), we obtainThen Equation (23) implies thatTherefore, the interference term is bounded as follows:Next, combining Equations (23) and (24), we obtainHence,We use the parametrization for λ and κ given by Equation (27), and apply Equations (29–33), to obtainCombining Equations (35) and (34) yieldsM is a one-dimensional projector, conditions (13–16) implyTherefore, when M is a two dimensional projector. Without loss of generality, we can assumeNext, consider the case in which A〉, |B〉 as followsAB) is given byThe requirements Equations (13) and (15) are satisfied by choosing the coefficients in |We apply condition (14) to obtainF, cos(γ2)) ≤ 1, Equation (40) implies thatSince We repeat the procedure used in the one-dimensional case to obtainSince M is a two-dimensional projector, conditions (13–16) implyTherefore, when We complete the proof by merging Equations (37) and (44).n for n > 3, doesn't provide additional modeling power since the condition given by Equation (17) remains. Also, the case 2 is more restrictive than the 3 case. In fact, membership data compatible with conditions (13–16) for 2 must satisfy μ(A) + μ(B) = 1  and μ(B), respectively. Moreover, since |C〉 as a whole represents the concept combination M ⊗ M is applied to |C〉 to obtain μ(AB).To recover the probabilistic structure of the former concepts in the combination, the operators The following definition summarizes how data is represented in the second sector.Let μ = {μ(A), μ(B), μ(AB)} be a triplet denoting the membership of conceptsand their conjunctionWe say that the triplet μ admits a representation in ℂn ⊗ ℂnif there exists a unit vector |C〉 ∈ ℂn ⊗ ℂn, and an operatorM:ℂn → ℂnsuch thatDefinition 2. n. Without loss of generality, we can take M to be an orthogonal projector on the subspace of ℂn spanned by the basis elements |1〉, …, |r〉, with r < n. Hence,Let C〉 be a unit vector in ℂn ⊗ ℂn. That is,andWe now prove that the operator M and the vector |C〉 above satisfy Equations (45–47) if and only if μ(A), μ(B), and μ(AB) are classical conjunction data.Next, let |Let μ = {μ(A), μ(B), μ(AB)} be a triplet denoting the membership of conceptsand their conjunctionThe triplet μ is classical conjunction data if and only if it admits a representation in ℂn ⊗ ℂnwith n = 2.Theorem 2. Proof. If μ admits a representation in ℂ2 ⊗ ℂ2, there exists a unit vector |C〉 ∈ ℂ2 ⊗ ℂ2 and an operator M such that Equations (45–47) are satisfied. If μ(A) = μ(B) = μ(AB) = 0 or 1, we can choose |C〉 to be any unit vector in ℂ2 ⊗ ℂ2, and M to be a zero- or two-dimensional projector, respectively. Otherwise, let {|1〉, |2〉} be the canonical basis for ℂ2. Without loss of generality, we can define |C〉 byand M by the one-dimensional projector into the subspace determined by |1〉. Note thatAB) ≤ μ(A), μ(AB) ≤ μ(B), and since |C〉 is a unit vector,Then, clearly μ is the semantic estimation of an exemplar pi with respect to conceptsbe a set of experimental data, where μand their conjunctionA representation of μ in ℂ3is defined as a pair of unit vectors |A〉, |B〉 ∈ ℂ3, and a collection of orthogonal projectorssuch that conditions (13–16) are satisfied for i = 1, …, k. We sayis a representation of μ in ℂ3.Definition 3. Leti(x) is the semantic estimation of exemplar pi with respect to conceptsbe a set of experimental data, where μand their conjunctionThe set of data μ has a representation in ℂ3if and only if for all i = 1, …, kTheorem 3. Proof. Let |A〉 = , |B〉 = , and |C〉 =  be the canonical basis for ℂ3. We prove that, if Equation (53) is satisfied for each i = 1, …, k then there exists an orthogonal projector Mi such that conditions (13–16) are satisfied for |A〉, |B〉, and Mi.i(A), μi(B) and μi(AB) satisfy (Equation 53), by Theorem 1 for each i ∈ {1, …, k} there exist two vectors,and an orthogonal projector Ai〉 and |Bi〉, as constructed in the proof of Theorem 1, are orthonormal. We set |Ci〉 = |Ai〉 × |Bi〉 so that the set {|Ai〉, |Bi〉, |Ci〉} forms an orthonormal basis for ℂ3 for any i ∈ {1, …, k}. Next, we define the operator Ui bySince μi is a unitary matrix whose action induces a change from the basis {|Ai〉, |Bi〉, |Ci〉} to the basis {|A〉, |B〉, |C〉}. Note that Ui|Ai〉 = |A〉, Ui|Bi〉 = |B〉, and Ui|Ci〉 = |C〉.Ui to represent A〉, |B〉, |C〉} as follows:We can also use the operator Ui = 1, …, k,We use the fact that A〉 and |B〉, and a set of projectors Mi, for i = 1, …, k, corresponding to the membership operator for each exemplar. Since the unitary transformations preserve the inner product between vectors and operators, the values of the membership estimations μi(A), μi(B), and μi(AB) are preserved.Theorem 3 provides a data representation in terms of a single pair of vectors |p =“filing cabinet” and q =“heated waterbed” mentioned in Section 1.3. These can now be represented by the states |A〉 = , |B〉 =  and the following measurement operatorsFrom a geometric perspective, the operators Mp and Mq correspond to rotations of the one-dimensional projector M →  in ℂ3.Consider for example the exemplars n ⊗ ℂn. We first define different types of representations for multiple exemplars, and then provide explicit representation theorems for the cases n = 2 and 3.We now apply unitary transformations in the concrete representations of the tensor product model in ℂA zero-type representation ofn ⊗on the tensor product space ℂ ℂnis a unit vector |C〉 ∈ ℂn ⊗ ℂn, and a collection of orthogonal projectorsfrom ℂn ⊗ ℂnto ℂn ⊗ ℂn, such that conditions (47)–(49) are satisfied withfor i = 1, …, k. We sayis a zero-type representation ofin ℂn ⊗ ℂn.Definition 4. C〉, and a collection of measurements that represent the membership weight estimations. However, this representation cannot be appropriately interpreted because i = 1, …, k.The zero-type representation is, mathematically speaking, the most general representation in the tensor product model that is consistent with the modeling principles of quantum cognition because it assumes a single concept state |i = 1, …, k. Therefore, these operators are not entangled because they act on different sides of ℂ3 ⊗ ℂ3.A more reasonable representation of data assumes that A first-type representation ofon the tensor product space ℂn ⊗ ℂnis a unit vector |C〉 ∈ ℂn ⊗ ℂn, and a collection of orthogonal projectorsMifrom ℂnto ℂn, for i = 1, …, k, such that  is a zero-type representation ofin ℂn ⊗ ℂn.Definition 5. C〉 describes the situation of having two concepts and their combination, and Mi represents the semantic estimation of exemplar pi, i = 1, …, k.The first-type representation is a direct extension of the representation of individual exemplars in Definition 2, and thus it is interpreted according to such representation: The state |The zero- and first-type representations require different conditions to model a collection of exemplars for a pair of concepts and their conjunction. While the first-type corresponds to the natural way to represent a pair of systems in quantum physics, and thus is the natural way to define a representation in the tensor product model for concepts, the zero-type provides a more general way to build concrete representations because it does not impose a product structure on the concept state or on the membership operators for the exemplars.In fact, from Definitions 4–5 it is trivial to deduce that a first-type representation is also a zero-type representation.2 ⊗ ℂ2.The following theorem characterizes the cases when a set of data has a zero-type representation in ℂThe set of datahas a zero-type representation in ℂ2 ⊗ ℂ2i is classical conjunction data for iif and only if μ = 1, …, k.Theorem 4. i = 1, …, k, we use the construction in the proof of Theorem 2 to obtain a tensor i. Next, we use unitary transformations to change this representation so that 2 ⊗ ℂ2. To facilitate the notation, we will make use of the isomorphism 𝕀 between ℂ2 ⊗ ℂ2 and ℂ4. LetProof. For each We defineCi〉 in ℂ4.The isomorphism 𝕀 allows us to represent Ci〉 to one of the canonical basis vectors of ℂ4, and use this transformation to represent the operators MA,MB, and M∧ in ℂ4. Next, we apply the the inverse isomorphism 𝕀−1 to map these new representations to ℂ2 ⊗ ℂ2.We can prove the theorem by building a unitary transformation that takes |Di〉, |Ei〉, |Fi〉 be three vectors in ℂ4 such thatLet |Ci〉, |Di〉, |Ei〉, and |Fi〉 form an orthonormal basis for ℂ4.The vectors |Leti is a unitary matrix whose action induces a change from the basis {|Ci〉, |Di〉, |Ei〉, |Fi〉} to the basis Note that Ui can now be used to change the basis in which The operator U−1iUi = UiU−1i, we obtainSince 𝟙 = U−1 to obtain a zero-type representation in ℂ2 ⊗ ℂ2:We then use the inverse isomorphism 𝕀Ci〉, M) for the exemplars pi with M →  obtained from Theorem 2.We have constructed a zero-type representation In the construction of Theorem 4, note that when Equation (66) entails operators Stating the necessary and sufficient conditions required for a set of data to have first-type representation is out of the scope of this paper. However, we now introduce another type of representation that is mathematically simpler, and can be used to obtain sufficient conditions for a first-type representation.A second-type representation ofon the tensor product space ℂn ⊗ ℂnis a pair of unit vectors |A〉, B〉 ∈ ℂn, and a collection of orthogonal projectorsMifrom ℂnto ℂn, for i = 1, …, k, such that  is a zero-type representation ofin ℂn ⊗ ℂn.Definition 6. C〉 to be a product state.The second-type is a mathematical simplification of the first-type representation that assumes |The set of datahas a second-type representation in ℂ2 ⊗ ℂ2if and only if for each i = 1, …, k there existsuch that Equations (45–47) are satisfied.Lemma 1. Ai〉 to |1〉 and |Bi〉 to |1〉 respectively, for i = 1, …, k. Then, it is straightforward to show that Proof. Let Theorem 4 and Lemma 1 characterize the sets of data that have a zero- and second-type representations. Since the first-type representation is less general than the zero-type representation, but more general than the second-type representation, these results can be applied to obtain an upper and lower bound for the number of exemplars that have a first-type representation in a given set of data.2 ⊗ ℂ2. We now extend our results to ℂ3 ⊗ ℂ3 so they become compatible with the representation analysis developed in Section 3.1 for a Hilbert space model in ℂ3. The next corollary extends the proof of Theorem 4 to the space ℂ3 ⊗ ℂ3.Note that Theorem 4 is built in ℂIf the set of datahas a zero-type representation in ℂ2 ⊗ ℂ2, thenhas a zero-type representation in ℂ3 ⊗ ℂ3.Corollary 2. Proof. Let 2 ⊗ ℂ2. We can create a vector3 ⊗ ℂ3 by choosing2 ⊗ ℂ2 are preserved. This completes the proof.Similarly, we can also create operators 3 ⊗ ℂ3.Since second-type representations are also first- and zero-type representations, we can apply Corollary 3.2 to obtain a first- and second-type representation in ℂIn quantum theory, measurement operators can be incompatible. That is, when we consider two different observables, the result of their sequential application can depend on the order in which they are applied. The fact that quantum measurements can be incompatible is related to fundamental differences between the quantum and classical realms, such as the observer phenomena, and the Heisenberg uncertainty principle , |B〉 = , and {M1, M2} be a representation in ℂ3ofand setWe say p1and p2are compatible with respect to the conceptsAif and only if c = 0, cB = 0, ABand c = 0, respectively.Definition 8. 3 ⊗ ℂ3.For simplicity, we will study compatibility for zero-type representations in ℂLet |C〉 =  ⊗ , and3 ⊗ ℂ3ofand setWe say p1and p2are compatible with respect to conceptsandif and only ifrespectively.Definition 9. 3 and in ℂ3 ⊗ ℂ3 using the data in Hampton  measurements.This is consistent with our expectations because the representation in the second sector ℂSince our data was collected presenting the exemplars in only one specific order Hampton, , these c3 and ℂ3 ⊗ ℂ3, respectively. Next, we introduced unitary transformations to provide concrete representations that are consistent with the cognitive principles of the quantum model of concepts, and used these concrete representations to study the question of measurement compatibility.In this paper, we have made some advances on the representational aspects of the quantum model for concept combinations. First, we proved that the first and second sectors of the two-sector Fock space model of concept conjunctions can be concretely represented in ℂThe representations introduced here could be an important tool for future applications. First, since they are consistent with the cognitive principles of the quantum model of concepts, the model could easily be introduced to a wider audience, and extended to produce concrete representations in the two-sector Fock space model. Second, they can be adopted as a representational standard for different groups who seek to develop their own computational implementations of the model. Third, the fact that all the measurements are represented in a single basis constitutes a tremendous mathematical advantage for studying the probabilistic structure of concepts.The evidence obtained in the application of our representations to the issue of exemplar compatibility is consistent with the assumptions of the model. Since the second sector entails logical reasoning, measurements in the tensor product model should be compatible. However, incompatible measurements are likely to be found in the Hilbert space model, since the first sector is associated with non-logical or intuitive reasoning. Moreover, this line of enquiry invites us to explore possible relations between the projector operator structure and the meaning of the exemplar.In summary, the introduction of unitary transformations and the subsequent application to develop concrete representations of concepts and their combinations seems to be a promising line of research that has the potential to expand both theoretical and applied research in quantum cognition.This research has been funded by an internal grant from the I.K Barber school of Arts and Sciences at UBC Okanagan.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


A necessary, but not sufficient, mathematical condition for the coexistence of short replicating species is presented here. The mathematical condition is obtained for a prebiotic environment, simulated as a fed-batch reactor, which combines monomer recycling, variable reaction order and a fixed monomer inlet flow with two replicator types and two monomer types. An extensive exploration of the parameter space in the model validates the robustness and efficiency of the mathematical condition, with nearly 1.7% of parameter sets meeting the condition and half of those exhibiting sustained coexistence. The results show that it is possible to generate a condition of coexistence, where two replicators sustain a linear growth simultaneously for a wide variety of chemistries, under an appropriate environment. The presence of multiple monomer types is critical to sustaining the coexistence of multiple replicator types.  Many models of early life demonstrate competition among chemical species, which leads to processes of natural selection and, eventually, to a decrease in the chemical diversity ,2. HowevMuch of the literature on replicator dynamic modeling has focused on the case where monomer resources are lost when a replicator decomposes ,3,4. HowThe species considered in this study are short biopolymers, of order 10–100 monomers—large enough to store significant information and possess potential for catalytic function, but limited in size by the instability of their associations. Such macromolecules or assemblies are not expected to follow kinetics based on elementary reaction orders, but rather, may possess observed non-integer reaction orders dependent upon nucleation kinetics and conformation ,14,15. MThe coupling to the environment is defined via a fixed inlet flow rate of building materials into the system, different from many closed-mass models ,8 in prei.e., predator-prey model), where the explicit interaction between the species lead to a coexistence scenario with oscillatory populations. More recent work in ecological models has focused in competitive scenarios for coexistence between multiple predators and a single prey specie [The combination of these three key effects—recycling, variable reaction order, and fixed monomer inlet flow—creates a dynamic scenario similar to a continuous stirred tank bioreactor with immobilized enzymes . When a y specie ,24,25, aOf course, the environment would not be expected to be constant over long periods of time, and modeling work has also considered the case of randomly fluctuating conditions  and direAnalysis of the reaction model for the two-replicator, two-monomer case provides a criterion for coexistence, according to the linear growth definition. From the chemical parameters and the inlet conditions, one can compute whether or not the linear growth solution is feasible. A search through many parameter sets supports the case that this criterion is, in fact, necessary for coexistence. Furthermore, about half of the scenarios satisfying this condition do, in fact, exhibit coexistence in simulation. Those that do not may be rationalized in terms of the stability of the linear growth solution. This criterion for coexistence provides a design tool to guide experimental studies. It also illustrates that most of these multi-dimensional parameter sets will not lead to coexistence. However, the set of parameters enabling coexistence is still infinite and could be discovered by a complex prebiotic soup. n replicator units, , which grow in an autocatalytic manner, and λ monomers , which serve as building materials for the replicators. F , while the larger replicating units accumulate inside the constant volume, V , similar to the cells in a well-mixed fed-batch bioreactor [The mathematical model of a prebiotic system includes the molar concentrations of two types of chemical species: oreactor . Previouoreactor ,27, suppLij. For the purposes of this work, two different replicator types, , and two different monomer types, , are included. Each of the replicator units has a composition of 20 building units, such that Lia + Lib = 20. Only the composition of each replicator is directly tracked in the model. The exact sequence is not directly modeled, although the impact of sequence on the kinetics could be modeled via the unique kinetic parameters for each replicator type. In Equations (1) and (2), the composition of the replicator units is represented by the parameters, ix, is represented by the constant, kr,i, whereas the dissociation of a replicator unit into free monomers is controlled by the constant, kd,i. The replicators do not interact directly, as reflected by the first-order reaction on ix, as well as the lack of xj terms in Equation (1). The autocatalytic replication rate of a replicator unit depends not only on the magnitude of kr,i, but also on its own concentration ix and the monomer concentrations, mj, inside the reactor. In simple reactions, the reaction orders are integer values associated with the stoichiometry coefficients of the corresponding reaction. This is referred to as an elementary reaction. If the mechanism of replication for replicator R1 is described by an elementary reaction, according to L1aA + L1bB + R1 → 2R1, then the monomer reaction orders in the reaction rate are α1a = L1a and α1b = L1b. Alternatively, Equations (1) and (2) employ an observed reaction order [αij may be obtained from parameter fits to experimental data  that lead to such non-integer values. This type of implementation is not new to the area of prebiotic chemistry. Parabolic replicators [r = ikx1/2, to represent the growth rate of replicating templates. In our work, the replication rate expression is an overall representation of the replication process without assuming a particular mechanism for how it happens. Evaluating reaction orders of the monomer concentrations in the replicator kinetics is a departure from the more common analysis of the order of the replicator concentration [In Equation (1), the formation of a new replicator unit, on order ,28, wherlicators ,30 use antration ,17,29,30ix, limits population growth, which could be hydrolysis in a condensation reaction. This step defines the monomer recycling of the building blocks back to the available pool of monomer in the system. As shown in Equations (1) and (2), the decomposition reaction depends only on the concentration of the replicator, ix, neglecting any interaction effects with other replicators or monomers. The individual n replicators in the model are coupled via sharing of available building material, described by Equation (2). Thus, they may compete for the limited amount of monomer that is supplied to the system, or they may even cooperate to best distribute and utilize the limited building material among the various species. Decomposition of a replicator unit, F , at the same time that they are consumed and released from the replication/dissociation process of the n replicator units. One of the unique features of this model for origins of life chemistry is that one can explicitly consider environmental dynamics in prebiotic conditions  using the inlet flow rate, F , and inlet monomer concentrations, min,j. Changing the values of these parameters during a simulation allows one to modify the net growth rate of each of the species inside the reactor,and to explore the potential effects of these environmental conditions in the growth of replicators in the reactor. Equation (2) describes the concentration dynamics of the monomers inside the system. This equation also represents the dynamic coupling between different replicator units in the model. The monomers flow in and out of the system at a flow rate, i.e., considering inlets and outlet streams of monomers) coupled to the surroundings, the model here is macroscopic, so stochastic effects due to low replicator concentrations are neglected [The mathematical description in Equations (1) and (2) also resembles the definitions of vesicle-like compartments or “protocells” ,31,32, ieglected . n = 2 replicators, x1, x2 and λ = 2, and monomers, ma, mb, the replicator growth rate is written as:As mentioned in the introduction, the definition of coexistence posed here is that multiple autocatalytic replicators sustain linear growth rates simultaneously, despite sharing common resources. Here, a mathematical description of this coexistence scenario is provided, based on the kinetic, composition and environmental parameters in Equations (1) and (2). In the particular case of the chemical system described by Equation (1), with x1 = c1t and x2 = c2t, where c1 and c2 represent the constant growth rates of each replicator. The value of the initial concentration of the replicators inside the system (which would correspond to the intercept of these lines) is neglected, relative to the long-term replicator populations. Using these proposed linear replicator profiles, and noticing that According to the proposed linear behavior, one may express the replicator concentration profiles as ma and mb, that enables the simultaneous linear growth of both replicators when c1 and c2 are positive. Notice then that the values of the monomer concentrations depend on the kinetic parameters of the replicators, but not on the composition of either replicator or on the environmental parameters. The solution of the nonlinear system of equations in Equations (5) and (6) is:Since the idea is to evaluate the sustained diversity of the replicators over long periods of time, one can assume that am and bm, can be derived by writing c1, c2, in order to construct a system of linear algebraic equations to solve for these unknown replicator growth rates. The steady-state equations for am and bm, according to Equation (2), are:These long-term monomer concentrations do not depend on variables that change over time. Equations (7) and (8) suggest that for a linear replicator growth, it is necessary that the monomer concentrations inside the fed-batch reactor reach a steady-state. The steady-state solution of the monomer concentration, c1, c2, are positive and increase rapidly. During the simulation, the monomer concentration decreases, due to the consumption by the replicators and the external outlet flow, but they continue to be positive, which means replicators are continuously being formed inside the bioreactor at a lower rate. Finally, the material balance in Equation (2) starts to reach a steady-state value as the replicator growth rates become equal to the rate of food supply to the bioreactor in Equations (9) and (10). The value of this steady-state for the monomer concentration is provided in Equations (7) and (8). In other words, the monomers A and B are the limiting reactants of the reactions, and the replication process cannot grow faster than the constant monomer supply rate. Equations (9) and (10) explain the rationale behind the assumption of a linear behavior for the replicators. At the beginning of the replication process, the replicators exhibit an exponential concentration profile, due to the initial concentration of monomers in the bioreactor and the addition of monomers in the system via the inlet flow L1a, L1b, L2a, L2b, one may evaluate if the two replicators will exhibit the coexistence linear behavior. If the replicator growth rates, c1 and c2, in Equations (9) and (10) are both positive, sustained coexistence may be possible, according to the linear growth definition proposed here. Equations (9) and (10) also incorporate elements from the environment via the inlet flow rate, F , and monomer concentrations, min,a, min,b, highlighting the importance of including the environment in the modeling of coexistence. Given the kinetic parameters of the autocatalytic replicators and the composition parameters, Coexistence of distinct species provides a mechanism to increase chemical diversity on the prebiotic Earth, allowing new species generated through mutation or spontaneous generation to take hold in the population. The model is used here to identify parameter sets that exhibit coexistence. Once the parameter sets are identified, suitable chemistries and environments can then be selected or designed. n = 2 replicator types and λ = 2 monomer types. Each replicator type is formed by 20 monomers. Given these four different chemical species, the parameter space of the model contains eight kinetic parameters  and two composition parameters . The exploration of the parameter space is made in two parts; first, a random sample selection is generated, having 10,000 different kinetic parameter sets using a statistical Latin Hypercube approach [The analysis is performed for a simple, but illustrative, case, with approach  with theLij. The equations are solved in MATLAB v.R2012a, using solver ode15s, due to the several orders of magnitude in the evaluated replication and dissociation rate constants that causes stiffness in the ODEs. The evaluation of Lij is constrained by forcing both replicator types to have at least one building unit of each monomer type. Therefore, since both replicators have a length of 20 units, 361 (19 × 19) possible combinations of the composition parameters are evaluated for each kinetic parameter set. Then, for each of the 10,000 kinetic parameter sets that have been generated, the ordinary differential equations (ODE) in Equations (1) and (2) are simulated using multiple combinations of the composition parameters, tf = 1 × 107 s), is several orders of magnitude greater than the decomposition timescales, Notice in 6 ODE simulations), the final total concentration of replicators, (x1 + x2 at t = tf), in each simulation is computed. For each of the kinetic parameter sets, only the combination of composition parameters that generates the maximum value of x1 + x2 at t = tf is selected, and then, the kinetic parameter sets are placed in ascendent order according to this value. x0,1 + x0,2 = 0.2 mol/m3). Over a longer simulation time, tf, these parameters lead to the extinction of the replicators and any information that they may contain. To organize the results of the large number of simulations in x1. It is clear from this figure that the most likely result in a constant monomer supply is a single-winner scenario (≃62% of the cases), since high x1 final concentration matches with the final total replicator concentration in x1 final concentration indicates that the other replicator has taken over the system. As for the remaining 62% of the kinetic parameter space, there are two possible scenarios—either one of the replicator types is able to take over the system as a “single-winner” or both replicator species are able to coexist over the simulation time. The main focus of this work is on the small fraction of the kinetic parameter space where both replicators are able to grow, despite sharing the monomers in the system. Among the parameter sets that exhibit coexistence at the end of the simulation, one of them is highlighted in . Therefore, the linear replicator profiles are based on how the reaction orders, αij, and the composition parameters, Lij, are used to manage the shared monomer resources. Lij is vital to developing the linear behavior observed in L1a = L2a = 10, describes a more competitive scenario between the replicators, since both of them equally require both monomers. In this case, the result of the simulation is a x2 single-winner scenario. Notice both replicators are less sensitive to the B concentration, given the low reaction orders, α1b and α2b. To highlight the role of the reaction orders as a metric of the sensitivity of the replicators to the monomer concentrations, an additional simulation of the parameter set in L1a = 10, L2a = 1 and α1b = 0.6 was performed, resulting in a x2 single-winner scenario. These examples suggest that both replicators are in a constant competition for the shared monomers and that replicators with low reaction orders are more robust to monomer variations and, therefore, less coupled to the dynamics of the remaining replicators in the system.Finding the right balance between αij and c1 and c2, are positive, then the desired linear behavior is possible. Here, Equations (9) and (10) are evaluated not only to screen for sustained diversity behavior, but also to screen for the complete extinction scenario. 6 different ODE simulations, evaluating all possible replicator compositions in the case study  for each of the 10,000 parameter sets used to explore the kinetics of these replicators. Notice that the sum of the percentages in the total column adds to 92.45%. In addition, 2.19% corresponds to unsuccessful parameter combinations, whose results presented numerical instabilities during the ODE simulation. The remaining difference (5.36%) corresponds to the successful simulations where the composition of the replicators was the same, (L1a = L2a). These results are not included in L1a = L2a) will be discussed later in this section. The diagonal values in c1 and c2 are both positive values. As for the quality in the identification of coexistence made by Equations (9) and (10), the probability of a Type I error for a particular parameter set is about 48%. These results indicate a key feature for the system of algebraic equations, since 0.9% of the entire parameter space leads to the coexistence of the replicators, and the system of algebraic equations is excluding most of the possible parameter combinations that can be evaluated for coexistence. The screening of the parameter space made by the system of algebraic equations in Equations (9) and (10) shows significant results for the case of the coexistence scenario. i.e., L1a = L2a). This table indicates that there is not a set of kinetic and composition parameters that led to the sustained linear behavior. Therefore, the system of algebraic equations accounts for all possible parameter combinations that exhibit coexistence. Overall, satisfying the system of linear equations in Equations (9) and (10) is a necessary, but not sufficient, mathematical condition for the coexistence of autocatalytic replicators in the model. L1a = L2a, coexistence is never observed, but rather, a single winner or extinction outcome. Having diverse replicator composition is a way to mitigate the kinetic competition between the replicators, as an additional degree of freedom in the coexistence of the system. x1 requires more monomer A and x2 requires more monomer B. The opposite scenario occurs for the α1a > α2a reinforces the x1 dependency on A, and α2b > α1b reinforces the x2 dependency on B  and (10) depends on the reaction orders and composition parameters only. Equations (9) and (10) show that coexistence of autocatalytic replicators requires a balance among all the parameters in the model, not only αij and Lij. However, the specialization of the replicators towards one particular monomer type is a conceptual explanation for the observations in min,a, min,b, and the lengths of both replicators are equal during the simulation. The system of algebraic equations in Equations (9) and (10) includes these variables into the parameter set to compute the coexistence condition. In the search for other coexistence scenarios, Equations (9) and (10) provide the relationship between the numerous degrees of freedom  in this design problem. Finally, the conjectures regarding the relationship between kinetics and composition of the replicators are limited to the scenario where the monomer inlet concentrations, Diversity is a prerequisite for selection and evolution, which motivates this study on chemical coexistence of replicating species. The kinetic model presented here includes a unique combination of features: monomer recycling, inlet and outlet monomer flow and variable reaction orders on the monomer concentration. Reversible linkages are a possible route to non-enzymatic replication in the prebiotic Earth, and this motivated the inclusion of recycling into the model. The monomer species may have been scarce in the prebiotic Earth, such that sustained replicator growth would be limited by the inlet flow rate of monomers into the system. Additionally, monomers may be lost in the outlet flow, so that a system that efficiently incorporates monomer would maximize its overall population. Monomer scavenged by one replicator type may be later transferred to another type via the recycling dynamic. Thus, aspects of cooperation, as well as competition are embodied in this model. The definition of coexistence presented here, that of sustained linear growth of multiple species, is in contrast to many common definitions of coexistence based on steady-state or oscillatory populations. This new definition is motivated by the model, in which the continuous inflow monomers, coupled with the monomer recycling, can yield a new dynamic behavior with sustained open-ended growth. A and B in the inlet stream were equal, and thus. coexistence was only possible when there was a dominant pairing of replicator and monomer . However, with unequal inlet concentrations, other combinations of kinetic parameters might also exhibit coexistence.In the simulation portion of this study, constraints were placed on the kinetic parameters, and constant values were used for the environmental parameters and initial conditions. However, the analysis in The algebraic conditions for coexistence do not include the initial conditions of the replicators or the monomers, and sensitivity of coexistence to the initial conditions was not presented in this paper. However, simulations from a range of replicator and monomer initial conditions showed no sensitivity of coexistence behavior to the initial conditions of the system. This suggests that the stability of the coexistence solution is independent of the initial condition. Observation of the system defined by This study focused on a simple yet dynamically rich scenario with two replicator types and two monomer types. However, a similar analysis to that presented in The dynamic model presented in this paper does not specify any explicit function, other than replication, and represents a very early stage of evolution. With a sustained pool of replicators, mutations would invariably also occur, enabling additional species to be generated. Depending upon their kinetics and composition, relative to the environment, these mutants might also be sustained within the system, further expanding its diversity. The definition of coexistence based on linear growth does not imply that the population sizes of the species are similar, only that all are growing. A species with a small population size could be viewed as insignificant, if population size is the only criterion. However, if that species has or develops a necessary function, it could be critical to the future performance of the system, even if its population is not large. Unlike other replicator studies, the model presented here does not aim to quantify replicator strength, via population size or other metrics, but rather focuses on the system-level dynamics. A diverse system could later develop complex function through cooperation, such as catalysis via a hypercycle , but thiCoexistence of diverse replicating species is necessary for evolution, but many replicator models predict the emergence of a single winner. Here, we present a chemically plausible kinetics model with a unique combination of effects that exhibits coexistence of two species for approximately 1% of the parameter space. The replicating species are not directly interacting, but rather, are coupled through shared monomer resources. The model is specified by parameters for the kinetics, composition and environment. The key features of the model are variable monomer reaction order, inlet and outlet flow of monomers and monomer recycling. Under appropriate parameter values, the populations of both replicating species grow with a linear profile. Algebraic conditions are derived to predict which parameter sets can exhibit coexistence, and in the simulation study, over half of the parameter sets meeting this condition do, in fact, have the stable linear growth solution, indicating sustained coexistence. Observation of these simulations suggests that the stability of this linear growth solution requires a weakened coupling between replicators, in which each replicator type is dominantly paired with one distinct monomer type. The algebraic coexistence conditions indicate that any system of replicators consistent with the kinetic model could exhibit coexistence—under an appropriate combination of compositional and environmental parameters. In a diverse prebiotic soup of monomers and replicators, coexisting replicators could be selected by the environment.