*PLoS One ; 19(4): e0301705, 2024.*

##### RESUMO

Introducing a strong form of soft continuity between soft topological spaces is significant because it can contribute to our growing understanding of soft topological spaces and their features, provide a basis for creating new mathematical tools and methods, and have significant applications in various fields. In this paper, we define soft super-continuity as a new form of soft mapping. We present various characterizations of this soft concept. Also, we show that soft super-continuity lies strictly between soft continuity and soft complete continuity and that soft super-continuity is a strong form of soft Î´-continuity. In addition, we give some sufficient conditions for the equivalence between soft super-continuity and other related concepts. Moreover, we characterize soft semi-regularity in terms of super-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and products by soft super-continuity. In addition to these, we study the relationship between soft super-continuity and soft Î´-continuity with their analogous notions in general topology. Finally, we give several sufficient conditions on a soft mapping to have a soft Î´-closed graph.

##### Assuntos

Matemática*PLoS One ; 19(4): e0294276, 2024.*

##### RESUMO

Past research has shown that growth mindset and motivational beliefs have an important role in math and science career interest in adolescence. Drawing on situated expectancy-value theory (SEVT), this study extends these findings by investigating the role of parental motivational beliefs (e.g., expectancy beliefs, utility values) and parent growth mindset in math on adolescent career interest in math-intensive fields (e.g., mathematics, computer science, statistics, and engineering; MCSE) through adolescent motivational beliefs in math. Structural equation modeling was used to test the hypothesized model using data from 290 adolescents (201 girls, 69.3%; Mage = 15.20), who participate in informal STEM (science, technology, engineering, mathematics) youth programs, and their parents (162 parents, 87.7% female) in the United Kingdom and the United States. As hypothesized, adolescent expectancy beliefs, utility values, and growth mindset in math had a significant direct effect on MCSE career interest. Further, there was a significant indirect effect of parental expectancy beliefs in math on MCSE career interest through adolescents' expectancy beliefs. Similarly, there was a significant indirect effect from parental utility values in math to MCSE career interest through adolescents' utility values. The findings suggest that parents' math motivational beliefs play a critical role in adolescent math motivational beliefs and their career interest in math-intensive fields.

##### Assuntos

Motivação , Pais , Humanos , Feminino , Adolescente , Estados Unidos , Masculino , Engenharia , Tecnologia , Matemática*PLoS One ; 19(4): e0296635, 2024.*

##### RESUMO

BACKGROUND: Overweight and obesity affect more than 18% of children and adolescents in the world. Obesity-related associations with brain morphology might be associated with reduced efficiency of inhibitory control. This association highlights a possible mechanism by which obesity impacts intelligence and academic achievement. Prior work indicates a mediating effect of inhibitory control on the relationship between body mass index (BMI) and intelligence and academic achievement. However, although obesity is associated with impaired math performance, we do not know whether inhibitory control also mediates the relationship between BMI and math performance. This study tests the hypothesis that inhibitory control statistically mediates the relationship between BMI and math performance. METHODS: 161 children (9 to 13 years old, 80 female) participated in the present study. We evaluated BMI; math performance, in a test composed of 20 arithmetic equations of the type x = (a × b) - c; and inhibitory control through the Flanker test. We carried out Spearman correlation tests, hierarchical multiple linear regression, and tested the confidence of the model where inhibitory control statistically mediates the indirect association between BMI and math performance. Mediation analysis in this cross-sectional study aimed to improve understanding of indirect relationships and offer insights into possible causal connections. RESULTS: Better math performance and lower BMI were associated with greater accuracy on the inhibitory control test and greater accuracy on the inhibitory control test was associated with better performance on math test. We found an indirect association between higher BMI in children and impairments in math performance, that was mediated by inhibitory control (a: -0.008, p = 0.025; b: 7.10, p = 0.0004; c: 0.05, p = 0.592; c': 0.11, p = 0.238; Indirect Effect: -0.0599, 95% CI: -0.13, -0.005). CONCLUSIONS: An indirect association between higher body mass indices in children and impairments in math performance was detected, through the impact that BMI has on inhibitory control.

##### Assuntos

Obesidade , Sobrepeso , Criança , Adolescente , Humanos , Feminino , Índice de Massa Corporal , Estudos Transversais , Matemática*Stud Hist Philos Sci ; 104: 48-60, 2024 Apr.*

##### RESUMO

Hermann Weyl's philosophical reflections remain a topic of considerable interest in the history and philosophy of science. In particular, Weyl's commitment to a form of idealism, as it pertains to his reading of Husserl and Fichte, has garnered much discussion. However, much less attention has been given to Weyl's later, and at that only partial, turn towards a form of empiricism (i.e. from the late 1920s onward). This lack of focus on Weyl's later philosophy has tended to obscure some of the most significant lessons that Weyl sought to draw from his decades of research in the foundations of mathematics and physics. In this paper, I develop some aspects of what I will term as Weyl's 'modest' empiricism. I will argue that Weyl's turn toward empiricism can be read in the context of a development of Helmholtz's epistemological program and his unique form of 'Kantianism'. The hope is that this reading will not only provide a better understanding of Weyl's later thought, especially his (1954) criticism of Cassirer, but that it may also provide the basis for a novel 'Weylian' account of the mathematization of nature underwriting the group-theoretic methodology of parts of modern physics.

##### Assuntos

Filosofia , Física , Humanos , Matemática , Conhecimento , Empirismo*Sensors (Basel) ; 24(5)2024 Feb 24.*

##### RESUMO

When performing lifting tasks at work, the Lifting Index (LI) is widely used to prevent work-related low-back disorders, but it presents criticalities pertaining to measurement accuracy and precision. Wearable sensor networks, such as sensorized insoles and inertial measurement units, could improve biomechanical risk assessment by enabling the computation of an adaptive LI (aLI) that changes over time in relation to the actual method of carrying out lifting. This study aims to illustrate the concepts and mathematics underlying aLI computation and compare aLI calculations in real-time using wearable sensors and force platforms with the LI estimated with the standard method used by ergonomists and occupational health and safety technicians. To reach this aim, 10 participants performed six lifting tasks under two risk conditions. The results show us that the aLI value rapidly converges towards the reference value in all tasks, suggesting a promising use of adaptive algorithms and instrumental tools for biomechanical risk assessment.

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Algoritmos , Remoção , Humanos , Medição de Risco , Matemática , Fenômenos Biomecânicos*WMJ ; 123(1): 34-38, 2024 02.*

##### RESUMO

BACKGROUND: Given the need for a diverse health care workforce, efforts must be made early in their education to support underrepresented minorities in medicine and the science, technology, engineering, and mathematics (STEM) fields. METHODS: The Eyes on the Future program introduces underrepresented minority 8th grade students to science and medicine via interactive science-based programming and mentorship by medical and graduate students. Program impact was evaluated using pre- and post-program surveys. RESULTS: Of 25 participating students, 24 and 22 responded to pre- and post-program surveys, respectively. Students showed strong interest in science concepts and STEM careers, with high, positively correlated, and statistically similar pre- and post-program survey responses. DISCUSSION: The Eyes on the Future program was well-received and represents a step towards addressing barriers to STEM careers faced by underrepresented minority students.

##### Assuntos

Instituições Acadêmicas , Tecnologia , Adolescente , Humanos , Escolaridade , Hispânico ou Latino , Matemática*Sci Rep ; 14(1): 6336, 2024 03 15.*

##### RESUMO

Hand stencils are a remarkable graphic expression in Prehistoric rock art, dating back to 42 ka BP. Although these stencils provide direct impressions of the artists' hands, the characterization of their biological profile (i.e., biological sex and age) is very challenging. Previous studies have attempted this analysis with traditional morphometrics (TM), whereas little research has been undertaken using Geometric Morphometrics (GM), a method widely used in other disciplines but only tentatively employed in rock art studies. However, the large variation in relative finger position in archaeological hands poses the question of whether these representations can be examined through GM, or, in contrast, if this creates an unmanageable error in the results. To address this issue, a 2D hand scans sample of 70 living individuals (F = 35; M = 35) has been collected in three standardized positions (n = 210) and digitized with 32 2D conventional landmarks. Results show that the intra-individual distance (mean Procrustes distance between Pos. 1-2 = 0.132; 2-3 = 0.191; 1-3 = 0.292) is larger than the inter-individual distance (mean in 1 = 0.122; 2 = 0.142; 3 = 0.165). Finally, it has been demonstrated that the relative finger positions, as well as the inclusion of all hand parts in the analysis, have an overshadowing effect on other variables potentially involved in the morphometric variability of the hand, such as biological sex.

##### Assuntos

Arqueologia , Arte , Humanos , Matemática*PLoS Comput Biol ; 20(3): e1011905, 2024 Mar.*

##### RESUMO

To design population topologies that can accelerate rates of solution discovery in directed evolution problems or for evolutionary optimization applications, we must first systematically understand how population structure shapes evolutionary outcome. Using the mathematical formalism of evolutionary graph theory, recent studies have shown how to topologically build networks of population interaction that increase probabilities of fixation of beneficial mutations, at the expense, however, of longer fixation times, which can slow down rates of evolution, under elevated mutation rate. Here we find that moving beyond dyadic interactions in population graphs is fundamental to explain the trade-offs between probabilities and times to fixation of new mutants in the population. We show that higher-order motifs, and in particular three-node structures, allow the tuning of times to fixation, without changes in probabilities of fixation. This gives a near-continuous control over achieving solutions that allow for a wide range of times to fixation. We apply our algorithms and analytic results to two evolutionary optimization problems and show that the rate of solution discovery can be tuned near continuously by adjusting the higher-order topology of the population. We show that the effects of population structure on the rate of evolution critically depend on the optimization landscape and find that decelerators, with longer times to fixation of new mutants, are able to reach the optimal solutions faster than accelerators in complex solution spaces. Our results highlight that no one population topology fits all optimization applications, and we provide analytic and computational tools that allow for the design of networks suitable for each specific task.

##### Assuntos

Evolução Biológica , Taxa de Mutação , Mutação , Algoritmos , Matemática*J Exp Child Psychol ; 242: 105892, 2024 Jun.*

##### RESUMO

Recent evidence suggests that using finger-based strategies is beneficial for the acquisition of basic numerical skills. There are basically two finger-based strategies to be distinguished: (a) finger counting (i.e., extending single fingers successively) and (b) finger number gesturing (i.e., extending fingers simultaneously to represent magnitudes). In this study, we investigated both spontaneous and prompted finger counting and finger number gesturing as well as their contribution to basic numerical skills in 3- to 5-year-olds (N = 156). Results revealed that only 6% of children spontaneously used their fingers for counting when asked to name a specific number of animals, whereas 59% applied finger number gesturing to show their age. This indicates that the spontaneous use of finger-based strategies depends heavily on the specific context. Moreover, children performed significantly better in prompted finger counting than in finger number gesturing, suggesting that both strategies build on each other. Finally, both prompted finger counting and finger number gesturing significantly and individually predicted counting, cardinal number knowledge, and basic arithmetic. These results indicate that finger counting and finger number gesturing follow and positively relate to numerical development.

##### Assuntos

Dedos , Conhecimento , Criança , Humanos , Pré-Escolar , Estudos Transversais , Matemática*Trends Neurosci Educ ; 34: 100220, 2024 03.*

##### RESUMO

BACKGROUND: Physical activity, fundamental motor skills, executive functions and early numeracy have shown to be related, but very little is known about the developmental relations of these factors. PROCEDURE: We followed 317 children (3-6 years) over two years. Fundamental motor skills and executive functions (inhibition+switching, updating) were measured at all time points (T1, T2, T3) and physical activity at T1 and early numeracy at T3. MAIN FINDINGS: Children with better fundamental motor skills at T1 developed slower in inhibition and switching. Fundamental motor skills developed faster in children who had better initial inhibition and switching ability. Vigorous physical activity at T1 was associated with a weaker initial inhibition and switching. The initial level and the developmental rate of updating were related to better early numeracy skills. CONCLUSIONS: Findings indicate that fundamental motor skills and executive functions are developmentally related, and updating is an important predictor for early numeracy in preschoolers.

##### Assuntos

Função Executiva , Destreza Motora , Criança , Humanos , Função Executiva/fisiologia , Destreza Motora/fisiologia , Exercício Físico , Inibição Psicológica , Matemática*PLoS One ; 19(3): e0301228, 2024.*

##### RESUMO

Determining if a sequence of numbers is ordered or not is one of the fundamental aspects of numerical processing linked to concurrent and future arithmetic skills. While some studies have explored the neural underpinnings of order processing using functional magnetic resonance imaging, our understanding of electrophysiological correlates is comparatively limited. To address this gap, we used a three-item symbolic numerical order verification task (with Arabic numerals from 1 to 9) to study event-related potentials (ERPs) in 73 adult participants in an exploratory approach. We presented three-item sequences and manipulated their order (ordered vs. unordered) as well as their inter-item numerical distance (one vs. two). Participants had to determine if a presented sequence was ordered or not. They also completed a speeded arithmetic fluency test, which measured their arithmetic skills. Our results revealed a significant mean amplitude difference in the grand average ERP waveform between ordered and unordered sequences in a time window of 500-750 ms at left anterior-frontal, left parietal, and central electrodes. We also identified distance-related amplitude differences for both ordered and unordered sequences. While unordered sequences showed an effect in the time window of 500-750 ms at electrode clusters around anterior-frontal and right-frontal regions, ordered sequences differed in an earlier time window (190-275 ms) in frontal and right parieto-occipital regions. Only the mean amplitude difference between ordered and unordered sequences showed an association with arithmetic fluency at the left anterior-frontal electrode. While the earlier time window for ordered sequences is consistent with a more automated and efficient processing of ordered sequential items, distance-related differences in unordered sequences occur later in time.

##### Assuntos

Mapeamento Encefálico , Potenciais Evocados , Adulto , Humanos , Tempo de Reação/fisiologia , Potenciais Evocados/fisiologia , Lobo Frontal , Matemática*Cogn Sci ; 48(2): e13412, 2024 Feb.*

##### RESUMO

Although children learn more when teachers gesture, it is not clear how gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second- and third-grade children. Participants received classroom-level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge.

##### Assuntos

Gestos , Aprendizagem , Criança , Humanos , Memória , Matemática , Atenção*J Biomech Eng ; 146(5)2024 Mar 01.*

##### RESUMO

Science, technology, engineering, and mathematics (STEM) education workshops and programs play a key role in promoting early exposure to scientific applications and questions. Such early engagement leads to growing not only passion and interest in science, but it also leads to skill development through hands-on learning and critical thinking activities. Integrating physiology and engineering together is necessary especially to promote health technology awareness and introduce the young generation to areas where innovation is needed and where there is no separation between health-related matters and engineering methods and applications. To achieve this, we created a workshop aimed at K-12 (grades 9-11) students as part of the Summer Youth Programs at Michigan Technological University. The aim of this workshop was to expose students to how engineering concepts and methods translate into health- and medicine-related applications and cases. The program consisted of a total of 15 h and was divided into three sections over a period of 2 weeks. It involved a combination of theoretical and hands-on guided activities that we developed. At the end of the workshop, the students were provided a lesson or activity-specific assessment sheet and a whole workshop-specific assessment sheet to complete. They rated the programs along a 1-5 Likert scale and provided comments and feedback on what can be improved in the future. Students rated hands-on activities the highest in comparison with case studies and individual independent research. Conclusively, this STEM summer-youth program was a successful experience with many opportunities that will contribute to the continued improvement of the workshop in the future.

##### Assuntos

Promoção da Saúde , Tecnologia , Adolescente , Humanos , Tecnologia/educação , Engenharia/educação , Instituições Acadêmicas , Matemática*J Exp Child Psychol ; 241: 105865, 2024 May.*

##### RESUMO

The current study examined how different features of corrective feedback influenced children's performance and motivational outcomes on a mathematics task. Elementary school-aged children from the United States (N = 130; Mage = 7.61 years; 35% female; 60% White) participated in a Zoom session with a trained researcher. During the learning activity, children solved a series of mathematical equivalence problems and were assigned to different feedback conditions that varied in feedback content (correct answer alone vs. correct answer with verification) and feedback source (computer alone vs. computer with person). In terms of content, feedback with verification cues led to decreased persistence, decreased strategy variability, and higher reliance on entrenched strategies relative to feedback that contained the correct answer alone. In terms of source, feedback from the computer alone enhanced children's accuracy; however, the most resilient children received feedback from the computer and a person. Findings are discussed in light of existing feedback theories.

##### Assuntos

Aprendizagem , Motivação , Criança , Humanos , Feminino , Masculino , Retroalimentação , Atenção , Matemática*CBE Life Sci Educ ; 23(1): ar11, 2024 03.*

##### RESUMO

Many students who enroll in a public U.S. 4-y college will not graduate. The odds of completing a college degree are even lower for students who have been marginalized in higher education, especially in Science, Technology, Engineering, and Math (STEM) fields. Can undergraduate research increase a student's likelihood of graduating college and close educational equity gaps in college completion? To answer this question, we use data from six public U.S. universities (N = 120,308 students) and use Propensity Score Matching to generate a comparison group for analyses. We conducted logistic regressions on graduation rates and equity gaps in 4 and 6 y using the matched comparison group and undergraduate researchers in STEM (n = 2727). When being compared with like-peers and controlling for background characteristics and prior academic performance, students who participated in undergraduate research were twice as likely to graduate in 4 y and over 10 times as likely to graduate in 6 y. We also found that equity gaps in 4-y graduation rates for students of color, low-income, and first-generation students were cut in half for undergraduate researchers. At 6 y, these gaps were completely closed for undergraduate researchers. As we seek ways to close education gaps and increase graduation rates, undergraduate research can be a meaningful practice to improve student success.

##### Assuntos

Engenharia , Estudantes , Humanos , Engenharia/educação , Tecnologia/educação , Avaliação Educacional , Matemática*Acta Psychol (Amst) ; 244: 104174, 2024 Apr.*

##### RESUMO

CONTEXT AND PROBLEM: The COVID-19 pandemic led to temporary closures of schools in Germany that were unpredictable, either short-term or sustained over many weeks depending on local COVID-19 incidence rates which varied in different regions over time. The COVID-19 pandemic created new stressors in schools to deliver the curriculum with reduced lessons and online teaching. COVID-19 also had a marked effect on research in schools. AIM: The INSIDE project is a nationwide German study that investigates the effects of inclusive schooling in secondary education. The data collection started in 2018 and is still ongoing. During the COVID-19 pandemic the drop-out of many schools lead to a sample attrition down to 39.3 % of the original sample. It is investigated whether imputation of missing values in the dependent variables school grades (N = 2999) produces different results than listwise deletion of cases (N = 383). HYPOTHESIS: It is hypothesized that missing data in the longitudinal data design were not missing at random (NMAR). It is further hypothesized based on previous research that in the larger, imputed sample, Math grades will deteriorate more than German grades. RESULTS: Two datasets with observed, respectively, imputed data showed no difference in parents' educational attainment and gender proportion. Larger integrative schools were less likely to drop out than smaller single type schools. Pupils of 'surviving' schools showed equivalent grades for German and Mathematics, while including predicted grades of pupils in 'stressed' drop-out schools showed a decline in Mathematics but not in German subject grades.

##### Assuntos

COVID-19 , Pandemias , Humanos , COVID-19/epidemiologia , Instituições Acadêmicas , Escolaridade , Matemática*Biosystems ; 237: 105153, 2024 Mar.*

##### RESUMO

The Hill numbers are statistics for biodiversity measurement in ecological studies, closely related to the Rényi and Shannon entropies from information theory. Recent developments in the mathematics of diversity in the setting of population genetics have produced mathematical constraints that characterize how standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we apply these constraints to diversity statistics in ecology, focusing on the Hill numbers and the Rényi and Shannon entropies. The mathematical bounds can shift perspectives on the diversities of communities, in that when upper and lower bounds on Hill numbers are evaluated in a classic butterfly example, Hill numbers that are initially larger in one community switch positions-so that associated normalized Hill numbers are instead smaller than those of the other community. The new bounds hence add to the tools available for interpreting a commonly used family of statistics for ecological data.

##### Assuntos

Biodiversidade , Entropia , Matemática , Probabilidade*J Exp Child Psychol ; 242: 105884, 2024 Jun.*

##### RESUMO

It is well established in the literature that fraction knowledge is important for learning more advanced mathematics, but the hierarchical relations among whole number arithmetic, fraction knowledge, and mathematics word problem-solving are not well understood. In the current study, Chinese Grade 6 students (N = 1160; 465 girls; Mage = 12.1 years, SD = 0.6) completed whole number arithmetic (addition, subtraction, multiplication, and division), fraction (mapping, equivalence, comparison, and arithmetic), and mathematics word problem-solving assessments. They also completed two control measures: number writing speed and nonverbal intelligence. Structural equation modeling was used to investigate the hierarchical relations among these assessments. Among the four fraction tasks, the correlations were low to moderate, suggesting that each task may tap into a unique aspect of fraction understanding. In the model, whole number arithmetic was directly related to all four fraction tasks, but was only indirectly related to mathematics word problem-solving, through fraction arithmetic. Only fraction arithmetic, the most advanced fraction skill, directly predicted mathematics word problem-solving. These findings are consistent with the view that students need to build these associations into their mathematics hierarchy to advance their mathematical competence.

##### Assuntos

Aprendizagem , Resolução de Problemas , Feminino , Humanos , Criança , Estudantes , Matemática , China*PLoS One ; 19(2): e0278593, 2024.*

##### RESUMO

The study explored the relationship between students' attitude towards, and performance in mathematics word problems (MWTs), mediated by the active learning heuristic problem solving (ALHPS) approach. Specifically, this study investigated the correlation between students' performance and their attitude towards linear programming word tasks (ATLPWTs). Tools for data collection were: the adapted Attitude towards Mathematics Inventory-Short Form (ATMI-SF), (α = .75) as a multidimensional measurement tool, and linear programming achievement tests (pre-test and post-test). A quantitative approach with a quasi-experimental pre-test, post-test non-equivalent control group study design was adopted. A sample of 608 eleventh-grade Ugandan students (291 male and 317 female) from eight secondary schools (both public and private) participated. Data were analyzed using PROCESS macro (v.4) for SPSS version 26. The results revealed a direct significant positive relationship between students' performance and their ATLPWTs. Thus, students' attitude positively and directly impacted their performance in solving linear programming word problems. The present study contributes to the literature on performance and attitude towards learning mathematics. Overall, the findings carry useful practical implications that can support theoretical and conceptual framework for enhancing students' performance and attitude towards mathematics word problems.

##### Assuntos

Atitude , Estudantes , Humanos , Masculino , Feminino , Resolução de Problemas , Instituições Acadêmicas , Matemática*Sci Rep ; 14(1): 3507, 2024 02 12.*

##### RESUMO

Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval [Formula: see text] and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.