Intuitive Set Research Articles

Alternative ways to initiate students’ intuition, and hence internalization, of why zero factorial is equal to one

Zero factorial, defined to be one, is often counterintuitive to students but nonetheless an interesting concept to convey in a classroom environment. The challenge is to delineate the concept in a simple and effective way through the practice of justification, a familiar concept in mathematics and science education. In this regard two algebraic and one statistical justification using the squeeze theorem are presented. To assess the effectiveness of the justifications, a student survey was conducted at a comprehensive university incorporating the analysis of the pre- and post-presentation statements. They clearly present that the justifications are useful in giving credence to zero factorial equals one. Overall, the result from the online survey supports that the students preferred Justification 1. The justifications provide instructors alternative ways to initiate exploration of students’ intuitive set up of comprehending unobvious facts like zero factorial equals one. For a range of learners with their varied abilities to perform various mental activities most closely associated with learning and problem-solving, the justifications as simple alternative methods offer the potential to raise the current level of cognitive skills to inspire differentiated paths of learning. These are evident from survey results noting the role of statistical thinking and techniques.

Animism, Eco‐Immanence, and Divine Transcendence: Toward an Integrated Religious Framework for Environmental Ethics

ABSTRACTIt is intuitive to think that divine transcendence is incompatible with the sacredness of nature, especially when transcendence is combined with the idea that God alone is valuable. Divine transcendence seems to demote this‐worldly values in favor of union with God in a disembodied afterlife. Divine transcendence also seems to legitimize hierarchies, including male–female and human‐nature hierarchies. Divine immanence seems a better alternative. This set of intuitions about transcendence appears regularly in the field of Religion and Ecology, sometimes as an implicit backdrop rather than an explicit position. This backdrop needs to be thematized and evaluated. For those with ecological concerns, divine transcendence and divine immanence need not be mutually exclusive. Rather, divine transcendence (understood non‐contrastively) complements divine immanence and is compatible with both animist and polytheist cosmologies. The extent of this mutual compatibility and its importance for environmental concerns has yet to be fully articulated.

Race in IR: toward empirical study

Errol Henderson writes “the banality of white supremacy, more than the democratic peace thesis, is probably ‘the closest thing to an empirical law in world politics.’” Such a view is likely shared by IR scholars that study race as kindred systems of hierarchy. By comparison, the collective field is now “noticing” its long silence on the subject. Renewed calls to mainstream race have come with an unsettling admission: the “norm against noticing” was not by mistake but an epistemic devotion to a set of intuitions that exclude the agency of a global majority. In our silence—inadvertent or otherwise—we forgo a more accurate account of outcomes where race is theoretically important or even banal as Henderson deciphers. What is made clear by his contribution is that we can and should change course. My response to Henderson seeks to reinforce the argument for a positivist approach to race in world politics—both its promises and challenges.

Toward a Moderate Hierarchical View About the Moral Status of Animals

In this essay, I develop a moderate hierarchical position about the moral status of animals that is based on two factors: on the level of mental development of a being who is affected and on the significance of the interests that are affected. I argue that this view accommodates two different sets of moral intuitions. On one hand, it explains why, in general, humans have the special moral standing that is typically attributed to us. On the other hand, it also allows us to accommodate much of our intuition about how animals ought to be treated. In addition, this view is supported also by plausible general theoretical considerations. Subsequently, I explore some implications of this view for some real-life examples of our interactions with animals, especially, for the practice of raising them for food using industrial methods. I argue that this practice is morally wrong and that the correct approach is to adopt a (nearly) plant-based lifestyle.

It cannot be fitting to blame God

This paper argues that it cannot be fitting to blame God. I show that divine immutability, even on a weak conception, implies that God's ethical character cannot change. I then argue that blame aims at a change in the ethical character of the one blamed. This claim is directly intuitive, explains a wide set of intuitions about when blame is unfitting, and is implied by most of the theories blame offered in the philosophical literature. Since blame targeted at God aims to change God's ethical character, an impossibility, such blame is not fitting. I then draw on this conclusion to sketch a new theodicy. I argue that a necessary condition on being blameworthy is that one can be blamed under some possible condition. So, God cannot be blameworthy. Further, I argue that if someone cannot be blameworthy, then they cannot do wrong. Wrong actions tend to make us blameworthy, but since God cannot be blameworthy nothing can tend to make him blameworthy – God cannot do wrong.

Legitimacy and two roles for flourishing in politics

Legitimacy and two roles for flourishing in politics

Preformation probability and kinematics of cluster emission yielding Pb-daughters* *Supported by the Fundamental Research Grant Scheme (FRGS/1/2019/STG02/UNIMAP/02/2) from the Ministry of Education Malaysia stipulated with the Institute of Engineering Mathematics (IMK) of the Faculty of Applied and Human Sciences UniMAP as the beholder, Science and Engineering Research Board (SERB, CRG/2021/001229), FOSTECT Project (FOSTECT.2019B.04), FAPESP Project (2017/05660-0)

In the present study, the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei, especially those that decay to the double shell closure Pb nucleus and its neighbors as daughters. The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry ( and ), cluster mass , and the Q-value, paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately. The cluster-daughter interaction potential is obtained by folding the relativistic mean-field (RMF) densities with the recently developed microscopic R3Y using the NL and the phenomenological M3Y NN potentials to compare their adaptability. The penetration probabilities are calculated from the WKB approximation. With the inclusion of the new preformation probability , the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data. Furthermore, a careful inspection reflects slight differences in the decay half-lives, which arise from their respective barrier properties. The for systems with double magic shell closure Pb daughter are found to be an order of higher than those with neighboring Pb daughter nuclei. By exploring the contributions of the decay energy, the recoil effect of the daughter nucleus is evaluated, in contrast to several other conjectures. Thus, the centrality of the -value in the decay process is demonstrated and redefined within the preformed cluster-decay model. Additionally, we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.

Dynamics of the SARS-CoV-2 main protease binding site.

The COVID-19 pandemic has been controlled through quarantines, travel bans, mask mandates, and vaccines. However, due to viral mutations and the unlikelihood of reaching herd immunity, there remains a need for therapeutics. The SARS-CoV-2 main protease (MPro) is necessary for the virus’ replication, thus it is a promising drug target. Additionally, it can be crystallized consistently and its sequence has few changes across virus mutants. MPro crystal structures depict general residue-residue interactions and backbone conformations, but they do not account for the dynamics of flexible regions. Instead, molecular dynamics (MD) simulations are used to identify the flexibility of the binding site, data we hypothesize is essential for successfully designing drugs to bind to MPro using computational drug docking methods. 600 ns of all-atom, explicit solvent MD simulations of the MPro homodimer were conducted, resulting in 1.2 million frames of monomeric data. Principal component analysis (PCA) was conducted on pairwise Cα-Cα distances between selected binding residues within apo and holo PDBs and the MD frames. These distances provide an intuitive set of measurements to characterize the dynamics of the binding site. Contour mapping was used to visualize the presence of clusters in the space defined by a few of the most contributive PC's. Snapshots representative of the most common conformations within the distribution of data were identified through the use of clustering methods and will be used in future drug docking simulations.

Contamination detection and microbiome exploration with GRIMER.

Contamination detection is a important step that should be carefully considered in early stages when designing and performing microbiome studies to avoid biased outcomes. Detecting and removing true contaminants is challenging, especially in low-biomass samples or in studies lacking proper controls. Interactive visualizations and analysis platforms are crucial to better guide this step, to help to identify and detect noisy patterns that could potentially be contamination. Additionally, external evidence, like aggregation of several contamination detection methods and the use of common contaminants reported in the literature, could help to discover and mitigate contamination. We propose GRIMER, a tool that performs automated analyses and generates a portable and interactive dashboard integrating annotation, taxonomy, and metadata. It unifies several sources of evidence to help detect contamination. GRIMER is independent of quantification methods and directly analyzes contingency tables to create an interactive and offline report. Reports can be created in seconds and are accessible for nonspecialists, providing an intuitive set of charts to explore data distribution among observations and samples and its connections with external sources. Further, we compiled and used an extensive list of possible external contaminant taxa and common contaminants with 210 genera and 627 species reported in 22 published articles. GRIMER enables visual data exploration and analysis, supporting contamination detection in microbiome studies. The tool and data presented are open source and available at https://gitlab.com/dacs-hpi/grimer.

Oxygen Deficiency and Migration-Mediated Electric Polarization in Magnetic Fe,Co-Substituted SrTiO3−δ

We use density functional theory (DFT) calculations to show that oxygen vacancies (vO) and mobility induce noncentrosymmetric polar structures in SrTi1−x−yFexCoyO3−δ (STFC, x=y=0.125) with δ={0.125,0.25}, enhance the saturation magnetization, and give rise to large changes in the electric polarization |ΔP|. We present an intuitive set of rules to describe the properties of STFC, which are based on the interplay between (Co/Fe)-vO defects, magnetic cation coordination, and topological vacancy disorder. STFC structures consist of layered crystals with sheets of linearly organized O4,5,6-coordinated Fe–Co pairs, sandwiched with layers of O5-coordinated Ti. (Co/Fe)-vO defects are the source of crystal distortions, cation off-centering and bending of the oxygen octahedra which, considering the charge redistribution mediated by vO and the cations’ electronegativity and valence states, triggers an effective electric polarization. Oxygen migration for δ=0.125 leads to |ΔP|>∼10 µC/cm2 due to quantum-of-polarization differences between δ=0.125 structures. Increasing the oxygen deficiency to δ=0.25 yields |ΔP|, the O migration of which resolved polarization for δ=0.25 is >∼3 µC/cm2. Magnetism is dominated by the Fe,Co spin states for δ=0.125, and there is a contribution from Ti magnetic moments (∼1 μB) for δ=0.25. Magnetic and electric order parameters change for variations of δ or oxygen migration for a given oxygen deficiency. Our results capture characteristics observed in the end members of the series SrTi(Co,Fe)O3, and suggest the existence of a broader set of rules for oxygen-deficient multiferroic oxides.

Dataset Feasibility Analysis Method based on Enhanced Adaptive LMS method with Min-max Normalization and Fuzzy Intuitive Sets

Dataset Feasibility Analysis Method based on Enhanced Adaptive LMS method with Min-max Normalization and Fuzzy Intuitive Sets

Neonatal Jaundice and Autism: Precautionary Principle Invocation Overdue.

Meta-analyses consistently find a substantial possible association between neonatal jaundice (hyperbilirubinemia) and later autism risk. The obvious question this poses is "what is the source of this risk?" This review explores the complementary roles of jaundice severity and time, racial and geographic disparities, and early infant feeding regime change, and discusses potential implications of these findings. A range of factors appears to increase the risk of autism development following neonatal jaundice, all of which are associated with the "exclusive breastfeeding" paradigm. Severity presents an intuitive risk factor in the context of bilirubin neurotoxicity; jaundice from the modal root cause of insufficient milk intake progresses as that condition persists. Racial and geographic disparities present another intuitive set of risk factors, including a heightened risk of missed diagnosis for darker-skinned neonates and delayed care access in poorer settings. In addition to these intuitive factors, near- or full-term as opposed to preterm status and phototherapy treatment may also heighten risk. These counter-intuitive findings provide additional support for deprivation/starvation as a crucial antecedent or independent variable, and time as a mediator to progression in and subsequent risk from jaundice; heightened medical monitoring and supplementation seem to protect preterms, and phototherapy risks iatrogenesis, having replaced without sufficient safety evidence the prior standard treatment of switching jaundiced, breastfed babies to formula. Critically, jaundice associated with insufficient milk intake due to breastfeeding insufficiencies is fully preventable and trivially treatable with appropriate supplemental milk. Feeding neonates adequately may play an important role in preventing autism and other neurodevelopmental disorders including attention deficit hyperactivity disorder, cerebral palsy, epilepsy, hearing impairment, learning disorders, and mood disorders. Precautionary principle invocation is overdue.

On the expressive power of Łukasiewicz square operator

Abstract The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: $\ast x=x\odot x$, where $\odot $ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form $n+1$ where $n$ belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations.

Basic Programming Concepts as Explained for Preschoolers

The development of information technologies has formed a socio-economic request to reduce the age at which children can be introduced to programming. After 6 years’ efforts, the authors managed to develop and on a large scale introduce a one-year programming course for preschoolers, which is built on a metaphor of programmed control. During the course development, a set of basic programming concepts was selected and specified to be mastered by preschoolers aged 6+ in the activity-game form. This set of concepts goes back to Seymour Papert's ideas about teaching programming by writing programs that control moving objects using intuitive sets of commands. The main feature of the proposed system of concepts, allow at the initial stage of training to demonstrate and assimilate all the elements of the concept in the real, not in the virtual world. In the picture of the World, which we explain and demonstrate to children, only one function remains at the computer - the execution of the program it has memorized. Everything else happens in the real world. In the real world, an environment is created in which a real robot will move. In the real world, a program is created from tangible objects, which will then be "shown" to the computer so that it stores it in its memory and can then execute it at the command of a human. In the real world, obeying the signals of the computer, the robot performs the work stipulated by the program. This allows you to begin acquaintance with the programming of children from 4 years old, without working individually or collectively with electronic screens, which in today's Russia is prohibited by federal medical authorities in the educational process of children under 5 years old. The course is built on the text-free pictographic programming system PiktoMir developed by Russian Academy of Sciences. The methodological content of the course allows each preschooler to gain experience in the development and debugging of 120-150 simple programs by the end of the course. The final part of the article discusses the authors' plans for the development of a three-year textless programming course, methodologically and instrumentally connected with the primary school programming course.

A SAS macro for modelling periodic data using cosinor analysis

Background and objectiveCosinor analysis, developed by Franz Hallberg and colleagues in the 1960s, allows for the fitting of a cosine curve to data of a known period. Cosinor analysis is frequently used in the analysis of biological rhythm data. While software exists to perform these analyses, we are not aware of any published SAS procedures or macros which would facilitate them. MethodsTo meet this gap, we herein describe SAS macros which perform cosinor analyses that assume either normally or gamma distributed outcomes and fixed period. The macros can 1) produce datasets with cosinor parameters including acrophase, mesor, amplitude, nadir and test for rhythmicity 2) output datasets with fitted and observed values from the model, and 3) plot the resulting curve and underlying data. ResultsWe demonstrate the use of these macros with data from our research on circadian rhythms of heart rate and sleep in critically ill patients. ConclusionsCosinor analysis provides a parsimonious and intuitive set of estimates to summarize periodic data. We are hopeful that the publication of our macro will allow a wider spectrum of users to avail themselves of this technique.

Video recoloring via spatial-temporal geometric palettes

Color correction and color grading are important steps in film production. Recent palette-based approaches to image recoloring have shown that a small set of representative colors provide an intuitive set of handles for color adjustment. However, a single, static palette cannot represent the time-varying colors in a video. We introduce a spatial-temporal geometry-based approach to video recoloring. Specifically, its core is a 4D skew polytope with a few vertices that approximately encloses the video pixels in color and time, which implicitly defines time-varying palettes through slicing of the 4D skew polytope at specific time values. Our geometric palette is compact, descriptive, and provides a correspondence between colors throughout the video, including topological changes when colors merge or split. Experiments show that our method produces natural, artifact-free recoloring.

Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

A new parametric generalized exponential entropy measure on intuitionistic vague sets

Entropy is a significant mathematical instrument for determining ambiguous/fuzzy information. Entropy is indispensable for measuring ambiguity, first familiarized by Shannon (Syst Tech J 27:379–423, 1948) to extent the degree of uncertainty in likelihood distributions. Complex info processes are extensively pragmatic in decision-making processes. Created as per the notion of an exponential exponent for the fuzzy set, our exertion offers a measure of the power of an intuitive set of exponents. This article identifies a new measure of the exponential theorem on an intuitive set of equations. In addition, the necessary properties are displayed. By analyzing the results of the examples, it has been shown that this method is faster and more effective in practice.

The Dawn of the Future-Like-Ours Argument Against Abortion

Although several scholars have held that the Greeks and the Romans viewed abortion as morally unproblematic, an examination of three ancient texts reveals that, starting around the first century CE, some Greek and Roman writers were willing to explore reasons for opposing abortion on ethical grounds (i.e., reasons based on the conviction that abortion is an injustice committed against the fetus). The three texts introduce a form of opposition to abortion that has come to be known in our time as the future-like-ours argument against abortion. The present paper explores the argument that emerges from the three ancient texts and compares it to the work of Don Marquis, the best-known contemporary defender of a future-like-ours argument against abortion. The comparison reveals significant similarities, which are ultimately attributable to a common set of intuitions about what makes killing wrong and premature death tragic.

Parsing Sage and Rosemary in Time: The Machine Learning Race to Crack Olfactory Perception.

Color and pitch perception are largely understandable from characteristics of physical stimuli: the wavelengths of light and sound waves, respectively. By contrast, understanding olfactory percepts from odorous stimuli (volatile molecules) is much more challenging. No intuitive set of molecular features is up to the task. Here in Chemical Senses, the Ray lab reports using a predictive modeling framework-first breaking molecular structure into thousands of features and then using this to train a predictive statistical model on a wide range of perceptual descriptors-to create a tool for predicting the odor character of hundreds of thousands of available but previously uncharacterized molecules (Kowalewski et al. 2021). This will allow future investigators to representatively sample the space of odorous molecules as well as identify previously unknown odorants with a target odor character. Here, I put this work into the context of other modeling efforts and highlight the urgent need for large new datasets and transparent benchmarks for the field to make and evaluate modeling breakthroughs, respectively.