New 63 knot and other knots in human proteome from AlphaFold predictions

AlphaFold is a new, highly accurate machine learning protein structure prediction method that outperforms other methods. Recently this method was used to predict the structure of 98.5% of human proteins. We analyze here the structure of these AlphaFold-predicted human proteins for the presence of knots. We found that the human proteome contains 65 robustly knotted proteins, including the most complex type of a knot yet reported in proteins. That knot type, denoted 63 in mathematical notation, would necessitate a more complex folding path than any knotted proteins characterized to date. In some cases AlphaFold structure predictions are not highly accurate, which either makes their topology hard to verify or results in topological artifacts. Other structures that we found, which are knotted, potentially knotted, and structures with artifacts (knots) we deposited in a database available at: https://knotprot.cent.uw.edu.pl/alphafold.

Iconicity in mathematical notation: Commutativity and symmetry

Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.

Developing Covariational Reasoning Among Students Using Contexts of Formulas

Multiple studies have been conducted to assess students’ ability to apply covariational reasoning to sketching graphs in physics. This study is supported by research on developing students’ skills in sketching functions in mathematics. It attempts to evaluate physics students’ ability to apply these skills to identify critical algebraic attributes of physics formulas for their potential to be sketched. Rather than seeking formulas’ physical interpretation, this study is posited to challenge students’ skills to merge their mathematical knowledge within physics structures. A group of thirty ([Formula: see text]) first-year college-level physics students were provided with two physically identical equations that described the object’s position. However, one equation was expressed in functional mathematical notation, whereas the other in a standard formula notation. The students were asked to classify the symbols in each formula as variables or parameters and determine these formulas’ potential to be graphed in respective coordinates. The analysis revealed that 93% of these students considered function notation as possessing sketchable potential against 13% who envisioned such potential in the standard formula notation. Further investigations demystified students’ confusion about the classification of the symbols used in the formula notation. These results opened up a gate for discussing the effects of algebraic notations in physics on activating students’ covariational skills gained in mathematics courses. Suggestions for improving physics instructions stemming from this study are discussed.

Theoretical Background

This chapter starts by briefly presenting the theoretical background of welfare economics and introducing key aspects such as the indirect utility function, the expenditure function, or the concepts of compensating surplus or equivalent surplus. Next, it draws attention to willingness to pay and willingness to accept, essential measures in environmental valuation. Finally, the chapter summarises the basic mathematical notation of the random utility maximisation models used throughout the book.

An Algorithmic Approach to Solve Continuum Hypothesis

The continuum hypothesis has been unsolved for hundreds of years. In other words, can I answer it completely? By refuting the culturally responsible continuum [1], one can link the problem to the mathematical continuum, and it is possible to disproof the continuum hypothesis [2] . To go ahead a step, one may extend our mathematical system (by employing a more powerful set theory) and solve the continuum problem by three conditional cases. This event is sim-ilar to the status cases in the discriminant of solving a quadratic equation. Hence, my proposed al-gorithmic flowchart can best settle and depict the problem. From the above, one can further con-clude that when people extend mathematics (like set theory — ZFC) into new systems (such as Force Axioms), experts can solve important mathematical problems (CH). Indeed, there are differ-ent types of such mathematical systems, similar to ancient mathematical notation. Hence, different cultures have different ways of representation, which is similar to a Chinese saying: “different vil-lages have different laws.” However, the primary purpose of mathematical notation was initially to remember and communicate. This event indicates that the basic purpose of developing any new mathematical system is to help solve a natural phenomenon in our universe.

The Accessibility of Mathematical Notation on the Web and Beyond

This paper serves two purposes. First, it offers an overview of the role of the Mathematical Markup Language (MathML) in representing mathematical notation on the Web, and its significance for accessibility. To orient the discussion, hypotheses are advanced regarding users’ needs in connection with the accessibility of mathematical notation. Second, current developments in the evolution of MathML are reviewed, noting their consequences for accessibility, and commenting on prospects for future improvement in the concrete experiences of users of assistive technologies. Recommendations are advanced for further research and development activities, emphasizing the cognitive aspects of user interface design.

The Effect of Ship Operator-Based Empty Container Imbalance on Container Circulation

The purpose of this study is to demonstrate that ship operator-based container imbalance (SOBCI) leads to empty container movement (ECM) beyond trade imbalance, which is described as additional ECM (AECM). This demonstration is supported by a feasible suggestion to overcome additional empty container circulation, critiquing the suggestion of a common container pool and initiating a further discussion to reduce AECM. Two hypotheses examining SOBCI, trade imbalance, and empty container circulation were tested for the container throughputs of Turkish ports using the Mann-Whitney U test and regression analysis. A thought experiment about how to calculate the potential amount of ECM beyond trade imbalance was conducted. Recently, a substantial amount of container accumulation beyond the trade imbalance in the terminals located in Istanbul-Kocaeli and Mersin for 20-foot containers and in Istanbul-Kocaeli and Gemlik for 40-foot containers has occurred due to SOBCI. In Turkish container terminals between 2013 and 2016, SOBCI explains 32.78% of AECM originating from the market effect. For 20-foot containers, the percentages of avoidable AECM are 30% for Istanbul-Kocaeli and 20% for Mersin. For 40-foot containers, the AECM is 50% for Mersin, 20%‐25% for Istanbul-Kocaeli and Gemlik, and 5% for Izmir-Aliaga. The concept of the market effect, its elements, SOBCI, and the magnitude of AECM arising from only the market effect (AECM-OME) were used for the empirical study. This study demonstrates the relationship between SOBCI and AECM-OME. Additionally, a unique thought experiment and its mathematical notation are presented to calculate the magnitude of AECM that has been released.

Penulisan Operasi Hitung dalam Bahasa Inggris melalui Game Take A Number

The implementation of this activity was carried out with the aim of improving the ability of ASM Mataram Banking Administration Management students in writing arithmetic operations using English both in mathematical notation and writing hundreds (hundreds) and thousands (thousands) in English. The stages of this activity begin with the initial stage (preparation), the core stage (implementation) and the final stage (evaluation). The initial stage is the preparation, at this stage the initial observation, the collection of material about the procedures for writing mathematical operations in English both writing mathematical notation and writing numbers in English and is equipped with questions of counting operations in English that are appropriate for the level students. The core stage is the implementation carried out by providing training in writing arithmetic in English through the game take a number for banking administration management students at ASM Mataram. The last stage is the evaluation carried out by giving some questions on the number counting operations in English that are done by students in accordance with the material that has been delivered, and comparing the results of the comparison before and after the training is given. Based on the implementation of the activity, the results showed that the arithmetic operations writing training had a good impact on mathematics and mastery of English. The addition of the game take a number aims to refresh the minds of students so that they can work on the questions while playing, as well as training the foresight, speed and accuracy in listening, writing, counting and adding numbers previously read in English.