Numerical Representation Research Articles

Layout pattern analysis and coverage evaluation in computational lithography.

In advanced semiconductor technology nodes, the model accuracy of optical proximity correction (OPC) is the key for integrated circuit (IC) chip mask tape out, yield ramp up, and product time-to-market. An accurate model means a small prediction error for the full chip layout. As the full chip layout usually has large pattern variety, an optimal pattern set with good coverage is desired during the model calibration process. Currently, no existing solutions can provide the effective metrics to evaluate the coverage sufficiency of the selected pattern set before a real mask tape out, which may potentially cause higher re-tape out cost and product time-to-market delay due to the multiple rounds of model calibration. In this paper, we construct the metrics to evaluate the pattern coverage before any metrology data is obtained. The metrics are based on either the pattern's intrinsic, numerical feature representation, or its potential model simulation behavior. Experimental results show a positive correlation between these metrics and lithographic model accuracy. An incremental selection method is also proposed based on the pattern simulation error. It reduces up to 53% of the model's verification error range. These pattern coverage evaluation methods can improve the efficiency of OPC model building, and are, in turn, beneficial to the whole OPC recipe development process.

University Experiences of Students in a Gender Minority

Academic and social-emotional experiences during the university years influence students’ academic achievement and emotional well-being. However, there is insufficient evidence on how the numerical representation of same-gendered persons affects such experiences in each group. The aim of this research was to analyze university experiences within degree programs where there is a large gender gap in students enrolled. The study is descriptive and cross-sectional and uses a mixed approach. An adaptation of the QVAr (questionnaire on academic experiences-reduced version) was administered to 726 students enrolled in degree programs with a large gender gap. Additionally, ten individual interviews were carried out with students belonging to minority gender groups. The obtained results show that, in these degree programs, students’ adaptation and coexistence processes are different, especially in interpersonal relationships between the majority and minority groups. Women in the minority require support from their female classmates in the early years of the degree program. Men in the minority, however, feel like part of the group from the start.

Problems of gender equality in sports: topical issues of combating discrimination

The article analyzes gender problems of discrimination in the field of sports activities. It was established that discrimination is anegative social phenomenon and manifests itself in all spheres, including sports. Despite a number of regulatory and institutional legal guarantees, athletes are exposed to negative situations, including oppression, intolerance, unequal treatment, and even violence. The goal of the modern ideology of legal regulation in the field of sports is to ensure somatic andpsychological well-being in all spheres of personal development of athletes, including the eradication of manifestations of discrimination, which is especially widespread on the basis of gender.Stereotyped thinking permeates sports activities, where certain sports are identified with a separate gender, resulting in genderdiscrimination against both women due to their supposedly strengthened masculine identity and men for choosing fragile sports.It is noted that the problems of stigmatization in sports have an ancient nature, but do not change in the context of the transformation of the phenomenon itself. Currently, the issue of eSports and its recognition at the professional level isbeing actively discussed. However, according to experts, the problem of gender discrimination in this area is particularly significant.Addressing systemic issues, including discrimination, requires good and open sports governance to create a culture that is trulyfair, accessible, inclusive and supportive. It has been established that increasing the numerical representation of women is an important feminist project in various institutional settings and promotes gender equality. However, the number in itself does not mean ensuring the principle of non-discrimination. The problems that have not been solved at the moment are forms of lower wages, lack of real equality in the occupation of managerial positions and coaching staff, uneven popularization in the mass media.

Numerical representation of tightly focused ultra-short laser pulses

A scheme for numerical representation for the fields of tightly focused laser pulses is presented going beyond the paraxial framework that gives accurate values up to near single-cycle pulses. The laser field is defined by a solution of the paraxial Helmholtz equation and a temporal pulse profile in light-cone coordinates, the fourth- and second-order corrections are provided for short pulses and vector beams, and the absolute error of these terms is presented. The method can give an accurate field description for any transverse electromagnetic mode, and it is suited for providing initial fields for existing solvers for Maxwell’s equations, such as in the particle-in-cell codes.

Pixel‐Level Grayscale Manipulation to Improve Accuracy in Digital Light Processing 3D Printing

AbstractDigital light processing (DLP) is a widely used additive manufacturing technique for functional applications due to its high accuracy and print speeds. However, a variety of factors such as pixel size, motion stage resolution, optical focus, and chemical properties of the resin limit DLP's minimum resolution. Recently, research into locally varying light intensities has led to the emergence of grayscale DLP printing, which offers new capabilities including sub‐pixel manipulation of the printed shape. Here, a methodology is developed to enhance accuracy beyond what is typically capable for a given projector resolution by using pixel‐level grayscale control to create round features from sharp pixels. A numerical representation of the DLP pixel shape is developed to account for the effects of the incident light patterns. A reaction‐diffusion model is then used to predict the printed shapes before and after grayscale enhancement. This model is used to determine the optimal pixel intensities to match a target shape. Finally, the minimum feature size allowed by the proposed method is explored. The promising results represent an important step forward in raising DLP printing to higher accuracy, which will allow the fabrication of functional and structural components with smaller features or smoother faces.

Biodiversity of Vitis vinifera endophytes in conventional and biodynamic vineyard

Plants are permanently exposed to biotic and abiotic stress and have therefore developed intricate resistance mechanisms, consequently. These include the presence of microbial endophytes, which can promote plant growth and ensure better resilience against unfavourable conditions. These microorganisms colonising plant tissues can directly affect plant growth by producing phytohormones, antioxidants, 1-aminocyclopropane-1-carboxylate (ACC) deaminase activity, or indirectly by the production of siderophores and antifungal agents. To the best of our knowledge, this is the first study devoted to assessing bacterial endophyte diversity and their plant growth-promoting properties in two utterly distinct vineyards in view of agricultural management (conventional, biodynamic) in the Czech Republic. With these different agricultural approaches, we hypothesised different numerical representations of bacterial endophytes acquired from vine shoots and leaves, which was not proved (P = 0.743, F = 0.129). A total of 470 distinct bacterial endophytes were isolated from the Vitis vinifera plants from the conventional and biodynamic vineyard and from which over 80% were identified by the matrix-assisted laser desorption-time-of-flight mass spectrometry (MALDI-TOF MS). In both vineyards, the dominant bacterial genus was Bacillus, followed by Pantoea, Pseudomonas and Staphylococcus. Plant-promoting endophyte properties varied with respect to the season and type of vineyard. The ability to produce indole-3-acetic acid (IAA) and ACC deaminase was higher in the biodynamic vineyard, in comparison with antioxidant activity, which was found in a higher proportion in isolates from the conventional vineyard.

Interpreting results from Rasch analysis 2. Advanced model applications and the data-model fit assessment

Purpose: The present paper presents developments and advanced practical applications of Rasch's theory and statistical analysis to construct questionnaires for measuring a person's traits. The flaws of questionnaires providing raw scores are well known. Scores only approximate objective, linear measures. The Rasch Analysis allows you to turn raw scores into measures with an error estimate, satisfying fundamental measurement axioms (e.g., unidimensionality, linearity, generalizability). A previous companion article illustrated the most frequent graphic and numeric representations of results obtained through Rasch Analysis. A more advanced description of the method is presented here. Conclusions: Measures obtained through Rasch Analysis may foster the advancement of the scientific assessment of behaviours, perceptions, skills, attitudes, and knowledge so frequently faced in Physical and Rehabilitation Medicine, not less than in social and educational sciences. Furthermore, suggestions are given on interpreting and managing the inevitable discrepancies between observed scores and ideal measures (data-model “misfit”). Finally, twelve practical take-home messages for appraising published results are provided.

Reads2Vec: Efficient Embedding of Raw High-Throughput Sequencing Reads Data.

The massive amount of genomic data appearing for SARS-CoV-2 since the beginning of the COVID-19 pandemic has challenged traditional methods for studying its dynamics. As a result, new methods such as Pangolin, which can scale to the millions of samples of SARS-CoV-2 currently available, have appeared. Such a tool is tailored to take as input assembled, aligned, and curated full-length sequences, such as those found in the GISAID database. As high-throughput sequencing technologies continue to advance, such assembly, alignment, and curation may become a bottleneck, creating a need for methods that can process raw sequencing reads directly. In this article, we propose Reads2Vec, an alignment-free embedding approach that can generate a fixed-length feature vector representation directly from the raw sequencing reads without requiring assembly. Furthermore, since such an embedding is a numerical representation, it may be applied to highly optimized classification and clustering algorithms. Experiments on simulated data show that our proposed embedding obtains better classification results and better clustering properties contrary to existing alignment-free baselines. In a study on real data, we show that alignment-free embeddings have better clustering properties than the Pangolin tool and that the spike region of the SARS-CoV-2 genome heavily informs the alignment-free clusterings, which is consistent with current biological knowledge of SARS-CoV-2.

GB-score: Minimally designed machine learning scoring function based on distance-weighted interatomic contact features.

In recent years, thanks to advances in computer hardware and dataset availability, data-driven approaches (like machine learning) have become one of the essential parts of the drug design framework to accelerate drug discovery procedures. Constructing a new scoring function, a function that can predict the binding score for a generated protein-ligand pose during docking procedure or a crystal complex, based on machine and deep learning has become an active research area in computer-aided drug design. GB-Score is a state-of-the-art machine learning-based scoring function that utilizes distance-weighted interatomic contact features, PDBbind-v2019 general set, and Gradient Boosting Trees algorithm to the binding affinity prediction. The distance-weighted interatomic contact featurization method used the distance between different ligand and protein atom types for numerical representation of the protein-ligand complex. GB-Score attains Pearson's correlation 0.862 and RMSE 1.190 on the CASF-2016 benchmark test in the scoring power metric. GB-Score's codes are freely available on the web at https://github.com/miladrayka/GB_Score.

PTGAC Model: A machine learning approach for constructing phylogenetic tree to compare protein sequences.

This work proposes a machine learning-based phylogenetic tree generation model based on agglomerative clustering (PTGAC) that compares protein sequences considering all known chemical properties of amino acids. The proposed model can serve as a suitable alternative to the Unweighted Pair Group Method with Arithmetic Mean (UPGMA), which is inherently time-consuming in nature. Initially, principal component analysis (PCA) is used in the proposed scheme to reduce the dimensions of 20 amino acids using seven known chemical characteristics, yielding 20 TP (Total Points) values for each amino acid. The approach of cumulative summing is then used to give a non-degenerate numeric representation of the sequences based on these 20 TP values. A special kind of three-component vector is proposed as a descriptor, which consists of a new type of non-central moment of orders one, two, and three. Subsequently, the proposed model uses Euclidean Distance measures among the descriptors to create a distance matrix. Finally, a phylogenetic tree is constructed using hierarchical agglomerative clustering based on the distance matrix. The results are compared with the UPGMA and other existing methods in terms of the quality and time of constructing the phylogenetic tree. Both qualitative and quantitative analysis are performed as key assessment criteria for analyzing the performance of the proposed model. The qualitative analysis of the phylogenetic tree is performed by considering rationalized perception, while the quantitative analysis is performed based on symmetric distance (SD). On both criteria, the results obtained by the proposed model are more satisfactory than those produced earlier on the same species by other methods. Notably, this method is found to be efficient in terms of both time and space requirements and is capable of dealing with protein sequences of varying lengths.

Do numbers make us handy? Behavioral and electrophysiological evidence for number-hand congruency effect

Finger counting facilitates numerical representations and mathematical processing. The current study investigated the association between finger counting habits and number processing by employing behavioral and electrophysiological measures. We explored whether small and large numerical primes influence the recognition of embodied target hand stimuli. Twenty-four right-handed participants that were grouped into right-starters (n = 13) and left-starters (n = 11) for finger counting performed a hand recognition task that consisted of numerical magnitudes as prime and hand recognition as targets. Based on the finger counting habits, congruent (i.e., left-starters: small number/left hand or large number/right hand; right-starters: small number/right hand or large number/left hand) and incongruent (i.e., left-starters: large number/left hand or small number/right hand; right-starters: large number/right hand or small number/left hand) conditions were presented to the participants. The participants were required to indicate whether the targets were left or right hand by simply pressing the left or the right key, respectively. Results indicated faster reaction times (RTs) for congruent as opposed to incongruent trials for all participants. The mean amplitude of the centro-parietal P300 component was significantly increased for the incongruent compared to congruent condition, indicating increased mental effort. Also, analysis of the latency of the P300 in terms of congruency effect in all participants revealed significant results. These combined results provide behavioral and electrophysiological evidence indicating the embodied nature of numbers. The results are interpreted in light of the general findings related to the P300 component. This research supports the association of number-hand representations and corroborates the idea of embodied numerosity.

Reconnecting Learning: An Educational Alternative For Dyscalculia Children In Elementary School

A math teacher uses a remedial education intervention to help one student with a counting dyscalculia problem. Dyscalculia is a catchy term for a variety of problems with math that affect learning and performance. The author of this study created this new theory-driven intervention with the aim of identifying primary school teachers using reconnect learning to help students with the potential to experience dyscalculia learn to count and in this case the ability to count to 10 which will be seen to achieve the learning goal. which is desired. the author used a qualitative approach to identify elementary school teachers using reconnective learning to help students with the potential to experience dyscalculia learn to count. Interviews, class observations, and introspective diaries all contributed to the data set. The author conducted the research, which was conducted at a public elementary school in Gresik, East Java, Indonesia, conducted in Grade 1 with a total of 20 students. After initial screening using the Indonesian Dyscalculia instrument. Students with dyscalculia have learning problems in mathematics that are characterized by underlying difficulties with numerical representation and processing. They can have problems with basic arithmetic such as counting and recognizing numbers. Helping students with Dyscalculia succeed in mathematics through early treatment is a promising area of research. A shortage of instructional scaffolding that helps Dyscalculia students organize their learning process while also addressing cognitive deficiencies and arithmetic competency gaps remains. Pseudonym Mrs. Sinta (elementary school math teacher) and Riki (a student potentially at risk of Dyscalculia) are involved in the current investigation. The results showed that the recommended interventions helped students become more proficient in calculations. Since most of the literature on remedial interventions for students with disabilities key significance to education is the focus of this research, an approach that shifts the emphasis from instructional tactics (devices, tools, interactions) to students' cognitive skills, an intervention that shows promise for helping students who are at risk of falling behind. in cognitive numbers. This study provides a solution to the posed question by showing how primary school teacher might use Reconnecting Learning to aid kids at risk for dyscalculia in their pursuit of numeric literacy. Mrs. Sinta (a pseudonym) is an elementary school teacher who employs the Reconnecting Learning paradigm in her own education. Success in learning to count to ten was shown to be one of Reconnecting Learning's intended outcomes.

A comparative study of different data representations under CNN and a novel integrated FDD architecture

AbstractIn recent years, deep‐learning‐based fault detection and diagnosis (FDD) methods have received extensive attention. As we all know, different input forms have a great impact on the final performance. In this paper, three categories and seven representation methods are discussed: numeric representations, image mapping representations (radar chart mapping and Gramian angular summation field (GASF) mapping), and signal transforming representations (fast Fourier transform (FFT) and wavelet). The tests on the Tennessee Eastman process (TEP) dataset prove that the FFT method has achieved the best performance on average. Based on this, a general FDD integration framework is proposed to integrate multiple base learners together to make decisions by weighted voting or maximum voting. Finally, the comparison between our proposed method and other five typical models (FFT, a GASF and a multi‐scale neural network (GASF–MSNN), convolutional neural network (CNN), Long Short‐Term Memory (LSTM), and Support Vector Machine (SVM)) illustrates the effectiveness of our method for FDD on the TEP. The proposed integrated method provides an effective platform for deep‐learning‐based FDD.

Characterizing SARS-CoV-2 Spike Sequences Based on Geographical Location.

With the rapid spread of COVID-19 worldwide, viral genomic data are available in the order of millions of sequences on public databases such as GISAID. This Big Data creates a unique opportunity for analysis toward the research of effective vaccine development for current pandemics, and avoiding or mitigating future pandemics. One piece of information that comes with every such viral sequence is the geographical location where it was collected-the patterns found between viral variants and geographical location surely being an important part of this analysis. One major challenge that researchers face is processing such huge, highly dimensional data to obtain useful insights as quickly as possible. Most of the existing methods face scalability issues when dealing with the magnitude of such data. In this article, we propose an approach that first computes a numerical representation of the spike protein sequence of SARS-CoV-2 using k-mers (substrings) and then uses several machine learning models to classify the sequences based on geographical location. We show that our proposed model significantly outperforms the baselines. We also show the importance of different amino acids in the spike sequences by computing the information gain corresponding to the true class labels.

Contrasting symbolic and non-symbolic numerical representations in a joint classification task

Both symbolic (digits) and non-symbolic (dots) numerals are spatially coded, with relatively small numbers being responded faster with a left key and large numbers being responded faster with a right key (spatial–numerical association of response codes [SNARC]). The idea of format independent SNARC seems to support the existence of a common system for symbolic and non-symbolic numerical representations, although evidence in the field is still mixed. The aim of the present study is to investigate whether symbolic and non-symbolic numerals interact in the SNARC effect when both information is simultaneously displayed. To do so, participants were presented with dice-like patterns, with digits being used instead of dots. In two separate magnitude classification tasks, participants had to respond either to the number of digits presented on the screen or to their numerical size. In the non-symbolic task, they had to judge whether the digits on the screen were more or less than three, irrespective of the numerical value of the digits. In the symbolic task, participants had to judge whether the digits on the screen were numerically smaller or larger than three, irrespective of the number of digits being present. The results show a consistent SNARC effect in the symbolic task and no effect in the non-symbolic one. Furthermore, congruency between symbolic and non-symbolic numerals did not modulate the response patterns, thus supporting the idea of independent representations and questioning some propositions of current theoretical accounts.

Face expression understanding by geometrical characterization of deep human face representation

Face expressions understanding is a key to have a better understanding of the human nature. In this contribution we propose an end-to-end pipeline that takes color images as inputs and produces a semantic graph that encodes numerically what are facial emotions. This approach leverages low-level geometric details as face representation which are numerical representations of facial muscle activation patterns to build this emotional understanding. It shows that our method recovers social expectations of what characterize facial emotions.

Tree visualizations of protein sequence embedding space enable improved functional clustering of diverse protein superfamilies.

Protein language models, trained on millions of biologically observed sequences, generate feature-rich numerical representations of protein sequences. These representations, called sequence embeddings, can infer structure-functional properties, despite protein language models being trained on primary sequence alone. While sequence embeddings have been applied toward tasks such as structure and function prediction, applications toward alignment-free sequence classification have been hindered by the lack of studies to derive, quantify and evaluate relationships between protein sequence embeddings. Here, we develop workflows and visualization methods for the classification of protein families using sequence embedding derived from protein language models. A benchmark of manifold visualization methods reveals that Neighbor Joining (NJ) embedding trees are highly effective in capturing global structure while achieving similar performance in capturing local structure compared with popular dimensionality reduction techniques such as t-SNE and UMAP. The statistical significance of hierarchical clusters on a tree is evaluated by resampling embeddings using a variational autoencoder (VAE). We demonstrate the application of our methods in the classification of two well-studied enzyme superfamilies, phosphatases and protein kinases. Our embedding-based classifications remain consistent with and extend upon previously published sequence alignment-based classifications. We also propose a new hierarchical classification for the S-Adenosyl-L-Methionine (SAM) enzyme superfamily which has been difficult to classify using traditional alignment-based approaches. Beyond applications in sequence classification, our results further suggest NJ trees are a promising general method for visualizing high-dimensional data sets.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age.

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Beyond the Numbers: How Focusing on Compositional Diversity Downplays Anti-Asian Racism

In Short Asian American students reported increasingly hostile racial climates, with misinformation and anti-Asian sentiments being spread on social media, other students physically shunning Asian students, and Asian internationals experiencing restrictions and fears of surveillance. Asian and Asian Americans remain on the fringe when it comes to higher education diversity, equity, and inclusion (DEI) discussions and efforts, under the stereotypical assumption that they are “model minorities.” Among the reasons there may be less attention on campus racial climates for Asian Americans is based a narrow and insufficient focus on compositional diversity—numerical representation of groups in higher education. A dynamic, multicontexual approach that incorporates faculty, staff, and students in better supporting Asian and Asian Americans in higher education is needed.

Arbitrary-Oriented Ellipse Detector for Ship Detection in Remote Sensing Images

At present, in arbitrary-oriented object detection, the angular periodicity problem of rotated bounding box described by angle causes an object to have different numerical representations, which leads to uncertainty of rotated bounding box regression. To eliminate the angular periodicity problem, in this paper, we propose a novel and simple ellipse parameters representation method for arbitrary-oriented object, which hides the angle of object in the focal vector of ellipse to avoid direct angle prediction. Moreover, the proposed representation method can enable the arbitrary-oriented object to have only one numerical representation, which is beneficial to alleviate the uncertainty of bounding box regression. In order to adapt the proposed ellipse parameters representation method, we adopt 2D Gaussian distribution label assign for coarse samples selection, then the KLD loss and SimOTA are used to refine the coarse samples to obtain the best positive samples. We extend the YOLOX with medium parameters as an oriented ship detector according to the proposed ellipse parameters representation method, and conduct the experiments on HRSC2016, RSDD-SAR and RHRSID to demonstrate the effectiveness of the proposed method. The experimental results show that the proposed representation method achieves impressive results compared with state-of-the-art arbitrary-oriented object detection methods.