Numerical Representation Research Articles

Planning in the face of diversity: A re-orientation of power relations

This paper explores the individuals' lived experiences of living next to different others. Its main focus is on diversity which signifies possible ways of working with differences. Hence, the analysis aims to explore individuals’ perceptions of diverse neighbourhoods, manifestations of differences’ co-existence and the procedure called planning for diversity. To these aims, a qualitative study encompassing interviewing 95 individuals in five neighbourhoods of Tehran, which is one of the most diverse cities in the middle east, is conducted through a phenomenographic approach. Results indicate that individuals' perceptions of diversity are location-based and related to structural inequity or welfare they experienced. Managerial, functional, sociological and physical aspects are the four main perceived pillars of a diverse neighbourhood, which as a spatial unit not only sets the scene for numerical and hierarchical representations of differences but is tolerant of differences. Nevertheless, residents’ lived experiences suggest that diverse populations in Tehran caused individuals' hunkering down – rooted in constrict theory – in general, although intergroup contacts – rooted in contact theory – are also frequent in neighbourhoods where diversity exists in all of its dimensions. Economic diversity is introduced as a catalyst for social diversity that can let outgroup interactions emerge whereas wealth concentration and indifference to differences are two primary components for the emergence of individualism in Tehran. Moreover, Conscious efforts through planning for diversity, which is people-oriented and procedural and looks for a reorientation of power relations, could let differences work, intergroup interactions form and interest-based identities, which introduce neighbourhood as ends, not means, emerge. Therefore, planning for diversity is more based on becoming ontology and is rooted in radical planning theory. Differences, which have always been run through a bottom-up approach, take the initiative and voice policy, set interest-based identities and try to reach them; that is how differences find the opportunity to be reunited.

Num2vec: Pre-Training Numeric Representations for Time Series Forecasting in the Sensing System

Time series forecasting in the sensing system aims to predict future values based on historical records that sensors have collected. Previous works, however, usually focus on improving model structure or algorithm for better performance but the perspective of learning proper numeric representations is overlooked. The inappropriate and coarse numeric representations are not expressive enough to capture the intrinsic characteristics of numbers, which will obviously degrade the prediction performance. In this article, we propose Num2vec, an algorithmic framework to learn numeric representations. Specifically, Num2vec lists three main logic characteristics of numbers: arithmetic, direction, and periodicity. By representing numbers into a transition space, Num2vec can translates numbers agilely to different Internet of Things tasks through selecting the corresponding characteristics. According to such a design, Num2vec enjoys flexible numeric representations to fit different Internet of Things time series tasks. Extensive experiments on four real-world datasets show that the approach achieves the best performance when compared with state-of-the-art baselines.

Impacts of Uncontrolled Operator Splitting Methods on Parameter Identification, Prediction Uncertainty, and Subsurface Flux Representation in Conceptual Hydrological Models

AbstractThe proper numerical representation of physical processes in mechanistic hydrological models is essential to produce robust predictions. A common problem with numerical schemes in hydrological models is that multiple concurrent fluxes are calculated sequentially. Although the importance of errors introduced by inappropriate numerical schemes is well recognized in the literature, many hydrological models calculate concurrent fluxes sequentially. Here, two versions of the HYPE model are used to investigate the limitations of sequential calculations. A fourth order Gear‐Nordsieck solution of the continuous state‐space formulation of HYPE (I‐HYPE) is developed to provide a robust solution, and a fixed‐step implicit Euler scheme (IE‐HYPE) is implemented to provide a computationally efficient and robust approximation of the I‐HYPE simulations. In contrast to I‐HYPE, results show that the original HYPE and the sequential calculation implemented in the continuous state‐space formulation of HYPE (SQ‐HYPE) typically simulate no interflow when soil moisture levels exceed the field capacity. The discrepancy between SQ‐HYPE and I‐HYPE grows with the size of the computation time step, and this implies a compromised representation of flow paths by sequential schemes. IE‐HYPE provides responses comparable with I‐HYPE for both daily and hourly time steps. IE‐HYPE and SQ‐HYPE are compared in terms of their groundwater representation, parameter identifiability, and predictive skills for two catchments. The sequential models have larger groundwater contributions to flow than IE‐HYPE because the splitting errors in SQ‐HYPE limit the interflow flux. IE‐HYPE estimates of the groundwater flux are more consistent with literature values of groundwater contributions to flow for the basins studied.

A Modelling on the Exponential Curves as $Cubic$, $5^{th}$ and $7^{th}$ B\'{e}zier Curve in Plane

In this study, it has been researched the exponential curve as a $3^{rd},$ $5^{th}$ and $7^{th}$ order B\'{e}zier curve in $\mathbf{E}^{2}$. Also, the numerical matrix representations of these curves have been calculated using the Maclaurin series in the plane via the control points.

How to Survive in a Totalitarian Regime: Education of Salesians in Slovakia in the Period of Socialism (1948–1989)

After the Communist coup in February 1948, all areas of society in Czechoslovakia were indoctrinated by the ideology of Marxism–Leninism. The Christian Churches became the biggest internal enemies of the state, since, especially in Slovakia, they had a strong tradition and numerous representations. The government tracked representatives and members of the Church and controlled all their activities. The activities of religious orders were prohibited, which de facto abolished them. The only possibility of their preservation was to continue the life, education and work of individual orders in secret. Our goal was to examine how the Salesian order survived in this situation; specifically, we focused on the forms of formation and illegal study of the Salesians during the totalitarian regime. Research in these activities is rather demanding, since they could not be documented for security reasons. So-called memoir literature, the oral history method, and private archival sources were used in the research. Despite the fact that it seems that religious orders would not survive in this historical situation, the opposite was true: in the period of persecution, the orders were not only able to survive, but also raised a new generation that ensured their continuity and the continuation of their activities.

Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

CARA PELAJAR LEPASAN MENENGAH MEWAKILKAN PENGAMIRAN TENTU

The problem of students’ understanding in learning Definite Integral is certainly one of the main issues in Calculus. Several cognitive barriers have been identified which cause the problems for students when learning for the first time on single function of integral. for this study. This article uses the theory of radical constructivism as a theoretical foundation, and focuses on the second sub-construct of the students’ understanding concept, which is the mode of post-secondary students make representations on Definite Integral. A case study is the design for this study. The method of selecting participants is through purposive sampling, which is selecting six participants who are among Diploma students in second semester at technical higher education institutions, especially those who are in technical engineering field. The results show that the mode of students representing definite integral can certainly be divided into three categories, namely Graphical Representation, Numerical Representation, and Schematic Representation.

On computation of neighbourhood degree sum-based topological indices for zinc-based metal–organic frameworks

AbstractThe permeable materials known as metal–organic frameworks (MOFs) have a large porosity volume, excellent chemical stability, and a unique structure that results from the potent interactions between metal ions and organic ligands. Work on the synthesis, architectures, and properties of various MOFs reveals their utility in a variety of applications, including energy storage devices with suitable electrode materials, gas storage, heterogeneous catalysis, and chemical assessment. A topological index, which is a numerical invariant, predicts the physicochemical properties of chemical entities based on the underlying molecular graph or framework. In this article, we consider two different zinc-based MOFs, namely zinc oxide and zinc silicate MOFs. We compute 14 neighbourhood degree sum-based topological indices for these frameworks, and the numerical and graphical representations of all the aforementioned 14 indices are made.

Hydrodynamic performance of a full-scale ship with a Pre-Swirl Duct: A numerical study with partially rotating grid method

This study investigates the hydrodynamic performance of a full-scale KVLCC2-S ship fitted with a Pre-Swirl Duct using CFD simulations. Four different propeller rotation representations are employed to evaluate the impact of the Pre-Swirl Duct on the ship’s performance. The study introduces a partially rotating grid method for two-phase flows, implemented within the Naval Hydro Pack library based on foam-extend software. The results of the study reveal that prediction of power savings depends on the accuracy of the numerical propeller representation. Non-inertial, partial, and inertial propeller representations predicted power savings while the actuator disc method predicted increase in delivered power. The partially rotating grid method provides a less computationally expensive alternative to the inertial propeller rotation representation, but at the cost of reduced accuracy. Furthermore, the study challenges the conventional analysis that attributes the power savings to improved propeller-hull interaction, suggesting that increased propeller efficiency is the primary cause.

Experimental validation of the dynamic thermal network approach in modeling buried pipes

The transient behavior of buried pipe systems plays a significant role in many heating and cooling systems, particularly in thermal energy networks and ground heat exchangers. In this study, the dynamic thermal network (DTN) approach’s validity as a response factor method in modeling dynamic conduction heat transfer in a buried pipe system is experimentally validated. A lab-scale representation of a buried pipe system has been excited by step changes in boundary temperatures and heat fluxes measured up to times approaching steady-state conditions. This data is used to derive weighting factors and also evaluate the validity of numerical representations of the buried pipe and to verify that the DTN method can reproduce the heat flux responses. It is demonstrated that the weighting factors required in this method can be derived from both numerical and experimental step-response time series data. The DTN method is found to be both accurate in reproducing the heat fluxes in the validation experiments but also significantly more computationally efficient than a conventional numerical model when simulating long timescale responses in buried pipe systems.

Representation of visible minorities in Canada's public service: Slow but significant progression

AbstractThis study examined the representation of visible minority (VM) employees in Canada's public service to clarify the extent to which Canada's Employment Equity Act (EEA) for diversity and equity management has influenced VM employment outcomes, with a focus on executive (leadership) and professional representation. Data from EEA annual reports (1997–2020) were analysed, and the results for VMs in the public service were juxtaposed with those for VMs in the broader labour market. VM employees' numerical representation under the EEA had increased and was slowly trending upwards in executive roles, exceeding their workforce availability in 2020. However, the representation of VMs in public service failed to match their actual proportion in the larger Canadian population. This group had a stronger representation in scientific and professional occupations, reflecting current immigration policies' support for skilled migration. The VM workforce in the broader labour market lacked equal representation, which indicates significant policy implications.

Improving deep learning model performance under parametric constraints for materials informatics applications

Modern machine learning (ML) and deep learning (DL) techniques using high-dimensional data representations have helped accelerate the materials discovery process by efficiently detecting hidden patterns in existing datasets and linking input representations to output properties for a better understanding of the scientific phenomenon. While a deep neural network comprised of fully connected layers has been widely used for materials property prediction, simply creating a deeper model with a large number of layers often faces with vanishing gradient problem, causing a degradation in the performance, thereby limiting usage. In this paper, we study and propose architectural principles to address the question of improving the performance of model training and inference under fixed parametric constraints. Here, we present a general deep-learning framework based on branched residual learning (BRNet) with fully connected layers that can work with any numerical vector-based representation as input to build accurate models to predict materials properties. We perform model training for materials properties using numerical vectors representing different composition-based attributes of the respective materials and compare the performance of the proposed models against traditional ML and existing DL architectures. We find that the proposed models are significantly more accurate than the ML/DL models for all data sizes by using different composition-based attributes as input. Further, branched learning requires fewer parameters and results in faster model training due to better convergence during the training phase than existing neural networks, thereby efficiently building accurate models for predicting materials properties.

What Do Arithmetic Errors in the Financial Context Reveal? A Preliminary Study of Individuals with Neurocognitive Disorders

Objectives: Arithmetic errors in the financial context have been investigated mainly in cognitively normal Parkinson’s disease (PD) patients and mildly impaired PD (PD-MCI) individuals. The aim of this study was to examine arithmetic errors in the financial context across neurocognitive disorders. Methods: Four hundred and twenty older adults from Greece were divided into four groups (110 patients with a diagnosis of Alzheimer’s disease (AD), 107 patients with a diagnosis of mild cognitive impairment (MCI), 109 healthy controls and 94 Parkinson’s disease dementia (PDD) patients). Their ages ranged from 65 to 98 years (M = 73.96, SD = 6.68), and the sample had a mean of 8.67 (SD = 4.08) years of education. For each of the AD patients, a counterpart matched by age, educational attainment and gender was selected from a larger group of participants. Results: Overall, the results reveal that healthy older adults did not commit arithmetic errors, but AD patients reported procedural errors in their responses to both questions. A high frequency of procedural errors was found in MCI patients’ responses to the first question, while the errors in their responses to the second question cannot be categorized. Finally, in PDD patients, place value errors were reported for the first question, while more magnitude errors were made when responding to the second question. Conclusions: These findings support that arithmetic errors within financial contexts are not the same across neurocognitive disorders, and numerical representations are not impaired not only in PDD, but also in AD and MCI. This information could be useful in cognitive assessments performed by neurologists and neuropsychologists as these types of errors may be indicators of specific brain pathologies.

A didactic sequence for the initial study of fractions

The present study is focused on the mathematical object of fractions. A didactic support sequence was elaborated and implemented as the first formal approach to its study for students in the third year of elementary level school, using, as a means, accessible manipulative materials to be used in the classroom. In order to identify the theoretical elements that served as a guide for the design of the activities and the manipulative materials, analyzes were carried out from the epistemological and didactic approaches. The didactic sequence consists of three parts: the first is based on the previous notions that the student has about fractions, using their experiences with daily life; in the second part it is contextualized, trying to formalize the object, going from a middle to a half; Finally, the use of numbers to represent fractions is introduced, making use of figural representations. It was applied to 6 students. It was concluded that the process of building their knowledge about fractions, starting with ½, associating it with their experiences, and using manipulative materials, allowed students to outline the concept of fractions and arrive at its numerical representation, giving meaning to the numerator and denominator.

On topological descriptor based heat of formation and entropy measure for actinium(III) fluoride

Silvery radioactive metallic element is known as actinium. Due to its high radioactivity and blue light, actinium glows in the dark. A recent discipline of applied chemistry is chemical graph theory. A topological index is a numerical value that links the thermodynamic properties of a chemical structure. Due to the importance of this structure, we computed the topological indices such as Randic, Zagreb Indices and so on. In this paper, we calculate topological indices of actinium(III) fluoride. A few degree-based entropies are computed from topological indices. Additionally, a connection has been made between the thermodynamic features of actinium(III) fluoride and Shannon entropy. The numerical and graphical representations of the computed data were combined with curve fitting between the calculated information entropies and the heat of formation.

Deep learning tumor heterogeneity metric from histopathology images vs next generation sequencing-derived scores for colon cancer prognostication.

3537 Background: Tumor heterogeneity is as an important determinant of clinical behavior in many cancer types, with increased heterogeneity thought to confer inferior clinical outcome. Sequencing based assessment of colon cancer has been used to quantify tumor heterogeneity and correlate it with survival, but is sensitive to the mutation calling algorithm utilized. Digitization of histopathology slides allows application of deep learning methods for image analysis. Automated slide annotation and feature extraction provides numeric representations of underlying phenotype from which tumor heterogeneity can be estimated. Here we compare the ability of a deep-learning tumor heterogeneity score (THS) to estimate overall survival in colon cancer patients to estimates produced by bulk sequencing derived mutant-allele tumor heterogeneity (MATH) and copy number variation (CNV) event scores. Methods: Digitized whole slide images (WSIs) from The Cancer Genome Atlas (TCGA) colon adenocarcinoma dataset are processed in a computational pipeline for tissue detection, numerical feature extraction, and cell type classification. WSIs are tiled and local THS calculated from imaging features. Corresponding MATH and CNV derived heterogeneity metrics are calculated from published sequencing data. Kaplan Meier curves are used to compare patient survival stratified by tumor heterogeneity as calculated by the three independent methods. Automated regional annotation identifies intra-tumoral and tumor-stromal boundary tiles and tumor THS is correlated to distance from the boundary. Results: Images from 379 patients (209 right-sided, 152 left-sided tumors) yielded 575,762 tiles. Automated annotation resulted in 272,791 intra-tumoral and 11,340 tumor-stromal boundary tiles. Stratification by imaging derived THS provided significant separation of overall survival curves (p < .01) in contrast to MATH and CNV methods (p > .05 for both). THS significantly separated the curves in right- but not left-sided cancers (p = .03 and .44, respectively). Evaluating THS as a function of distance from the tumor-stromal boundary, right-sided tumors showed significant decrease in THS with increasing distance from tumor edge. Conclusions: Our novel pipeline produced spatially resolved imaging data informed by underlying tumor phenotype without need for pathologist annotation. The resultant THS correlated with outcome and outperformed sequencing-based prognostication methods. The spatial information identified higher heterogeneity at the tumor edge than interior regions of right-sided, but not left-sided tumors, capturing known but poorly understood differences in colon tumors by location. Deep learning image analysis provided reproducible and cost-effective data with great potential both in clinical biomarker discovery and as a research tool.

A novel, AI-generated morphologic biomarker to predict prostate cancer recurrence in patients with intermediate risk of progression.

e17097 Background: About half of the prostate cancer (PCa) patients within an intermediate-risk group return to the clinic with disease progression after the first line of therapy. While these patients can be stratified into Gleason Grades (GG) 3+4 and 4+3, studies indicate that high-risk patients can still be found in both groups. Using our AI platform, we have developed a morphometric biomarker by analyzing digitized H&E slide images (WSIs), which can accurately predict early biochemical recurrence (within 36 months post-surgery) and the risk of metastatic disease more accurately than GG, TNM staging, and genomic tools. Methods: 125 intermediate-risk (n = 67, 3+4; n = 58, 4+3) samples were collected from the Icahn School of Medicine at Mount Sinai (ISSMS) to form a held-out test set. Seventy-eight patients within the test set had an associated genomic score. A series of deep learning models trained using data from ISMMS, the University of Wisconsin-Madison, and TCGA generated a high dimensional vector for each WSI to provide a numerical representation of observed morphologies, which is then converted into a single score to predict biochemical recurrence within 36 months (BCR) and rank risk of metastasis (MET). Area-under-the-receiver operating characteristic (AROC) was used to measure the accuracy of BCR, and the concordance index (CI) was used to measure the performance of MET. The high and low-risk groups' hazard ratios (HR) for patients within grades 3+4 and 4+3 show that our model can further stratify GG. Results: Our method was significantly better at predicting BCR (AROC: 0.801) and ranking MET (CI: 0.764) relative to GG, TNM, and genomic tool (Table 1). We further sub-stratified the patients into GG 3+4 and 4+3 and identified high-risk patients within each GG. Patients in GG 3+4 with high PATHOMIQ scores had a significantly higher risk of BCR (HR 3.3; 95% CI 1.44 – 7.56; p < 0.005) compared to the low PATHOMIQ score patients. A similar trend was seen in the GG 4+3 group (HR 3.0; 95% CI 1.32 – 6.83; p < 0.01). Conclusions: Our histopathology-based prognostic biomarker significantly improves over standard clinical markers in stratifying patients with intermediate-risk PCa for BCR and MET. Our method overcomes several limitations of genomic testing: We only need digitized WSIs. Our method is non-destructive and preserves the tissue for further interrogation. Moreover, our turn-around time is a few hours. Thus, the PATHOMIQ scoring method may strongly impact the management of intermediate-risk PCa patients and clinical trial patient selection for the successful development of new therapies for early-stage PCa. [Table: see text]

The numerical stroop effect on consumer preference to order healthy food

This article explores an alternative strategy to subtly nudge decisions in preference for healthy menu items – managing calorie presentation to create a Numerical Stroop Effect drawing upon the numerical magnitude representation theory. Across two experiments, the research finds that incongruent (vs. congruent) numerical magnitude representation of food calories (e.g., small 7 and large 5) increases consumers' preference to order healthy items. The study reveals the effect’s underlying mechanism through perceived healthiness along with the boundary factors of consumers’ health consciousness and time pressure. Specifically, low health-conscious consumers show a preference to order healthy items when exposed to incongruent magnitude representation of food calories, particularly when they experience high time pressure. The research contributes to the hospitality literature with an in-depth understanding of the less explored effect of numerical magnitude representation. This research also provides an easily implementable menu strategy to influence consumers’ dining preferences for healthier alternatives.

"Head of the Class": equity discourses related to department head appointments at one Canadian medical school.

Equitable appointments of departmental leaders in medical schools have lagged behind other Equity, Diversity, and Inclusion (EDI) advancements. The purpose of this research was to 1) analyze how policy documents communicate changing ideas of EDI, employment equity, and departmental leadership; and 2) investigate department heads' (DH) perspectives on EDI policies and practices. We conducted a critical discourse analysis to examine underlying assumptions shaping EDI and departmental leadership in one Canadian medical school. We created and analyzed a textual archive of EDI documents (n = 17, 107 pages) and in-depth interviews with past (n = 6) and current (n = 12) DH (830 minutes; 177 pages). Documents framed EDI as: a legal requirement; an aspiration; and historical reparation. In interviews, participants framed EDI as: affirmative action; relationships; numerical representation; and relinquishing privilege. We noted inconsistent definitions of equity-deserving groups. Change is slowly happening, with emerging awareness of white privilege, allyship, co-conspiracy, and the minority tax. However, there is more urgent work to be done. This work requires an intersectional lens. Centering the voices, and taking cues from equity-deserving leaders and scholars will help ensure that EDI pathways, such as those used to cultivate department leaders, are more inclusive, effective, and aligned with intentions.

Sem2vec : Semantics-aware Assembly Tracelet Embedding

Binary code similarity is the foundation of many security and software engineering applications. Recent works leverage deep neural networks (DNN) to learn a numeric vector representation (namely, embeddings ) of assembly functions, enabling similarity analysis in the numeric space. However, existing DNN-based techniques capture syntactic-, control flow-, or data flow-level information of assembly code, which is too coarse-grained to represent program functionality. These methods can suffer from low robustness to challenging settings such as compiler optimizations and obfuscations. We present sem2vec , a binary code embedding framework that learns from semantics . Given the control-flow graph (CFG), 34 pages. of an assembly function, we divide it into tracelets , denoting continuous and short execution traces that are reachable from the function entry point. We use symbolic execution to extract symbolic constraints and other auxiliary information on each tracelet. We then train masked language models to compute embeddings of symbolic execution outputs. Last, we use graph neural networks, to aggregate tracelet embeddings into the CFG-level embedding for a function. Our evaluation shows that sem2vec extracts high-quality embedding and is robust against different compilers, optimizations, architectures, and popular obfuscation methods including virtualization obfuscation. We further augment a vulnerability search application with embeddings computed by sem2vec and demonstrate a significant improvement in vulnerability search accuracy.