Vector Arithmetic Research Articles

ScPerb: Predict single-cell perturbation via style transfer-based variational autoencoder

IntroductionTraditional methods for obtaining cellular responses after perturbation are usually labor-intensive and costly, especially when working with multiple different experimental conditions. Therefore, accurate prediction of cellular responses to perturbations is of great importance in computational biology. Existing methodologies, such as graph-based approaches, vector arithmetic, and neural networks, either mix perturbation-related variances with cell-type-specific patterns or implicitly distinguish them within black-box models. ObjectivesThis study aims to introduce and demonstrate a novel framework, scPerb, which explicitly extracts perturbation-related variances and transfers them from unperturbed to perturbed cells to accurately predict the effect of perturbation in single-cell level. MethodsscPerb utilizes a style transfer strategy by incorporating a style encoder into the architecture of a variational autoencoder. The style encoder captures the differences in latent representations between unperturbed and perturbed cells, enabling accurate prediction of post-perturbation gene expression data. ResultsComprehensive comparisons with existing methods demonstrate that scPerb delivers improved performance and higher accuracy in predicting cellular responses to perturbations. Notably, scPerb outperforms other methods across multiple datasets, achieving superior R2 values of 0.98, 0.98, and 0.96 on three benchmarking datasets. ConclusionscPerb offers a significant advancement in predicting cellular responses by effectively separating and transferring perturbation-related variances. This framework not only enhances prediction accuracy but also provides a robust tool for computational biology, addressing the limitations of current methodologies.

Digital Transformation and Corporate ESG Performance – Evidence from China

The focal point of this paper is to study environmental, social, and governance (ESG) performance consequences of digital transformation for companies, as well as green technological innovation, corporate social responsibility, and internal control as mediating variables. A set of digital transformation indicators was developed utilizing data from 355 listed industrial companies in China between 2011 and 2019 and vector arithmetic. The study’s findings suggested that digital transformation has considerably raised ESG performance, with green technological innovation, corporate social responsibility, and internal control as significant mediating variables. The paper has several contributions; for example, it provides theoretical and empirical evidence for ESG improvement in Chinese firms and an essential factor associated with ESG performance, among others. The non-economic impacts of digital transformation on ESG performance are essential insights offered by this study. They also provide insight into these impacts' mechanisms, including green technology, corporate social responsibility, and internal control.

Predictive Modeling of UHPC Compressive Strength: Integration of Support Vector Regression and Arithmetic Optimization Algorithm

Based on an in-depth analysis of the factors influencing the compressive strength of ultra-high-performance concrete (UHPC), this study examined the impact of both single factorsand combined factors on UHPC performance using experimental data. The correlation analysis indicates that cement content, water content, steel fiber, and fly ash significantly affect the strength of UHPC, whereas silica fume, superplasticizers, and slag powder have a relatively smaller influence. This analysis provides a scientific basis for model development. Furthermore, the support vector regression (SVR) model was optimized using the arithmetic optimization algorithm (AOA). The superior performance and computational efficiency of the AOA–SVR model in predicting UHPC compressive strength were validated. Compared to SVR, support vector machine (SVM), and other single models, the AOA–SVR model achieves the highest R2 value and the lowest error rates. The results demonstrate that the optimized AOA–SVR model possesses excellent generalization ability and can more accurately predict the compressive strength of UHPC.

A Survey of Polynomial Multiplications for Lattice-Based Cryptosystems

We survey various mathematical tools used in software works multiplying polynomials in ℤ q [ x ] ⟨ x n − α x − β ⟩ . In particular, we survey implementation works targeting polynomial multiplications in lattice-based cryptosystems Dilithium, Kyber, NTRU, NTRU Prime, and Saber with instruction set architectures/extensions Armv7-M, Armv7E-M, Armv8-A, and AVX2. There are three emphases in this paper: (i) modular arithmetic, (ii) homomorphisms, and (iii) vectorization. For modular arithmetic, we survey Montgomery, Barrett, and Plantard multiplications. For homomorphisms, we survey (a) various homomorphisms such as Cooley–Tukey FFT, Good–Thomas FFT, Bruun's FFT, Rader's FFT, Karatsuba, and Toom–Cook; (b) various algebraic techniques for adjoining nice properties to the coefficient rings, including localization, Schönhage's FFT, Nussbaumer's FFT, and coefficient ring switching; and (c) various algebraic techniques related to the polynomial moduli, including twisting, composed multiplication, evaluation at ∞ , truncation, incomplete transformation, striding, and Toeplitz matrix-vector product. For vectorization, we survey the relations between homomorphisms and vector arithmetic. We then go through several case studies: We compare the implementations of modular multiplications used in Dilithium and Kyber, explain how the matrix-to-vector structure was exploited in Saber, and review the design choices of transformations for NTRU and NTRU Prime with vectorization. Finally, we outline several interesting implementation projects.

Deciphering Soil-Plant and Soil-Insect Interactions: A Mathematical Modeling Approach

Abstract The Pev and Rv functions were introduced as a way of summarizing the mechanical phenomenon of root-soil interactions and the effect of root growth on soil volume. The Mohr-Coulomb criterion was applied to the Rv function to demonstrate the relationship between root morphology, soil mechanical properties, and soil stability. The theory of elasticity and plasticity was applied in the analysis of the Bio-Geo Interface, which showed that the force F generated by the roots increased with time due to the growth of the roots and the increase in their volume. The forces acting on the Bio-Geo Interface were represented mathematically through the use of vector arithmetic, which helped to calculate the direction of the forces acting on the system. The Pev function was used to study the evolution of the plant and how it affected the Rv function. The results showed that the interplay between plant growth and soil mechanics is crucial in understanding the behavior of the Bio-Geo Interface, and can provide valuable insights into the interactions between plants and soil in natural and engineered systems. In the study of soil-insect interaction, a mathematical function, Iev, was proposed to represent the insect’s evolution in the soil environment. The function takes into account factors such as food sources and void ratio, which are important indicators of the biological and geotechnical aspects of the soil respectively. Despite the potential impact of insects on the soil environment, it has been concluded that their force resulting from their movement and behavior is negligible according to theories of elasticity and plasticity. This means that the impact of insects on the soil is minimal and does not significantly affect the soil’s mechanical properties. However, the biological aspects of the soil, such as food sources, remain important factors in the study of insect evolution in the soil environment.

An encoding framework for binarized images using hyperdimensional computing.

Hyperdimensional Computing (HDC) is a brain-inspired and lightweight machine learning method. It has received significant attention in the literature as a candidate to be applied in the wearable Internet of Things, near-sensor artificial intelligence applications, and on-device processing. HDC is computationally less complex than traditional deep learning algorithms and typically achieves moderate to good classification performance. A key aspect that determines the performance of HDC is encoding the input data to the hyperdimensional (HD) space. This article proposes a novel lightweight approach relying only on native HD arithmetic vector operations to encode binarized images that preserves the similarity of patterns at nearby locations by using point of interest selection and local linear mapping. The method reaches an accuracy of 97.92% on the test set for the MNIST data set and 84.62% for the Fashion-MNIST data set. These results outperform other studies using native HDC with different encoding approaches and are on par with more complex hybrid HDC models and lightweight binarized neural networks. The proposed encoding approach also demonstrates higher robustness to noise and blur compared to the baseline encoding.

A two-stage model extraction attack on GANs with a small collected dataset

Due to their capacity for image generation, GAN models may be considered as a solution for the use of private data, which enhances their commercial value. However, unlike discriminative models such as CNNs, extraction attacks on GANs have not received significant attention, with only a few relevant works available. This paper proposes a novel two-stage extraction attack on GANs that does not require access to the victim GAN model. In the first stage, data augmentation is performed using GAN inversion techniques and vector arithmetic, tailored to scenarios with small query budgets. The second stage comprises two types of training: the innocent transfer training on unprocessed collected samples and the additional training on the augmented set. We provide three options for additional training: training of the discriminator alone (D), training of the generator alone (G), and training of both (D+G). We then conduct a quantity and quality evaluation of our extraction attacks compared to the baseline attack. Experiment results demonstrate that our proposed approach can successfully extract a GAN model, where the distribution of the extracted GAN closely resembles the distribution of the target GAN, even with a hundred generated images of the target GAN. Specifically, we achieve stable performance with better extraction, a more disentangled latent space for the extracted GAN, and significant semantic attribute editing performance using the two-stage extraction with additional training of the discriminator (D). By demonstrating that even a hundred leaked images may result in severe extraction, this study raises serious concerns regarding GAN model leakage.

A deep generative framework with embedded vector arithmetic and classifier for sample generation, label transfer, and clustering of single-cell data

Multiple-source single-cell datasets have accumulated quickly and need computational methods to integrate and decompose into meaningful components. Here, we present inClust (integrated clustering), a flexible deep generative framework that enables embedding auxiliary information, latent space vector arithmetic, and clustering. All functional parts are relatively modular, independent in implementation but interrelated at runtime, resulting in an all-in general framework that could work in supervised, semi-supervised, or unsupervised mode. We show that inClust is superior to most data integration methods in benchmark datasets. Then, we demonstrate the capability of inClust in the tasks of conditional out-of-distribution generation in supervised mode, label transfer in semi-supervised mode, and spatial domain identification in unsupervised mode. In these examples, inClust could accurately express the effect of each covariate, distinguish the query-specific cell types, or segment spatial domains. The results support that inClust is an excellent general framework for multiple-task harmonization and data decomposition.

Gender Asymmetry of Visegrád Group Languages as Reflected by Word Embeddings

Abstract Today, word embeddings have become a standard method in natural language processing, largely due to the availability of large language corpora. The models effectively reflect the semantic relationships between words without any additional linguistic input. Recently, more emphasis has been placed on interpreting the seemingly discriminatory results of some queries, with the goal of de-biasing language models. However, if we consider the vector space to be a reasonably valid model of a linguistic semantic space, does not the asymmetry and subsequent discrimination in word embeddings reflect the (average) discriminatory tendencies inherent in the language? This article explores word embedding models for the Visegrád group languages and we apply basic vector arithmetic to demonstrate the basic language asymmetry present in the models. It is well known that in English models, vector transfers result in eerily accurate predictions when swapping genders (the famous king – man + woman = queen), but these transfers also result in rather uncomplimentary roles for certain occupations (doctor – man + woman = nurse, or computer programmer – man + woman = homemaker). The article explores similar transfers in models of V4 languages – Slovak, Czech, Polish, and Hungarian. With Hungarian gender neutrality, Polish strong generic masculine, and close parallels between Slovak and Czech, we hope to uncover interesting similarities and differences in gender asymmetry in these languages, based on real language data.

Nature-inspired architected materials using unsupervised deep learning

Nature-inspired material design is driven by superior properties found in natural architected materials and enabled by recent developments in additive manufacturing and machine learning. Existing approaches to push design beyond biomimicry typically use supervised deep learning algorithms to predict and optimize properties based on experimental or simulation data. However, these methods constrain generated material designs to abstracted labels and to “black box” outputs that are only indirectly manipulable. Here we report an alternative approach using an unsupervised generative adversarial network (GAN) model. Training the model on unlabeled data constructs a latent space free of human intervention, which can then be explored through seeding, image encoding, and vector arithmetic to control specific parameters of de novo generated material designs and to push them beyond training data distributions for broad applicability. We illustrate this end-to-end with new materials inspired by leaf microstructures, showing how biological 2D structures can be used to develop novel architected materials in 2 and 3 dimensions. We further utilize a genetic algorithm to optimize generated microstructures for mechanical properties, operating directly on the latent space. This approach allows for transfer of information across manifestations using the latent space as mediator, opening new avenues for exploration of nature-inspired materials.

Interactive Visualizations of Word Embeddings for K-12 Students

Word embeddings, which represent words as dense feature vectors, are widely used in natural language processing. In their seminal paper on word2vec, Mikolov and colleagues showed that a feature space created by training a word prediction network on a large text corpus will encode semantic information that supports analogy by vector arithmetic, e.g., "king" minus "man" plus "woman" equals "queen". To help novices appreciate this idea, people have sought effective graphical representations of word embeddings. We describe a new interactive tool for visually exploring word embeddings. Our tool allows users to define semantic dimensions by specifying opposed word pairs, e.g., gender is defined by pairs such as boy/girl and father/mother, and age by pairs such as father/son and mother/daughter. Words are plotted as points in a zoomable and rotatable 3D space, where the third ”residual” dimension encodes distance from the hyperplane defined by all the opposed word vectors with age and gender subtracted out. Our tool allows users to visualize vector analogies, drawing the vector from “king” to “man” and a parallel vector from “woman” to “king-man+woman”, which is closest to “queen”. Visually browsing the embedding space and experimenting with this tool can make word embeddings more intuitive. We include a series of experiments teachers can use to help K-12 students appreciate the strengths and limitations of this representation.

Generative Deep Learning of the Single Cell Dose Response of 2,3,7,8 Tetrachlorodibenzo‐p‐dioxin in Mouse Liver

Single cell RNA‐seq provides a new opportunity to study the heterogeneity of chemical perturbation within tissues. However, exploring the space of all cell type – chemical combinations is experimentally and financially unfeasible. This space is significantly expanded by the dose axis of chemical perturbation. Computational tools are needed to predict responses not only across tissues, but also across doses while capturing the nuances of cell type specific gene expression. Generative deep learning architectures such as autoencoders simplify the single cell expression space allowing cross‐tissue, ‐organ, ‐organism and ‐dose predictions using simple vector arithmetic. However, differing sensitivities and non‐linearities make cell type specific gene expression predictions following treatment at higher doses challenging. Here, improvements to vector arithmetic in the latent space achieve high dose cell type specific predictions better than other state of the art algorithms. We specifically look at a well‐studied toxicant, 2,3,7,8 Tetrachlorodibenzo‐p‐dioxin (TCDD), in the mouse liver as a case study. TCDD binds to and activates the aryl hydrocarbon receptor (AhR) to regulate gene expression associated with several physiological processes including xenobiotic metabolism, development, and circadian rhythm. Prediction of the effects of TCDD across liver cell types is non‐trivial as AhR is not only differentially expressed across cell types but is also differentially expressed within certain cell types along the porto‐central axis of the liver lobule. Our model predicts dose‐dependent gene expression across liver zones (i.e., portal to central hepatocytes), and across liver cell types (e.g., endothelial to stellate cells) using basal gene expression data. The model is also able to predict low dose TCDD gene expression using high dose data. Finally, using outputs from the model, an algorithm was developed to order cells based on their sensitivities to a particular toxicant by assigning a “pseudo‐dose” value to each cell. Given the model’s high performance on these tasks, the tool developed here will aid the exploration of the gene expression space of chemical perturbation.

Building an allocentric travelling direction signal via vector computation.

Many behavioural tasks require the manipulation of mathematical vectors, but, outside of computational models1-7, it is not known how brains perform vector operations. Here we show how the Drosophila central complex, a region implicated in goal-directed navigation7-10, performs vector arithmetic. First, we describe a neural signal in the fan-shaped body that explicitly tracks the allocentric travelling angle of a fly, that is, the travelling angle in reference to external cues. Past work has identified neurons in Drosophila8,11-13 and mammals14 that track the heading angle of an animal referenced to external cues (for example, head direction cells), but this new signal illuminates how the sense of space is properly updated when travelling and heading angles differ (for example, when walking sideways). We then characterize a neuronal circuit that performs an egocentric-to-allocentric (that is, body-centred to world-centred) coordinate transformation and vector addition to compute the allocentric travelling direction. This circuit operates by mapping two-dimensional vectors onto sinusoidal patterns of activity across distinct neuronal populations, with the amplitude of the sinusoid representing the length of the vector and its phase representing the angle of the vector. The principles of this circuit may generalize to other brainsand to domains beyond navigation where vector operations or reference-frame transformations are required.

Chinese sentiment classification based on Word2vec and vector arithmetic in human–robot conversation

With the aim of enhancing human–chatbot interactions, this paper presents a novel sentiment classification framework that recognizes both semantics emotion terms and emojis. Underpinned by Word2vec and vector arithmetic, a deep model learns the vectors of emotion words and emojis from a large-scale corpus of conversations. The vectors are then assembled into a dictionary, evaluated with an improved k-means similarity calculation, and assigned to a category of emotions. To accommodate negative grammar constructions, e.g., “not happy” as opposed to “unhappy”, a separate module combines the vectors of negatives and emotion words using vector addition. The final sentiment classification results are derived by calculating the similarity between an utterance and the emotion categories. Experiments show this strategy results in multi-emotion and polarity classifications between 3 and 4% more precise than the next best performing baseline classifier.

Poetic Sound Similarity Vectors Using Phonetic Features

A procedure that uses phonetic transcriptions of words to produce a continuous vector-space model of phonetic sound similarity is presented. The vector dimensions of words in the model are calculated using interleaved phonetic feature bigrams, a novel method that captures similarities in sound that are difficult to model with orthographic or phonemic information alone. Measurements of similarity between items in the resulting vector space are shown to perform well on established tests for predicting phonetic similarity. Additionally, a number of applications of vector arithmetic and nearest-neighbor search are presented, demonstrating potential uses of the vector space in experimental poetry and procedural content generation.

Vector Arithmetic in the Triangular Grid.

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Semantic Deep Learning: Prior Knowledge and a Type of Four-Term Embedding Analogy to Acquire Treatments for Well-Known Diseases.

BackgroundHow to treat a disease remains to be the most common type of clinical question. Obtaining evidence-based answers from biomedical literature is difficult. Analogical reasoning with embeddings from deep learning (embedding analogies) may extract such biomedical facts, although the state-of-the-art focuses on pair-based proportional (pairwise) analogies such as man:woman::king:queen (“queen = −man +king +woman”).ObjectiveThis study aimed to systematically extract disease treatment statements with a Semantic Deep Learning (SemDeep) approach underpinned by prior knowledge and another type of 4-term analogy (other than pairwise).MethodsAs preliminaries, we investigated Continuous Bag-of-Words (CBOW) embedding analogies in a common-English corpus with five lines of text and observed a type of 4-term analogy (not pairwise) applying the 3CosAdd formula and relating the semantic fields person and death: “dagger = −Romeo +die +died” (search query: −Romeo +die +died). Our SemDeep approach worked with pre-existing items of knowledge (what is known) to make inferences sanctioned by a 4-term analogy (search query −x +z1 +z2) from CBOW and Skip-gram embeddings created with a PubMed systematic reviews subset (PMSB dataset). Stage1: Knowledge acquisition. Obtaining a set of terms, candidate y, from embeddings using vector arithmetic. Some n-gram pairs from the cosine and validated with evidence (prior knowledge) are the input for the 3cosAdd, seeking a type of 4-term analogy relating the semantic fields disease and treatment. Stage 2: Knowledge organization. Identification of candidates sanctioned by the analogy belonging to the semantic field treatment and mapping these candidates to unified medical language system Metathesaurus concepts with MetaMap. A concept pair is a brief disease treatment statement (biomedical fact). Stage 3: Knowledge validation. An evidence-based evaluation followed by human validation of biomedical facts potentially useful for clinicians.ResultsWe obtained 5352 n-gram pairs from 446 search queries by applying the 3CosAdd. The microaveraging performance of MetaMap for candidate y belonging to the semantic field treatment was F-measure=80.00% (precision=77.00%, recall=83.25%). We developed an empirical heuristic with some predictive power for clinical winners, that is, search queries bringing candidate y with evidence of a therapeutic intent for target disease x. The search queries -asthma +inhaled_corticosteroids +inhaled_corticosteroid and -epilepsy +valproate +antiepileptic_drug were clinical winners, finding eight evidence-based beneficial treatments.ConclusionsExtracting treatments with therapeutic intent by analogical reasoning from embeddings (423K n-grams from the PMSB dataset) is an ambitious goal. Our SemDeep approach is knowledge-based, underpinned by embedding analogies that exploit prior knowledge. Biomedical facts from embedding analogies (4-term type, not pairwise) are potentially useful for clinicians. The heuristic offers a practical way to discover beneficial treatments for well-known diseases. Learning from deep learning models does not require a massive amount of data. Embedding analogies are not limited to pairwise analogies; hence, analogical reasoning with embeddings is underexploited.

On the Almansi-Michell solution and its numerical implementation for heterogeneous beams with periodic microstructures subject to periodically-varying loads

This paper aims to present a general solution to the Almansi-Michell problem of heterogeneous beam structures with periodic microstructures, which take the most general form of periodic configurations with different constituent materials, subject to periodically varying external loads. By analogy with Ieşan’s rational scheme, the displacement solution is generated by introducing periodic functions in place of warping functions for constant cross-sectional beams. The governing equations for unknown displacements and the linear system of equations for undetermined coefficients are non-trivially derived in detail. By properly handling surface integrals, improved FE equations for the displacement solution and unknown coefficients, which are more efficient in numerical computation, are then formulated. A novel numerical implementation approach is further developed, which adopts general FE software/in-house FE code as a black box and calculates the Almansi-Michell solution with simple vector arithmetic. The proposed numerical implementation approach can effectively handle a wide range of microstructures. Several numerical examples are given to show the correctness of the Almansi-Michell solution and the effectiveness of the numerical implementation approach.

Automorphisms of Finite Quasi-Groups without Sub-Quasi-Groups

Finite quasi-groups without sub-quasi-groups are considered. It is shown that polynomially complete quasi-groups with this property are quasi-primal. The case in which the automorphism groups act transitively on these quasi-groups is considered. Quasi-groups of prime-power order defined on an arithmetic vector space over a finite field are also studied. Necessary conditions for a multiplication in this space given in coordinate form to determine a quasi-group are found. The case of a vector space over the two-element field is considered in more detail. A criterion for a multiplication given in coordinate form by Boolean functions to determine a quasi-group is obtained. Under certain assumptions, quasi-groups of order 4 determined by Boolean functions are described up to isotopy. Polynomially complete quasi-groups are important in that the problem of solving polynomial equations is NP-complete in such quasi-groups. This property suggests using them for protecting information, because cryptographic transformations are based on quasi-group operations. In this context, an important role is played by quasi-groups containing no sub-quasi-groups.

ScGen predicts single-cell perturbation responses.

Accurately modeling cellular response to perturbations is a central goal of computational biology. While such modeling has been based on statistical, mechanistic and machine learning models in specific settings, no generalization of predictions to phenomena absent from training data (out-of-sample) has yet been demonstrated. Here, we present scGen (https://github.com/theislab/scgen), a model combining variational autoencoders and latent space vector arithmetics for high-dimensional single-cell gene expression data. We show that scGen accurately models perturbation and infection response of cells across cell types, studies and species. In particular, we demonstrate that scGen learns cell-type and species-specific responses implying that it captures features that distinguish responding from non-responding genes and cells. With the upcoming availability of large-scale atlases of organs in a healthy state, we envision scGen to become a tool for experimental design through in silico screening of perturbation response in the context of disease and drug treatment.