Reviewerly/exHarmony huggingface dataset:
Some New Methods to Generate Short Addition Chains

Modular exponentiation and scalar multiplication are important operations in most public-key cryptosystems, and their efficient computation is essential to cryptosystems. The shortest addition chain is one of the most important mathematical concepts to realize the optimization of computation. However, finding a shortest addition chain of length r is generally regarded as an NP-hard problem, whose time complexity is comparable to O(r!). This paper proposes some novel methods to generate short addition chains. We firstly present a Simplified Power-tree method by deeply deleting the power-tree whose time complexity is reduced to O(r2). In this paper, a Cross Window method and its variant are introduced by improving the Window method. The Cross Window method uses the cross correlation to deal with the windows and its pre-computation is optimized by a new Addition Sequence Algorithm. The theoretical analysis is conducted to show the correctness and effectiveness. Meanwhile, our experiments show that the new methods can obtain shorter addition chains compared to the existing methods. The Cross Window method with the Addition Sequence algorithm can attain 44.74% and 9.51% reduction of the addition chain length, in the best case, compared to the Binary method and the Window method respectively.
A neurodynamic model of a high-dimensional vector associative memory for road traffic control optimization

&lt;p&gt;The manuscript introduces a novel perspective and approach to tackling traffic control. Bypassing the need for computationally expensive constrained optimization of spatiotemporal cues describing the road traffic state, the system exploits the causal relation between traffic light green light timing and the flow of cars. This way the system can store traffic contexts as memories used to simply recall plausible green time timings matching the flow of cars. This behavior amounts to an autoassociative memory, efficiently implemented in spiking neural networks, that provides a good trade-off between execution time and accuracy. We believe the approach has very high potential in real-world deployments. Our initial results on four real datasets demonstrate the benefits that the approach has and, of course, the lightweight and efficient computation steps and learning paradigm. Our goal is to raise awareness in the traffic engineering community on how neural associative memories can be a suitable candidate for traffic control, a problem without straightforward solutions. The flexibility in representing traffic data through vectors, causal learning of memories, and fast recall provide outstanding benefits demonstrated through our experiments. We hope the work will contribute to both the neural network community, through a novel autoassociative memory system using high-dimensional vectors, and the traffic engineering community, through a novel solution to traffic control.&lt;/p&gt;
Articulación entre Modelización y Espacios de Trabajo Matemático. Análisis de una Tarea bajo el ciclo de Blomhøj en Educación Superior

Background: The Mathematical Working Spaces (MWS) theoretical framework has developed a growing interest in how mathematical modelling is recognised, analysed, and articulated from its theoretical and empirical scopes. Given the articulations identified in the literature, it is interesting to determine whether new networks with the MWS provide powerful strategies for analysing mathematical modelling task resolution. Objective: to characterise the modelling activity from the network composed by the Blomhøj modelling cycle and the MWS in engineering students. Design: This work is a case study with a qualitative approach, which analyses the resolution of a modelling task through the proposed network. Setting and participants: The experimentation was carried out in an integral calculus course for a computer civil engineering career at a Chilean university. Modelling practices are not usual in this second-year subject, although enhancing their use in professional education is necessary. Data collection and analysis: We collected the written records of the students, selecting one to perform the in-depth analysis due to its high representativeness and clarity, as evidenced in the documents. Three steps were followed to characterise the modelling activity in the written record: description, analysis, and interpretation. Results: The Blomhøj modelling cycle might present connections with the MWS at the formulation of the problem and not only at the systematisation, which is a novelty in this field of research. Conclusions: A novel approach with which to develop the network between the MWS and modelling emerges, emphasising the investigation of mathematical problems using the student’s reality in higher education.
Motley String Theory Overview

Copenhagen Update of Motley String Theory (aka MST) Overview includes several new results author obtained during his first two years in Denmark. Paper provides Overview of the basic principles of MST and demonstrates how it solved major problems of High Energy Physics and Astrophysics. New version also describes what "elementary particles" are made of from the MST point of view and provides details of the process of their creation. We mention that MST based analysis suggests that neutrinos are Majorana fermions and therefore neutrinoless double beta decay is to be detected sooner or later. After that we provide evidence for the rotational symmetry of MST being the fundamental reason for the principle of Gauge Invariance, which plays key role in the "classical" Particle Physics the Standard Model is based upon as well as in the Quantum Field Theory
We Don’t Really Need Quaternions in Geometric Modeling, Computer Graphics and Animation: Here Is Why

With the increased use of light-emitting diode technology, the design freedom of taillight shapes has improved, and the shape design of taillights has become a major design focus and breakthrough point for new energy vehicles.As traditional taillight shape design normally depends on the individual experience of designers who make considerable effort to capture design inspiration by manually searching for design references, taillight shape creative design in the field of computer-aided design is studied to assist designers' creative thinking and design efficiency.In this research, generative adversarial networks are applied to explore the creative generation mechanism of taillight shape designs.First, a dataset of high-quality vehicle taillight shape images is established, which combines safety and aesthetic taillight shape design rules and insights.Then, deep convolutional generative adversarial networks and progressive growing of generative adversarial networks are both introduced to train and construct the taillight shape generative design model, and the commonalities and differences between the two are further compared.Finally, the optimal creative generation design model of the taillight shape is constructed.This research provides a new idea for taillight shape design, and the constructed taillight shape creative generation design model is helpful in realizing efficient, diversified and innovative taillight shape design and provides designers with rapid and sustainable preliminary design proposals and creative inspiration support.
Reengineering Small-Scale Business Enterprises as Predictors of Youth Employment and Poverty Alleviation

The study examines the reengineering of small-scale business enterprises as predictors of youth employment and poverty alleviation. Four objectives and four research questions were posed. The population of the study was two hundred and sixty (260) registered businesses. The study was carried out using a survey research design. A research-created questionnaire titled "Reengineering of Small-Scale Business Enterprises as Predictors of Youth Employment and Poverty Alleviation" was used to collect data (RSCBEPYEPA scale). The instrument was validated by one test and measurement expert and two vocational education experts. A trial/pilot test was conducted on 40 registered businessmen and women in Akwa Ibom State who were not part of the main study population, and the study received an overall reliability coefficient of 0.92 using Cronbach's alpha data analysis. The survey was given to 260 registered businesses. The entire study population was used. To answer the research questions, the data was analyzed using means and standard deviation, and the multivariate analysis of variance (MANOVA) statistic was used to test the hypothesis at the 0.05 level of significance. The result showed that the government provided small-scale businesses in Cross River State with financial support, capacity-building programs, legislative support, and the provision of facilities for youth employment and poverty alleviation. It was recommended, among other things, that small-scale business entrepreneurs should take advantage of the financial support provided by the government to boost their businesses.&#x0D; &#x0D; Received: 10 January 2023 / Accepted: 26 February 2023 / Published: 6 March 2023
Quotient on some Generalizations of topological group

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.
Operations on Signed Distance Function Estimates

With the increased use of light-emitting diode technology, the design freedom of taillight shapes has improved, and the shape design of taillights has become a major design focus and breakthrough point for new energy vehicles.As traditional taillight shape design normally depends on the individual experience of designers who make considerable effort to capture design inspiration by manually searching for design references, taillight shape creative design in the field of computer-aided design is studied to assist designers' creative thinking and design efficiency.In this research, generative adversarial networks are applied to explore the creative generation mechanism of taillight shape designs.First, a dataset of high-quality vehicle taillight shape images is established, which combines safety and aesthetic taillight shape design rules and insights.Then, deep convolutional generative adversarial networks and progressive growing of generative adversarial networks are both introduced to train and construct the taillight shape generative design model, and the commonalities and differences between the two are further compared.Finally, the optimal creative generation design model of the taillight shape is constructed.This research provides a new idea for taillight shape design, and the constructed taillight shape creative generation design model is helpful in realizing efficient, diversified and innovative taillight shape design and provides designers with rapid and sustainable preliminary design proposals and creative inspiration support.
Bounding the quantum value of compiled nonlocal games: from CHSH to BQP verification

We present a step towards the goal of producing a general cryptographic 'compilation' procedure which can translate any entangled nonlocal game into a single-prover interactive protocol while preserving quantum completeness and soundness, using cryptography to simulate the separation between the provers. A candidate for such a procedure was introduced by Kalai et al. (STOC '23), who defined a black-box cryptographic compilation procedure that applies to any nonlocal game and showed that it preserves classical value. In this work, we make progress towards a full understanding of the quantum value of the single-prover protocols that result from applying the Kalai et al. compilation procedure to entangled games. For the special case of CHSH, we prove that the Tsirelson bound holds under the compilation procedure introduced by Kalai et al., and we also recover a strong version of the 'rigidity' property that makes CHSH so useful. As an application, we give a single-prover cryptographically sound classical verification protocol for BQP, and we prove its soundness using our CHSH rigidity analysis. Our protocol replicates the functionality of Mahadev's protocol (FOCS '18) but with two advantages: (1) the protocol is conceptually intuitive and requires fewer bespoke ingredients, and the soundness analysis is simpler and directly follows the analysis of the nonlocal case, and (2) the soundness analysis does not explicitly use the assumption of a TCF or an adaptive hardcore bit, and only requires QFHE as a black box (though currently the only known constructions of QFHE use TCFs).
Conflict-Based Model Predictive Control for Scalable Multi-Robot Motion Planning

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.
Separated and Shared Effects in Higher-Order Languages

Effectful programs interact in ways that go beyond simple input-output, making compositional reasoning challenging. Existing work has shown that when such programs are ``separate'', i.e., when programs do not interfere with each other, it can be easier to reason about them. While reasoning about separated resources has been well-studied, there has been little work on reasoning about separated effects, especially for functional, higher-order programming languages. We propose two higher-order languages that can reason about sharing and separation in effectful programs. Our first language $\lambda_{\text{INI}}$ has a linear type system and probabilistic semantics, where the two product types capture independent and possibly-dependent pairs. Our second language $\lambda_{\text{INI}}^2$ is two-level, stratified language, inspired by Benton's linear-non-linear (LNL) calculus. We motivate this language with a probabilistic model, but we also provide a general categorical semantics and exhibit a range of concrete models beyond probabilistic programming. We prove soundness theorems for all of our languages; our general soundness theorem for our categorical models of $\lambda_{\text{INI}}^2$ uses a categorical gluing construction.
Certified Randomness from Quantum Supremacy

We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based on random circuit sampling, that Google and USTC have successfully carried out starting in 2019. We show that, whenever the outputs of these experiments pass the now-standard Linear Cross-Entropy Benchmark (LXEB), under plausible hardness assumptions they necessarily contain $\Omega(n)$ min-entropy, where $n$ is the number of qubits. To achieve a net gain in randomness, we use a small random seed to produce pseudorandom challenge circuits. In response to the challenge circuits, the quantum computer generates output strings that, after verification, can then be fed into a randomness extractor to produce certified nearly-uniform bits -- thereby "bootstrapping" from pseudorandomness to genuine randomness. We prove our protocol sound in two senses: (i) under a hardness assumption called Long List Quantum Supremacy Verification, which we justify in the random oracle model, and (ii) unconditionally in the random oracle model against an eavesdropper who could share arbitrary entanglement with the device. (Note that our protocol's output is unpredictable even to a computationally unbounded adversary who can see the random oracle.) Currently, the central drawback of our protocol is the exponential cost of verification, which in practice will limit its implementation to at most $n\sim 60$ qubits, a regime where attacks are expensive but not impossible. Modulo that drawback, our protocol appears to be the only practical application of quantum computing that both requires a QC and is physically realizable today.
Evolutionary Augmentation Policy Optimization for Self-supervised Learning

Self-supervised Learning (SSL) is a machine learning algorithm for pretraining Deep Neural Networks (DNNs) without requiring manually labeled data. The central idea of this learning technique is based on an auxiliary stage aka pretext task in which labeled data are created automatically through data augmentation and exploited for pretraining the DNN. However, the effect of each pretext task is not well studied or compared in the literature. In this paper, we study the contribution of augmentation operators on the performance of self supervised learning algorithms in a constrained settings. We propose an evolutionary search method for optimization of data augmentation pipeline in pretext tasks and measure the impact of augmentation operators in several SOTA SSL algorithms. By encoding different combination of augmentation operators in chromosomes we seek the optimal augmentation policies through an evolutionary optimization mechanism. We further introduce methods for analyzing and explaining the performance of optimized SSL algorithms. Our results indicate that our proposed method can find solutions that outperform the accuracy of classification of SSL algorithms which confirms the influence of augmentation policy choice on the overall performance of SSL algorithms. We also compare optimal SSL solutions found by our evolutionary search mechanism and show the effect of batch size in the pretext task on two visual datasets.
Study of Distractors in Neural Models of Code

Finding important features that contribute to the prediction of neural models is an active area of research in explainable AI. Neural models are opaque and finding such features sheds light on a better understanding of their predictions. In contrast, in this work, we present an inverse perspective of distractor features: features that cast doubt about the prediction by affecting the model's confidence in its prediction. Understanding distractors provide a complementary view of the features' relevance in the predictions of neural models. In this paper, we apply a reduction-based technique to find distractors and provide our preliminary results of their impacts and types. Our experiments across various tasks, models, and datasets of code reveal that the removal of tokens can have a significant impact on the confidence of models in their predictions and the categories of tokens can also play a vital role in the model's confidence. Our study aims to enhance the transparency of models by emphasizing those tokens that significantly influence the confidence of the models.
Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddings

We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate modeling approach for efficiently handling a large number of binary and categorical parameters. The key idea is to select a number of discrete structures from the input space (the dictionary) and use them to define an ordinal embedding for high-dimensional combinatorial structures. This allows us to use existing Gaussian process models for continuous spaces. We develop a principled approach based on binary wavelets to construct dictionaries for binary spaces, and propose a randomized construction method that generalizes to categorical spaces. We provide theoretical justification to support the effectiveness of the dictionary-based embeddings. Our experiments on diverse real-world benchmarks demonstrate the effectiveness of our proposed surrogate modeling approach over state-of-the-art BO methods.
Revisiting Adversarial Training for ImageNet: Architectures, Training and Generalization across Threat Models

While adversarial training has been extensively studied for ResNet architectures and low resolution datasets like CIFAR, much less is known for ImageNet. Given the recent debate about whether transformers are more robust than convnets, we revisit adversarial training on ImageNet comparing ViTs and ConvNeXts. Extensive experiments show that minor changes in architecture, most notably replacing PatchStem with ConvStem, and training scheme have a significant impact on the achieved robustness. These changes not only increase robustness in the seen $\ell_\infty$-threat model, but even more so improve generalization to unseen $\ell_1/\ell_2$-attacks. Our modified ConvNeXt, ConvNeXt + ConvStem, yields the most robust $\ell_\infty$-models across different ranges of model parameters and FLOPs, while our ViT + ConvStem yields the best generalization to unseen threat models.
Quantum Merlin-Arthur proof systems for synthesizing quantum states

Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely the complexity of synthesizing quantum states. We investigate a state-synthesizing counterpart of the class NP, referred to as stateQMA, which is concerned with preparing certain quantum states through a polynomial-time quantum verifier with the aid of a single quantum message from an all-powerful but untrusted prover. This is a subclass of the class stateQIP recently introduced by Rosenthal and Yuen (ITCS 2022), which permits polynomially many interactions between the prover and the verifier. Our main result consists of error reduction of this class and its variants with an exponentially small gap or a bounded space, as well as how this class relates to other fundamental state synthesizing classes, i.e., states generated by uniform polynomial-time quantum circuits (stateBQP) and space-uniform polynomial-space quantum circuits (statePSPACE). Furthermore, we establish that the family of UQMA witnesses, considered as one of the most natural candidates, is in stateQMA. Additionally, we demonstrate that stateQCMA achieves perfect completeness.
Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and introduce an energy-conserving shooting method that allows robust inference from both short and long trajectories. We demonstrate the method's success in learning Hamiltonian systems in various data settings.