Search

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

Frameworks and DSLs auto-generating code have traditionally relied on human experts developing them to have in place rigorous methods to assure the legality of the applied code transformations. Machine Learning (ML) is gaining wider adoption as a means to auto-generate code optimised for the hardware target. However, ML solutions, and in particular black-box DNNs, provide no such guarantees on legality. In this paper we propose a library, Tadashi, which leverages the polyhedral model to empower researchers seeking to curate datasets crucial for applying ML in code-generation. Tadashi provides the ability to reliably and practically check the legality of candidate transformations on polyhedral schedules applied on a baseline reference code. We provide a proof that our library guarantees the legality of generated transformations, and demonstrate its lightweight practical cost. Tadashi is available at https://github.com/vatai/tadashi/., Comment: Submitted to CGO

A novel method was developed to detect double-$\Lambda$ hypernuclear events in nuclear emulsions using machine learning techniques. The object detection model, the Mask R-CNN, was trained using images generated by Monte Carlo simulations, image processing, and image-style transformation based on generative adversarial networks. Despite being exclusively trained on $\prescript{6\ }{\Lambda\Lambda}{\rm{He}}$ events, the model achieved a detection efficiency of 93.8$\%$ for $\prescript{6\ }{\Lambda\Lambda}{\rm{He}}$ and 82.0$\%$ for $\prescript{5\ }{\Lambda\Lambda}{\rm{H}}$ events in the produced images. In addition, the model demonstrated its ability to detect the $\prescript{6\ }{\Lambda\Lambda}{\rm{He}}$ event named the Nagara event, which is the only uniquely identified double-$\Lambda$ hypernuclear event reported to date. It also exhibited a proper segmentation of the event topology. Furthermore, after analyzing 0.2$\%$ of the entire emulsion data from the J-PARC E07 experiment utilizing the developed approach, six new candidates for double-$\Lambda$ hypernuclear events were detected, suggesting that more than 2000 double-strangeness hypernuclear events were recorded in the entire dataset. This method is sufficiently effective for mining more latent double-$\Lambda$ hypernuclear events recorded in nuclear emulsion sheets by reducing the time required for manual visual inspection by a factor of five hundred.

The global population growth from 10,000 BC to 2023 is discussed within the Verhulst scaling equation and its extensions framework. The analysis focuses on per the capita global population rate coefficient Gp(P)=[dP(t)/P(t)]/dt=dlnP(t)/d, which reveals two linear domains: from 700CE till 1966 and from 1966 till 2023. Such a pattern can be considered a universal reference for reliable scaling relations describing P(t) changes. It is also the distortions-sensitive test indicating domains of their applicability and yielding optimal values of parameters. For models recalling the Verhulst equation, a single pair of growth rate and system capacity coefficients (r,s) should describe global population rise in the mentioned periods. However, the Verhulst equation with such effective parameters does not describe P(t) changes. Notable is the new way of data preparation, based on collecting data from various sources and their numerical filtering to obtain a smooth set of optimal values enabling the derivative-based analysis. The analysis reveals links between P(t) changes and some historical and pre-historical references influencing the global scale., Comment: 29 pages, 3 figures

In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.

We describe integral representations of the alternating group $A_4$, in particular, the Auslander-Reiten quiver of its 2-adic representations. Using these results we calculate Tate cohomologies of all $A_4$-lattices., Comment: 11 pages

Pretrained language models underpin several AI applications, but their high computational cost for training limits accessibility. Initiatives such as BLOOM and StarCoder aim to democratize access to pretrained models for collaborative community development. However, such existing models face challenges: limited multilingual capabilities, continual pretraining causing catastrophic forgetting, whereas pretraining from scratch is computationally expensive, and compliance with AI safety and development laws. This paper presents Aurora-M, a 15B parameter multilingual open-source model trained on English, Finnish, Hindi, Japanese, Vietnamese, and code. Continually pretrained from StarCoderPlus on 435 billion additional tokens, Aurora-M surpasses 2 trillion tokens in total training token count. It is the first open-source multilingual model fine-tuned on human-reviewed safety instructions, thus aligning its development not only with conventional red-teaming considerations, but also with the specific concerns articulated in the Biden-Harris Executive Order on the Safe, Secure, and Trustworthy Development and Use of Artificial Intelligence. Aurora-M is rigorously evaluated across various tasks and languages, demonstrating robustness against catastrophic forgetting and outperforming alternatives in multilingual settings, particularly in safety evaluations. To promote responsible open-source LLM development, Aurora-M and its variants are released at https://huggingface.co/collections/aurora-m/aurora-m-models-65fdfdff62471e09812f5407 ., Comment: Preprint

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic phase of rod-like liquid crystalline compounds, are evidenced on approaching liquid-solid discontinuous phase transition. The 'supercriticality' can be an additional factor for supporting the unique pro-health properties of linseed oil. It can also be significant for numerous technological applications. The report also reveals properties significant for melting/freezing discontinuous phase transition cognitive puzzle. Broadband dielectric spectroscopy studies revealed long-range premelting (heating from the solid phase) and post-freezing (cooling from the liquid phase) effects with critical-like parametrizations. They can be correlated with the 'grain model' for premelting and its development by the Lipovsky model. The evidence for the post-freezing effect, with the critical-like portrayal, may indicate a specific granular solidification associated with pretransitional fluctuations. Numerous hallmarks of liquid-liquid and solid-solid phase transitions have also been found. Notably, the melting temperature surrounding is related to the minimum and the freezing temperature to the maximum of dielectric loss factor D=tan(delta). Regarding dynamics, three primary relaxation processes have been found. Their changes in subsequent temperature intervals, related to the apparent activation enthalpy, follow critical-like patterns with the same singular temperature. For relaxation times evolution, it leads to optimal parameterizations via the 'critical and activated' equation, recently proposed., Comment: 14 Figures , 15 equations

We use deep reinforcement learning (RL) to optimize a weapons to target assignment (WTA) policy for multi-vehicle hypersonic strike against multiple targets. The objective is to maximize the total value of destroyed targets in each episode. Each randomly generated episode varies the number and initial conditions of the hypersonic strike weapons (HSW) and targets, the value distribution of the targets, and the probability of a HSW being intercepted. We compare the performance of this WTA policy to that of a benchmark WTA policy derived using non-linear integer programming (NLIP), and find that the RL WTA policy gives near optimal performance with a 1000X speedup in computation time, allowing real time operation that facilitates autonomous decision making in the mission end game.

The model discussion focused on links between the unique properties of relaxor ceramics and the basics of critical phenomena physics and glass transition physics. It indicates the significance of uniaxiality for appearing mean-field features near paraelectric_ferroelectric transition. Pretransitional fluctuations, increasing up to grain size and leading to inter-grain, random, local electric fields, are indicated to be responsible for relaxor ceramics characteristics. Their impacts yield the pseudo spinodal behavior associated with weakly discontinuous local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions PNRs. It explains coherently dielectric constant changes with the diffused maximum near paraelectric_ferroelectric transition, the sensitivity even to moderate electric fields, tunability, and the glassy dynamics. These considerations are confronted with experimental results for the complex dielectric permittivity studies in relaxor ceramic, covering the 200K range, from the paraelectric to the deep ferroelectric phase. The distortions-sensitive and derivative-based analysis revealed the preference for the exponential scaling pattern in the paraelectric phase and the surroundings of the paraelectric-ferroelectric transition. It may suggest the Griffith phase behavior associated with the mean-field criticality disturbed by random local impacts. The discussion of experimental results is supplemented by relaxation times changes and the coupled energy losses analysis. The studies also led to the description of tunability temperature changes with scaling relations., Comment: 39 PAGES, 20 Figures

In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel Bernoulli used an elementary version of compartmental modeling to find the effectiveness of deliberate smallpox inoculation on life expectancy. We have used the well-known SIR (Susceptible, Infected and Recovered) model of Kermack & McKendrick to extend the analysis further by including exposure, quarantining, insusceptibility and deaths in a SEIQRDP model. Further, we have generalized this model by using the solutions of Fractional Differential Equations to test the accuracy and validity of the mathematical modeling techniques against Canadian COVID-19 trends and spread of real-world disease. Our work also emphasizes the importance of Personal Protection Equipment (PPE) and impact of social distancing on controlling the spread of COVID-19., Comment: 14 Pages of Text, 24 Figures on 6 Pages

This study developed a novel method for detecting hypernuclear events recorded in nuclear emulsion sheets using machine learning techniques. The artificial neural network-based object detection model was trained on surrogate images created through Monte Carlo simulations and image-style transformations using generative adversarial networks. The performance of the proposed model was evaluated using $\alpha$-decay events obtained from the J-PARC E07 emulsion data. The model achieved approximately twice the detection efficiency of conventional image processing and reduced the time spent on manual visual inspection by approximately 1/17. The established method was successfully applied to the detection of hypernuclear events. This approach is a state-of-the-art tool for discovering rare events recorded in nuclear emulsion sheets without any real data for training., Comment: 32 pages, 13 figures

The report discusses the emergence of the Socio-Economic Soft Matter (SE-SM) as the result of interactions between physics and economy. First, demographic changes since the Industrial Revolution onset are tested using Soft Matter science tools. Notable in the support of innovative derivative-based and distortions-sensitive analytic tools. It revealed the Weibull type powered exponential increase, with a notably lesser rising rate since the crossover detected near the year 1970. Subsequently, demographic (SE-SM) patterns are tested for Rapa Nui (Easter) Island model case and for four large 'hallmark cities' where the rise and decay phases have occurred. They are Detroit and Cleveland in the USA and Lodz (former textile industry center) and Bytom (former coal mining center) in Poland. The analysis explicitly revealed scaling patterns for demographic changes, influenced by the historical and socio-economic backgrounds and the long-lasting determinism in population changes. Universalistic features of demographic changes are discussed within the Socio-Economic Soft Matter concept., Comment: 17 pages, 9 Figures

In this thought-provoking article, we discuss certain myths and legends that are folklore among members of the high-performance computing community. We gathered these myths from conversations at conferences and meetings, product advertisements, papers, and other communications such as tweets, blogs, and news articles within and beyond our community. We believe they represent the zeitgeist of the current era of massive change, driven by the end of many scaling laws such as Dennard scaling and Moore's law. While some laws end, new directions are emerging, such as algorithmic scaling or novel architecture research. Nevertheless, these myths are rarely based on scientific facts, but rather on some evidence or argumentation. In fact, we believe that this is the very reason for the existence of many myths and why they cannot be answered clearly. While it feels like there should be clear answers for each, some may remain endless philosophical debates, such as whether Beethoven was better than Mozart. We would like to see our collection of myths as a discussion of possible new directions for research and industry investment.

Landau - de Gennes mean field model predicts the discontinuous transition for the Isotropic - Nematic transition, associated with uniaxial and quadrupolar order parameter in three dimensions. This report shows pressure-related dielectric studies for rod-like nematogenic pentylcyanobiphenyl (5CB) and its nanocolloids with BaTiO3 nanoparticles. The scan of dielectric constant revealed the continuous I-N transition in a compressed nanocolloid with a tiny amount of nanoparticles (x=0.1%). For the nematic phase in 5CB and its x=1% nanocolloid the enormous values of dielectric constant and the bending-type long-range pretransitional behavior were detected. The 'shaping' influence of pretransitional fluctuations was also detected for the ionic-related contribution to dielectric permittivity in the isotropic phase. For the high-frequency relaxation domain, this impact was tested for the primary relaxation time and the translational-orientaional decoupling., Comment: 28 pages, 7 figures

The report presents pressure-related broadband dielectric spectroscopy (BDS) studies in liquid crystalline octyloxycyanbiphenyl and its nanocolloid with BaTiO3 nanoparticles, focused on the low-frequency ionic domain and the impact of pretransitional fluctuations. Hence basic exogenic (pressure) and endogenic (nanoparticles) impacts on dielectric properties are addressed. The innovative derivative-based analysis revealed functional 'critical-like' descriptions of ionic contributions to dielectric permittivity and electric conductivity. The supplementary dielectric constant scan, yielding insight into dipole-diple arrangements, is also presented. Studies cover the puzzling case of complex liquid (SmA) - Solid crystal phase transition, revealing relatively strong critical-like premelting effects, which have hardly been observed for the discontinuous 'melting transition' so far., Comment: 29 pages, 12 Figures

The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent tendency for local self-organization. The hypothesis is validated by studying population growth evolution using universalistic scaling patterns developed in Soft Matter science. It is supported by the innovative derivative-based and distortions-sensitive analysis, showing the extended Malthus-type trend from 10 000 B till ca. the year 1200. Subsequently, the explicit evidence of the powered exponential population rise pattern is shown, with the unique crossover near 1970. Following this year, the population growth systematically slows down compared to earlier trends. Population growth is confronted with global food demand evolution, which changes and also follows an exponential pattern. The rise of networking and innovations are indicated as the driving force leading to the crossover from the Malthus-type exponential behavior to the powered exponential one. It is supported by the analysis of the number of patents for innovations. The authors introduced the derivative-based and distortions-sensitive analysis for the optimal implementation of the powered exponential function for describing dynamic data., Comment: 6 figures, 24 pages