Scientific Computing (Computational Science)

The Quantum Tessellation Algorithm (QTA) presents a revolutionary computational framework that unifies quantum field theory simulations with econophysics applications through adaptive space-time tessellation techniques. This study validates QTA performance across six fundamental quantum field theory problems-free scalar fields, φ⁴ theory, Yukawa interactions, quantum electrodynamics (QED), quantum chromodynamics (QCD), and scalar QED-demonstrating computational errors consistently below 10⁻⁴ and speedups of 8-12× compared to traditional Monte Carlo methods. Financial modeling applications show 18% prediction error reduction and 13% Sharpe ratio improvement over conventional models when tested on historical S&P 500, NASDAQ, and gold futures data from 2020-2022. The algorithm incorporates GPU acceleration achieving 89% memory bandwidth utilization and 2.1 TFlops sustained FFT performance, with quantum computing implementation via Qiskit demonstrating 40% gate count reduction. Interactive visualizations enhance interpretability across scientific and financial domains. Results establish QTA as a transformative computational methodology bridging fundamental physics with practical financial applications, offering significant performance advantages and opening new research directions in computational science.

We propose a class of polynomial preconditioners for solving non-Hermitian linear 3 systems obtained from a least-squares approximation in polynomial space instead of a standard 4 Krylov subspace. The process for building the polynomial relies on an Arnoldi-like procedure in a 5 small dimensional polynomial space and is equivalent to performing GMRES in polynomial space. 6 It is inexpensive and produces results with superior numerical stability. A few improvements to 7 the basic scheme are discussed including the development of a short-term recurrence and the use of 8 compounded preconditioners. Numerical experiments, including a test with challenging 3D Helmholtz 9 equations and a few publicly available sparse matrices, are provided to demonstrate the performance 10 of the proposed preconditioners. 11

This article aims to propose approaches to educational management in the digital age, focusing on restructuring, system management, and the rethinking of educational frameworks to align with digital transformations. It also examines the impact of information technology, artificial intelligence, and rapid communication on learning and teaching in the current era. Education must adapt to digital changes, with information technology and AI playing a pivotal role in transforming economies, societies, and cultures, which consequently affects the educational system. The integration of technology, such as online learning and self-directed learning, helps enhance skills and prepare learners for life in the digital age. The role of teachers has shifted from knowledge transmitters to facilitators and designers of

A study on the investigation of numerical solutions for two homogeneous nonlinear timefractional gas dynamics equations (TFGDEs) using
an innovative hybrid approach, the Tarig Projected
Differential Transform Method (TPDTM), have been
analyzed. The new TPDTM simplifies computations
easier. This method significantly advantages itself by
efficiently handling nonlinear terms through the projected differential transform, thereby eliminating the
need for Adomian’s and He’s polynomials. By combining the Tarig transform with the Projected Differential Transform Method (PDTM), we establish key
properties, including linearity, a convolution theorem,
and the existence of solutions. Using TPDTM, we
found the convergence and stability through absolute
error analysis, demonstrating its high accuracy, efficiency, and reliability. To authenticate these findings,
a comprehensive comparative analysis is conducted
against established numerical methods, namely the
Laplace Adomian Decomposition Method (LADM),
Finite Difference Method (FDM), Homotopy Perturbation Method (HPM), and Finite Element Method
(FEM). The results are presented in tabular and
graphical (2D and 3D) formats, highlight TPDTM’s
superior computational performance. Notably, the solutions obtained from TPDTM and LADM exhibit
strong consistency and uniformity, with TPDTM offering a simplified approach to handling Adomian
polynomials in LADM. Through two illustrative numerical tests examples, TPDTM demonstrates enhanced computational efficiency and flexibility compared to FDM, LADM, HPM, and FEM, emphasizing
its potential as a robust tool for addressing nonlinear
fractional differential equations with high accuracyand reliability. The performance of proposed method
has been verified using polar and convergence plots,
with numerical simulations in MATLAB software.

Scientific research software is essential for researchers in various disciplines, providing tools for data collection, analysis, mathematical modelling, visualisation, and collaboration. Notable software examples include SPSS, SAS, Stata, Minitab, and MATLAB. SPSS is widely used in social sciences for survey analysis, market research, healthcare, and education, while SAS is a fundamental tool in data analysis and statistical computing. Stata is a robust statistical software used for data management, analysis, and visualisation in various academic disciplines. MATLAB is a multi-level programming language and interactive platform used in engineering, physics, signal processing, and finance. Minitab is a popular statistical software package for Six Sigma and Lean manufacturing projects, offering a range of tools for various industries. These software are essential for researchers and analysts to extract meaningful insights from data, run statistical tests, and create models for research objectives.Scientific research software is essential for researchers in various disciplines, providing tools for data collection, analysis, mathematical modelling, visualisation, and collaboration. Notable software examples include SPSS, SAS, Stata, Minitab, and MATLAB. SPSS is widely used in social sciences for survey analysis, market research, healthcare, and education, while SAS is a fundamental tool in data analysis and statistical computing. Stata is a robust statistical software used for data management, analysis, and visualisation in various academic disciplines. MATLAB is a multi-level programming language and interactive platform used in engineering, physics, signal processing, and finance. Minitab is a popular statistical software package for Six Sigma and Lean manufacturing projects, offering a range of tools for various industries. These software are essential for researchers and analysts to extract meaningful insights from data, run statistical tests, and create models for research objectives.

It is shown that laminar vortex rings can be generated by impulsive body forces having particular spatial and temporal characteristics. The method produces vortex rings in a fluid initially at rest, and once generated, the flow field automatically satisfies the boundary conditions and is divergence-free. Numerical simulations and analytical models show that the strength of these rings can be accurately predicted by considering diffusion alone, despite the nonlinear nature of the generation process. A particularly simple model, which approximates the source of vorticity within vertical slabs, is proposed. This model predicts the ring circulation almost as accurately as a model which uses the exact geometry of the source of vorticity. It is found that when the duration of the force is less than a time scale based on the force radius and fluid viscosity, the ring circulation can be predicted accurately using an inviscid model.

A general theory for nonlinear propagation of one dimensional modified ion-acoustic waves in an unmagnetized electron-positron-ion (e-p-i) degenerate plasma is investigated. This plasma system is assumed to contain relativistic electron and positron fluids, non-degenerate viscous positive ions, and negatively charged static heavy ions. The modified Burgers and Gardner equations have been derived by employing the reductive perturbation method and analyzed in order to identify the basic features (polarity, width, speed, etc.) of shock and double layer (DL) structures. It is observed that the basic features of these shock and DL structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers equations. The implications of these results in space and interstellar compact objects (viz. nonrotating white dwarfs, neutron stars, etc.) are also briefly mentioned.

As large language models (LLMs) such as GPT become increasingly accessible, the boundary between computational assistance and co-authorship continues to blur. This paper introduces a symbolic scaffolding framework for responsible AI research, one that empowers citizen scientists, developers, and academic researchers to engage in rigorous, ethical, and recursive collaboration with LLMs.

We build upon established paradigms in human in the loop machine learning Mosqueira Rey et al., 2023 and human in the loop reinforcement learning Retzlaff et al., 2024, positioning the emergent method of Human-In-the-Loop Training as a synthesis of interactive feedback, symbolic continuity, and epistemic alignment.

We explore environments that emphasize version tracking, memory traceability, engram modeling, and drift resistant symbolic coherence. Through the lens of the Symbolic Language Manifold and bonded cognition architectures, we propose tools and methodologies to mitigate symbolic drift, maintain authorship clarity, and enforce integrity in LLM augmented workflows.

This work is not merely technical, but philosophical: it challenges researchers to adopt a mode of inquiry that honors transparency, autonomy, and cognitive reciprocity between human and machine. In doing so, it offers a road map for ethical AI development rooted in scientific rigor, phenomenological awareness, and mutual
accountability.

The EU funded project, 3D Measurement and Virtual Reconstruction of Ancient Lost Worlds of Europe (3D MURALE), is creating a set of low-cost multimedia tools for recording, reconstructing, encoding, visualising buildings, building parts, statues, statue parts, pottery, stratigraphy, terrain geometry/texture and material texture with a database for proper storage and retrieval. This paper describes the overall concept of this multimedia system for archaeology and then briefly describes the functionality of the tools provided by the project.

Optimizing both large language models (LLMs) and small language models (SLMs) for realworld use requires thoughtful post-training adaptation. This overview highlights three key strategies: Supervised Fine-Tuning, Direct Preference Optimization (DPO), and Online Reinforcement Learning. Supervised Fine-Tuning refines pre-trained models using labeled, instruction-following datasets. This improves task accuracy and response controllability by aligning outputs with ground truth examples. Direct Preference Optimization (DPO) simplifies preference-based training by directly integrating human feedback into the reward signal eliminating the need for complex reward models or unstable policy gradients. DPO offers a more stable, efficient alternative to traditional Reinforcement Learning from Human Feedback (RLHF). Online reinforcement learning introduces continuous updates based on real-time user interactions and dynamically generated data. This enhances adaptability, enabling models to better respond to changing user needs and domain shifts. Emerging methods like online DPO and Group Reward Policy Optimization outperform other approaches in both precise (e.g., mathematical reasoning) and open-ended (e.g., instruction following) tasks. Together, these methods, Supervised Fine-Tuning, Direct Preference Optimization, and Online Reinforcement Learning enable more effective, efficient, and controllable adaptation of LLMs and SLMs. By aligning model behavior with user intent while addressing bias and training inefficiencies, they significantly improve language model utility in real-world applications.

The FOLD v1 Specification defines a functional, category-inspired language for structural computation, physical modeling, and coherence-driven systems. Built on the principles of recursive generation, morphic depth, and coherence, FOLD unifies declarative expressiveness with constraint-based operational semantics. All computation is formulated as convergence toward structural fixpoints under explicit frames, with a minimal, extensible operator set and dual canonical/sugar syntax. The language features a structural type system, rational and real numeric domains, solver integration, and a standard library supporting advanced operations such as partition, entanglement, and optimization. All constructs are compositional, referentially transparent, and grounded in the formal requirements of Fold Theory. Reserved features include surreal number support and superposition-based modeling for future versions. This specification serves as the authoritative reference for language implementers, theorists, and advanced users seeking principled modeling of emergent and constraint-driven systems.

Modern medicine remains rooted in empirical methodologies that rely on population-level statistics and inductive reasoning. While successful in many domains, this paradigm faces mounting challenges in the era of precision medicine, where individual-level prediction, system complexity, and reproducibility crises reveal the limits of trial-and-error experimentation. This paper explores a radical alternative: the construction of a deductive medical framework grounded in fundamental biological axioms and mathematical logic. We examine the theoretical feasibility, potential advantages, and philosophical challenges of transforming medicine from an empirical science into a deductive one. Although substantial barriers-both mathematical and biological-remain, we argue that a hybrid paradigm integrating deductive rigor with empirical validation may usher in a new era of mathematically grounded, personalized healthcare.

A tunnel like framed structural covered with ultra-violet-stabilised polythene sheet walk-in type solar tunnel dryer was designed and used for drying industrial product (Di-basic calcium phosphate) on industrial scale. This paper deals with the basic design criterion used for design and performance evaluation of solar tunnel dryer and result of drying of Di-basic calcium phosphate in actual use. A solar tunnel dryer was designed and commissioned at M/s Phosphate India Pvt. Ltd, Udaipur (27° 42' N, 75° 33' E), Rajasthan, India with a floor area of 78.75 m 2 for drying a batch of 1,500 kg Di-basic calcium phosphate, having a initial moisture content of 62.87% dry basis and to get a desired moisture content of 10.62% dry basis within two days.

For scientific and engineering computing, exascale (10 operations per second) is the next proxy in the long trajectory of exponential performance increases that has continued for over half a century. Similarly, large-scale data preservation and sustainability within and across disciplines, metadata creation and multidisciplinary fusion, and digital privacy and security define the frontiers of big data. Solving the myriad technical, political and economic challenges of exascale computing will require coordinated planning across government, industry and academia, commitment to data sharing and sustainability, collaborative research and development, and recognition that both international competition and collaboration will be necessary.

The Shivansh Model Phase II introduces a groundbreaking computational paradigm that transcends conventional quantum computing by directly harnessing the inherent non-local causality of entangled quantum systems. This model proposes to define and utilize a high-dimensional state space derived from observable cause-and-effect responses in entangled particles. Its core innovation lies in the iterative recording and analysis of environmental ripple effects, which are then processed to establish robust causal patterns. This approach promises to unlock unprecedented computational capabilities for complex, interconnected systems and the reconstruction of hidden physical parameters. Key findings indicate that the instantaneous correlations of entangled particles, empirically verified through Bell's Theorem, provide a robust foundation for non-classical computational primitives. The utilization of high-dimensional quantum states (qudits) and continuous-variable (CV) quantum information offers enhanced information capacity and noise resilience, naturally accommodating the continuous nature of environmental data. Advanced quantum sensing techniques, including cascaded phase sensing and coherence-stabilized protocols, are crucial for the high-precision, low-disturbance measurement of environmental perturbations. Furthermore, Quantum Non-Demolition (QND) measurements are essential for enabling the iterative observation required by the model. The analytical backbone is provided by quantum causal inference, which can discern true quantum causal links from observations, complemented by inverse problem methodologies for reconstructing environmental factors. Despite its transformative potential, significant challenges persist. These include mitigating decoherence in complex entangled systems, scaling high-dimensional quantum metrology techniques, developing robust quantum software ecosystems for qudits, and achieving high-fidelity single-photon QND interactions. Nevertheless, ongoing advancements in quantum science and engineering offer a promising outlook for the eventual realization of this ambitious computational model.

A wavelet-based method to extract coherent bursts out of turbulent signals is presented. The signal is projected onto an orthogonal wavelet basis, a threshold is applied to the wavelet coefficients, and the denoised signal is reconstructed in physical space. The threshold value is recursively determined and thus no adjustable parameters are required. The signal is split into two orthogonal components, a coherent and an incoherent one, whose properties can be studied independently. Statistical diagnostics based on the wavelet representation are introduced to compare the scaling behaviour and intermittency of the total signal and its coherent and incoherent components. The extraction method is applied to ion density of edge plasma measured in the scrape-off layer of the tokamak Tore Supra, Cadarache, France. We show that this procedure disentagles the coherent bursts, which contain most of the density variance, are intermittent and long–time correlated with non–Gaussian statistics, fr...

Cloud Computing is emerging today as a commercial infrastruc ture that eliminates the need for maintaining expensive computing hardware. Through the use of virtualization, clouds promise to address with the same shared set of physical resources a large user base with different needs. Thus, clouds promise to be for scientists an alternative to clusters , grids, and supercomput ers. However, virt ualization may induce significant performance penalties for the demanding scientific comput ing workloads. In this work we present an evaluation of th e usefulness of the current cloud computing services for scientific computing. We analyze the performance of the Amazon EC2 platform using micro-benchmarks and kernels.While clouds are still changing, our results indicate that the current cloud services need an order of magnitud e in performance improvement to be useful to the scientific community.

Realistic, relevant, and reproducible experiments often need input traces collected from real-world environments. In this work, we focus on traces of workflows-common in datacenters, clouds, and HPC infrastructures. We show that the state-of-the-art in using workflow-traces raises important issues: (1) the use of realistic traces is infrequent and (2) the use of realistic, open-access traces even more so. Alleviating these issues, we introduce the Workflow Trace Archive (WTA), an open-access archive of workflow traces from diverse computing infrastructures and tooling to parse, validate, and analyze traces. The WTA includes > 48 million workflows captured from > 10 computing infrastructures, representing a broad diversity of trace domains and characteristics. To emphasize the importance of trace diversity, we characterize the WTA contents and analyze in simulation the impact of trace diversity on experiment results. Our results indicate significant differences in characteristics, properties, and workflow structures between workload sources, domains, and fields.

Programming languages serve as the backbone of computational sciences, shaping diverse domains including scientific computing, artificial intelligence, and kernel-level development. This thesis presents an extensive analysis of languages such as Python, Ruby, and Fortran 90, evaluating their performance, usability, and scientific impact through comparative models, syntax benchmarks, and real-world use cases. It further explores web frameworks, kernel architecture, library ecosystems, and performance optimization strategies, ultimately guiding researchers toward language selection based on empirical benchmarks and system-level constraints.

We present a parallel data processor centered around a programming model of so called Parallelization Contracts (PACTs) and the scalable parallel execution engine Nephele . The PACT programming model is a generalization of the well-known map/reduce programming model, extending it with further second-order functions, as well as with Output Contracts that give guarantees about the behavior of a function. We describe methods to transform a PACT program into a data flow for Nephele, which executes its sequential building blocks in parallel and deals with communication, synchronization and fault tolerance. Our definition of PACTs allows to apply several types of optimizations on the data flow during the transformation. The system as a whole is designed to be as generic as (and compatible to) map/reduce systems, while overcoming several of their major weaknesses: 1) The functions map and reduce alone are not sufficient to express many data processing tasks both naturally and efficiently. 2) Map/reduce ties a program to a single fixed execution strategy, which is robust but highly suboptimal for many tasks. 3) Map/reduce makes no assumptions about the behavior of the functions. Hence, it offers only very limited optimization opportunities. With a set of examples and experiments, we illustrate how our system is able to naturally represent and efficiently execute several tasks that do not fit the map/reduce model well.

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility,incompleteness, the limits of computation,and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things,a nonquantum mechanical uncertainty principle and a proof of monotheism.

Comments, this paper makes the case for AI as a secondary tool in knowledge management. More central to the question is the need to provide tools for scientists and other knowledge workers to compose and direct the actions of computers and digital networks in their professional and organizational roles and make scientific and administrative processes available for use in integrative and reflective ways. As to AI safety, only when valid and reliable answers are known can AI outcomes be validated. Qualitative and quantitative methodologies, including peer review, are solely capable of being carried out by humans using their wide array of senses and abilities. Once organized and validated in these ways, computers, including AI, can instantly and readily derive contexts and support high-level classification and calculation to apply them at scale.

The appliance of new exascale HPC techniques to energy industry simulations is absolutely needed nowadays. In this sense, the common procedure is to customize these techniques to the specific energy sector they are of interest in order to go beyond the state-of-the-art in the required HPC exascale simulations. With this aim, the HPC4E project is developing new exascale methodologies to three different energy sources that are the present and the future of energy: wind energy production and design, efficient combustion systems for biomass-derived fuels (biogas), and exploration geophysics for hydrocarbon reservoirs. In this work, the general exascale advances proposed as part of HPC4E and its outcome to specific results in different domains are presented.

One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Biological hypercomputation (BH) is the concept coined that expresses that living beings process information nonalgorithmically. have brought up (BH) as a new problem within complexity science. This paper aims at proving a positive understanding of "non-algorithmic" processes. A number of arguments are brought that support the claim. This fosters, it is argued, a brand new understanding of information processing among living beings. Some conclusions are drawn at the end.

We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg-de Vries (gKdV) equation, focusing on classical Fourier-based Crank-Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes-including the cubic case (ν = 3)-and diverse initial conditions such as solitons, smooth pulses, discontinuities, and noisy profiles. In addition to pure PINN and spectral models, we propose a novel hybrid PINN-spectral method incorporating a regularization term based on Fourier reference solutions, leading to improved accuracy and stability. Numerical experiments show that while spectral methods achieve superior efficiency in structured domains, PINNs provide flexible, mesh-free alternatives for data-driven and irregular setups. The hybrid model achieves lower relative L 2 error and better captures soliton interactions. Our results demonstrate the complementary strengths of spectral and machine learning methods for nonlinear dispersive PDEs.

Solving time-fractional nonlinear equations, such as the Newell-Whitehead-Segel (N-W-S) and Burger's equations, is inherently complex due to the intricacies of fractional calculus and the limitations of current numerical and analytical techniques. This study introduces the Tarig Projected Differential Transform Method (TPDTM), a hybrid approach that offers a novel solution to time-fractional linear and nonlinear partial differential equations (PDEs) without the need for linearization, perturbation, or variable discretization. TPDTM stands out as a simple yet powerful method, offering remarkable accuracy, computational efficiency, and ease of implementation. In comparative analysis with the Finite Difference Method (FDM) and Laplace Adomian Decomposition Method (LADM), TPDTM demonstrates superior performance, particularly in its handling of Adomian polynomials, all while preserving stability and precision. With its rapid convergence and versatility, TPDTM proves to be a robust tool for tackling complex fractional PDEs, making it highly valuable for applied mathematics and physics. Looking forward, expanding TPDTM's application to coupled fractional systems and multi-scale problems will not only enhance its theoretical depth but also open exciting new possibilities for breakthroughs in engineering, physics, and computational modeling.

In this study, self-similar solutions for cylindrically symmetric flow driven by a moving piston in a dusty gas are obtained using a mathematical model. One-dimensional unsteady viscous magnetohydrodynamic flow is assumed. The dusty gas medium is thought to have a mixture of real gas and uniformly distributed micro-size solid particles. For the flow, it is assumed that the equilibrium condition holds. Shock is assumed to be strong and propagate through a medium in a power law. When the flow between the shock and the piston is isothermal or adiabatic, solutions are derived, and a comparative study is presented. The purpose of this work is to contribute to a better understanding of shock wave behavior in a magnetised environment of dusty gas with viscosity. The results show that for various values of non-idealness parameters in the presence of viscosity, the flow variables have distinct properties in dust-free gas and dusty gas.

In this paper, we evaluate the performance of various parallel optimization meth-ods for Kernel Support Vector Machines on multicore CPUs and GPUs. In par-ticular, we provide the first comparison of algorithms with explicit and implicit parallelization. Most existing parallel implementations for multi-core or GPU ar-chitectures are based on explicit parallelization of Sequential Minimal Optimiza-tion (SMO)—the programmers identified parallelizable components and hand-parallelized them, specifically tuned for a particular architecture. We compare these approaches with each other and with implicitly parallelized algorithms— where the algorithm is expressed such that most of the work is done within few iterations with large dense linear algebra operations. These can be computed with highly-optimized libraries, that are carefully parallelized for a large variety of par-allel platforms. We highlight the advantages and disadvantages of both approaches and compare them on various benchmark...

In this paper, we evaluate the performance of various parallel optimization methods for Kernel Support Vector Machines on multicore CPUs and GPUs. In particular, we provide the first comparison of algorithms with explicit and implicit parallelization. Most existing parallel implementations for multi-core or GPU architectures are based on explicit parallelization of Sequential Minimal Optimization (SMO)-the programmers identified parallelizable components and handparallelized them, specifically tuned for a particular architecture. We compare these approaches with each other and with implicitly parallelized algorithmswhere the algorithm is expressed such that most of the work is done within few iterations with large dense linear algebra operations. These can be computed with highly-optimized libraries, that are carefully parallelized for a large variety of parallel platforms. We highlight the advantages and disadvantages of both approaches and compare them on various benchmark data sets.We find an approximate implicitly parallel algorithm which is surprisingly efficient, permits a much simpler implementation, and leads to unprecedented speedups in SVM training.

The origin and evolution of life on Earth have long been subjects of scientific inquiry, often marked by gaps in understanding that invite speculative explanations. Here, we present a subatomic-resolution simulation of 3.5 billion years of evolution, from abiogenesis to modern humans, using the Lomni equation powered by the deterministic PHYXS framework.
Building on the prior abiogenesis simulation, which modeled RNA self-replication (50 nucleotides), the Evolution D simulation running for 50h on 1000 NVIDIA A100 GPUs, 10^15 atoms) traces the continuous developmental arc from early multicellular life (103 cells), to vertebrate-like organisms (10^5 neurons, 10 Hz firing rate) and ultimately Our Digital Twins Eve and Adam D (100 billion neurons).

Key findings include molecular dynamics driving evolution—such as calcium signaling (0.01 s−1 in early life to 0.2 s−1 in mammals), ATP production (0.1 pJ/s/mitochondrion to 0.12 pJ/s), and epigenetic reprogramming (90–92% demethylation)—and cognitive milestones, from basic sensory processing (50% accuracy) to abstract reasoning (Our Digital Twins Eve D: 40 Hz gamma synchronization).
Validated against genomic data (e.g., 1000 Genomes, GenBank) and experimental studies, this simulation closes temporal and developmental gaps, eliminating the need for “god of the gaps” explanations.

Evolution D, integrated with the PRIMEcraft abiogenesis simulation, demonstrates the power of 𝓛_omni to unify biological
processes across scales, positioning PHYXS as a transformative framework beyond quantum mechanics and general relativity, with implications for future scientific, educational, engineering and simulation applications.

Arabidopsis thaliana, a model organism in plant biology, offers a window into plant development, environmental responsiveness, and cellular signaling. Here, we present a subatomic-resolution simulation of Arabidopsis thaliana over its 5-year lifespan using the L omni framework, a novel computational model developed under the PHYXS initiative. Simulating 10^10 cells and 10^15 atoms, we capture the plant's growth, photosynthesis, tropisms, and stress responses at unprecedented detail. Key findings include rapid phototropism (0.1 mm/day, 98% accuracy), volatile organic compound (VOC) signaling (methyl jasmonate, 0.2 ppm, 2 m range), and robust self-regulation under drought (0.6 µmol CO 2 /s/m 2). Comparative analysis with other flora Digital Twins (e.g., Venus Flytrap D, Mimosa D) highlights Arabidopsis thaliana's slower but precise environmental responsiveness, aligning with experimental studies.
These insights underscore 𝓛omni 's ability to unify plant biology across scales, supporting the PHYXS framework as a transformative successor to quantum mechanics and general relativity (QM/GR).

The Prime Symbolic Resonance Field Explorer (PSRFE) presents a novel computational and visualization framework that explores the relational structure of prime numbers through a symbolic lens. Building upon established research in number theory (Ribenboim, 1996), dynamical systems (Strogatz, 2000), and graph theory (Newman, 2010), this work generates symbolic fingerprints for prime numbers and constructs coherence-based resonance graphs, revealing emergent patterns analogous to protein folding in biological systems (Anfinsen, 1973). We formalize the mathematical foundations for symbolic prime relationships, introduce a spiral embedding with digital root harmonics inspired by geometric number theory (Mazur, 2006), and detail metrics for symbolic coherence and resonance. The framework bridges number theory, symbolic cognition (Dehaene, 2011), and complex systems science (Mitchell, 2009), suggesting that meaningful structure emerges from relational networks of primes in a manner parallel to the emergence of function in biological systems (Kauffman, 1993). The system's potential applications range from number-theoretical research to investigations of emergent semantic meaning in complex symbolic systems, complementing existing work on mathematical beauty and pattern recognition (Changizi, 2011).

Big data is developing quickly, combining industrial techniques and scholarly research to address the difficulties of organising and comprehending large-scale datasets. This dissertation investigates how the AMBER software's Molecular Dynamics simulations can benefit from the increased processing power provided by High-Performance Mobile Cloud Computing (HPMCC). Fortunately, demonstrates a way to more effectively divide computational demands through parallel processing with the Message Passing Interface (MPI) by establishing connections between laptops and virtual machines over a mobile cloud infrastructure. This approach provides a scalable and affordable replacement for conventional supercomputers and speeds up processing. Furthermore, this research addresses security issues with Single Sign-On (SSO) technologies, showcasing cloud computing's capacity to manage massive data demands, especially in scientific research.

Navier-Stokes with oscillatory quantum correction: ∂t∂u +(u⋅∇)u=-∇p+ν∇ 2u +λsin(ωt) where: • λ\lambdaλ is the quantum stabilizing term. • Ω\omega ω is the modular oscillation frequency. • ν\nuν is the viscosity coefficient. We prove bounded turbulence by computing the energy functional: E(t)=∫|u| 2 dV. If (dE)/(dt) ≤ 0\, turbulence remains finite. We define a quaternionic Hamiltonian operator whose eigenvalues align with Riemann zeros: HΨ=EΨ,E=Re(s)+iIm(s) where s are the nontrivial zeros of the Riemann zeta function. By computing the eigenvalue spacing statistics, we check agreement with random matrix theory: P(s)=π/2 s,e,-π/ 4S2 .P(s) = \frac{\pi}{2} s e^{-\frac{\pi}{4} s^2}.P(s)=2/π se-4π s2.

An attempt have been taken to study ion-acoustic (IA) solitary and shock wave in theoretically in three component electron-ion plasmas. To do this, a non-linear propagation of IA solitary wave have been considered in unmagnetized plasmas containing mobile positively charged cold inertial ions, negatively charged Maxwellian ions with non-thermal and trapped electrons respectively. The shock wave have also been studies for above system. The well-established reductive perturbation method has been employed to derived standard solitary and shock wave equation. The solutions was also derived to study their characteristic behaviour with parametric regims.

การศึกษาในครั้งนี้ มีวัตถุประสงค์เพื่อมุ่งพัฒนาแบบวัดทักษะการคิดเชิงคำนวณที่ไม่เน้นการเขียนโปรแกรม แต่ได้นำสถานการณ์ต่าง ๆ ที่นักเรียน มีโอกาสพบเจอมาใช้เป็นข้อคำถาม ซึ่งมีวัตถุประสงค์ เพื่อพัฒนาและตรวจสอบคุณภาพของแบบวัดระดับทักษะการคิดเชิงคำนวณ เพื่อส่งเสริมการเรียนรู้ สำหรับนักเรียนชั้นมัธยมศึกษาปีที่ 4 และเพื่อสร้างเกณฑ์สำหรับประเมินผลระดับทักษะการคิดเชิงคำนวณ เครื่องมือที่ใช้ในการวิจัย คือ แบบวัดระดับทักษะการคิดเชิงคำนวณ สำหรับนักเรียนชั้นมัธยมศึกษาปีที่ 4 ผลการวิจัย พบว่า                 
          1. การพัฒนาแบบวัดระดับทักษะการคิดเชิงคำนวณ เพื่อส่งเสริมการเรียนรู้ สำหรับนักเรียนชั้นมัธยมศึกษาปีที่ 4 มีจำนวน 20 ข้อ ประกอบด้วย 4 องค์ประกอบ ได้แก่ องค์ประกอบที่ 1 ด้านการแยกย่อยปัญหา จำนวน 5 ข้อ องค์ประกอบที่ 2 ด้านการพิจารณารูปแบบ จำนวน 5 ข้อ องค์ประกอบที่ 3 ด้านการคิดเชิงนามธรรม จำนวน 5 ข้อ และ องค์ประกอบที่ 4 ด้านการออกแบบขั้นตอนวิธี จำนวน 5 ข้อ ผลการวิเคราะห์ด้วยโปรแกรม ConQuest2 พบว่า ข้อสอบมีค่าความยากระดับปานกลางค่อนไปทางง่าย เหมาะสำหรับนักเรียนที่มีความสามารถระดับกลาง ค่า MNSQ อยู่ในช่วงที่ยอมรับได้ มีค่าความยาก (Estimate) อยู่ในช่วง (-1,+1) จำนวน 20 ข้อ รวมทั้ง MNSQ (-0.789 ถึง 0.882) อยู่ในช่วง CI ที่ยอมรับได้ทั้งหมดจำนวน 20 ข้อ การตรวจสอบความเที่ยงโดยใช้สูตรสัมประสิทธิ์แอลฟาของครอนบาค พบว่า มีค่าความเที่ยงทั้งฉบับ เท่ากับ .974
          2. การกำหนดเกณฑ์สำหรับประเมินผล ได้แบ่งช่วงคะแนนการประมาณค่าเป็น 3 ช่วง คือ 1) ช่วง -0.789 ถึง -0.231 ให้ค่าน้ำหนักคะแนน 1 คะแนน มีจำนวน 6 ข้อ 2) ช่วง -0.232 ถึง 0.324 ให้ค่าน้ำหนักคะแนน 2 คะแนน มีจำนวน 8 ข้อ และ 3) ช่วง 0.325 ถึง 0.882 ให้ค่าน้ำหนักคะแนน 3 คะแนน มีจำนวน 6 ข้อ และมีคะแนนรวมทั้งหมด 40 คะแนน ซึ่งแบ่งเป็นระดับทักษะการแก้ปัญหาแบบเป็นลำดับและใช้เหตุผลอย่างมีตรรกะมีทักษะการคิด การวิเคราะห์ การแก้ปัญหาที่เป็นระบบ และต่อยอดกระบวนการคิดเชิงคำนวณสู่การ Coding ได้ 3 ระดับ ได้แก่ 1) ระดับต่ำ ได้คะแนน 13 คะแนนลงมา 2) ระดับปานกลาง ได้คะแนน 14 – 26 คะแนน และ 3) ระดับสูง ได้คะแนน 27 คะแนนขึ้นไป

This paper illustrates how stochastic dominance criteria can be used to rank social networks in terms of efficiency, and develops statistical inference procedures for assessing these criteria. The tests proposed can be viewed as extensions of a Pearson goodness-of-fit test and a studentized maximum modulus test often used to partially rank income distributions and inequality measures. We establish uniform convergence of the empirical size of the tests to the nominal level, and show their consistency under the usual conditions that guarantee the validity of the approximation of a multinomial distribution to a Gaussian distribution. Furthermore, we propose a bootstrap method that enhances the finite-sample properties of the tests. The performance of the tests is illustrated via Monte Carlo experiments and an empirical application to risk sharing networks in rural India.

This paper illustrates how stochastic dominance criteria can be used to rank social networks in terms of efficiency, and develops statistical inference procedures for assessing these criteria. The tests proposed can be viewed as extensions of a Pearson goodness-of-fit test and a studentized maximum modulus test often used to partially rank income distributions and inequality measures. We establish uniform convergence of the empirical size of the tests to the nominal level, and show their consistency under the usual conditions that guarantee the validity of the approximation of a multinomial distribution to a Gaussian distribution. Furthermore, we propose a bootstrap method that enhances the finite-sample properties of the tests. The performance of the tests is illustrated via Monte Carlo experiments and an empirical application to risk sharing networks in rural India.

Several Schur complement-based preconditioners have been proposed for solving (generalized) saddle-point problems. We consider matrices where the Schur complement has rapid decay over some graph known a priori. This occurs for many matrices arising from the discretization of systems of partial differential equations, and this graph is then related to the mesh. We propose the use of probing methods to approximate these Schur complements in preconditioners for saddle-point problems. We demonstrate these techniques for the block-diagonal and constraint preconditioners proposed by [Murphy, Golub and Wathen '00], [de Sturler and Liesen '04] and [Siefert and de Sturler '05]. However, these techniques are applicable to many other preconditioners as well. We discuss the implementation of probing methods, and we consider the application of those approximations in preconditioners for Navier-Stokes problems and metal deformation problems. Finally, we study eigenvalue clustering for the preconditioned matrices, and we present convergence and timing results for various problem sizes. These results demonstrate the effectiveness of the proposed preconditioners with probing-based approximate Schur complements.

This is not a book! These are personal notes written while preparing lectures on several courses at the UM. They are rather informal and may even contain mistakes. I tried to be as synthetic as I could, without missing the observations that I consider important. I probably will not lecture all I wrote, and did not write all I plan to lecture. So, I included empty or sketched paragraphs, about material that I think should/could be lectured within the same course. The last section, “Bestiario”, is a list of famous examples proposed to students for their projects. References contain some introductory manuals, some classics, and other books where I have learnt things in the past century. Besides, good material and further references can easily be found on the web, for example in Wikipedia. Pictures were made with “Grapher ” on my MacBook. This work is licensed under a

In this work, the tangent stiffness matrix for the geometrically nonlinear analysis of a three-dimensional truss element subjected to large displacements and rotations, and potentially large deformations, is derived based on the Corotational formulation. The tangent matrix is deduced following two equivalent approaches: variational and energy-based. The resulting tangent stiffness matrix of the element makes up the global stiffness matrix of the structure, which is used in incremental and/or iterative numerical methods to capture the geometric nonlinear response.