General Framework Research Articles

Directional integration and pathway enrichment analysis for multi-omics data

Omics techniques generate comprehensive profiles of biomolecules in cells and tissues. However, a holistic understanding of underlying systems requires joint analyses of multiple data modalities. We present DPM, a data fusion method for integrating omics datasets using directionality and significance estimates of genes, transcripts, or proteins. DPM allows users to define how the input datasets are expected to interact directionally given the experimental design or biological relationships between the datasets. DPM prioritises genes and pathways that change consistently across the datasets and penalises those with inconsistent directionality. To demonstrate our approach, we characterise gene and pathway regulation in IDH-mutant gliomas by jointly analysing transcriptomic, proteomic, and DNA methylation datasets. Directional integration of survival information in ovarian cancer reveals candidate biomarkers with consistent prognostic signals in transcript and protein expression. DPM is a general and adaptable framework for gene prioritisation and pathway analysis in multi-omics datasets.

A hybrid quantum–classical algorithm for mixed-integer optimization in power systems

Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing has been tested as a potential solution towards reducing the computational burden imposed by these problems, providing promising results, motivating the can be used to speedup the solution of MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum–classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum–classical algorithms for power system mixed integer optimization problems.

A Diffusion-Based Approach for Simulating Forward-in-Time State-Dependent Speciation and Extinction Dynamics.

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios.

New Paradigm of Identifiable General-response Cognitive Diagnostic Models: Beyond Categorical Data.

Cognitive diagnostic models (CDMs) are a popular family of discrete latent variable models that model students' mastery or deficiency of multiple fine-grained skills. CDMs have been most widely used to model categorical item response data such as binary or polytomous responses. With advances in technology and the emergence of varying test formats in modern educational assessments, new response types, including continuous responses such as response times, and count-valued responses from tests with repetitive tasks or eye-tracking sensors, have also become available. Variants of CDMs have been proposed recently for modeling such responses. However, whether these extended CDMs are identifiable and estimable is entirely unknown. We propose a very general cognitive diagnostic modeling framework for arbitrary types of multivariate responses with minimal assumptions, and establish identifiability in this general setting. Surprisingly, we prove that our general-response CDMs are identifiable under -matrix-based conditions similar to those for traditional categorical-response CDMs. Our conclusions set up a new paradigm of identifiable general-response CDMs. We propose an EM algorithm to efficiently estimate a broad class of exponential family-based general-response CDMs. We conduct simulation studies under various response types. The simulation results not only corroborate our identifiability theory, but also demonstrate the superior empirical performance of our estimation algorithms. We illustrate our methodology by applying it to a TIMSS 2019 response time dataset.

Loops of loops expansion in the amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the ‘loops of loops’ expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

Integrated workflows and interfaces for data-driven semi-empirical electronic structure calculations.

Modern software engineering of electronic structure codes has seen a paradigm shift from monolithic workflows toward object-based modularity. Software objectivity allows for greater flexibility in the application of electronic structure calculations, with particular benefits when integrated with approaches for data-driven analysis. Here, we discuss different approaches to create deep modular interfaces that connect big-data workflows and electronic structure codes and explore the diversity of use cases that they can enable. We present two such interface approaches for the semi-empirical electronic structure package, DFTB+. In one case, DFTB+ is applied as a library and provides data to an external workflow; in another, DFTB+receives data via external bindings and processes the information subsequently within an internal workflow. We provide a general framework to enable data exchange workflows for embedding new machine-learning-based Hamiltonians within DFTB+ or enabling deep integration of DFTB+ in multiscale embedding workflows. These modular interfaces demonstrate opportunities in emergent software and workflows to accelerate scientific discovery by harnessing existing software capabilities.

Probabilistic Models and Statistics for Electronic Financial Markets in the Digital Age

AbstractThe scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreover highlight and explain the important role played by some classical concepts of probability and statistics. We focus on three main aspects: Testing for jumps; rough fractional stochastic volatility; and limit order microstructure noise. We review jump tests based on extreme value theory and complement the literature proposing new statistical methods. They are based on asymptotic theory of order statistics and the Rényi representation. The second stage of our journey visits a recent strand of research showing that volatility is rough. We further investigate this and establish a minimax lower bound exploring frontiers to what extent the regularity of latent volatility can be recovered in a more general framework. Finally, we discuss a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices and its probabilistic and statistical foundation.

Research and Application of a Generalized Power Communication Framework with Joint Security Protection Mechanism

Background: The rapid development of Industry 4.0 has opened up new power systems, which face a more complex network topology and a broader range of security threats. This has led to an urgent demand for a coordinated, lightweight, and secure communication management method. Methods: This paper presents a general power communication framework with a joint security protection mechanism that is suitable for coordinated management and transmission safety. The framework manages the protocol’s thread management of the device by converting it to the framework’s process management. It formulates specifications for protocols and equipment that access the framework to achieve support for multiple protocols and equipment. This reduces the difficulty of system operation and maintenance, as well as system complexity, and improves management efficiency. Additionally, the joint security protective mechanism for plugin authentication and protocol encryption is introduced to enable secure data transmission and guarantee the framework's security management. Finally, two experiments have been conducted to discuss and confirm the effectiveness and safety of the framework. Results: The results of the two experiments and the following analysis show that our framework is superior to the chosen well-known industrial commercial communication platforms, and the time delay cost by our mechanism doesn’t significantly affect the real-time data transmission in the power industry, proving its feasibility in both IoT and power applications. Conclusion: Our framework demonstrates exceptional performance in terms of time lag and packet loss during the experiment, surpassing other IoT communication frameworks. Furthermore, it maintains its high standards even under rigorous security analysis.

Modal reduction principles: a parametric shift to graphs

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks.

Classifying topology in photonic crystal slabs with radiative environments

In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

Two-scale asymptotic homogenization analysis of piezoelectric composite materials in generalized curvilinear coordinates

This paper presents a comprehensive study on applying the two-scale asymptotic homogenization method to derive the effective properties of piezoelectric composite materials characterized by generalized periodicity in curvilinear coordinates. The methodology involves formulating the homogenization problem in a general curvilinear framework suitable for materials with complex geometric configurations. By systematically deriving the homogenized equations and effective coefficients, the paper provides a robust theoretical foundation for understanding the macroscopic behavior of piezoelectric composites under various loading conditions. The model’s versatility is demonstrated through its application to specific curvilinear coordinate systems, including the helix coordinate system and cylindrical coordinates with wavy geometry. These examples highlight the potential of the proposed approach in analyzing and designing piezoelectric materials with intricate geometries. The state-of-the-art numerical homogenization methods have also validated the proposed homogenization method, ensuring its accuracy and robustness.

Adaptive Ferroelectric States in KNN-based Piezoceramics: Unveiling the Mechanism of Enhancing Piezoelectric Properties through Multiple Phase Boundary Engineering

Developing high performance lead-free piezoceramics, such as (K,Na)NbO3 (KNN) material, is critical to achieving environmental sustainability in next-generation electromechanical devices. Although substantial advancements have been made in KNN-based ceramics, a general coherent framework is lacking that links microscopic structure to the enhancement of macroscopic properties. Our findings indicate that the enhanced performance of KNN-based ceramics in multiphase coexistence boundaries can be attributed to the formation of self-adjusting nanodomains in response to strong local structural heterogeneity. The self-adjusting behavior of domain structure is an outcome of minimizing the local stress generated by the lattice mismatch within KNN-based ceramics, which conforms to the thermodynamic principles that favor minimizing total free energy. Guided by this strategy, the present work achieves a significant improvement of electromechanical properties, including a piezoelectric coefficient (d33) of ~585 pC N-1, an electromechanical coupling factor (kp) of ~62%, and a figure of merit (d33 × g33) of ~12.78 ×10-12 m2 N-1. This study offers a new strategy for developing lead-free piezoceramics through dedicated design of novel phase boundaries.

Greta: Towards a General Roadside Unit Deployment Framework

<i>Greta:</i> Towards a General Roadside Unit Deployment Framework

Synchronizing short-, mid-, and long-term operations of hydro-wind-photovoltaic complementary systems

Hydro-wind-photovoltaic (PV) complementary power systems (HWPCSs) offer a promising solution for integrating intermittent wind and PV power, leveraging the long-term energy storage capacity of reservoirs and the short-term flexible adjustability of hydro units. However, existing studies often neglect the reciprocal influences among short-, mid-, and long-term operations of HWPCSs, resulting in suboptimal operating strategies. To tackle this issue, the study proposes a generic framework for synchronizing operations of HWPCSs across multiple time scales. The framework simultaneously optimizes long-term operating rule curves, mid-term water consumption allocation, day-ahead power generation plan scheduling, and intraday economic operation of HWPCSs. A HWPCS located in the Yalong River Basin is selected as the case study. The results indicate that: (1) synchronized operation effectively reduces the output shortage risk (from 4.86% to 0%) and average absolute water consumption deviation (from 2.07% to 0.09%) compared to the conventional method; (2) synchronized operation provides more reasonable boundaries for short-term operations, reducing the average online time percentage (from 65.08% to 63.57%) and start-up/shut-down times (from 3185 to 2981) of hydro units, leading to an increase in the average hydropower efficiency (from 9.05 to 9.12). This study highlights the impracticality of the conventional method, underscoring the necessity of synchronized operation for HWPCSs. The proposed method provides a practical framework for the efficient operation of HWPCSs.

Long-term follow-up in congenital diaphragmatic hernia

With improvements in initial care for patients with congenital diaphragmatic hernia (CDH), the number of CDH patients with severe disease who are surviving to discharge has increased. This growing population of patients faces a unique set of long-term challenges, multisystem adverse outcomes, and post-intervention complications requiring specialized multidisciplinary follow-up. Early identification and intervention are essential to mitigate the potential morbidity associated with these challenges. This manuscript outlines a general framework for long-term follow-up for the CDH patient, including cardiopulmonary, gastrointestinal, neurodevelopmental, surgical, and quality of life outcomes.

Statistical Divergence and Paths Thereof to Socioeconomic Inequality and to Renewal Processes

This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable from that of the other. The general framework is then applied to the topics of socioeconomic inequality and renewal processes. The general framework and its applications are shown to yield and to relate to the following: f-divergence, Hellinger divergence, Renyi divergence, and Kullback–Leibler divergence (also known as relative entropy); the Lorenz curve and socioeconomic inequality indices; the Gini index and its generalizations; the divergence of renewal processes from the Poisson process; and the divergence of anomalous relaxation from regular relaxation. Presenting a `fresh’ perspective on statistical divergence, this paper offers its readers a simple and transparent construction of statistical-divergence gauges, as well as novel paths that lead from statistical divergence to the aforementioned topics.

GEORGIAN COMPETITION LAW IN THE DIGITAL AGE – GEORGIAN PRACTICE AND EXISTING CHALLENGES

The article identifies, systematizes the decisions taken by the Georgian Competition and Consumer Agency regarding digital markets/competition and reviews the practices established by the Agency based on the said decisions. The introduction of the article highlights the significant challenge of modern competition law, which implies that competition law does not exist independently of era and context, and it is important that competition law and its enforcement mechanisms function effectively in the conditions of the modern digital economy. The article then defines the digital economy and describes two of its key features, (big) data and digital platforms. A number of theoretical problems are then mentioned which may hinder the effective enforcement of competition law in relation to similar economic agents/markets. The main part of the article will concern the review of the decisions made by the Competition Agency in relation to online markets and digital platforms. Since there are currently no special legislative or by-law norms necessary for the effective enforcement of competition law in the digital age, the Competition Agency is guided by the general legislative framework regulating competition law to resolve similar issues. The analysis of the decisions revealed that the practice of the Agency develops in the direction of only two: (I) unfair competition (II) agreements restricting competition, and currently there is no, for example, a decision of the Competition Agency regarding the abuse of a dominant position by digital platforms.

Influential individuals can promote prosocial practices in heterogeneous societies: a mathematical and agent-based model.

In this paper, we examine how different governance types impact prosocial behaviors in a heterogenous society. We construct a general theoretical framework to examine a game-theoretic model to assess the ease of achieving a cooperative outcome. We then build a dynamic agent-based model to examine three distinct governance types in a heterogenous population: monitoring one's neighbors, despotic leadership, and influencing one's neighbors to adapt strategies that lead to better fitness. In our research, we find that while despotic leadership may lead towards high prosociality and high returns it does not exceed the effects of a local individual who can exert positive influence in the community. This may suggest that greater individual gains can be had by cooperating and that global hierarchical leadership may not be essential as long as influential individuals exert their influence for public good and not for public ill.

A Factory of Fractional Derivatives

This paper aims to demonstrate that, beyond the small world of Riemann–Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to different paths taken. The notions of time and scale sequences are introduced, and general associated basic derivatives, namely, right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to obtain both known and new fractional-order derivatives. Several fractional derivatives are considered, mainly Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

Fragment-Fusion Transformer: Deep Learning-Based Discretization Method for Continuous Single-Cell Raman Spectral Analysis.

Raman spectroscopy has become an important single-cell analysis tool for monitoring biochemical changes at the cellular level. However, Raman spectral data, typically presented as continuous data with high-dimensional characteristics, is distinct from discrete sequences, which limits the application of deep learning-based algorithms in data analysis due to the lack of discretization. Herein, a model called fragment-fusion transformer is proposed, which integrates the discrete fragmentation of continuous spectra based on their intrinsic characteristics with the extraction of intrafragment features and the fusion of interfragment features. The model integrates the intrinsic feature-based fragmentation of spectra with transformer, constructing the fragment transformer block for feature extraction within fragments. Interfragment information is combined through the pyramid design structure to improve the model's receptive field and fully exploit the spectral properties. During the pyramidal fusion process, the information gain of the final extracted features in the spectrum has been enhanced by a factor of 9.24 compared to the feature extraction stage within the fragment, and the information entropy has been enhanced by a factor of 13. The fragment-fusion transformer achieved a spectral recognition accuracy of 94.5%, which is 4% higher compared to the method without fragmentation and fusion processes on the test set of cell Raman spectroscopy identification experiments. In comparison to common spectral classification models such as KNN, SVM, logistic regression, and CNN, fragment-fusion transformer has achieved 4.4% higher accuracy than the best-performing CNN model. Fragment-fusion transformer method has the potential to serve as a general framework for discretization in the field of continuous spectral data analysis and as a research tool for analyzing the intrinsic information within spectra.