Iterative Integration Research Articles

Change plane model averaging for subgroup identification.

Central to personalized medicine and tailored therapies is discovering the subpopulations that account for treatment effect heterogeneity and are likely to benefit more from given interventions. In this article, we introduce a change plane model averaging method to identify subgroups characterized by linear combinations of predictive variables and multiple cut-offs. We first fit a sequence of statistical models, each incorporating the thresholding effect of one particular covariate. The estimation of submodels is accomplished through an iterative integration of a change point detection method and numerical optimization algorithms. A frequentist model averaging approach is then employed to linearly combine the submodels with optimal weights. Our approach can deal with high-dimensional settings involving enormous potential grouping variables by adopting the sparsity-inducing penalties. Simulation studies are conducted to investigate the prediction and subgrouping performance of the proposed method, with a comparison to various competing subgroup detection methods. Our method is applied to a dataset from a warfarin pharmacogenetics study, producing some new findings.

Algorithmic study of the algebraic parameter estimation problem for a class of perturbations

We consider the algebraic parameter estimation problem for a class of standard perturbations. We assume that the measurement z(t) of a solution x(t) of a linear ordinary differential equation -- whose coefficients depend on a set θ := {θ₁, ..., θᵣ} of unknown constant parameters -- is affected by a perturbation γ(t) whose structure is supposed to be known (e.g., an unknown bias, an unknown ramp), i.e., z(t)=x(t, θ)+γ(t). We investigate the problem of obtaining closed-form expressions for the parameters θᵢ's in terms of iterative indefinite integrals or convolutions of z. The different results are illustrated by explicit examples computed using the NonA package -- developed in Maple -- in which we have implemented our main contributions.

MAPPING THE INTERPLAY OF SOCIAL HEALTH AND COGNITIVE FUNCTIONING: A MIXED RESEARCH KNOWLEDGE SYNTHESIS

Abstract Introduction Dementia is a syndrome with complex underlying bio-psycho-social mechanisms relevant for prevention and intervention. This work presents a mixed research knowledge synthesis, mapping the multidimensional interplay of social health and cognitive functioning in dementia. Methods Data integration from 1) systematic review, 2) group model building workshops, (3) iterative integration of multi-national cohort studies (4) ongoing revisions of the social health concept via expert discussions. Results The map comprises more than 50 markers, clustered in six domains (social health, psychological pathways, physiological pathways, health behavior pathways, brain/cognitive reserve, cognitive functioning). The social health domain is structured in six sub-domains representing a novel conceptual understanding. Three pathways (physiological, psychological, health behavior) reflect principal mechanisms connecting social health with brain/cognitive reserve and cognitive functioning. Conclusion The map depicts dynamic relationships between social health and cognitive functioning that can serve as a basis for recommendations, both for prevention and for improved dementia care.

Resolving charged hadrons in QED — gauge invariant interpolating operators

Standard interpolating operators for charged mesons, e.g. JB = overline{b} iγ5u for B−, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by adding an auxiliary charged scalar ΦB, {mathcal{J}}_B^{(0)} = JB ΦB, which reproduces all the universal soft and collinear logs. The modified LSZ-factor is shown to be infrared finite which is a necessary condition for validating the approach. At mathcal{O} (α), this is equivalent to a specific Dirac dressing of charged operators. A generalisation thereof, using iterated integrals, establishes the equivalence to all orders and provides a transparent alternative viewpoint. The method is discussed by the example of the leptonic decay B−→ ℓ− overline{nu} for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. B−→ π0ℓ− overline{nu} ).

Three-Dimensional ANP Evaluation Method Based on Spatial Position Uncertainty under RNP Operation

Performance-based navigation (PBN) operations based on the required navigation performance (RNP) operations are the trend for civil aviation in the future. In order to further ensure the safety and efficiency of civil aviation operation, RNP will transition from 2D to 3D/4D. Accurately evaluating the actual navigation performance in three-dimensional directions (3D ANP) under civil aircraft RNP operation is important to guarantee the safe flight of civil aircraft. However, the traditional two-dimensional ANP evaluation method mainly focuses on plane navigation performance along the track, lacks the evaluation of the vertical direction. Moreover, the traditional three-dimensional accuracy evaluation method is based on the assumption of three-dimensional independence and uniformity, which can only carry out approximate calculation, and the evaluation result is inaccurate. Therefore, this paper constructs a three-dimensional ellipsoid error probability (EEP) evaluation model for the spatial position uncertainty of the navigation output of the flight management system in three-dimensional directions, and gives the three-dimensional accurate ANP calculation results through iterative numerical integration. The simulation results show that the evaluation method proposed in this paper can accurately evaluate the actual navigation performance of the airborne navigation system in all directions of 3D space, and has higher evaluation accuracy and precision than the traditional ANP evaluation method, which is of great significance to ensure the flight safety of civil aircraft under 3D/4D RNP operation in the future.

$\mathrm{SL}_{2}(\mathbb{R})$-developments and signature asymptotics for planar paths with bounded variation

The signature transform, defined by the formal tensor series of global iterated path integrals, is a homomorphism between the path space and the tensor algebra that has been studied in geometry, control theory, number theory as well as stochastic analysis. An elegant isometry conjecture states that the length of a bounded variation path \gamma can be recovered from the asymptotics of its normalised signature: \text{Length}(\gamma)= \lim_{n\rightarrow\infty} \Big\Vert n! \int_{0<t_{1}<\cdots<t_{n}<T} d\gamma_{t_{1}}\otimes\cdots\otimes d\gamma_{t_{n}} \Big\Vert^{1/n}. This property depends on a key topological non-degeneracy notion known as tree-reducedness (namely, with no tree-like pieces). Existing arguments have relied crucially on \gamma having a continuous derivative under the unit speed parametrisation. In this article, we prove the above isometry conjecture for planar paths by assuming only local bounds on the angle of \gamma' (which ensures the absence of tree-like pieces). Our technique is based on lifting the path onto the special linear group \mathrm{SL}_{2}(\mathbb{R}) and analysing the behaviour of the associated angle dynamics at a microscopic level.

The thalamocortical inhibitory network controls human conscious perception

Although conscious perception is a fundamental cognitive function, its neural correlates remain unclear. It remains debatable whether thalamocortical interactions play a decisive role in conscious perception. To clarify this, we used functional magnetic resonance imaging (fMRI) where flickering red and green visual cues could be perceived either as a non-fused colour or fused colour. Here we show significantly differentiated fMRI neurodynamics only in higher-order thalamocortical regions, compared with first-order thalamocortical regions. Anticorrelated neurodynamic behaviours were observed between the visual stream network and default-mode network. Its dynamic causal modelling consistently provided compelling evidence for the involvement of higher-order thalamocortical iterative integration during conscious perception of fused colour, while inhibitory control was revealed during the non-fusion condition. Taken together with our recent magnetoencephalography study, our fMRI findings corroborate a thalamocortical inhibitory model for consciousness, where both thalamic inhibitory regulation and integrative signal iterations across higher-order thalamocortical regions are essential for conscious perception.

Analytic Detection in Homotopy Groups of Smooth Manifolds

In this paper, for the mapping of a sphere into a compact orientable manifold Sn → M, n ≥ 1, we solve the problem of determining whether it represents a nontrivial element in the homotopy group of the manifold πn(M). For this purpose, we consistently use the theory of iterated integrals developed by Chen. It should be noted that the iterated integrals as repeated integration were previously meaningfully used by Lappo-Danilevsky to represent solutions of systems of linear differential equations and by Whitehead for the analytical description of the Hopf invariant for mappings f : S2n−1 → Sn, n ≥ 2.We give a brief description of Chen’s theory representing Whitehead’s and Haefliger’s formulas for the Hopf invariant and generalized Hopf invariant. Examples of calculating these invariants using the technique of iterated integrals are given. Further, it is shown how one can detect any element of the fundamental group of a Riemann surface using iterated integrals of holomorphic forms. This required to prove that the intersection of the terms of the lower central series of the fundamental group of a Riemann surface is a unit group.

DNA sequence and chromatin modifiers cooperate to confer epigenetic bistability at imprinting control regions

Genomic imprinting is regulated by parental-specific DNA methylation of imprinting control regions (ICRs). Despite an identical DNA sequence, ICRs can exist in two distinct epigenetic states that are memorized throughout unlimited cell divisions and reset during germline formation. Here, we systematically study the genetic and epigenetic determinants of this epigenetic bistability. By iterative integration of ICRs and related DNA sequences to an ectopic location in the mouse genome, we first identify the DNA sequence features required for maintenance of epigenetic states in embryonic stem cells. The autonomous regulatory properties of ICRs further enabled us to create DNA-methylation-sensitive reporters and to screen for key components involved in regulating their epigenetic memory. Besides DNMT1, UHRF1 and ZFP57, we identify factors that prevent switching from methylated to unmethylated states and show that two of these candidates, ATF7IP and ZMYM2, are important for the stability of DNA and H3K9 methylation at ICRs in embryonic stem cells.

Smart Governance of Urban Ecological Environment Driven by Digital Twin Technology: A Case Study on the Ecological Restoration and Management in S island of Chongqing

China is undergoing rapid urbanization, which has caused undesirable urban sprawl and ecological deterioration. Combining information technology for ecological environment governance is an effective measure to improve governance efficiency. In this paper, based on the analysis of the ecological restoration and governance case of S Island in Chongqing, an ecological intelligent governance system architecture based on the integration of multiple information technologies such as digital twin is extracted. The research shows that the S Island is based on the technical concept of the digital twin, and integrates a variety of information technology integration, collects and processes a large amount of data generated in the whole process of S Island repair and operation, and builds it based on the digital twin concept and accurately maps the physical space. This system model can be stored and processed based on the integrated data, realize knowledge graph visualization, algorithm optimization, and iterative integration for different objects and application scenarios, and finally serve different functional modules in ecological governance, which can be used to support Smart governance of cities.

Iterative Design and Integration of a Microlearning Mobile App for Performance Improvement and Support for NATO Employees.

This case study details microlearning content development, testing, and implementation of the NATO Headquarters Supreme Allied Command Transformation (HQ SACT) e-Learning Networking App (NeNA) conducted by an AECT microlearning consulting team. NeNA was designed to provide microlearning “just-in-time” content, to create socialization (affinity spaces), channel organizational content, and increase employee motivation. The purpose of the AECT and HQ SACT partnership was to test the NeNA app as a viable way to develop and deliver microlearning content that personalizes self-directed learning, reduces cognitive load, meets the changing needs of the younger workforce, and captures implicit knowledge of employees prior to the end of their military duties. Primary lessons learned surrounded the importance of practitioner awareness of organizational and contextual challenges, including usability of solutions and essential steps to onboarding (training and integration), when adopting mobile learning solutions to provide performance support and improvement to employees.

Psychiatric diagnosis and treatment in the 21st century: paradigm shifts versus incremental integration.

Psychiatry has always been characterized by a range of different models of and approaches to mental disorder, which have sometimes brought progress in clinical practice, but have often also been accompanied by critique from within and without the field. Psychiatric nosology has been a particular focus of debate in recent decades; successive editions of the DSM and ICD have strongly influenced both psychiatric practice and research, but have also led to assertions that psychiatry is in crisis, and to advocacy for entirely new paradigms for diagnosis and assessment. When thinking about etiology, many researchers currently refer to a biopsychosocial model, but this approach has received significant critique, being considered by some observers overly eclectic and vague. Despite the development of a range of evidence-based pharmacotherapies and psychotherapies, current evidence points to both a treatment gap and a research-practice gap in mental health. In this paper, after considering current clinical practice, we discuss some proposed novel perspectives that have recently achieved particular prominence and may significantly impact psychiatric practice and research in the future: clinical neuroscience and personalized pharmacotherapy; novel statistical approaches to psychiatric nosology, assessment and research; deinstitutionalization and community mental health care; the scale-up of evidence-based psychotherapy; digital phenotyping and digital therapies; and global mental health and task-sharing approaches. We consider the extent to which proposed transitions from current practices to novel approaches reflect hype or hope. Our review indicates that each of the novel perspectives contributes important insights that allow hope for the future, but also that each provides only a partial view, and that any promise of a paradigm shift for the field is not well grounded. We conclude that there have been crucial advances in psychiatric diagnosis and treatment in recent decades; that, despite this important progress, there is considerable need for further improvements in assessment and intervention; and that such improvements will likely not be achieved by any specific paradigm shifts in psychiatric practice and research, but rather by incremental progress and iterative integration.

Developing adaptive management guidance for groundwater planning and development

Adaptive management (AM) uses targeted monitoring, and structured and iterative integration of new knowledge of project operations to improve future management practices. AM is increasingly cited in groundwater management plans because it purportedly overcomes inherent uncertainties in estimating future environmental responses to human activities. Yet, there are currently only general recommendations available for applying AM for groundwater management. In response, we develop preliminary guidance on the application of “adaptive groundwater management” (AGM) by amending existing AM theory to better account for the management challenges of groundwater-affecting activities. Three key factors emerge that are critical in the design of AGM strategies, including: (1) the severity of groundwater impacts from project operations, (2) the permanence of groundwater impacts, and (3) the level of uncertainty in groundwater system responses to project operations. These three factors are especially important considerations in stakeholder engagement and in assessing the applicability of AGM. The above three key factors are integrated into definitions of “active” and “passive” forms of AGM. Passive AGM strategies meet minimum thresholds for structured and iterative management approaches that incorporate uncertainty reduction, while active AGM strategies include additional constraints that place a greater emphasis on uncertainty quantification and reduction. The preliminary guidance on AGM given in this paper should be extended through consultation with groundwater industry groups and regulators to urgently develop formal AGM guidelines, thereby improving awareness and accountability of the risks and manageability of future groundwater impacts.

MULTI-SCULPT: Multiplex Integration via Selective, CRISPR-Mediated, Ultralong Pathway Transformation in Yeast for Plant Natural Product Synthesis.

Yeast has been a versatile model host for complex and valuable natural product biosynthesis via the reconstruction of heterologous biosynthetic pathways. Recent advances in natural product pathway elucidation have uncovered many large and complicated plant pathways that contain 10-30 genes for the biosynthesis of structurally complex, valuable natural products. However, the ability to reconstruct ultralong pathways efficiently in yeast does not match the increasing demand for valuable plant natural product biomanufacturing. Here, we developed a one-pot, multigene pathway integration method in yeast, named MULTI-SCULPT for multiplex integration via selective, CRISPR-mediated, ultralong pathway transformation. Leveraging multilocus genomic disruption via CRISPR/Cas9, newly developed native and synthetic genetic parts, and fine-tuned gene integration and characterization methods, we managed to integrate 21 DNA inserts that contain a 12-gene plant isoflavone biosynthetic pathway into yeast with a 90-100% success rate in 12 days. This method enables fast and efficient ultralong biosynthetic pathway integration and can allow for the fast iterative integration of even longer pathways in the future. Ultimately, this method will accelerate combinatorial optimization of elucidated plant natural product pathways and accelerate putative pathway characterization heterologously.

Differential Equation Based Path Integral for Open Quantum Systems

We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems. In this method, a system of partial differential equations is derived based on the continuation of a classical numerical method called iterative quasi-adiabatic propagator path integral (i-QuAPI). While the resulting system has infinite equations, we introduce a reasonable closure to obtain a series of finite systems. New numerical schemes can be derived by discretizing these differential equations. It is numerically verified that in certain cases, by selecting appropriate systems and applying suitable numerical schemes, the memory cost required in the i-QuAPI method can be significantly reduced.

A Trident Quaternion Framework for Inertial-Based Navigation Part I: Rigid Motion Representation and Computation

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity, and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This article proposes a compact and elegant representation of the body's attitude/velocity/position, with the aid of a devised trident quaternion tool, which is an extension of dual quaternions. And the position is accounted for by adding a second dual part to the dual quaternion. Eventually, the kinematics of the strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion differential equation. In addition, the numerical solution to this trident quaternion-based kinematic equation is dealt with the recently proposed functional iterative integration approach. Numerical results are provided to verify the analysis. The new representation not only provides an elegant kinematic form of inertial navigation, but gives birth to precision inertial navigation algorithm.

On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua

In the theory of second-gradient continua, the internal virtual work functional can be considered as a second-order distribution in which the virtual displacements take the role of test functions. In its easiest representation, the internal virtual work functional is represented as a volume integral over a subset of the three-dimensional Euclidean vector space and involves first and second derivatives of the virtual displacements. In this paper, we show by an iterative integration by parts procedure how an alternative representation of such a functional can be obtained when the integration domain is a subset that contains also edges and wedges. Since this procedure strongly relies on the divergence theorem for submanifolds of a Euclidean vector space, it is a main goal to derive this divergence theorem for submanifolds starting from Stokes’ theorem for manifolds. To that end, results from Riemannian geometry are gathered and applied to the submanifold case.

Real-time wear monitoring of hob cutter based on statistical analysis

Real-time wear monitoring of hob cutters is of great significance to the quality and efficiency of gear hobbing. To achieve this goal, a strategy based on statistical analysis is proposed in this paper. First, vibration signals during the entire life cycle of a hob cutter are collected. Then, a feature iterative integration method is proposed to integrate the initial features of vibration signals. The integrated features have obvious stages, reflecting the different wear status of hob cutters. Next, a probability tabular cumulative sum control chart method is established to monitor the wear status of hob cutters in real time. Finally, the verification results of two different data sets prove the effectiveness and transferability of the proposed methods.

Pairwise connected tensor network representation of path integrals

It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized using matrix product states, taking advantage of the finite length of the non-Markovian memory. Tensor networks promise to provide a new, unified language to express the structure of path integral. Here, a generalized tensor network is derived and implemented specifically incorporating the pairwise interaction structure of the influence functional, allowing for a compact representation and efficient evaluation. This pairwise connected tensor network path integral (PCTNPI) is illustrated through applications to typical spin-boson problems and explorations of the differences caused by the exact form of the spectral density. The storage requirements and performance are compared with iterative quasi-adiabatic propagator path integral and iterative blip-summed path integral. Finally, the viability of using PCTNPI for simulating multistate problems is demonstrated taking advantage of the compressed representation.

A Novel Iterative Inner-Pulse Integration Target Detection Method for Bistatic Radar

A large time-bandwidth product bistatic radar offers several advantages in high-resolution target detection and motion parameter estimation, but the scale factor and inner-pulse Doppler will also be introduced in the radar echoes when detecting high-speed targets. Under this condition, the conventional matched filter will cause a certain energy loss and a non-negligible shift of the range center, which is called mismatch effect. Considering the special geometries of the bistatic radar, we first establish the precise echo signal model to describe the radar echoes for high-speed targets in a space-air based bistatic radar system. By analyzing the mismatch effect within the pulse and the migration between pulses, we have obtained the mathematic relationship between the scale factor, inner-pulse Doppler shift, range, equivalent velocity and accelerate. Following that, we perceive that the parameters of the matched filter are related to the target motion parameters, i.e., a priori unknown, which inspires us to propose an iterative coherent integration method to achieve the intra-pulse and inter-pulse integration. A precise echo signal model matched filter with initial parameters is defined and a roughly motion parameter estimation is acquired by the precise echo signal model-based Keystone transform and inner-pulse chirp Fourier transform. The estimated parameters are used for matched filter construction and coherent integration. This process is performed over multiple iterations to provide an accurate motion parameter result. In the end, a target detection experiment is given to show the effectiveness of the proposed method using space-air based bistatic radar.