Component Modal Synthesis (CMS) is a reduced order modelling method widely used for large-scale complex systems. It can effectively approximate system-level models through component synthesis, in which the repetitive geometrical components are modelled once and synthesised together. However, the conventional CMS only applies to systems with stationary components connected by strictly compatible ports, limiting it from modelling systems with moving components. This paper presents an adaptive port (AP) technique to extend CMS approaches for modelling parametric systems with rotational parts. To demonstrate the capability of the AP technique, we apply it to the Static Condensation Reduced Basis Element (SCRBE), one widely used variant of CMS approaches. The AP-based SCRBE (AP-SCRBE) can enforce the synthesis of rotational-stationary components over a shared adaptive port when the connecting surfaces of two components are discretisation-wise incompatible, which happens when one component moves relative to the others. Numerical experiments on the NREL 5MW wind turbine show that, in the context of rotational-stationary component synthesis, the AP-SCRBE can accurately and efficiently mode
Modern software systems increasingly integrate machine learning (ML) due to its advancements and ability to enhance data-driven decision-making. However, this integration introduces significant challenges for software engineering, especially in software product lines (SPLs), where managing variability and reuse becomes more complex with the inclusion of ML components. Although existing approaches have addressed variability management in SPLs and the integration of ML components in isolated systems, few have explored the intersection of both domains. Specifically, there is limited support for modeling and managing variability in SPLs that incorporate ML components. To bridge this gap, this article proposes a structured framework designed to extend Software Product Line engineering, facilitating the integration of ML components. It facilitates the design of SPLs with ML capabilities by enabling systematic modeling of variability and reuse. The proposal has been partially implemented with the VariaMos tool.
The description of the intersections of components of a Springer fiber is a very complex problem. Up to now only two cases have been described completely. The complete picture for the hook case has been obtained by N. Spaltenstein and J.A. Vargas, and for two-row case by F.Y.C. Fung. They have shown in particular that the intersection of a pair of components of a Springer fiber is either irreducible or empty. In both cases all the components are non-singular and the irreducibility of the intersections is strongly related to the non-singularity. As it has been shown in [8] a bijection between orbital varieties and components of the corresponding Springer fiber in GL_n extends to a bijection between the irreducible components of the intersections of orbital varieties and the irreducible components of the intersections of components of Springer fiber preserving their codimensions. Here we use this bijection to compute the intersections of the irreducible components of Springer fibers for two-column case. In this case the components are in general singular. As we show the intersection of two components is non-empty. The main result of the paper is a necessary and sufficient condition f
This paper proposes a method for generating software components for embedded systems, integrating seamlessly into existing implementations without developer intervention. We demonstrate this by automatically generating hardware abstraction layer (HAL) code for GPIO operations on the STM32F407 microcontroller. Using Abstract Syntax Trees (AST) for code analysis and Retrieval-Augmented Generation (RAG) for component generation, our approach enables autonomous code completion for embedded applications.
In this paper we study substitutions on $A^\mathbb{Z}$ where $A$ is a finite alphabet. We precisely characterize the minimal components of substitution subshifts, give an optimal bound for their number and describe their dynamics. The explicitness of these results provides a method to algorithmically compute and count the minimal components of a given substitution subshift.
Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components for each univariate functional feature. In this paper, we present extensive simulations to investigate choosing the number of principal components to retain. We show empirically that the conventional approach of using a percentage of variance explained threshold for each univariate functional feature may be unreliable when aiming to explain an overall percentage of variance in the multivariate functional data, and thus we advise practitioners to exercise caution.
Component graphs $Γ_{0}(F)$ are defined for arrays of sets $F$, and in particular for arrays of path components for Vietoris-Rips complexes and Lesnick complexes. The path components of $Γ_{0}(F)$ are the {\it stable components} of the array $F$. The stable components for the system of Lesnick complexes $\{ L_{s,k}(X) \}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.
Consider polynomial maps $f:\C\to\C$ of degree $d\ge 2$, or more generally polynomial maps from a finite union of copies of $\C$ to itself. In the space of suitably normalized maps of this type, the hyperbolic maps form an open set called the hyperbolic locus. The various connected components of this hyperbolic locus are called hyperbolic components, and those hyperbolic components with compact closure (or equivalently those contained in the "connectedness locus") are called bounded hyperbolic components. It is shown that each bounded hyperbolic component is a topological cell containing a unique post-critically finite map called its center point. For each degree $d$, the bounded hyperbolic components can be separated into finitely many distinct types, each of which is characterized by a suitable reduced mapping scheme $\bar S_f$. Any two components with the same reduced mapping scheme are canonically biholomorphic to each other. There are similar statementsfor real polynomial maps, for polynomial maps with marked critical points, and for rational maps. Appendix A, by Alfredo Poirier, proves that every reduced mapping scheme can be represented by some classical hyperbolic component
In this work, we study the entropies of photons, dust (baryonic matter), dark matter, and dark energy in the context of cosmology. When these components expand freely with the universe, we calculate the entropy and specific entropy of each component from the perspective of statistics. Under specific assumptions and conditions, the entropies of these components can satisfy the second law of thermodynamics independently. Our calculations show that the specific entropy of matter cannot be a constant during the expansion of the universe except for photons. When these components interact with the space-time background, there could exist the phenomenon of particle production (annihilation). We study the influence of the interaction on the entropies of these components, and obtain the conditions guaranteeing that the entropy of each component satisfies the second law of thermodynamics.
Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time series that linearly transforms the observed series into several groups of lower-dimensional multivariate subseries. These multivariate subseries have non-zero spectral coherence among components within a group but have zero spectral coherence among components across groups. The observed series is expressed as a sum of frequency components whose variances are proportional to the spectral matrices at the respective frequencies. The demixing matrix is then estimated using an eigendecomposition on the sum of the variance matrices of these frequency components and its asymptotic properties are derived. Finally, a consistent test on the cross-spectrum of pairs of components is used to find the desired segmentation into the lower-dimensional subseries. The numerical performance of the proposed method is illustrated through simulation examples and an application to modeling and forecasting wind data is presented.
The action potential propagating in a nerve fibre generates accompanying mechanical and thermal effects. The whole signal is therefore an ensemble which includes primary and secondary components. The primary components of a signal are the action potential itself and longitudinal mechanical waves in axoplasm and surrounding biomembrane. These components are characterized by corresponding velocities. The secondary components of a signal are derived from primary components and include transverse displacement of a biomembrane and the temperature -- these have no independent velocities but have been measured in several experiments. A robust mathematical model is presented based on differential equations describing the signal primary components which are coupled into a system by coupling forces. The model includes also mathematical formulation for establishing the secondary components following the ideas from experimental studies.
Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms, it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course, rarely happens in real life, where almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. Recently, Lustig and Vardi introduced dataflow and control-flow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while control-flow synthesis is decidable. In this work, we consider the problem of control-flow synthesis from libraries of probabilistic components . We show that this more general problem is also decidable.
The reuse at the component level is generally more effective than the one at the object-oriented class level. This is due to the granularity level where components expose their functionalities at an abstract level compared to the fine-grained object-oriented classes. Moreover, components clearly define their dependencies through their provided and required interfaces in an explicit way that facilitates the understanding of how to reuse these components. Therefore, several component identification approaches have been proposed to identify components based on the analysis object-oriented software applications. Nevertheless, most of the existing component identification approaches did not consider co-usage dependencies between API classes to identify classes/methods that can be reused to implement a specific scenario. In this paper, we propose an approach to identify reusable software components in object-oriented APIs, based on the interactions between client applications and the targeted API. As we are dealing with actual clients using the API, dynamic analysis allows to better capture the instances of API usage. Approaches using static analysis are usually limited by the difficulty
Which components of the singular value decomposition of a signal-plus-noise data matrix are most informative for the inferential task of detecting or estimating an embedded low-rank signal matrix? Principal component analysis ascribes greater importance to the components that capture the greatest variation, i.e., the singular vectors associated with the largest singular values. This choice is often justified by invoking the Eckart-Young theorem even though that work addresses the problem of how to best represent a signal-plus-noise matrix using a low-rank approximation and not how to best_infer_ the underlying low-rank signal component. Here we take a first-principles approach in which we start with a signal-plus-noise data matrix and show how the spectrum of the noise-only component governs whether the principal or the middle components of the singular value decomposition of the data matrix will be the informative components for inference. Simply put, if the noise spectrum is supported on a connected interval, in a sense we make precise, then the use of the principal components is justified. When the noise spectrum is supported on multiple intervals, then the middle components mig
Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such `exotic' components in moduli spaces of SO(p,q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO(p,q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO(2,q), with q> 3).
We generalize an earlier result of Segev, which shows that {\em some\/} component in a minimal counterexample to Quillen's conjecture must admit an outer automorphism. We show in fact that {\em every\/} component must admit an outer automorphism. Thus we transform his restriction-result on components to an elimination-result: namely one which excludes any component which does not admit an outer automorphism. Indeed we show that the outer automorphisms admitted must include $p$-outers: that is, outer automorphisms of order divisible by $p$. This gives stronger, concrete eliminations: for example if $p$ is odd, it eliminates sporadic and alternating components -- thus reducing to Lie-type components (and typically forcing $p$-outers of field type). For $p = 2$, we obtain similar but less restrictive results. We also provide some tools to help eliminate suitable components that do admit $p$-outers in a minimal counterexample.
We take a process component as a pair of an interface and a behaviour. We study the composition of interacting process components in the setting of process algebra. We formalize the interfaces of interacting process components by means of an interface group. An interesting feature of the interface group is that it allows for distinguishing between expectations and promises in interfaces of process components. This distinction comes into play in case components with both client and server behaviour are involved.
Utilizing third party software components in the development of new systems became somewhat unfavourable approach among many organizations nowadays. This reluctance is primarily built due to the lack of support to verify the quality attributes of software components in order to avoid potential mismatches with systems requirements. This paper presents an approach to overcome this problem by providing a tool support to check component compatibility to a specification provided by developers. So, components compatibility can be checked and developers can verify components that match their quality attributes prior of integrating them into their system.
In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well-suited for Bayesian density estimation, many investigators are using them for inferences about the number of components, by considering the posterior on the number of components represented in the observed data. We show that this posterior is not consistent --- that is, on data from a finite mixture, it does not concentrate at the true number of components. This result applies to a large class of nonparametric mixtures, including DPMs and PYMs, over a wide variety of families of component distributions, including essentially all discrete families, as well as continuous exponential families satisfying mild regularity conditions (such as multivariate Gaussians).
Time series with multiple periodically correlated components is a complex problem with comparatively limited prior research. Most existing time series models are designed to accommodate simple periodically correlated components and tend to be sensitive to over-parameterization and optimization issues and are also unable to model complex PC components patterns in a time series. Frequency separation techniques can be used to maintain the correlation structure of each specific PC component, whereas Bayesian techniques can combine new and existing prior information to update beliefs about these components. This study introduces a method to combine the frequency separation techniques and Bayesian techniques to forecast PC and MPC time series data in a two stage form which is expected to show the new method's suitability in modeling MPC components compared to classical methods.