Classical Representation Research Articles

Retargetable Optimizing Compilers for Quantum Accelerators via a Multilevel Intermediate Representation

We present a multilevel quantum–classical intermediate representation (IR) that enables an optimizing, retargetable compiler for available quantum languages. Our work builds upon the multilevel intermediate representation (MLIR) framework and leverages its unique progressive lowering capabilities to map quantum languages to the low-level virtual machine (LLVM) machine-level IR. We provide both quantum and classical optimizations via the MLIR pattern rewriting subsystem and standard LLVM optimization passes, and demonstrate the programmability, compilation, and execution of our approach via standard benchmarks and test cases. In comparison to other standalone language and compiler efforts available today, our work results in compile times that are 1,000× faster than standard Pythonic approaches, and 5–10× faster than comparative standalone quantum language compilers. Our compiler provides quantum resource optimizations via standard programming patterns that result in a 10× reduction in entangling operations, a common source of program noise. We see this work as a vehicle for rapid quantum compiler prototyping.

Violences subies, violences agies : la place de l’expression somatique du repérage à l’expertise

Being a victim of violence and neglect during childhood can expose minors to significant health repercussions on the physical, psychological, psycho-affective and neuro-developmental levels.. Self- and hetero-aggressive violences in all age groups are now considered to be possible consequences of these severe adverse experiences.The place of the body is essential in this context. The body, often considered as the only tangible and opposable marker of violence, has a singular and integral place in the psyche and overall health.It is an important vector in order for professionals to have access to the child. The examination of the body allows the expression of violence and its formulation from a very young age, especially during clinical examinations in situations of possible danger. It also “speaks” in situations of malaise, growth disorder, self or heteroaggressive acts. During the adolescence, it can also be attacked by scarification, dietary restrictions, mutilations, early and risky sexual activity, prostitution..By taking jointly both the body and the psyche, children and adolescents find a unity, are no longer fragmented. It is this unity that will allow the continuation of more specific care and more specifically child psychiatric support.This joint concern of paediatricians, general practitioners, child psychiatrists and psychologists will also ensure, particularly during adolescence, the continuation of health monitoring.It is essential to think about these collaborations from the first meeting with children and adolescents who are victims or perpetrators of violence.Encountering child and adolescent victims of violence confronts practitioners with a reality that is difficult to see and to conceive. Although the continuum between suffered violence and perpetrated violence seems to be better known today, these different situations remain difficult to understand and to manage. We believe that the violence that is perpetrated can be a screen for the causes of the violence and for the response to the needs of minors, particularly in terms of health.For practitioners, going to meet children and adolescents who are perpetrators of violence entails to be able to take a “step aside” from the classical representations of aggression or aggressiveness, whether they are directed towards third parties or towards the minor himself. Access to the somatic examination and medical history of these children or adolescents must be fully integrated from the first meeting. Associating health in all its aspects (somatic, psychic and social) then allows for specific care to be provided, regardless of their nature and place. This initial integrated practice allows us to take care of children and adolescents and highlights the notion of otherness that is undermined in situations of violence or neglect, particularly when they occur in the family environment. This initial joint somatic and psychological care in a single unit enables re-establishment of a dialogue with the minors and their parents. The shared competencies and the links that unite these different professionals together constitutes already therapeutic care.By reintroducing a dialogue about the children and adolescents and their overall health, the response to their needs can be perceived as a common and reachable objective that inscribes the minor in the temporality and extracts him or her from the immediacy of a punctually repressed act.

Idiopathic remitting seronegative symmetrical synovitis with pitting edema syndrome mimicking symptoms of polymyalgia rheumatica: a case report

BackgroundRemitting seronegative symmetrical synovitis with pitting edema is a rare rheumatic condition of the elderly population that is well described but whose mechanisms remain little studied. This syndrome is characterized by symmetrical swelling located mainly on the dorsal part of the hands and the feet. Because of possible heterogeneous clinical presentation, it can easily mimic the onset of other rheumatic diseases or appear associated with them. Here we report a case of a patient who developed remitting seronegative symmetrical synovitis with pitting edema with preexisting shoulder and hip girdle pain associated with progressive fatigue, indicating a possible differential diagnosis of polymyalgia rheumatica. We reviewed and compared classification for remitting seronegative symmetrical synovitis with pitting edema and polymyalgia rheumatica and discussed other differential diagnoses.Case presentationAn 84-year-old Caucasian woman presented to our General Medicine Unit with acute onset of symmetrical hands and feet edema, leading to functional limitation due to pain and stiffness. Additionally, she was complaining about neck, shoulder, and pelvic girdle pain present for about 2 months associated with worsening asthenia. Blood tests showed an elevated level of C-reactive protein and erythrocyte sedimentation rate, as well as absence of anti-cyclic citrullinated peptide antibodies and rheumatoid factor. As all criteria of remitting seronegative symmetrical synovitis with pitting edema syndrome were present, the patient was treated with low-dose prednisone, with a rapid and complete resolution of symptoms. She remains asymptomatic without treatment 2 years after the onset of symptoms, without any evident oncologic etiology.ConclusionsThis case is an example of a classic representation of remitting seronegative symmetrical synovitis with pitting edema syndrome with clinical elements suggesting a concomitant existing early stage of polymyalgia rheumatica. These two entities, classified in the group of seronegative arthritis, can coexist (up to 10% of cases), with remitting seronegative symmetrical synovitis with pitting edema appearing as an initial or late manifestation of polymyalgia rheumatica. It is essential to remind that remitting seronegative symmetrical synovitis with pitting edema is associated with a higher risk of cancer (30%). A proper diagnosis allows the clinician to precisely define the appropriate therapy duration to limit its side effects in the elderly and remain aware of the potential risk of underlying malignancy.

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. This paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

Learning hyperelastic anisotropy from data via a tensor basis neural network

Anisotropy in the mechanical response of materials with microstructure is common and yet is difficult to assess and model. To construct accurate response models given only stress–strain data, we employ classical representation theory, novel neural network layers, and L1 regularization. The proposed tensor-basis neural network can discover both the type and orientation of the anisotropy and provide an accurate model of the stress response. The method is demonstrated with data from hyperelastic materials with off-axis transverse isotropy and orthotropy, as well as materials with less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward neural networks and input-convex neural network formulations are developed and tested. Using the latter, a polyconvex potential can be established, which, by satisfying the necessary growth condition can guarantee the existence of boundary value problem solutions.

얼굴성 해체와 디지털 캐릭터 창출과의 접목 가능성 고찰

This paper examines the possibility that the discourse of dismantlement of faciality can be combined with character creation in the digital age by analyzing the facial images in Jean Dubuffet's Art Brut painting focusing on Gilles Deleuze's concept of 'faciality'. According to Deleuze, the face is a layer of linguistic expression deterritorialized from the body, and it is the mechanism of faciality that fixes humans to signifiance and subjectification by a single code that dominates Western civilization. This paper attempts to capture the prototype of the face that the mechanism of faciality do not penetrate through the raw image of faces in Art Brut, which breaks down the classical representation system. These informel faces of Art Brut and Deleuze's undecidable faces suggest the possibility of various expressions of face and body images through the undecidability between faciality and body, and the relationship with material objects. In other words, the deconstruction of faciality as claimed in this paper can open the infinite possibilities of creating digital characters with another vitality as a new approach to face representation.

The Backhaul Profit Maximization Problem: Optimization Models and Solution Procedures

We present a compact mixed integer program (MIP) for the backhaul profit maximization problem in which a freight carrier seeks to generate profit from an empty delivery vehicle’s backhaul trip from its last scheduled delivery to its depot by allowing it to deviate from the least expensive (or fastest) route to accept pickup-and-delivery requests between various points on the route as allowed by its capacity and required return time. The MIP is inspired by a novel representation of multicommodity flow that significantly reduces the size of the constraint matrix compared with a formulation based on the classical node-arc representation. This, in turn, leads to faster solution times when using a state-of-the-art MIP solver. In an empirical study of both formulations, problem instances with 10 potential pickup/drop-off locations and up to 72 pickup-and-delivery requests were solved an average 1.44 times faster in real time with our formulation, whereas instances with 20 locations and up to 332 pickup-and-delivery requests were solved an average of 11.88 times faster. The largest instances in the comparative study had 60 locations and up to 3,267 pickup-and-delivery requests; these instances required an average of more than 54 hours of real time to solve with the node-arc–based formulation but were solved in an average of under two hours of real time using our compact formulation. We also present a heuristic algorithm based on our compact formulation that finds near optimal solutions to each of the 60-location instances within 22 minutes of real time and near optimal solutions to instances with up to 80 locations within four and a half hours of real time.

Quantum to classical mapping of the two-dimensional toric code in an external field

Kitaev's toric code Hamiltonian in dimension D=2 has been extensively studied for its topological properties, including its quantum error correction capabilities. While the Hamiltonian is quantum, it lies within the class of models that admits a D+1-dimensional classical representation. In these notes, we provide details of a Suzuki-Trotter expansion of the partition function of the toric code Hamiltonian in the presence of an external magnetic field. By coupling additional degrees of freedom in the form of a matter field that can subsequently be gauged away, we explicitly derive a classical Hamiltonian on a cubic lattice which takes the form of a non-isotropic 3D Ising gauge theory.

Integrated Smart-Home Architecture for Supporting Monitoring and Scheduling Strategies in Residential Clusters

The monitoring of power consumption and the forecasting of load profiles for residential appliances are essential aspects of the control of energy savings/exchanges at multiple hierarchical levels: house, house cluster, neighborhood, and city. External environmental factors (weather conditions) and inhabitants’ behavior influence power consumption, and their usage as part of forecasting activity may lead to added value in the estimation of daily-load profiles. This paper proposes a distributed sensing infrastructure for supporting the following tasks: the monitoring of appliances’ power consumption, the monitoring of environmental parameters, the generation of records for a database that can be used for both identifying load models and testing load-scheduling algorithms, and the real-time acquisition of consumption data. The hardware/software codesign of an integrated architecture that can combine the typical distributed sensing and control networks present in modern buildings (targeting user comfort) with energy-monitoring and management systems is presented. Methods for generating simplified piecewise linear (PWL) representations of the load profiles based on these records are introduced and their benefits compared with classic averaged representations are demonstrated for the case of peak-shaving strategies. The proposed approach is validated through implementing and testing a smart-meter node with wireless communication and other wired/wireless embedded modules, enabling the tight integration of the energy-monitoring system into smart-home/building-automation systems. The ability of this node to process power measurements with a programable granularity level (seconds/minutes/hours) at the edge level and stream the processed measurement results at the selected granularity to the cloud is identified as a valuable feature for a large range of applications (model identification, power saving, prediction).

MATHEMATICAL MODEL OF MAINTENANCE OF SAMPLES OF WEAPONS AND MILITARY EQUIPMENT USING THE DISTRIBUTION OF TIME OF TROUBLE-FREE OPERATION OF PRODUCTS IN THE FORM OF WEIBUL'S LAW

The article considers the mathematical model of maintenance of samples of armaments and military equipment according to the state with parameter control, for which the distribution of time of trouble-free operation of weapons in the form of Weibul's law is used as a model of failures. Probable physical distributions have a certain advantage over simply probable distributions, because their parameters can be determined on the basis of both statistical characteristics of failures and analysis of failures of the physical process. In addition, diffusion distribution laws, such as diffusion-monotone and diffusion-nonmonotonic distributions, are now the most relevant. These facts have significant practical value, which determines the relevance of the research. Also, the article considers the dependences of the coefficient of technical use of the object on different characteristics of the service system and the object itself are determined. For the mathematical description of the processes inherent in the maintenance system, the apparatus of semi-Markov random processes in the classical representation is used. Weibul's distribution law is one of the least used due to its complexity. The main results of the work are obtained by numerical method. The dependences obtained as a result of the calculations show the existence of the optimal period of preventive maintenance of the object of control, in which the maximum value of its coefficient of technical use is achieved. The result of the work allows to establish the quantitative dependence of the coefficient of technical use on the reliability of control means, scale and form in the form of Weibul's distribution law in a wide range of periodicity of preventive maintenance.

Simulation of fully nonstationary random processes using generalized harmonic wavelets

Simulation of nonstationary random processes plays an important role to probabilistic response analysis of structures and systems under stochastic excitations via Monte Carlo methods. Based on the evolutionary spectral representation theory, this article proposes a novel approach to simulate one-dimensional nonstationary random processes by using generalized harmonic wavelet (GHW). According to the explicit relationship between the evolutionary power spectral density (EPSD) and GHW coefficients, the samples of a random process can be generated by superposing GHWs with stochastic phase angles. The attractive features of the proposed approach are (1) the sample time histories obtained by the proposed method can accurately match the target EPSD and reflect the evolutionary probabilistic characteristics of the random process, (2) the number of GHWs used in the simulation is fixed due to the constraint relationship between the frequency and time resolutions of GHWs, and (3) the proposed method has better computational efficiency than the classical spectrum representation method (SRM). To demonstrate the accuracy and efficiency of the proposed GHW-based approach, three case studies involving the generation of time history samples from a given EPSD model, the simulation of an actual earthquake record, and a comparison between the proposed method and the SRM are presented respectively.

Three alternative boundary integral flow representations for wave diffraction-radiation by offshore structures

Three alternatives to the classical boundary integral representation of diffraction-radiation of regular waves by large stationary bodies, such as offshore structures and moored ships, that underlies existing panel methods are defined. These three alternative flow representations are associated with two alternative linear flow models, called ‘free waterplane flow model’ and ‘rigid waterplane flow model’, of potential flow around an offshore structure in regular waves. As was shown previously, these two alternative linear flow models of diffraction-radiation of regular waves by stationary bodies yield identical boundary integral flow representations and are then consistent, although the rigid waterplane flow model precludes irregular frequencies. Moreover, this flow model – and mathematical transformations – yield two other boundary integral flow representations, so that three alternatives to the classical boundary integral flow representation used in existing panel methods are defined. These three alternative flow representations are weakly singular. The first of these flow representations, given previously, involves a surface integral over the waterplane inside the body, while the second flow representation involves a line integral around the waterline of the body, i.e. the intersection curve between the body and the undisturbed free surface. The third flow representation is of particular interest because it involves neither a surface integral over the waterplane nor a line integral around the waterline. Moreover, this boundary integral flow representation does not involve a distribution of dipoles over the body surface; indeed, it expresses the flow potential in terms of the normal and tangential components of the flow velocity at the surface of the body. It is also notable that this boundary integral flow representation is identical to the boundary integral representation previously obtained for flows around ships advancing at a constant speed in calm water or in regular waves, and thus provides a common basis for the analysis of three major classes of flows in ship and offshore hydrodynamics.

Graph-Based Integration of Histone Modification Profiles

In this work, we introduce a similarity-network-based approach to explore the role of interacting single-cell histone modification signals in haematopoiesis—the process of differentiation of blood cells. Histones are proteins that provide structural support to chromosomes. They are subject to chemical modifications—acetylation or methylation—that affect the degree of accessibility of genes and, in turn, the formation of different phenotypes. The concentration of histone modifications can be modelled as a continuous signal, which can be used to build single-cell profiles. In the present work, the profiles of cell types involved in haematopoiesis are built based on all the major histone modifications (i.e., H3K27ac, H3K27me3, H3K36me3, H3K4me1, H3K4me3, H3K9me3) by counting the number of peaks in the modification signals; then, the profiles are used to compute modification-specific similarity networks among the considered phenotypes. As histone modifications come as interacting signals, we applied a similarity network fusion technique to integrate these networks in a unique graph, with the aim of studying the simultaneous effect of all the modifications for the determination of different phenotypes. The networks permit defining of a graph-cut-based separation score for evaluating the homogeneity of subgroups of cell types corresponding to the myeloid and lymphoid phenotypes in the classical representation of the haematopoietic tree. Resulting scores show that separation into myeloid and lymphoid phenotypes reflects the actual process of haematopoiesis.

Stopping power of Hetero nuclear di-cluster ions from partial-wave analysis based on semi classical phase shifts


 We apply a semi classical partial-wave scattering method based on the induced density approach (IDA) model. For ion electron scattering, the transport cross section is used to calculate the energy loss. This method yields a non-perturbative exemplification of energy loss, bridging the difference among classical and quantal representations. The focus of this work is the interaction of hetero nuclear di-cluster (He-H) ions with a free gas. The results show three kinds of stopping power in (a.u) (cluster stopping power, self-stopping power and correlated stopping power) of hetero nuclear di-cluster ions (He-H) with velocity at different atomic di-cluster distances at different densities and temperatures. We find that Bragg’s peak of stopping power is directly proportional to density and temperatures and inversely with atomic di-cluster distance . The equations in present work are programmed in fortran-90 for numerical calculations.

Partial and Global Representations of Finite Groups

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from Dokuchaev et al. (J. Algebra 226(1), 505–532, 2000) (which correspond to the case H = {1G}), we develop further an effective theory that allows explicit computations. As a case study, we apply our theory to the symmetric group $\mathfrak {S}_{n}$ and its subgroup $\mathfrak {S}_{n-1}$ of permutations fixing 1: this provides a natural extension of the classical representation theory of $\mathfrak {S}_{n}$ .

Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems

This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described. A generating functional method to constructing irreducible current algebra representations is reviewed, and the ergodicity of the corresponding representation Hilbert space measure is mentioned. The algebraic properties of the so called coherent states are also reviewed, generated by cyclic representations of the Heisenberg algebra on Hilbert spaces. Unbelievable and impressive applications of coherent states to the theory of nonlinear dynamical systems on Hilbert spaces are described, along with their linearization and integrability. Moreover, we present a further development of these results within the modern Lie-algebraic approach to nonlinear dynamical systems on Poissonian functional manifolds, which proved to be both unexpected and important for the classification of integrable Hamiltonian flows on Hilbert spaces. The quantum current Lie algebra symmetry properties and their functional representations, interpreted as a universal algebraic structure of symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics on functional manifolds, are analyzed in detail. Based on the current algebra symmetry structure and their functional representations, an effective integrability criterion is formulated for a wide class of completely integrable Hamiltonian systems on functional manifolds. The related algebraic structure of the Poissonian operators and an effective algorithm of their analytical construction are described. The current algebra representations in separable Hilbert spaces and the factorized structure of quantum integrable many-particle Hamiltonian systems are reviewed. The related current algebra-based Hamiltonian reconstruction of the many-particle oscillatory and Calogero–Moser–Sutherland quantum models are reviewed and discussed in detail. The related quasi-classical quantum current algebra density representations and the collective variable approach in equilibrium statistical physics are reviewed. In addition, the classical Wigner type current algebra representation and its application to non-equilibrium classical statistical mechanics are described, and the construction of the Lie–Poisson structure on the phase space of the infinite hierarchy of distribution functions is presented. The related Boltzmann–Bogolubov type kinetic equation for the generating functional of many-particle distribution functions is constructed, and the invariant reduction scheme, compatible with imposed correlation functions constraints, is suggested and analyzed in detail. We also review current algebra functional representations and their geometric structure subject to the analytical description of quasi-stationary hydrodynamic flows and their magneto-hydrodynamic generalizations. A unified geometric description of the ideal idiabatic liquid dynamics is presented, and its Hamiltonian structure is analyzed. A special chapter of the review is devoted to recent results on the description of modified current Lie algebra symmetries on torus and their Lie-algebraic structures, related to integrable so-called heavenly type spatially many-dimensional dynamical systems on functional manifolds.

A probabilistic framework for particle-based reaction–diffusion dynamics using classical Fock space representations

The modeling and simulation of stochastic reaction–diffusion processes is a topic of steady interest that is approached with a wide range of methods. At the level of particle-resolved descriptions, where chemical reactions are coupled to the spatial diffusion of individual particles, there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is relatively underdeveloped. The aim of this paper is to provide a framework to systematically formulate the probabilistic evolution equation, termed chemical diffusion master equation (CDME), that governs particle-based stochastic reaction–diffusion processes. To account for the non-conserved and unbounded particle number of this type of open systems, we employ a classical analogue of the quantum mechanical Fock space that contains the symmetrized probability densities of the many-particle configurations in space. Following field-theoretical ideas of second quantization, we introduce creation and annihilation operators that act on single-particle densities and provide natural representations of symmetrized probability densities as well as of reaction and diffusion operators. These operators allow us to consistently and systematically formulate the CDME for arbitrary reaction schemes. The resulting form of the CDME further serves as the foundation to derive more coarse-grained descriptions of reaction–diffusion dynamics. In this regard, we show that a discretization of the evolution equation by projection onto a Fock subspace generated by a finite set of single-particle densities leads to a generalized form of the well-known reaction–diffusion master equation, which supports non-local reactions between grid cells and which converges properly in the continuum limit.

CLIFF CHANGE DETECTION USING SIAMESE KPCONV DEEP NETWORK ON 3D POINT CLOUDS

Abstract. Mainly depending on their lithology, coastal cliffs are prone to changes due to erosion. This erosion could increase due to climate change leading to potential threats for coastal users, assets, or infrastructure. Thus, it is important to be able to understand and characterize cliff face changes at fine scale. Usually, monitoring is conducted thanks to distance computation and manual analysis of each cliff face over 3D point clouds to be able to study 3D dynamics of cliffs. This is time consuming and inclined to each one judgment in particular when dealing with 3D point clouds data. Indeed, 3D point clouds characteristics (sparsity, impossibility of working on a classical top view representation, volume of data, …) make their processing harder than 2D images. Last decades, an increase of performance of machine learning methods for earth observation purposes has been performed. To the best of our knowledge, deep learning has never been used for 3D change detection and categorization in coastal cliffs. Lately, Siamese KPConv brings successful results for change detection and categorization into 3D point clouds in urban area. Although the case study is different by its more random characteristics and its complex geometry, we demonstrate here that this method also allows to extract and categorize changes on coastal cliff face. Results over the study area of Petit Ailly cliffs in Varengeville-sur-Mer (France) are very promising qualitatively as well as quantitatively: erosion is retrieved with an intersection over union score of 83.86 %.

Simulation of non-stationary and non-Gaussian random processes by 3rd-order Spectral Representation Method: Theory and POD implementation

This paper introduces the 3rd-order Spectral Representation Method for simulation of non-stationary and non-Gaussian stochastic processes. The proposed method extends the classical 2nd-order Spectral Representation Method to expand the stochastic process from an evolutionary bispectrum and an evolutionary power spectrum, thus matching the process completely up to third-order. A Proper Orthogonal Decomposition (POD) approach is further proposed to enable an efficient FFT-based implementation that reduces computational cost significantly. Two examples are presented, including the simulation of a fully non-stationary seismic ground motion process, highlighting the accuracy and efficacy of the proposed method.

Verifying Provable Stability Domains for Discrete-Time Systems Using Ellipsoidal State Enclosures

Stability contractors, based on interval analysis, were introduced in recent work as a tool to verify stability domains for nonlinear dynamic systems. These contractors rely on the property that - in case of provable asymptotic stability - a certain domain in a multi-dimensional state space is mapped into its interior after a certain integration time for continuous-time processes or after a certain number of discretization steps in a discrete-time setting. However, a disadvantage of the use of axis-aligned interval boxes in such computations is the omnipresent wrapping effect. As shown in this contribution, the replacement of classical interval representations by ellipsoidal domain enclosures reduces this undesirable effect. It also helps to find suitable ratios for the edge lengths if interval-based domain representations are investigated. Moreover, ellipsoidal domains naturally represent the possible regions of attraction of asymptotically stable equilibrium points that can be analyzed with the help of quadratic Lyapunov functions, for which stability criteria can be cast into linear matrix inequality (LMI) constraints. For that reason, this paper further presents possible interfaces of ellipsoidal enclosure techniques with LMI approaches. This combination aims at the maximization of those domains that can be proven to be stable for a discrete-time range-only localization algorithm in robotics. There, an Extended Kalman Filter (EKF) is applied to a system for which the dynamics are characterized by a discrete-time integrator disturbance model with additive Gaussian noise. In this scenario, the measurement equations correspond to the distances between the object to be localized and beacons with known positions.