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[Display omitted] Transition metal phosphides have been demonstrated to be promising non-noble catalysts for water splitting, yet their electrocatalytic performance is impeded by unfavorable free energies of adsorbed intermediates. The achievement of nanoscale modulation in morphology and electronic states is imperative for enhancing their intrinsic electrocatalytic activity. Herein, we propose a strategy to expedite the water splitting process over NiCoP/FeNiCoP hollow ellipsoids by modulating the electronic structure and d-band center. These unique phosphorus (P) vacancies-rich ellipsoids are synthesized through an ion-exchange reaction between uniform NiCo-nanoprisms and K 3 [Fe(CN) 6 ], followed by NaH 2 PO 2 -assisted phosphorization under N 2 atmosphere. Various characterizations reveals that the titled catalyst possesses high specific surface area, abundant porosity, and accessible inner surfaces, all of which are beneficial for efficient mass transfer and gas diffusion. Moreover, density functional theory (DFT) calculations further confirms that the NiCoP/FeNiCoP heterojunction associated with P vacancies regulate the electronic structures of d-electrons and p-electrons of Co and P atoms, respectively, resulting in a higher desorption efficiency of adsorbed H* intermediates with a lower energy barrier for water splitting. Due to the aforementioned advantages, the resultant NiCoP/FeNiCoP hollow ellipsoids exhibit remarkably low overpotentials of 45 and 266 mV for hydrogen and oxygen evolution reaction to achieve the current densities of 10 and 50 mA cm−2, respectively. This work not only reports the synthesis of a hollow double-shell structure of NiCoP/FeNiCoP but also introduces a novel strategy for constructing a multifunctional electrocatalyst for water splitting. [ABSTRACT FROM AUTHOR]

The present study focuses on controller design for high-order fully actuated systems that experience input saturation and are affected by bounded disturbances, such as nonlinear uncertainties and time-varying unknown parameters. A saturated adaptive controller is developed via the fully actuated system approach and the Lyapunov stability theory to achieve output control and reject disturbances. The disturbances are treated as an extended state and then estimated by introducing an extended state observer. An adaptive variable is used to handle the estimation error between the actual and estimated values of the disturbances. An auxiliary system is designed to mitigate the saturation effect. Lyapunov's direct method verifies that the estimation error, the tracking error, the adaptive state, and the auxiliary system state will eventually stabilise within a bounded ellipsoid. An illustration of spacecraft attitude control demonstrates the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Our objective is to construct a model of the velocity ellipsoid and the retrieved Solar velocity for two programs of ultra-cool L dwarfs with 49 points (UCDs 49) and 39 points (UCDs 39) within 85◦ ≥ b ≥ -85◦. Firstly, we calculated the velocity dispersion (σ1, σ2, σ3; km s-1) ratios (σ2/σ1 = 0.78 ± 0.06; UCDs 49 &0.79 ± 0.05; UCDs 39) and (σ3/σ1 = 0.41 ± 0.04; UCDs 49 & 0.51 ± 0.03; UCDs 39), the vertex longitude (l2) which has often differed significantly from zero in many analyses (i.e., l2 = -0◦8967; UCDs 49 & -0.4454; UCDs 39). Here, we have computed the Solar velocity (S⊙; km s-1) as (32.13±0.18; UCDs 49 & 21.73± 0.22) and the other Solar elements (lA, bA). Finally, we have computed Oort's constants (A,B; km s-1 kpc1) and the angular velocities for UCDs 49 and UCDs 39 programs where their numerical values are in the same manner. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces. Design/methodology/approach: The research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality. Findings: The study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions. Originality/value: This study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models. [ABSTRACT FROM AUTHOR]

Collision avoidance presents a challenging problem for multi-segment continuum robots owing to their flexible structure, limited workspaces, and restricted visual feedback, particularly when they are used in teleoperated minimally invasive surgery. This study proposes a comprehensive control framework that allows these continuum robots to automatically avoid collision and self-collision without interfering with the surgeon's control of the end effector's movement. The framework implements the early detection of collisions and active avoidance strategies by expressing the body geometry of the multi-segment continuum robot and the differential kinematics of any cross-section using screw theory. With the robot's parameterized shape and selected checkpoints on the obstacle's surface, we can determine the minimum distance between the robot and arbitrary obstacle, and locate the nearest point on the robot. Furthermore, we expand the null-space-based control method to accommodate redundant, non-redundant, and multiple continuum robots. An assessment of the avoidance capability is provided through an instantaneous and global criterion based on ellipsoids and possible movement ranges. Simulations and physical experiments involving continuum robots of different degrees of freedom performing various tasks were conducted to thoroughly validate the proposed framework. The results demonstrated its feasibility and effectiveness in minimizing the risk of collisions while maintaining the surgeon's control over the end effector. [ABSTRACT FROM AUTHOR]

Knot filtered embedded contact homology was first introduced by Hutchings in 2015; it has been computed for the standard transverse unknot in irrational ellipsoids by Hutchings and for the Hopf link in lens spaces L(n,n−1)$L(n,n-1)$ via a quotient by Weiler. While toric constructions can be used to understand the ECH chain complexes of many contact forms adapted to open books with binding the unknot and Hopf link, they do not readily adapt to general torus knots and links. In this paper, we generalize the definition and invariance of knot filtered embedded contact homology to allow for degenerate knots with rational rotation numbers. We then develop new methods for understanding the embedded contact homology chain complex of positive torus knotted fibrations of the standard tight contact 3‐sphere in terms of their presentation as open books and as Seifert fiber spaces. We provide Morse–Bott methods, using a doubly filtered complex and the energy filtered perturbed Seiberg–Witten Floer theory developed by Hutchings and Taubes, and use them to compute the T(2,q)$T(2,q)$ knot filtered embedded contact homology, for q$q$ odd and positive. [ABSTRACT FROM AUTHOR]

We construct integrable Hamiltonian systems with magnetic fields of the ellipsoidal, paraboloidal and conical type, i.e. systems that generalize natural Hamiltonians separating in the respective coordinate systems to include nonvanishing magnetic field. In the ellipsoidal and paraboloidal case each this classification results in three one–parameter families of systems, each involving one arbitrary function of a single variable and a parameter specifying the strength of the magnetic field of the given fully determined form. In the conical case the results are more involved, there are two one–parameter families like in the other cases and one class which is less restrictive and so far resists full classification. [ABSTRACT FROM AUTHOR]

Let |$K$| be a smooth, origin-symmetric, strictly convex body in |${\mathbb{R}}^{n}$|⁠. If for some |$\ell \in \textrm{GL}(n,{\mathbb{R}})$|⁠ , the anisotropic Riemannian metric |$\frac{1}{2}D^{2} \left \Vert \cdot \right \Vert_{\ell K}^{2}$|⁠ , encapsulating the curvature of |$\ell K$|⁠ , is comparable to the standard Euclidean metric of |${\mathbb{R}}^{n}$| up-to a factor of |$\gamma> 1$|⁠ , we show that |$K$| satisfies the even |$L^{p}$| -Minkowski inequality and uniqueness in the even |$L^{p}$| -Minkowski problem for all |$p \geq p_{\gamma }:= 1 - \frac{n+1}{\gamma }$|⁠. This result is sharp as |$\gamma \searrow 1$| (characterizing centered ellipsoids in the limit) and improves upon the classical Minkowski inequality for all |$\gamma < \infty $|⁠. In particular, whenever |$\gamma \leq n+1$|⁠ , the even log-Minkowski inequality and uniqueness in the even log-Minkowski problem hold. [ABSTRACT FROM AUTHOR]

Let K ⊂ R d be a convex body. Let X1,... , Xk, where k ≤ d, be random points independently and uniformly chosen in K, and let ξk be a uniformly distributed random linear k-plane. It is proved that if p ≥ −d + k + 1, then E K ∩ ξ k d + p ≤ c d , k , p · K k E conv 0 , X 1 , ⋯ , X k p , where | · | and conv denote the volume of the corresponding dimension and the convex hull, respectively. The constant cd,k,p is such that if k > 1, then the equality holds if and only if K is an ellipsoid centered at the origin, and if k = 1, then the inequality turns to equality. The inequality reduces to the Busemann intersection inequality if p = 0 and to the Busemann random simplex inequality if k = d. An affine version of this inequality which in a similar way generalizes the Schneider inequality and the Blaschke-Grömer inequality is also presented. [ABSTRACT FROM AUTHOR]

Land and sea vertical datums have traditionally been separate reference levels, due to the different methodologies and observations used in their derivations. However, the need for a seamless connection of these datums has become important due to a wide range of applications in the coastal zone. This study evaluates existing methods, oceanographic and geodetic models and observations for the development of an operational model of coastal heights called AUSHYDROID. We use a complex study area in north west Australia to gain a new insight into how accurately the separation between the lowest astronomical tide (LAT) and a reference ellipsoid can be estimated from existing models, which could form the basis of a national AUSHYDROID model for Australia. Our results are the first attempt to use this combination of existing data in this location, suggesting that ellipsoidal heights of LAT can be estimated to an accuracy of ∼0.2 m at the coast, with the combination of DTU18MSS and FES2014b having the lowest RMS of 0.125 m. However, in some complex coastline areas such as bays and estuaries, the differences increase to >0.5 m so that additional tide gauge observations with GNSS levelling connections and improved models are needed in these regions. [ABSTRACT FROM AUTHOR]

Four new wood-inhabiting fungi, Trechispora albofarinosa, T. bisterigmata, T. pileata and T. wenshanensis spp. nov., are proposed based on a combination of morphological features and molecular evidence. Trechispora albofarinosa is characterized by the farinose basidiomata with flocculence hymenial surface, a monomitic hyphal system with clamped generative hyphae, and ellipsoid, warted basidiospores. Trechispora bisterigmata is characterized by the membranous basidiomata with odontioid hymenial surface, rhizomorphic sterile margin, barrelled basidia and subglobose to broad ellipsoid, smooth basidiospores. Trechispora pileata is characterized by the laterally contracted base, solitary or imbricate basidiomata, fan shaped pileus, radially striate-covered surface with appressed scales, odontioid hymenophore surface, and subglobose to broad ellipsoid, thin-walled, smooth basidiospores. Trechispora wenshanensis is characterized by a cottony basidiomata with a smooth hymenial surface, and ellipsoid, thin-walled, warted basidiospores. Sequences of ITS and LSU marker of the studied samples were generated, and phylogenetic analyses were performed with the maximum likelihood, maximum parsimony, and Bayesian inference methods. The phylogenetic tree inferred from the ITS+nLSU sequences highlighted that four new species were grouped into the genus Trechispora. [ABSTRACT FROM AUTHOR]

The aim of this study is the determination of the best fit ellipsoid to given points by quaternions. The problem of the fitting ellipsoid is frequently encountered in image processing, computer games, medicine, engineering and science applications, geodesy, etc. The ellipsoid fitting problem is the process of determining the ellipsoid that best fits a given set of points in 3D. In the fitting process, it is generally done over two models. The first of these is the algebraic method and the second one is orthogonal (geometric) method. In this study, we tried to solve the problem of algebraic and orthogonal ellipsoid fitting based on Euler angles for the first time over quaternions. The superiority of quaternions over Euler rotation angles is well known. In addition, the variance–covariance matrix of the parameters of the fitted ellipsoid will also be calculated. Numerical applications show that the proposed method can be used successfully. [ABSTRACT FROM AUTHOR]

Ellipsoidal orthogonal curvilinear coordinates referred to a triaxial reference ellipsoid are not used in geodesy perhaps because of their theoretical complexity. However, many surveying and geodetic problems could be resolved by simply transforming variables between local frames. Herein it is shown that the computations of local displacements and variance-covariance matrices referred to currently used local curvilinear geodetic coordinate frames gives approximately the same answers than when referred to local ellipsoidal (triaxial) curvilinear frames. The theoretical procedures to obtain the required transformations between local geodetic and local ellipsoidal (triaxial) frames are introduced and examples explained. [ABSTRACT FROM AUTHOR]

In this longitudinal retrospective image analysis, conducted on patients diagnosed with dry age-related macular degeneration (AMD) and 5 years of follow-up imaging data, the study aimed to investigate the relationship between ellipsoid zone (EZ) integrity on spectral domain optical coherence tomography (SD-OCT) and visual acuity (VA). Using a machine learning-enabled feature extraction tool, quantitative EZ parameters were derived from SD-OCT images. The analysis revealed significant correlations between EZ integrity metrics and VA. Eyes with excellent VA (≥20/25 Snellen) exhibited higher EZ integrity, including less EZ attenuation, thicker ellipsoid zone-retinal pigment epithelium (EZ-RPE) thickness, and higher EZ intensity, in contrast to eyes with worse VA (≤20/40 Snellen). Additionally, eyes with geographic atrophy (GA) in the foveal region displayed compromised EZ integrity compared to those without GA. Notably, baseline EZ integrity metrics were predictive of future VA loss. These findings suggest that quantitative SD-OCT measurements of EZ integrity could potentially detect early changes in dry AMD and serve as valuable indicators for predicting future functional outcomes. Furthermore, these measurements hold promise for use in clinical trial screenings, offering insights into the progression of the disease and its impact on visual acuity. This study underscores the importance of EZ integrity assessment in understanding and managing dry AMD. [ABSTRACT FROM AUTHOR]

Background: Screening for hydroxychloroquine (HCQ) retinopathy is crucial to detecting early disease. A novel machine-learning-based optical coherence tomography (OCT) biomarker, Ellipsoid Zone (EZ) At-Risk, can quantitatively measure EZ alterations and at-risk areas for progressive EZ loss in a fully automated fashion. The purpose of this analysis was to compare the EZ At-Risk burden in eyes with HCQ toxicity to eyes without toxicity. Methods: IRB-approved image analysis study of 83 subjects on HCQ and 44 age-matched normal subjects. SD-OCT images were reviewed for evidence of HCQ retinopathy. A ML-based, fully automatic measurement of the percentage of the macular area with EZ At-Risk was performed. Results: The mean age for HCQ subjects was 67.1 ± 13.2 years and 64.2 ± 14.3 years for normal subjects. The mean EZ At-Risk macular burden in the "toxic" group (n = 38) was significantly higher (10.7%) compared to the "non-toxic" group (n = 45; 2.2%; p = 0.023) and the "normal" group (1.4%; p = 0.012). Additionally, the amount of EZ At-Risk burden was significantly correlated with the HCQ dose based on the actual (p = 0.016) and ideal body weight (p = 0.033). Conclusions: The novel biomarker EZ-At Risk was significantly higher in subjects with evidence of HCQ retinopathy as well as significantly associated with HCQ dose. This novel biomarker should be further evaluated as a potential screening tool for subjects on HCQ. [ABSTRACT FROM AUTHOR]

The realization of high interconnect densities for three-dimensional integration demands development of new wafer-to-wafer bonding approaches. Recently introduced Cu-to-Cu wafer-to-wafer hybrid bonding schemes overcome scaling limitations, but like other Cu-based interconnect structures, they are prone to electromigration. Migration and growth of voids, induced by electromigration and mechanical stress, cause Cu-to-Cu hybrid bonds to fail. A comprehensive modeling approach is required to fully understand the complex dynamics of voids with their influencing factors, such as current density, temperature, and mechanical stress. In this work, we utilize such a modeling approach to perform studies of void migration through Cu-to-Cu hybrid bonds. The calculated velocities of the evolving void surface fully correspond to the experimentally observed behavior of voids migrating from the lower pad to the upper diffusion barrier of the upper pad, where they cause electrical failure. The migration velocity of a void in the upper pad is 20% higher than the migration velocity of a void in the bottom pad. Unbalance of the normal velocity distribution at the void surface leads to the transformation of the originally ellipsoid void into a teardrop shape. The simulations provide full insight in the impact of layout geometry, material properties, and operating conditions on void dynamics. In addition, the results enable targeted adjustments of the influencing factors to inhibit void migration and growth in order to delay or to fully prevent Cu-to-Cu hybrid bond failure. [ABSTRACT FROM AUTHOR]

Trajectory-based methods that propagate classical nuclei on multiple quantum electronic states are often used to simulate nonadiabatic processes in the condensed phase. A long-standing problem of these methods is their lack of detailed balance, meaning that they do not conserve the equilibrium distribution. In this article, we investigate ideas for restoring detailed balance in mixed quantum–classical systems by tailoring the previously proposed spin-mapping approach to thermal equilibrium. We find that adapting the spin magnitude can recover the correct long-time populations but is insufficient to conserve the full equilibrium distribution. The latter can however be achieved by a more flexible mapping of the spin onto an ellipsoid, which is constructed to fulfill detailed balance for arbitrary potentials. This ellipsoid approach solves the problem of negative populations that has plagued previous mapping approaches and can therefore be applied also to strongly asymmetric and anharmonic systems. Because it conserves the thermal distribution, the method can also exploit efficient sampling schemes used in standard molecular dynamics, which drastically reduces the number of trajectories needed for convergence. The dynamics does however still have mean-field character, as is observed most clearly by evaluating reaction rates in the golden-rule limit. This implies that although the ellipsoid mapping provides a rigorous framework, further work is required to find an accurate classical-trajectory approximation that captures more properties of the true quantum dynamics. [ABSTRACT FROM AUTHOR]

With the development of high-performance computing technology, the number of scientific publications regarding computational modelling of applications with the Discrete Element Method/Modelling (DEM) approaches in agricultural engineering has risen in the past decades. Many granular materials, e.g. grains, fruits and soils in agricultural engineering are processed, and thus a better understanding of these granular media with DEM is of great significance in design and optimization of tools and process in agricultural engineering. In this review, the theory and background of DEM have been introduced. Some improved contact models discussed in the literature for accurately predicting the contact force between two interacting particles have been compared. Accurate approximation of irregular particle shapes is of great importance in DEM simulations to model real particles in agricultural engineering. New algorithms to approximate irregular particle shapes, e.g. overlapping multi-sphere approach, ellipsoid, etc., have been summarized. Some remarkable engineering applications of the improved numerical models developed and implemented in DEM are discussed. Finally, potential applications of DEM and some suggested further works are addressed in the last section of this review. [ABSTRACT FROM AUTHOR]

Besides amplitude variation, phase variation of seismic wave is also an important carrier of geological information at the fault slip interface. To analyze the seismic propagation through the fault slip interface, which is assumed to be a flat, horizontal and imperfectly welded contact (nonwelded) interface between two different tilted anisotropic (TTI) media, we derived the analytical formulae for amplitude and phase variations of reflected and transmitted seismic waves with longitudinal wave (qP), the slow and fast waves (qS and SH) generated simultaneously. The derived formulae could satisfy the fracture model, in which the symmetry axis planes of the upper and lower media coincide. Also, we provided the exact and approximate methods for velocities and polarizations as well as the reflected and transmitted angles based on the slowness ellipsoid. Moreover, weakly anisotropic parameters are taken into consideration by the approximate amplitude (AVO) and phase formulae of qP and qS. The approximations also clearly show the effect of anisotropic parameters on the amplitude and phase change. The derived results show that the compliance parameters affect the phase change rather than amplitude, while anisotropic parameters affect both. The numerical model shows that with respect to the incident P-wave, the phase change of the reflected qP wave is more significant than the other generating waves due to the linear slip boundary; the coefficients could be used to determine the fracture dip and strike; the frequency hardly affects the real part of the coefficient, while the imaginary part of the coefficient. Moreover, the derived formulae for phase change will contribute to the seismic inversion with the formulae for amplitude variation simultaneously. [ABSTRACT FROM AUTHOR]

We investigated three-dimensional (3D) eyeball protrusion and its association with the offset between the lamina cribrosa (LC) and Bruch's membrane opening (BMO). 3D-MRI scans were taken from 93 subjects (186 eyes). An ellipsoid was fitted along the posterior 2/3 contour of each eyeball. Eyeball asymmetry with focal bulging was determined by the existence of an adjacent outward protrusion/reciprocal inward depression pair, and the angular deviation of the outermost protruded point (OPP) was measured from the nasal side of the fovea-BMO axis. The LC/BMO offset was evaluated by measuring the central retinal vascular trunk (CRVT) location from the BMO center: (1) the angular deviation and (2) the offset index as the ratio between the CRVT-BMO center distance and the BMO radius in the same direction. Seventy-nine eyes (42%) were classified as having eyeball asymmetry, which had a more superior LC/BMO offset (P < 0.001) and a larger offset index (P = 0.002). In those eyes, the angular deviation of the OPP showed a significant correlation with that of the LC/BMO offset (r = -0.724, P < 0.001), as did protrusion depth with the offset index (r = 0.291, P = 0.009). The presence of eyeball asymmetry was associated with superior LC/BMO offset (P = 0.004) and larger offset index (P = 0.009). Superior LC/BMO offset was associated with older age (P < 0.001), shorter axial length (P < 0.001) and inferior location of OPP (P < 0.001). The location and extent of focal bulging were closely associated with those of LC/BMO offset. This indicates that focal bulging during expansion might be associated with diverse directionality of LC/BMO offset. [ABSTRACT FROM AUTHOR]

The genus Favolaschia within the family Mycenaceae is characterised by the gelatinous basidiomata with poroid hymenophore and most species inhabit monocotyledonous plants. In this study, many samples covering a wide geographic range in China were examined morphologically and phylogenetically using concatenated ITS1-5.8S-ITS2-nLSU sequence data. Three new species clustering in Favolaschia sect. Anechinus, namely Favolaschia imbricata, F. miscanthi and F. sinarundinariae, are described. Favolaschia imbricata is characterised by imbricate basidiomata with pale grey to greyish colour when fresh and broadly ellipsoid basidiospores measuring 7–9 × 5–6.8 µm; F. miscanthi is characterised by satin white basidiomata when fresh, broadly ellipsoid basidiospores measuring 7.5–10 × 5.5–7 µm and inhabit rotten Miscanthus; F. sinarundinariae is characterised by greyish-white basidiomata when fresh, dark grey near the base upon drying, broadly ellipsoid to subglobose basidiospores measuring 7–9 × 5–7 µm and inhabit dead Sinarundinaria. The differences amongst the new species and their morphologically similar and phylogenetically related species are discussed. In addition, an updated key to 19 species of Favolaschia found in China is provided. [ABSTRACT FROM AUTHOR]

Purpose: Additive Manufacturing (AM) conventionally necessitates an intermediary slicing procedure using the standard tessellation language (STL) data, which can be computationally burdensome, especially for intricate microcellular architectures. This study aims to propose a direct slicing method tailored for digital light processing-type AM processes for the efficient generation of slicing data for microcellular structures. Design/methodology/approach: The authors proposed a direct slicing method designed for microcellular structures, encompassing micro-lattice and triply periodic minimal surface (TPMS) structures. The sliced data of these structures were represented mathematically and then convert into 2D monochromatic images, bypassing the time-consuming slicing procedures required by 3D STL data. The efficiency of the proposed method was validated through data preparations for lattice-based nasopharyngeal swabs and TPMS-based ellipsoid components. Furthermore, its adaptability was highlighted by incorporating 2D images of additional features, eliminating the requirement for complex 3D Boolean operations. Findings: The direct slicing method offered significant benefits upon implementation for microcellular structures. For lattice-based nasopharyngeal swabs, it reduced data size by a factor of 1/300 and data preparation time by a factor of 1/8. Similarly, for TPMS-based ellipsoid components, it reduced data size by a factor of 1/60 and preparation time by a factor of 1/16. Originality/value: The direct slicing method allows for bypasses the computational burdens associated with traditional indirect slicing from 3D STL data, by directly translating complex cellular structures into 2D sliced images. This method not only reduces data volume and processing time significantly but also demonstrates the versatility of sliced data preparation by integrating supplementary features using 2D operations. [ABSTRACT FROM AUTHOR]

Algorithms for generating uniform random points on a triaxial ellipsoid are non-trivial to verify because of the non-analytical form of the surface area. In this paper, a formula for the surface area of an ellipsoidal patch is derived in the form of a one-dimensional numerical integration problem, where the integrand is expressed using elliptic integrals. In addition, analytical formulae were obtained for the special case of a spheroid. The triaxial ellipsoid formula was used to calculate patch areas to investigate a set of surface sampling algorithms. Particular attention was paid to the efficiency of these methods. The results of this investigation show that the most efficient algorithm depends on the required coordinate system. For Cartesian coordinates, the gradient rejection sampling algorithm of Chen and Glotzer is best suited to this task, when paired with Marsaglia's method for generating points on a unit sphere. For outputs in polar coordinates, it was found that a surface area rejection sampler is preferable. [ABSTRACT FROM AUTHOR]

A new edaphic green alga, Oedocladium sahyadricum sp. nov was identified from a natural forest in Kerala, India. In the present study, the new species is described and compared with its related species. The primary distinguishing characteristics of O. sahyadricum include its dioecious and terrestrial nature, superior operculum, ellipsoid oogonium, and oospore. The study highlights the presence of Oedocladium in Kerala and emphasize the need for exploration of soil algae to further understand the diversity of this genus. [ABSTRACT FROM AUTHOR]

In the past decade, there has been significant attention on the sudden transition and freezing phenomena of quantum correlations in open system dynamics. In this study, we aim to explore how the quantum steering ellipsoid can be used to characterize the sudden transition of decoherence. Our findings reveal that the shape of the quantum steering ellipsoid undergoes a qualitative change at the transition point during the decoherence process under two commonly encountered noise channels. This observation provides valuable insights into the connection between the sudden transition of decoherence and the geometric properties of the quantum steering ellipsoid. We gain a deeper understanding of this relationship by visually analyzing the changes in the ellipsoid's shape. Additionally, we compare these results with those obtained using the one-norm geometric quantum discord. This comparison further validates the significance of the sudden transition observed in the quantum steering ellipsoid and highlights the advantages of using this geometric measure. Overall, our study contributes to the understanding of quantum correlations in open systems and provides a visually appealing and intuitive way to analyze the sudden transitions of decoherence using the quantum steering ellipsoid. [ABSTRACT FROM AUTHOR]

Let n ≥ 3 and let K ⊂ ℝn be a convex body. A point p ∈ int K is said to be a Larman point of K if for every hyperplane Π passing through p, the section Π ∩ K has an (n – 2)-plane of symmetry. If p is a Larman point of K and for every section Π ∩ K, p is in the corresponding (n – 2)-plane of symmetry, then we call p a revolution point of K. We conjecture that if K contains a Larman point which is not a revolution point, then K is either an ellipsoid or a body of revolution. This generalizes a conjecture of Bezdek for n = 3. We prove several results related to the conjecture for strictly convex origin symmetric bodies. Namely, if K ⊂ ℝn is a strictly convex origin symmetric body that contains a revolution point p which is not the origin, then K is a body of revolution. This generalizes the False Axis of Revolution Theorem in [7]. We also show that if p is a Larman point of K ⊂ ℝ3 and there exists a line L such that p ∉ L and, for every plane Π passing through p, the line of symmetry of the section Π ∩ K intersects L, then K is a body of revolution (in some cases, K is a sphere). We obtain a similar result for projections of K. Additionally, for K ⊂ ℝn with n ≥ 4, we show that if every hyperplane section or projection of K is a body of revolution and K has a unique diameter D, then K is a body of revolution with axis D. [ABSTRACT FROM AUTHOR]

In this paper, we address the comment provided by Zheng and Palffy-Muhoray regarding our previous work on computing the closest approach distance of two ellipsoids. Additionally, we present experimental results that assess the numerical error bounds in the authors' own implementation of the analytic solution for the closest approach distance of two ellipses. We report very rare cases where the closest approach distances of two ellipses are erroneously calculated as zero, which is impossible given that the radii of the ellipses are not zero. [ABSTRACT FROM AUTHOR]

Ellipsoidal plasmonic particles are of huge importance in the biosensing field due to their orientation-specific light scattering properties and higher area of surface-adhesive interactions. In this paper, we present a computational investigation of the orientation-specific plasmonic properties of graphene-wrapped—Au nano ellipsoids of various aspect ratios and graphene layer thicknesses using the discontinuous Galerkin time domain (DGTD) method. We could observe that both the dipolar and quadrapolar resonances of Au ellipsoids are strongly modulated by graphene layer. Furthermore, we have modelled graphene wrapped Au ellipsoidal nanoarray biosensor with optimized orientation having very high sensitivity (484 nm/RIU) towards refractive index changes associated with various fibrillation stages of beta amyloid (biomarker for Alzheimer's disease) compared to the bare Au nanoellipsoidal biosensor. [ABSTRACT FROM AUTHOR]

A new passivity-based voltage tracker for islanded Direct Current (DC) microgrids is presented in this paper. The proposed design develops a new sufficient condition for passivity-based state feedback with proportional and integral control using the attracting ellipsoid method. In this paper, we consider the time behavior of the extended vector, which completely describes the principle properties of the closed-loop system such as the boundedness of the trajectories within some ellipsoid and the dependence of its "size" on the feedback gains. The next step, which we are realizing in this paper, is the minimization of the attractive ellipsoid by selecting the "best" admissible feedback parameters. Here, it is important to note that the applied feedback is of PD-type (proportional differential) on the system state and I-type (integral) on the output. This is a new construction of the suggested feedback which gives several advantages for a designer. The suggested control is decentralized and uses only the local states; it is cost-effective and avoids the time delays in the communication networks which are needed if centralized control is used. The suggested control is carried out in the bilinear matrix inequality (BMI) framework. Extensive simulation is performed on a test system composed of renewable energy sources, under plug and play (PnP) operations, and uncertainties in distribution lines and loads. The performance of the proposed decentralized voltage controller is compared with that of a voltage tracker present in the literature. The comparison shows the improvements introduced by the proposed control ensure the stability of the dc bus voltage and a quick response under different scenarios of operating conditions. [ABSTRACT FROM AUTHOR]

We consider minimization of the supporting function of a convex compact set on the unit sphere. In essence, this is the problem of projecting zero onto a compact convex set. We consider sufficient conditions for solving this problem with a linear rate using a first order algorithm—the gradient projection method with a fixed step-size and with Armijo's step-size. We consider some applications for problems with set-valued mappings. The mappings in the work basically are given through the set-valued integral of a set-valued mapping with convex and compact images or as the Minkowski sum of finite number of convex compact sets, e.g., ellipsoids. Unlike another solution ways, e.g., with approximation in a certain sense of the mapping, the considered algorithm much weaker depends on the dimension of the space and other parameters of the problem. It also allows efficient error estimation. Numerical experiments confirm the effectiveness of the considered approach. [ABSTRACT FROM AUTHOR]

In this present study, five new wood-inhabiting fungal taxa, Botryobasidium gossypirubiginosum, Botryobasidium incanum, Botryobasidium yunnanense, Coltricia zixishanensis, and Coltriciella yunnanensis are proposed. Botryobasidium gossypirubiginosum is distinguished by its slightly rubiginous hymenial surface, monomitic hyphal system, which branches at right angles, and subglobose, smooth basidiospores (14–17.5 × 13–15.5 µm); B. incanum is characterized by its white to incanus basidiomata having a hypochnoid hymenial surface, and ellipsoid, smooth basidiospores (6.5–8.5 × 3.5–5 µm); B. yunnanense is characterized by its buff to slightly yellowish hymenial surface, monomitic hyphal system, and broadly ellipsoid to globose, smooth, thick-walled basidiospores (11.5–14.5 × 9.5–10.5 µm); Coltricia zixishanensis differs in its rust brown pileal surface, and ellipsoid, thick-walled basidiospores (5–6.5 × 4–4.5 µm). Coltriciella yunnanensis is distinguished by its tiny pilei, short stipe, and navicular, verrucose basidiospores (10.5–12.5 × 6–7 µm). Sequences of ITS and nLSU genes were used for phylogenetic analyses using the maximum likelihood, maximum parsimony, and Bayesian inference methods. The phylogenetic results inferred from ITS sequences revealed that B. gossypirubiginosum was closely related to B. robustius; the species B. incanum was grouped with B. vagum; B. yunnanense was related to B. indicum. The species C. zixishanensis was grouped with C. confluens and C. perennis. ITS sequences revealed that C. zixishanensis was grouped into the genus Coltriciella, in which it was grouped with Co. globosa and Co. pseudodependens. [ABSTRACT FROM AUTHOR]

Four new wood-inhabiting fungi were found in Southwestern China within the genera Phanerochaete, Phlebiopsis, Asterostroma, and Vararia of the families Phanerochaetaceae and Peniophoraceae, belonging to the orders Polyporales and Russulales individually. Combined with their morphological characteristics and molecular biological evidence, the present study describes them as new fungal taxa. Asterostroma yunnanense is characterized by the resupinate, membranaceous to pellicular basidiomata with a cream to salmon-buff hymenial surface, hyphal system dimitic bearing simple-septa, thin- to thick-walled, yellowish brown asterosetae with acute tips, and thin-walled, echinulate, amyloid, globose basidiospores. Phanerochaete tongbiguanensis is characterized by the resupinate basidiomata with a white to cream hymenial surface, a monomitic hyphal system with simple-septa generative hyphae, the presence of subclavate cystidia covered with a lot of crystals, and oblong ellipsoid basidiospores (6–9 × 3–4.5 µm). Phlebiopsis fissurata is characterized by the membranaceous, tuberculate basidiomata with a buff to slightly brown hymenial surface, a monomitic hyphal system with simple-septa, conical cystidia, and broadly ellipsoid. Vararia yingjiangensis is characterized by a corky basidiomata with a pinkish buff to cinnamon-buff hymenial surface, cracking, yellowish dichohyphae with slightly curved tips, subulate gloeocystidia, and thick-walled, ellipsoid basidiospores (6.5–11.5 × 5–7 µm). The phylogenetic analyses of ITS + nLSU revealed that the two new species were nested into the genera Phanerochaete and Phlebiopsis within the family Phanerochaetaceae (Polyporales), in which Phanerochaete tongbiguanensis was sister to P. daliensis; Phlebiopsis fissurata was grouped with P. lamprocystidiata. Two new species were clustered into the genera Asterostroma and Vararia within the family Peniophoraceae (Russulales), in which Asterostroma yunnanense was sister to A. cervicolor; Vararia yingjiangensis formed a single branch. [ABSTRACT FROM AUTHOR]

The particle shape plays an important role in the macroscopic response of granular materials. Based on discrete element method (DEM) simulation results of triaxial tests on samples with different particle shapes, this study focuses on the microcharacteristics of contact network and anisotropy in granular media during shearing by a quad-partition method. Numerical results show that the interlocking is enhanced, and stronger contact force will be generated along the loading direction as the deviation of particle shape from a sphere, causing the increase of shear strength. Sliding mainly occurs in weak contacts, and the microscopic dissipative behavior in weak contact sliding plays a key role in the transformation from contraction to dilation. The samples with different particle shapes all reach the maximum proportion of sliding contacts at the phase transformation state that is the transition points of volumetric change. The anisotropy of samples increases as the deviation of particle shape from a sphere, and the contribution of the normal contact force anisotropy to the shear strength is the largest one. With the increase of the particle axial ratio, the mean coordination number and geometrical anisotropy increase due to the oriented alignment occurring at the critical state. Compared with superball particles, the ellipsoid particles have lower compressibility with a smaller axial strain and volumetric strain at the peak state. [ABSTRACT FROM AUTHOR]

Interpreting transient electromagnetic (TEM) anomalies in terms of conductive rectangular plates is effective in many situations. However, not all conductors are thin and planar. Triaxial ellipsoid conductors are an attractive alternative: geometrically simple (corner-free), mathematically tractable at early and late time limits, and able to encompass shapes ranging from discs to elongate lenses to equi-dimensional pods. Accordingly a fast magnetostatic algorithm has been developed to compute the resistive limit (RL) response of a ellipsoidal conductor, which may also be permeable. The algorithm has been validated against new analytic resistive limit solutions for spherical and spheroidal conductors and against 3D multigrid finite difference modelling for a triaxial ellipsoidal conductor. A uniformly conductive ellipsoid supports three fundamental current modes in the resistive limit, an independent mode for excitation parallel to each of the principal axes. The RL current density increases linearly with radial distance from the ellipsoid centre. A formula for the time constant of an oblate spheroid has been derived for excitation parallel to its rotational axis, namely $ {\tau _3} \approx \sigma {\mu _0}bc/(4 + 6c/b) $ τ 3 ≈ σ μ 0 b c / (4 + 6 c / b) , where $ \sigma $ σ is the conductivity and $ c $ c and $ b $ b are respectively the minor and major radii. [ABSTRACT FROM AUTHOR]

The auxiliary latitudes are essential tools in cartography. This paper summarizes methods for converting between them with an emphasis on providing full double-precision accuracy. This includes series expansions in the third flattening, where the truncation error is precisely measured and where estimates of the radii of convergence are given. Also new formulas are given for computing the rectifying and authalic latitudes with minimal roundoff error. [ABSTRACT FROM AUTHOR]

Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enclosed within a triaxial ellipsoid, which is stratified in density with a constant Brunt–Väisälä frequency (using the Boussinesq approximation) and uniformly rotating along a (possibly) tilted axis with respect to gravity. The wave problem is then governed by a mixed hyperbolic-elliptic equation for the velocity. As in the rotating non-stratified case considered by Vantieghem (2014, Proc. R. Soc. A, 470, 20140093. (doi:10.1098/rspa.2014.0093)), we find that the spectrum is pure point in ellipsoids (i.e. only consists of eigenvalues) with polynomial eigenvectors. Then, we characterize the spectrum using numerical computations (obtained with a bespoke Galerkin method) and asymptotic spectral theory. Finally, the results are discussed in light of natural applications (e.g. for Mediterranean eddies or Jupiter's vortices). [ABSTRACT FROM AUTHOR]

This study mathematically examines chemical and biomaterial models by employing the finite element method. Unshaped biomaterials' complex structures have been numerically analyzed using Gaussian quadrature rules. It has been analyzed for commercial benefits of chemical engineering and biomaterials as well as biorefinery fields. For the computational work, the ellipsoid has been taken as a model, and it has been transformed by subdividing it into six tetrahedral elements with one curved face. Each curved tetrahedral element is considered a quadratic and cubic tetrahedral element and transformed into standard tetrahedral elements with straight faces. Each standard tetrahedral element is further decomposed into four hexahedral elements. Numerical tests are presented that verify the derived transformations and the quadrature rules. Convergence studies are performed for the integration of rational, weakly singular, and trigonometric test functions over an ellipsoid by using Gaussian quadrature rules and compared with the generalized Gaussian quadrature rules. The new transformations are derived to compute numerical integration over curved tetrahedral elements for all tests, and it has been observed that the integral outcomes converge to accurate values with lower computation duration. [ABSTRACT FROM AUTHOR]

This paper focuses on the analytical procedure for determining novel exact expressions for internal forces and displacements of hemi-ellipsoidal shells formed as an axisymmetric shell of revolution under uniformly distributed load such as imposed loads. The simplest form of expressions for solutions is derived based on the linear membrane theory under symmetrical loading that is formed as a shell of revolution. The results have been validated and have a good consistency with numerical solutions from the finite-element method (FEM) which are derived based on the principle of virtual work and differential geometry. The obtained analytical exact solution is only valid for small displacements or if the response does not exceed the linearity limit. In cases of large displacements, geometrical nonlinear finite-element analysis is recommended to determine the solution. The linearity limit determination is demonstrated, and the effects of shells' geometry, thickness, and magnitude of applied loads are presented. Additionally, the linear buckling analysis has been performed. The study found that the size ratio, thickness, and support condition have a significant effect on the critical load of the first mode, and the hemispherical shells have the highest buckling resistance due to the geometry. [ABSTRACT FROM AUTHOR]

Species of Grifola are famous edible mushrooms and are deeply loved by consumers around the world. Most species of this genus have been described and recorded in Oceania, Europe and South America, with only Grifola frondosa being recorded in Asia. In this study, two novel species of Grifola from southwestern China (Asia) are introduced. Macro and micromorphological characters are described. Grifola edulis sp. nov. present medium-size basidiomata with gray to gray-brown lobes upper surface, mostly tibiiform or narrowly clavate, rarely narrowly lageniform or ellipsoid chlamydospores, cuticle hyphae terminal segments slightly enlarged. Grifola sinensis sp. nov. has white to grayish white lobes upper surface, mostly ellipsoid, rarely narrowly utriform chlamydospores, and broadly ellipsoid to ellipsoid basidiospores (4.6-7.9 × 3.0-5.9 µm). The two new species are supported by phylogenetic analyses of combined nuclear rDNA internal transcribed spacer ITS1-5.8S-ITS2 rDNA (ITS) and ß-tubulin (TUBB). Moreover, the genetic distance between TUBB sequences of those specimen from GenBank was 1.76-1.9%. Thus, the conspecificity relationship of our specimens remains uncertain, and further specimens are required to conclusively confirm its identity. [ABSTRACT FROM AUTHOR]

The permeability tensor is a critical parameter for analyzing the hydraulic behavior of anisotropic permeability in fractured rock masses. However, determining this tensor for three-dimensional (3D) fractured rock masses has proven to be challenging and resource-intensive. Both field tests, requiring numerous costly in situ tests, and numerical experiments, hindered by complex discrete fracture networks with a high fracture density, present difficulties in obtaining accurate results. In response, this study proposes a semi-theoretical method for determining the permeability tensor of 3D fractured rock masses, significantly reducing labor and economic costs. The proposed method focuses on establishing the theoretical relationship of directional permeabilities in a 3D space, with emphasis on the properties of the permeability tensor and the influence of fractures' geometry on the flow rate. To facilitate the construction of the method, anisotropic ellipse and ellipsoid are introduced, providing a description of permeability anisotropy. With this innovative approach, engineers can calculate the permeability tensor even when only one value of permeability is available along any flow direction. The utilization of the anisotropic ellipse and ellipsoid concepts helps simplify the determination process. Through numerical experiments, the method is validated and its accuracy demonstrated, making it a valuable tool for analyzing the hydraulic behavior of 3D fractured rock masses. [ABSTRACT FROM AUTHOR]

The thermal conductivity parameter of the materials is a fundamental parameter for thermal design and study of heat transfer processes. In our study, we combined the homogenization theory based on the finite element with the thermal conductivity order-of-magnitude analysis and similarity principle, to construct structural models of fibers, spheres, ellipsoids, sheets, and interfaces, and establish the topology of intermingling and encapsulation of different structures. Combined thermal conductivity calculations of mesoscopic composites and microscopic interface models using finite element and molecular dynamics methods. The anisotropy model of thermal conductivity was established by coordinate transformation. Based on the numerical verification of the reliability of the method, the mechanisms of the influence on the thermal transport of composites were analyzed for parameters such as volume fraction of different structural fillers, structural shape, thermal conductivity ratio, thickness of highly thermally conductive coatings, and spatial orientation distribution. The results showed that the effective thermal conductivity (ETC) of the continuous structural reinforced composite was mainly influenced by the volume fraction of the filler; the modulation of ETC with ellipsoidal particle structure form and distribution mode was comparable to the effect of changing the volume fraction modulation; the mutual fusion between ellipsoids randomly distributed in the plane could effectively enhance the heat transport effect of the composite, and as the volume fraction increased to more than 3%, the heat transport gain from mutual fusion was more obvious; spraying high thermally conductive copper coating on ellipsoidal particles could significantly enhance the ETC of the composites. The present work could provide reference for composites in terms of structural improvement and thermal performance enhancement. [ABSTRACT FROM AUTHOR]

We extend the ideas of finding sheared maps discussed in [10], and continue a matrix decomposition called TRD decomposition which has an interesting geometric interpretation. Let M be a three times three invertible matrix with real entries. The matrix M can be written as product of three matrices T, R and D, M = TRD, where D is a diagonalizable matrix with two equal eigenvalues, R is an orthogonal matrix and finally T is a shear matrix. The product TRD is corresponding to a series of linear transformations that send the unit sphere to the same ellipsoid that M does. The decomposition for a general ellipsoid has been discussed in [6]. In this paper, the decomposition is applied on a locus ellipsoid LE(Σ), resulted from a linear transformation LE that is applied on an ellipsoid Σ, which is discussed in ([9]) and ([8]). Moreover, LE (Σ) can be represented by a positive definite M. we adopt a different approach when decompose M into TRD. We relate the given ellipsoid to an ellipsoid that is in its standard form through a transition matrix. Next, we apply the SVD decomposition on a sheared ellipsoid to obtain the final decomposition for the given locus ellipsoid LE(Σ). [ABSTRACT FROM AUTHOR]

In this paper, we consider the matter of on-line clustering of hyperplanes within the presence of bounded noise. This is often a challenging problem that involves the segmentation of the data and the estimation of the hyperplanes parameters. The proposed algorithm consists in two successive steps. At whenever, the first step allows to assign the current data point to the most appropriate hyperplane and therefore the second step realizes an update of the parameters of the hyperplane that contains the data point. The second step springs from an Outer Bounding Ellipsoid type algorithm suitable for on-line parameters estimation within the presence of bounded noise. The performance of our algorithm is proven using synthetic and real data. [ABSTRACT FROM AUTHOR]

Generalized restricted three body problems consist of adding some extra hypotheses to the Restricted three body problem (RTBP) in order to have a new problem, not very different of the original RTBP. However, not any additional hypothesis is allowed; it must satisfy the laws of Physics. Among the several generalizations found in literature, we prove that at least there are two hypotheses that cannot be used, namely: 1) Perturbation in Coriolis and/or centrifugal forces, and 2) primaries are spheroids moving on elliptical orbits. [ABSTRACT FROM AUTHOR]

Due to the large number of layers and different thickness of partings, the poor caving performance of top coal (CPTC) in thick coal seam with complex structure has always been an important problem affecting the top-coal recovery rate (TCRR) in the fully mechanized caving face. Based on the theory of coal-caving ellipsoid, a mechanical model of a long cantilever structure formed by the fracture of the thick parting crossing coal-caving ellipsoid was established, and the influence mechanism of the long cantilever beam structure on CPTC was revealed. Besides, a method to distinguish the influence of multi-layer partings on CPTC was put forward, and the influence of parting thickness, position and the number of parting layers on CPTC was obtained. The results show that the critical parting thickness hg increases with the increase of axial deflection angle θ, mining thickness h and volume weight of parting γg, and hg decreases with the increase of tensile strength of the parting Rt. The main influencing factors of hg can be ordered as follows: h > θ > Rt > γg. The position of the thick parting plays a controlling role in CPTC. The fundamental measure to improve CPTC is to reduce the cantilever beam length formed by the thick parting so that top coal above the parting can be caved. Based on this, the technical scheme of hydraulic fracturing for promoting top-coal caving was proposed and applied. During the initial mining period of the working face, TCRR was effectively increased from 45.99 to 77.18%. Highlights: The influencing factors of the critical thickness of partings affecting the caving performance of top coal include h, θ, Rt, and γg. The layer of thick parting plays a controlling role in the caving performance of top coal of coal seam with multi-layer partings. A scheme of hydraulic fracturing to reduce the cantilever beam structure formed by the fracture of partings was proposed and applied. [ABSTRACT FROM AUTHOR]

The work used data on Saturn's satellite Hyperion obtained from the flight results of the Cassini spacecraft due to their completeness, resolution, and image quality. They pointed out the chaotic nature of Hyperion's rotation, as a result of which there was an ambiguity in determining its coordinate system associated with the body. The dimensions of the approximating ellipsoid and the parameters of the transition from the coordinate system, initially adopted under the assumption of uniform rotation of Hyperion around Saturn, to a coordinate system whose axes coincide with the axes of the found ellipsoid were obtained. A digital model of the Hyperion surface was also created, on the basis of which geodetic heights were calculated relative to a triaxial ellipsoid with certain parameters. The method for calculating heights is based on the combined use of the equation of the normal to the surface passing through a given point and the equation of the surface itself. As a result of the research, a map of Hyperion was compiled in the projection of the triaxial ellipsoid with horizontal lines constructed on the basis of calculated geodetic heights. An original method for studying the nature of Hyperion's rotation is presented using the projection of Saturn's position onto the surface of Hyperion for all known moments in time in an object-centric coordinate system. The implementation of this technique allowed us to assume that Hyperion's own rotation axis precesses relative to the largest axis of the body in a counterclockwise direction. [ABSTRACT FROM AUTHOR]

An essential aspect of human motor learning is the formation of inverse models, which map desired actions to motor commands. Inverse models can be learned by adjusting parameters in neural circuits to minimize errors in the performance of motor tasks through gradient descent. However, the theory of gradient descent establishes limits on the learning speed. Specifically, the eigenvalues of the Hessian of the error surface around a minimum determine the maximum speed of learning in a task. Here, we use this theoretical framework to analyze the speed of learning in different inverse model learning architectures in a set of isometric arm-reaching tasks. We show theoretically that, in these tasks, the error surface and, thus the speed of learning, are determined by the shapes of the force manipulability ellipsoid of the arm and the distribution of targets in the task. In particular, rounder manipulability ellipsoids generate a rounder error surface, allowing for faster learning of the inverse model. Rounder target distributions have a similar effect. We tested these predictions experimentally in a quasi-isometric reaching task with a visuomotor transformation. The experimental results were consistent with our theoretical predictions. Furthermore, our analysis accounts for the speed of learning in previous experiments with incompatible and compatible virtual surgery tasks, and with visuomotor rotation tasks with different numbers of targets. By identifying aspects of a task that influence the speed of learning, our results provide theoretical principles for the design of motor tasks that allow for faster learning. [ABSTRACT FROM AUTHOR]