Classifying rockburst with confidence:A novel conformal prediction approach

The scientific community recognizes the seriousness of rockbursts and the need for effective mitigation measures.The literature reports various successful applications of machine learning(ML)models for rockburst assessment;however,a significant question remains unanswered:How reliable are these models,and at what confidence level are classifications made?Typically,ML models output single rockburst grade even in the face of intricate and out-of-distribution samples,without any associated confidence value.Given the susceptibility of ML models to errors,it becomes imperative to quantify their uncertainty to prevent consequential failures.To address this issue,we propose a conformal prediction(CP)framework built on traditional ML models(extreme gradient boosting and random forest)to generate valid classifications of rockburst while producing a measure of confidence for its output.The proposed framework guarantees marginal coverage and,in most cases,conditional coverage on the test dataset.The CP was evaluated on a rockburst case in the Sanshandao Gold Mine in China,where it achieved high coverage and efficiency at applicable confidence levels.Significantly,the CP identified several“confident”classifications from the traditional ML model as unreliable,necessitating expert verification for informed decision-making.The proposed framework improves the reliability and accuracy of rockburst assessments,with the potential to bolster user confidence.

3D‑Printed Carbon‑Based Conformal Electromagnetic Interference Shielding Module for Integrated Electronics

Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern electronics.However,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electronics,posing a major obstacle to the integra-tion of electronics.The innovation of integrating 3D-printed conformal shielding(c-SE)modules with packaging materials onto core electronics offers infinite possibilities to satisfy ideal SE func-tion without occupying additional space.Herein,the 3D printable carbon-based inks with various proportions of graphene and carbon nanotube nanoparticles are well-formulated by manipulating their rheological peculiarity.Accordingly,the free-constructed architectures with arbitrarily-customized structure and multifunctionality are created via 3D printing.In particular,the SE performance of 3D-printed frame is up to 61.4 dB,simultaneously accompanied with an ultralight architecture of 0.076 g cm^(-3) and a superhigh specific shielding of 802.4 dB cm3 g^(-1).Moreover,as a proof-of-concept,the 3D-printed c-SE module is in situ integrated into core electronics,successfully replacing the traditional metal-based module to afford multiple functions for electromagnetic compatibility and thermal dissipa-tion.Thus,this scientific innovation completely makes up the blank for assembling carbon-based c-SE modules and sheds a brilliant light on developing the next generation of high-performance shielding materials with arbitrarily-customized structure for integrated electronics.

Gelatin-Based Metamaterial Hydrogel Films with High Conformality for Ultra-Soft Tissue Monitoring

Implantable hydrogel-based bioelectronics(IHB)can precisely monitor human health and diagnose diseases.However,achieving biodegradability,biocompatibility,and high conformality with soft tissues poses significant challenges for IHB.Gelatin is the most suitable candidate for IHB since it is a collagen hydrolysate and a substantial part of the extracellular matrix found naturally in most tissues.This study used 3D printing ultrafine fiber networks with metamaterial design to embed into ultra-low elastic modulus hydrogel to create a novel gelatin-based conductive film(GCF)with mechanical programmability.The regulation of GCF nearly covers soft tissue mechanics,an elastic modulus from 20 to 420 kPa,and a Poisson’s ratio from-0.25 to 0.52.The negative Poisson’s ratio promotes conformality with soft tissues to improve the efficiency of biological interfaces.The GCF can monitor heartbeat signals and respiratory rate by determining cardiac deformation due to its high conformability.Notably,the gelatin characteristics of the biodegradable GCF enable the sensor to monitor and support tissue restoration.The GCF metamaterial design offers a unique idea for bioelectronics to develop implantable sensors that integrate monitoring and tissue repair and a customized method for endowing implanted sensors to be highly conformal with soft tissues.

Momentum as Translations at Conformal Infinity

Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.

Conformal Human–Machine Integration Using Highly Bending‑Insensitive,Unpixelated,and Waterproof Epidermal Electronics Toward Metaverse

Efficient and flexible interactions require precisely converting human intentions into computer-recognizable signals,which is critical to the breakthrough development of metaverse.Interactive electronics face common dilemmas,which realize highprecision and stable touch detection but are rigid,bulky,and thick or achieve high flexibility to wear but lose precision.Here,we construct highly bending-insensitive,unpixelated,and waterproof epidermal interfaces(BUW epidermal interfaces)and demonstrate their interactive applications of conformal human–machine integration.The BUW epidermal interface based on the addressable electrical contact structure exhibits high-precision and stable touch detection,high flexibility,rapid response time,excellent stability,and versatile“cut-and-paste”character.Regardless of whether being flat or bent,the BUW epidermal interface can be conformally attached to the human skin for real-time,comfortable,and unrestrained interactions.This research provides promising insight into the functional composite and structural design strategies for developing epidermal electronics,which offers a new technology route and may further broaden human–machine interactions toward metaverse.

Joint polarization and DOA estimation based on improved maximum likelihood estimator and performance analysis for conformal array

The conformal array can make full use of the aperture,save space,meet the requirements of aerodynamics,and is sensitive to polarization information.It has broad application prospects in military,aerospace,and communication fields.The joint polarization and direction-of-arrival(DOA)estimation based on the conformal array and the theoretical analysis of its parameter estimation performance are the key factors to promote the engineering application of the conformal array.To solve these problems,this paper establishes the wave field signal model of the conformal array.Then,for the case of a single target,the cost function of the maximum likelihood(ML)estimator is rewritten with Rayleigh quotient from a problem of maximizing the ratio of quadratic forms into those of minimizing quadratic forms.On this basis,rapid parameter estimation is achieved with the idea of manifold separation technology(MST).Compared with the modified variable projection(MVP)algorithm,it reduces the computational complexity and improves the parameter estimation performance.Meanwhile,the MST is used to solve the partial derivative of the steering vector.Then,the theoretical performance of ML,the multiple signal classification(MUSIC)estimator and Cramer-Rao bound(CRB)based on the conformal array are derived respectively,which provides theoretical foundation for the engineering application of the conformal array.Finally,the simulation experiment verifies the effectiveness of the proposed method.

CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM

In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

2D Curves in Conformal Hyperquaternion Algebras H⊗2m

The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H⊗2m in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H⊗2m is the object of this work.

Nonlinear Conformal Gravitation

In 1909 the brothers E. and F. Cosserat discovered a new nonlinear group theoretical approach to elasticity (EL), with the only experimental need to measure the EL constants. In a modern framework, they used the nonlinear Spencer sequence instead of the nonlinear Janet sequence for the Lie groupoid defining the group of rigid motions of space. Following H. Weyl, our purpose is to compute for the first time the linear and nonlinear Spencer sequences for the Lie groupoid defining the conformal group of space-time in order to provide the mathematical foundations of both electromagnetism (EM) and gravitation (GR), with the only experimental need to measure the EM and GR constants. With a manifold of dimension n ≥ 3, the difficulty is to deal with the n nonlinear transformations that have been called “elations” by E. Cartan in 1922. Using the fact that dimension n = 4 has very specific properties for the computation of the Spencer cohomology, we also prove that there is no conceptual difference between the (nonlinear) Cosserat EL field or induction equations and the (linear) Maxwell EM field or induction equations. As for gravitation, the dimension n = 4 also allows to have a conformal factor defined everywhere but at the central attractive mass because the inversion law of the isotropy subgroupoid made by second order jets transforms attraction into repulsion. The mathematical foundations of both electromagnetism and gravitation are thus only depending on the structure of the conformal pseudogroup of space-time.

N ＝ 4 Superconformal Quantum Mechanics in One Dimension and Its Algebraic Structure

N = 4 superconformal quantum mechanics of nonrelativistic particles in the typical 1/x2-potentials, which holds not only supersymmetry but also dynamical conformal symmetry, is studied. The corresponding superconformal quantum mechanical algebra, which contains supersymmetric quantum mechanical algebra with four supercharges and conformal algebra as subalgebras, and its two canonical group chains are established.

Conformal structure-preserving method for damped nonlinear Schrdinger equation

In this paper,we propose a conformal momentum-preserving method to solve a damped nonlinear Schrodinger(DNLS) equation.Based on its damped multi-symplectic formulation,the DNLS system can be split into a Hamiltonian part and a dissipative part.For the Hamiltonian part,the average vector field(AVF) method and implicit midpoint method are employed in spatial and temporal discretizations,respectively.For the dissipative part,we can solve it exactly.The proposed method conserves the conformal momentum conservation law in any local time-space region.With periodic boundary conditions,this method also preserves the total conformal momentum and the dissipation rate of momentum exactly.Numerical experiments are presented to demonstrate the conservative properties of the proposed method.

A novel DOA estimation algorithm using directional antennas in cylindrical conformal arrays

In this paper, a novel direction of arrival(DOA) estimation algorithm using directional antennas in cylindrical conformal arrays(CCAs) is proposed. To eliminate the shadow effect, we divide the CCAs into several subarrays to obtain the complete output vector. Considering the anisotropic radiation pattern of a CCA, which cannot be separated from the manifold matrix, an improved interpolation method is investigated to transform the directional subarray into omnidirectional virtual nested arrays without non-orthogonal perturbation on the noise vector. Then, the cross-correlation matrix(CCM) of the subarrays is used to generate the consecutive co-arrays without redundant elements and eliminate the noise vector. Finally, the full-rank equivalent covariance matrix is constructed using the output of co-arrays,and the unitary estimation of the signal parameters via rotational invariance techniques(ESPRIT) is performed on the equivalent covariance matrix to estimate the DOAs with low computational complexity. Numerical simulations verify the superior performance of the proposed algorithm, especially under a low signal-to-noise ratio(SNR) environment.

RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

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Stereotactic conformal radiotherapy of hepatic metastases:clinical analysis of 8 cases

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Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.

A Bifunctional-Modulated Conformal Li/Mn-Rich Layered Cathode for Fast-Charging,High Volumetric Density and Durable Li-Ion Full Cells

Lithium-and manganese-rich(LMR)layered cathode materials hold the great promise in designing the next-generation high energy density lithium ion batteries.However,due to the severe surface phase transformation and structure collapse,stabilizing LMR to suppress capacity fade has been a critical challenge.Here,a bifunctional strategy that integrates the advantages of surface modification and structural design is proposed to address the above issues.A model compound Li_(1.2)Mn_(0.54)Ni_(0.13)Co_(0.13)O_(2)(MNC)with semi-hollow microsphere structure is synthesized,of which the surface is modified by surface-treated layer and graphene/car-bon nanotube dual layers.The unique structure design enabled high tap density(2.1 g cm^(−3))and bidirectional ion diffusion pathways.The dual surface coatings covalent bonded with MNC via C-O-M linkage greatly improves charge transfer efficiency and mitigates electrode degradation.Owing to the synergistic effect,the obtained MNC cathode is highly conformal with durable structure integrity,exhibiting high volumetric energy density(2234 Wh L^(−1))and predominant capacitive behavior.The assembled full cell,with nanograph-ite as the anode,reveals an energy density of 526.5 Wh kg^(−1),good rate performance(70.3%retention at 20 C)and long cycle life(1000 cycles).The strategy presented in this work may shed light on designing other high-performance energy devices.

A CONFORMAL SUPFRUNIFIED THEORY

In this paper we have established a superspace U for supergauge actions, constructed a confermal supergroup SU (2, 2|N) and a conformal extended SU (2, 2|N) supergravity theory. Using the Lagrangian Higgs evolution mechanism under the supergroup SU(2, 2|N)SU(N)actions on the superspace U, we have advanced a SU(2, 2|N)SU【N’】 superunified theory of a superunited system, discussed the Lagrangian evolution of the superunified theory, and given the fiber bundle geometry of all above mechanisms.

CONFORMAL TRANSFORMATION SOLUTION FOR THE ATTENUATION CONSTANT OF TEM TRANSMISSION LINES

The conformal transformation solution is presented for the attenuation constant ofTEM transmission lines which can be mapped into the coaxial or the parallel plate lines by certainconformal transformations including the numerical ones.The analytic and numerical results ofsome examples are also given.

Cycle Time Reduction in Injection Molding by Using Milled Groove Conformal Cooling

This paper presents simulation study on Milled Grooved conformal cooling channels(MGCCC)in injection molding.MGCCC has a more effective cooling surface area which helps to provide efficient cooling as compared to conventional cooling.A case study of Encloser part is investigated for cycle time reduction and quality improvement.The performance designs of straight drilled are compared with MGCCC by using Autodesk Moldflow Insight(AMI)2016.The results show total 32.1% reduction of cooling time and 9.86% reduction of warpage in case of MGCCC as compared to conventional cooling.

M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds

We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.