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In this paper, we consider the sparse phase retrieval problem, recovering an s -sparse signal x ♮ ∈ R n from m phaseless samples y i = | 〈 x ♮ , a i 〉 | for i = 1 , ... , m. Existing sparse phase retrieval algorithms are usually first-order and hence converge at most linearly. Inspired by the hard thresholding pursuit (HTP) algorithm in compressed sensing, we propose an efficient second-order algorithm for sparse phase retrieval. Our proposed algorithm is theoretically guaranteed to give an exact sparse signal recovery in finite (in particular, at most O (log ⁡ m + log ⁡ (‖ x ♮ ‖ 2 / | x min ♮ |)) steps, when { a i } i = 1 m are i.i.d. standard Gaussian random vector with m ∼ O (s log ⁡ (n / s)) and the initialization is in a neighborhood of the underlying sparse signal. Together with a spectral initialization, our algorithm is guaranteed to have an exact recovery from O (s 2 log ⁡ n) samples. Since the computational cost per iteration of our proposed algorithm is the same order as popular first-order algorithms, our algorithm is extremely efficient. Experimental results show that our algorithm can be several times faster than existing sparse phase retrieval algorithms. [ABSTRACT FROM AUTHOR]

The first numerical solution of the 3-D travel time tomography problem is presented. The globally convergent convexification numerical method is applied. • The first numerical solution of the Travel Time Tomography Problem in the 3D case. • Globally convergent convexification numerical method is the key. • Rigorous convergence analysis based on a Carleman estimate. [ABSTRACT FROM AUTHOR]

We propose an inverse scattering scheme of recovering a polyhedral obstacle in R n , n = 2 , 3 , by only a few high-frequency acoustic backscattering measurements. The obstacle could be sound-soft or sound-hard. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior, from which one can determine the exterior normal directions of the front sides/faces. Then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions, one can determine the exterior unit normal vector of each side/face of the obstacle. After the determination of the exterior unit normals, the recovery is reduced to a finite-dimensional problem of determining a location point of the obstacle and the distance of each side/face away from the location point. For the latter reconstruction, we need to make use of the far-field data with phases. Numerical experiments are also presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract: We consider the inverse scattering problem of reconstructing multiple impenetrable bodies embedded in an unbounded, homogeneous and isotropic elastic medium. The inverse problem is nonlinear and ill-posed. Our study is conducted in an extremely general and practical setting: the number of scatterers is unknown in advance; and each scatterer could be either a rigid body or a cavity which is not required to be known in advance; and moreover there might be components of multiscale sizes presented simultaneously. We develop several locating schemes by making use of only a single far-field pattern, which is widely known to be challenging in the literature. The inverse scattering schemes are of a totally “direct” nature without any inversion involved. For the recovery of multiple small scatterers, the nonlinear inverse problem is linearized and to that end, we derive sharp asymptotic expansion of the elastic far-field pattern in terms of the relative size of the cavities. The asymptotic expansion is based on the boundary-layer-potential technique and the result obtained is of significant mathematical interest for its own sake. The recovery of regular-size/extended scatterers is based on projecting the measured far-field pattern into an admissible solution space. With a local tuning technique, we can further recover multiple multiscale elastic scatterers. [Copyright &y& Elsevier]

Abstract: We develop two enhanced techniques for the multilevel linear sampling method (MLSM) proposed in [32] for inverse scattering problems. Under some practical situations, the MLSM suffers certain undesirable “breakage cells” problem. We propose to avoid the curse of “breakage cells” by incorporating “expanding” and “searching” techniques. The new techniques are shown to significantly improve the robustness of the MLSM, and meanwhile they possess the same optimal computational complexity as the MLSM. Numerical experiments are presented to illustrate the promising features of the enhanced MLSMs. [Copyright &y& Elsevier]

Abstract: This article is devoted to the construction of a family of universal extension operators for the Sobolev spaces of differential forms of degree l () in a Lipschitz domain (, ) for any . It generalizes the construction of the first universal extension operator for standard Sobolev spaces , , on Lipschitz domains, introduced by Stein [E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, NJ, 1970, Theorem 5, p. 181]. We adapt Steinʼs idea in the form of integral averaging over the pullback of a parametrized reflection mapping. The new theory covers extension operators for and in as special cases for , respectively. Of considerable mathematical interest in its own right, the new theoretical results have many important applications: we elaborate existence proofs for generalized regular decompositions. [Copyright &y& Elsevier]

The molecular chaperone Hsp40 functions as a dimer. The dimer formation is critical for Hsp40 molecular chaperone activity to facilitate Hsp70 to refold non-native polypeptides. We have determined the crystal structure of the C-terminal fragment of yeast Hsp40 Ydj1 that is responsible for Ydj1 dimerization by MAD method. The C-terminal fragment of Ydj1 comprises of the domain III of Ydj1 and the Ydj1 C-terminal dimerization motif. The crystal structure indicates that the dimerization motif of type I Hsp40 Ydj1 differs significantly from that of yeast type II Hsp40. The C terminus of type I Hsp40 Ydj1 from one monomer forms β-strands with the domain III from the other monomer in the homo-dimer. The L372 from Ydj1 C terminus inserts its side-chain into a hydrophobic pocket on domain III. The modeled full-length Ydj1 dimer structure reveals that a large cleft is formed between the two monomers. The domain IIs of Ydj1 monomers that contain the zinc-finger motifs points directly against each other. [Copyright &y& Elsevier]

E. coli Hsp100 ClpB was recently identified as a critical part in a multi-chaperone system to play important roles in protein folding, protein transport and degradation in cell physiology. ClpB contains two nucleotide-binding domains (NBD1 and NBD2) within their primary sequences. NBD1 and NBD2 of ClpB can be classified as members of the large ATPase family known as ATPases associated with various cellular activities (AAA). To investigate how ClpB performs its ATPase activities for its chaperone activity, we have determined the crystal structure of ClpB nucleotide-binding domain 1 (NBD1) by MAD method to 1.80 A˚ resolution. The NBD1 monomer structure contains one domain that comprises 11 α-helices and six β-strands. When compared with the typical AAA structures, the crystal structure of ClpB NBD1 reveals a novel AAA topology with six-stranded β-sheet as its core. The N-terminal portion of NBD1 structure has an extra β-strand flanked by two extra α-helices that are not present in other AAA structures. Moreover, the NBD1 structure does not have a C-terminal helical domain as other AAA proteins do. No nucleotide molecule is bound with ClpB NBD1 in the crystal structure probably due to lack of the C-terminal helix domain in the structure. Isothermal titration calorimetry (ITC) studies of ClpB NBD1 and other ClpB deletion mutations showed that either ClpB NBD1 or NBD2 alone does not bind to nucleotides. However, ClpB NBD2 combined with ClpB C-terminal fragment can interact with one ADP or ATP molecule. ITC data also indicated that full-length ClpB could bind two ADP molecules or one ATP analogue ATPγS molecule. Further ATPase activity studies of ClpB and ClpB deletion mutants showed that only wild-type ClpB have ATPase activity. None of ClpB NBD1 domain, NBD2 domain and NBD2 with C-terminal fragment has detectable ATPase activities. On the basis of our structural and mutagenesis data, we proposed a “see-saw” model to illustrate the mechanisms by which ClpB performs its ATPase activities for chaperone functions. [Copyright &y& Elsevier]

The aim of this paper is to compute the mean field and variance of solutions to three-dimensional Maxwell's equations with random interfaces via shape calculus and pivoted low-rank approximation. Based on the perturbation theory and shape calculus, we characterize the statistical moments of solutions to Maxwell's equations with random interfaces in terms of the perturbation magnitude via the first order shape-Taylor expansion. In order to capture oscillations with high resolution close to the interface, an adaptive finite element method using Nédélec's third order edge elements of the first kind is employed to solve the deterministic Maxwell's equations with the mean interface to approximate the expectation of solutions. For the second moment computation, an efficient low-rank approximation of the pivoted Cholesky decomposition is proposed to compute the two-point correlation function to approximate the variance of solutions. Numerical experiments are presented to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers numerical design of finite sound-hard lining (FSHL)-based approximate cloaks with arbitrary shapes. Regarding the complexity of the shape, two new approaches are proposed to design the transformation map from the virtual space to the physical space via transformation optics. For star-shaped geometry, we propose an explicit global transformation map which can be easily differentiated and inverted. For more general shapes, an Initialize-Untangle-Extend (IUE) approach is initiated to build locally piecewise differentiable deformations, which can be locally inverted with the help of an approximate triangulation. With the locally piecewise-constructed transformation, the parameters of acoustic scattering models in physical space can be determined in both approaches based on the transformation invariance of the Helmholtz system. Then the cloaking effects for an arbitrary shape FSHL-based cloak can be realized following Li et al. (2012) [5] . Extensive numerical experiments are presented to illustrate both the effectiveness of cloak design and the efficiency of the proposed FSHL-based cloaks with arbitrary shapes. [ABSTRACT FROM AUTHOR]

The presence of magnetized anomalies in the shell of the Earth interrupts its geomagnetic field. We consider the inverse problem of identifying the anomalies by monitoring the variation of the geomagnetic field. Motivated by the theoretical unique identifiability result in [7] , we develop a novel numerical scheme of locating multiple magnetized anomalies. In our study, we do not assume the source that generates the geomagnetic field, and the medium configurations of the Earth's core and the magnetized anomalies are a-priori known. The core of the reconstruction scheme is a novel imaging functional whose quantitative behaviours can be used to identify the anomalies. Both rigorous analysis and extensive numerical experiments are provided to verify the effectiveness and promising features of the proposed reconstruction scheme. • Magnetic anomalies detection from geomagnetic monitoring is practically important and challenging. • Based on a sophisticated geomagnetic model, a novel reconstruction scheme is proposed and developed. • In our method, the geomagnetic source and the medium configuration of the Earth's core are both not a-priori known. • The core is a novel imaging functional whose promising features are both theoretically and computationally verified. [ABSTRACT FROM AUTHOR]

We propose an approach to design an optimized heterogeneous interconnected porous structure over a fixed macro-design mesh for performance optimization, which has seldom been addressed despite its extensive potential industrial applications. We achieve this by introducing the concept of the extended triply periodic minimal surface (ETPMS), defined by an implicit function with additional control parameters that can prescribe the element anisotropy and heterogeneity consistently. The control parameters are expressed as continuous explicit functions of spatial coordinates, and ultimately generate a porous structure with perfect geometric connections and fully interconnected pore networks. The modeling advantages of the ETPMS come at the cost of challenges in its efficient simulation and optimization owing to its large number of varied ETPMS elements and their geometric validity requirements. These issues are further resolved using a strategy of offline pre-computation; in particular, parametric homogenization and several carefully designed optimization techniques. The performance of the approach is demonstrated using a suite of three-dimensional benchmark examples. [ABSTRACT FROM AUTHOR]

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method. [ABSTRACT FROM AUTHOR]

This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally “direct” involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations. [ABSTRACT FROM AUTHOR]

Abstract: Many mitochondrial proteins are synthesized as preproteins carrying amino-terminal presequences in the cytosol. The preproteins are imported by the translocase of the outer mitochondrial membrane and the presequence translocase of the inner membrane. Tim50 and Tim23 transfer preproteins through the intermembrane space to the inner membrane. We report the crystal structure of the intermembrane space domain of yeast Tim50 to 1.83 Å resolution. A protruding β-hairpin of Tim50 is crucial for interaction with Tim23, providing a molecular basis for the cooperation of Tim50 and Tim23 in preprotein translocation to the protein-conducting channel of the mitochondrial inner membrane. [Copyright &y& Elsevier]