Compact Domain Research Articles

Statistics of boundary encounters by a particle diffusing outside a compact planar domain

We consider a particle diffusing outside a compact planar set and investigate its boundary local time ℓ t , i.e., the rescaled number of encounters between the particle and the boundary up to time t. In the case of a disk, this is also the (rescaled) number of encounters of two diffusing circular particles in the plane. For that case, we derive explicit integral representations for the probability density of the boundary local time ℓ t and for the probability density of the first-crossing time of a given threshold by ℓ t . The latter density is shown to exhibit a very slow long-time decay due to extremely long diffusive excursions between encounters. We briefly discuss some practical consequences of this behavior for applications in chemical physics and biology.

Compact class-conditional domain invariant learning for multi-class domain adaptation

Neural network-based models have recently shown excellent performance in various kinds of tasks. However, a large amount of labeled data is required to train deep networks, and the cost of gathering labeled training data for every kind of domain is prohibitively expensive. Domain adaptation tries to solve this problem by transferring knowledge from labeled source domain data to unlabeled target domain data. Previous research tried to learn domain-invariant features of source and target domains to address this problem, and this approach has been used as a key concept in various methods. However, domain-invariant features do not mean that a classifier trained on source data can be directly applied to target data because it does not guarantee that data distribution of the same classes will be aligned across two domains. In this paper, we present novel generalization upper bounds for domain adaptation that motivates the need for class-conditional domain invariant learning. Based on this theoretical framework, we then propose a class-conditional domain invariant learning method that can learn a feature space in which features in the same class are expected to be mapped nearby. We empirically experimented that our model showed state-of-the-art performance on standard datasets and showed effectiveness by visualization of latent space.

Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet

We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal families in such setting. Using an algebro-geometric integration technique, we prove that the billiard within generalized ellipses of each type is integrable in the sense of Liouville. Further, we prove a generalization of the Poncelet theorem and derive Cayley-type conditions for periodic trajectories and explore geometric consequences.

Research on sparsity of frequency modulated signal in fractional Fourier transform domain

Frequency modulated (FM) signal is extensively applied in sonar, radar, laser and emerging optical cross-research, its sparsity is a common basic issue for the sampling, denoising and compression of FM signal. This paper mainly studies the sparsity of FM signal in the fractional Fourier transform (FRFT) domain, and a maximum singular value method (MSVM) is proposed to estimate the compact FRFT domain of FM signal. This method uses the maximum singular value of amplitude spectrum of FM signal to measure the compact domain, and WOA is used to search the compact domain, which effectively improves the shortcomings of the existing methods. Compared with MNM and MACF, this method gives a sparser representation of FM signal in the FRFT domain, which has less number of significant amplitudes. Finally, the primary application of this method in the FM signal filtering is given.

A phaseless inverse problem for electrodynamic equations in the dispersible medium

ABSTRACT For electrodynamic equations related to non-conducting dispersible medium we consider the inverse problem of recovering two variable coefficients from a given phaseless information of solutions to the equations. One of these coefficients is the permittivity while the second one characterizes the time dispersion of the medium. We suppose that unknown coefficients differ from given constants inside of a compact domain Ω. A plane electromagnetic wave going in the direction ν from infinity fall down on this domain and modulus of the electric strength is measured on a part of the boundary of Ω for all . The inverse problem consists in determining unknown functions from this information. We reduce the inverse problem to two problems: (1) the inverse kinematic problem for recovering the refractive index and (2) the integral geometry problem for recovering the second coefficient related to the dispersion. An uniqueness theorem for the first problem is stated on the base of known results. The second problem differs from have studied by the more general weight function and it is still open. Then we demonstrate that under some natural assumption the weight function uniformly close to 1. Replacing the weight function by 1, we obtain the integral geometry problem for which the uniqueness theorem and stability estimate are established and some numerical algorithms are proposed.

The solution structure of the complement deregulator FHR5 reveals a compact dimer and provides new insights into CFHR5 nephropathy

The human complement Factor H-related 5 protein (FHR5) antagonizes the main circulating complement regulator Factor H, resulting in the deregulation of complement activation. FHR5 normally contains nine short complement regulator (SCR) domains, but a FHR5 mutant has been identified with a duplicated N-terminal SCR-1/2 domain pair that causes CFHR5 nephropathy. To understand how this duplication causes disease, we characterized the solution structure of native FHR5 by analytical ultracentrifugation and small-angle X-ray scattering. Sedimentation velocity and X-ray scattering indicated that FHR5 was dimeric, with a radius of gyration (Rg ) of 5.5 ± 0.2 nm and a maximum protein length of 20 nm for its 18 domains. This result indicated that FHR5 was even more compact than the main regulator Factor H, which showed an overall length of 26-29 nm for its 20 SCR domains. Atomistic modeling for FHR5 generated a library of 250,000 physically realistic trial arrangements of SCR domains for scattering curve fits. Only compact domain structures in this library fit well to the scattering data, and these structures readily accommodated the extra SCR-1/2 domain pair present in CFHR5 nephropathy. This model indicated that mutant FHR5 can form oligomers that possess additional binding sites for C3b in FHR5. We conclude that the deregulation of complement regulation by the FHR5 mutant can be rationalized by the enhanced binding of FHR5 oligomers to C3b deposited on host cell surfaces. Our FHR5 structures thus explained key features of the mechanism and pathology of CFHR5 nephropathy.

Incipient Fault Detection for Air Brake System of High-Speed Trains

The ideal air brake system is to provide accurate brake pressures, which ensures the normal braking performance of high-speed trains. For the high-speed trains in China, a univariate monitoring strategy has been adopted to monitor the state of each brake cylinder of the air brake system separately. In practice, this kind of strategy is effective for faults with large amplitude, but it is always ineffective for all kinds of incipient faults with small amplitude. Due to nonstationary and multimode properties inherent in air brake systems, conventional detection methods are difficult to be used. In this article, we develop novel detection strategies for three kinds of incipient faults in the air brake systems, including sensor deviation fault, leakage fault, and brake cylinder component fault. Starting from the characteristics of actual data from air brake systems, some variables with high level of consistency are selected. Then, a linear data transformation is conducted to obtain approximate stationary properties, and all the data in multiple modes are mapped into a compact domain. In addition, a fault-to-signal ratio (FSR) is proposed to reflect the sensitivity of the proposed detection statistic to the fault. In particular, the multistage control limits and sliding window strategies are integrated into the detection statistic, which effectively lowers the control limits and enhances robustness to noise, respectively. Finally, experiments on the braking test platform are provided to show the effectiveness of our proposed strategies.

Parallel implementation of a VIScous Vorticity Equation (VISVE) method in 3-D laminar flow

This paper presents a newly developed parallel implementation of solving the 3–D vorticity equation to fully simulate the incompressible laminar flow in the Eulerian frame. This method is designed to solve 3–D problems with irregular wall boundaries in small and compact computational domains in general shapes efficiently. The curl form of vorticity equation is discretized using the Finite Volume Method (FVM) by applying Stokes' theorem, which automatically guarantees the divergence–free condition of vorticity field at all times. The vorticity preserving velocity field is recovered by an explicit scheme without solving any linear system, and this velocity field is reprojected onto a divergence–free space by solving only one scalar velocity–potential Poisson's equation. The vorticity boundary condition is satisfied by employing a vorticity creation scheme, that can handle arbitrary wall boundary shapes. Numerical results of the flow past a 3–D NACA0012 hydrofoil with one periodic direction, the flow past a sphere, and the flow past a 3–D rectangular wing are presented to validate the scheme.

A Functional Busemann Intersection Inequality

The Busemann intersection inequality states that if K is a compact domain in $${\mathbb {R}}^n$$ then where $$c(n)>0$$ is an explicit constant, with equality if and only if K is an ellipsoid centered at the origin. In this paper, we prove a functional version of the Busemann intersection inequality. We also demonstrate an “equivalent” sharp entropy inequality for dual mixed volumes of functions.

Outer entropy equals Bartnik-Bray inner mass and the gravitational ant conjecture

Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall's ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass. Lastly, we discuss some implications of taking quantum matter into consideration in the semiclassical setting.

Zinc Interactions with a Soluble Mutated Rat Amylin to Mimic Whole Human Amylin: An Experimental and Simulation Approach to Understand Stoichiometry, Speciation and Coordination of the Metal Complexes.

Islet amyloid polypeptide (IAPP) is a hormone co-secreted with insulin and zinc from pancreatic β-cells. To overcome the low solubility of human IAPP, we characterized zinc complexes species formed with 1) a mutated form of rat-IAPP(1-37; R18 H) able to mimic the human IAPP, 2) the r-IAPP(1-37) and the IAPP(1-8) fragment. Stoichiometry, speciation and coordination features of zinc(II) complexes were unveiled by ESI-MS, potentiometry and NMR measurements combined with DFT and free-energy simulations. Mononuclear species start to form around pH 6; Zn2+ binds both His18 and N-amino terminus in rat-IAPP(1-37; R18 H). The in silico study allows us to assess not only a structured turn compact domain in r-IAPP(1-37) and r-IAPP(1-37; R18 H) featured by a different free energy barrier for the transition from the compact to elongated conformation upon the coordination of Zn2+ , but also to bring into light a coordination shell further stabilized by noncovalent interactions.

Structural analysis of the LDL receptor–interacting FERM domain in the E3 ubiquitin ligase IDOL reveals an obscured substrate-binding site

Hepatic abundance of the low-density lipoprotein receptor (LDLR) is a critical determinant of circulating plasma LDL cholesterol levels and hence development of coronary artery disease. The sterol-responsive E3 ubiquitin ligase inducible degrader of the LDLR (IDOL) specifically promotes ubiquitination and subsequent lysosomal degradation of the LDLR and thus controls cellular LDL uptake. IDOL contains an extended N-terminal FERM (4.1 protein, ezrin, radixin, and moesin) domain, responsible for substrate recognition and plasma membrane association, and a second C-terminal RING domain, responsible for the E3 ligase activity and homodimerization. As IDOL is a putative lipid-lowering drug target, we investigated the molecular details of its substrate recognition. We produced and isolated full-length IDOL protein, which displayed high autoubiquitination activity. However, in vitro ubiquitination of its substrate, the intracellular tail of the LDLR, was low. To investigate the structural basis for this, we determined crystal structures of the extended FERM domain of IDOL and multiple conformations of its F3ab subdomain. These reveal the archetypal F1-F2-F3 trilobed FERM domain structure but show that the F3c subdomain orientation obscures the target-binding site. To substantiate this finding, we analyzed the full-length FERM domain and a series of truncated FERM constructs by small-angle X-ray scattering (SAXS). The scattering data support a compact and globular core FERM domain with a more flexible and extended C-terminal region. This flexibility may explain the low activity in vitro and suggests that IDOL may require activation for recognition of the LDLR.

Mapping epigenetic modifications on chicken lampbrush chromosomes

BackgroundThe epigenetic regulation of genome is crucial for implementation of the genetic program of ontogenesis through establishing and maintaining differential gene expression. Thus mapping of various epigenetic modifications to the genome is relevant for studying the regulation of gene expression. Giant transcriptionally active lampbrush chromosomes are an established tool for high resolution physical mapping of the genome and its epigenetic modifications. This study is aimed at characterizing the epigenetic status of compact chromatin domains (chromomeres) of chicken lampbrush macrochromosomes.ResultsDistribution of three epigenetic modifications – 5-methylcytosine, histone H3 trimethylated at lysine 9 and hyperacetylated histone H4 – along the axes of chicken lampbrush chromosomes 1–4, Z and W was analyzed in details. Enrichment of chromatin domains with the investigated epigenetic modifications was indicated on the cytological chromomere-loop maps for corresponding chicken lampbrush chromosomes. Heterogeneity in the distribution of 5-methylcytosine and histone H3 trimethylated at lysine 9 along the chromosome axes was revealed.ConclusionsOn examples of certain chromomeres of chicken lampbrush chromosomes 1, 3, 4 and W we demonstrated that a combination of immunofluorescent staining and fluorescence in situ hybridization allows to relate the epigenetic status and a DNA sequence context of individual chromomeres.

Notions of Stein spaces in non-Archimedean geometry

Let k k be a non-Archimedean complete valued field and let X X be a k k -analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: (1) for every complete valued extension k ′ k’ of k k , every coherent sheaf on X × k k ′ X \times _{k} k’ is acyclic; (2) X X is Stein in the sense of complex geometry (holomorphically separated, holomorphically convex), and higher cohomology groups of the structure sheaf vanish (this latter hypothesis is crucial if, for instance, X X is compact); (3) X X admits a suitable exhaustion by compact analytic domains considered by Liu in his counter-example to the cohomological criterion for affinoidicity. When X X has no boundary the characterization is simpler: in (2) the vanishing of higher cohomology groups of the structure sheaf is no longer needed, so that we recover the usual notion of Stein space in complex geometry; in (3) the domains considered by Liu can be replaced by affinoid domains, which leads us back to Kiehl’s definition of Stein space.

Compressed Sensing MIMO Radar System for Extended Target Detection

The article presents a multiple-input–multiple-output (MIMO) radar system for which transmit-receive beamforming in conjunction with a compact frequency domain representation of the radar signals yields a sparse representation of the radar scene. Compressed sensing (CS) methods are then applied to design the radar waveforms for detecting the presence within the radar scene of multiple extended targets with known impulse responses, as well as for designing the receiver filters to reconstruct the radar scene. The detection performance of the MIMO radar system based on noisy scene reconstruction is illustrated with numerical examples obtained from simulations. These show that the receiver operating characteristic curves obtained using the MIMO radar waveforms and receiver filters designed based on CS methods outperform those obtained when statically defined waveforms and receiver filters are used for target detection in the reconstructed scene.

Realistic classical binding energies in the \u03c9-Skyrme model

An omega-meson extension of the Skyrme model — without the Skyrme term but including the pion mass — first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained energy minimisation problem within a natural geometric framework and studied analytically on compact domains, and numerically on Euclidean space. Using a constrained second-order Newton flow algorithm, classical energy minimisers are constructed for various values of the omegapion coupling. At high coupling, these Skyrmion solutions are qualitatively similar to the Skyrmions of the standard Skyrme model with massless pions. At sufficiently low coupling, they show similarities with those in the lightly bound Skyrme model: the Skyrmions of low baryon number dissociate into lightly bound clusters of distinct 1-Skyrmions, and the classical binding energies for baryon numbers 2 through 8 have realistic values.

Analysis of a two-layer neural network via displacement convexity

Fitting a function by using linear combinations of a large number $N$ of “simple” components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is nonconvex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here, we consider the problem of learning a concave function $f$ on a compact convex domain $\Omega \subset {\mathbb{R}}^{d}$, using linear combinations of “bump-like” components (neurons). The parameters to be fitted are the centers of $N$ bumps, and the resulting empirical risk minimization problem is highly nonconvex. We prove that, in the limit in which the number of neurons diverges, the evolution of gradient descent converges to a Wasserstein gradient flow in the space of probability distributions over $\Omega $. Further, when the bump width $\delta $ tends to $0$, this gradient flow has a limit which is a viscous porous medium equation. Remarkably, the cost function optimized by this gradient flow exhibits a special property known as displacement convexity, which implies exponential convergence rates for $N\to \infty $, $\delta \to 0$. Surprisingly, this asymptotic theory appears to capture well the behavior for moderate values of $\delta $, $N$. Explaining this phenomenon, and understanding the dependence on $\delta $, $N$ in a quantitative manner remains an outstanding challenge.

An intrinsic hyperboloid approach for Einstein Klein–Gordon equations

Klainerman introduced in [7] the hyperboloidal method to prove global existence results for nonlinear Klein–Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to Lorentzian spacetimes. This approach is developed in [15] for proving, under the maximal foliation gauge, the global nonlinear stability of Minkowski space for Einstein equations with massive scalar fields, which states that, the sufficiently small data in a compact domain, surrounded by a Schwarzschild metric, leads to a unique, globally hyperbolic, smooth and geodesically complete solution to the Einstein Klein–Gordon system. In this paper, we set up the geometric framework of the intrinsic hyperboloid approach in the curved spacetime. By performing a thorough geometric comparison between the radial normal vector field induced by the intrinsic hyperboloids and the canonical $\partial_r$, we manage to control the hyperboloids when they are close to their asymptote, which is a light cone in the Schwarzschild zone. By using such geometric information, we not only obtain the crucial boundary information for running the energy method in [15], but also prove that the intrinsic geometric quantities including the Hawking mass all converge to their Schwarzschild values when approaching the asymptote.

Compact Hybrid Domain based Human Recognition using Face Images

Compact Hybrid Domain based Human Recognition using Face Images

Solution structure of the cytoplasmic domain of NhaP2 a K+/H+ antiporter from Vibrio cholera

NhaP2 is a K+/H+ antiporter from Vibrio cholerae which consists of a transmembrane domain and a cytoplasmic domain of approximately 200 amino acids, both of which are required for cholera infectivity. Here we present the solution structure for a 165 amino acid minimal cytoplasmic domain (P2MIN) form of the protein. The structure reveals a compact N-terminal domain which resembles a Regulator of Conductance of K+ channels (RCK) domain connected to a more open C-terminal domain via a flexible 20 amino acid linker. NMR titration experiments showed that the protein binds ATP through its N-terminal domain, which was further supported by waterLOGSY and Saturation Transfer Difference NMR experiments. The two-domain organisation of the protein was confirmed by BIOSAXS, which also revealed that there are no detectable-ATP-induced conformational changes in the protein structure. Finally, in contrast to all known RCK domain structures solved to date, the current work shows that the protein is a monomer.