Simplification method for nonlinear equations of monotone type in Banach space

In a Banach space, we study an operator equation with a monotone operator T. The operator is an operator from a Banach space to its conjugate, and T=AC, where A and C are operators of some classes. The considered problem belongs to the class of ill-posed problems. For this reason, an operator regularization method is proposed to solve it. This method is constructed using not the operator T of the original equation, but a more simple operator A, which is B-monotone, B=C−1. The existence of the operator B is assumed. In addition, when constructing the operator regularization method, we use a dual mapping with some gauge function. In this case, the operators of the equation and the right-hand side of the given equation are assumed to be perturbed. The requirements on the geometry of the Banach space and on the agreement conditions for the perturbation levels of the data and of the regularization parameter are established, which provide a strong convergence of the constructed approximations to some solution of the original equation. An example of a problem in Lebesgue space is given for which the proposed method is applicable.

Capturing the Signature of Topological Evolution from the Snapshots of Road Networks

Road networks serve as the backbone of cities, shaping urban structure as well as providing the critical function of transport for people, goods, and services. The design and management of resilient road infrastructure, therefore, is essential for building a sustainable city. Road networks grow and evolve over time, such that their topology shifts from an initially planned state to the one that emerges from self-organization and urban growth. In this work, we use a dual mapping approach to compare the topological features of road networks in 25 districts in Seoul, South Korea. By using average node degree as an indicator of the level of self-organization, we present that multiple topological variables including power-law exponent gradually shift as a network grows. By testing static error and attack tolerance of these networks, we also show that the gradual shift in topology also has an important implication in network resilience. We suggest a new method, inspired by Lorenz curve, for quantifying network vulnerability. This modified Lorenz curve enables calculating the relative impact of intensive attacks to random failures and shows that a more self-organized road network tends to become more vulnerable to selective attacks.

Lights, camera, path splitter: a new approach for truly simultaneous dual optical mapping of the heart with a single camera

Background Optical mapping of transmembrane voltage and intracellular calcium is a powerful tool for investigating cardiac physiology and pathophysiology. However, simultaneous dual mapping of two fluorescent probes remains technically challenging. We introduce a novel, easy-to-use approach that requires a path splitter, single camera and excitation light to simultaneously acquire voltage and calcium signals from whole heart preparations, which can be applied to other physiological models – including neurons and isolated cardiomyocytes. Results Complementary probes were selected that could be excited with a single wavelength light source. Langendorff-perfused hearts (rat, swine) were stained and imaged using a sCMOS camera outfitted with an optical path splitter to simultaneously acquire two emission fields at high spatial and temporal resolution. Voltage (RH237) and calcium (Rhod2) signals were acquired concurrently on a single sensor, resulting in two 384 × 256 images at 814 frames per second. At this frame rate, the signal-to-noise ratio was 47 (RH237) and 85 (Rhod2). Imaging experiments were performed on small rodent hearts, as well as larger pig hearts with sufficient optical signals. In separate experiments, each dye was used independently to assess crosstalk and demonstrate signal specificity. Additionally, the effect of ryanodine on myocardial calcium transients was validated – with no measurable effect on the amplitude of optical action potentials. To demonstrate spatial resolution, ventricular tachycardia was induced –resulting in the novel finding that spatially discordant calcium alternans can be present in different regions of the heart, even when electrical alternans remain concordant. The described system excels in providing a wide field of view and high spatiotemporal resolution for a variety of cardiac preparations. Conclusions We report the first multiparametric mapping system that simultaneously acquires calcium and voltage signals from cardiac preparations, using a path splitter, single camera and excitation light. This approach eliminates the need for multiple cameras, excitation light patterning or frame interleaving. These features can aid in the adoption of dual mapping technology by the broader cardiovascular research community, and decrease the barrier of entry into panoramic heart imaging, as it reduces the number of required cameras.

Lights, Camera, Path Splitter: A New Approach for Truly Simultaneous Dual Optical Mapping of the Heart with a Single Camera

ABSTRACTBackgroundOptical mapping of transmembrane voltage and intracellular calcium is a powerful tool for investigating cardiac physiology and pathophysiology. However, simultaneous dual mapping of two fluorescent probes remains technically challenging. We introduce a novel, easy-to-use approach that requires a path splitter, single camera and excitation light to simultaneously acquire voltage and calcium signals from whole heart preparations, which can be applied to other physiological models – including neurons and isolated cardiomyocytes.ResultsComplementary probes were selected that could be excited with a single wavelength light source. Langendorff-perfused hearts (rat, swine) were stained and imaged using a sCMOS camera outfitted with an optical path splitter to simultaneously acquire two emission fields at high spatial and temporal resolution. Voltage (RH237) and calcium (Rhod2) signals were acquired concurrently on a single sensor, resulting in two 384×256 images at 814 frames per second. At this frame rate, the signal-to-noise ratio was 47 (RH237) and 85 (Rhod2). Imaging experiments were performed on small rodent hearts, as well as larger pig hearts with sufficient optical signals. In separate experiments, each dye was used independently to assess crosstalk and demonstrate signal specificity. Additionally, the effect of ryanodine on myocardial calcium transients was validated – with no measurable effect on the amplitude of optical action potentials. To demonstrate spatial resolution, ventricular tachycardia was induced –resulting in the novel finding that spatially discordant calcium alternans can be present in different regions of the heart, even when electrical alternans remain concordant. The described system excels in providing a wide field of view and high spatiotemporal resolution for a variety of cardiac preparations.ConclusionsWe report the first multiparametric mapping system that simultaneously acquires calcium and voltage signals from cardiac preparations, using a path splitter, single camera and excitation light. This approach eliminates the need for multiple cameras, excitation light patterning or frame interleaving. These features can aid in the adoption of dual mapping technology by the broader cardiovascular research community, and decrease the barrier of entry into panoramic heart imaging, as it reduces the number of required cameras.

A flexible data hiding scheme using differential dual mapping

Steganography is the approach with invisible communication. In our proposed system maximum of 3000 characters can be embedded in the image which is chosen from a video and a different type of frame work for hiding and extracting are provided at both nodes. As an extension of this work, the same algorithm can be implemented in three channels of the colour image. A lossless data hiding technique based on the differential pair mapping algorithm by embedding data bits in an image is proposed, then a generated image is embedded with large amount of data in the form of bits in the mean-removed via the proposed algorithm. Experimental outputs shows that stego-image in our method has high capacity and security with certain robustness and the PSNR value is higher than the other techniques.

Differences in phonetic-to-lexical perceptual mapping of L1 and L2 regional accents

This study investigates how second language (L2) listeners match an unexpected accented form to their stored form of a word. The phonetic-to-lexical mapping for L2 as compared to L1 regional varieties was examined with early and late Italian-L2 speakers who were all L1-Australian English speakers. AXB discrimination and lexical decision tasks were conducted in both languages, using unfamiliar regional accents that minimize (near-merge) consonant contrasts maintained in their own L1-L2 accents. Results reveal that in the L2, early bilinguals’ recognition of accented variants depended on their discrimination capacity. Late bilinguals, for whom the accented variants were not represented in their L2 lexicon, instead mapped standard and accented exemplars to the same lexical representations (i.e., dual mapping: Samuel & Larraza, 2015). By comparison, both groups showed the same broad accommodation to L1 accented variants. Results suggest qualitatively different yet similarly effective phonetic-to-lexical mapping strategies both for L2 versus L1 regional accents.