Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications

This is the first installment in a series of papers aimed at generalizing symplectic capacities and homologies. The main purposes of this paper are to construct analogues of Ekeland-Hofer and Hofer-Zehnder symplectic capacities based on a class of Hamiltonian boundary value problems motivated by Clarke's and Ekeland's work, and to study generalizations of some important results about the original these two capacities (for example, the famous Weinstein conjecture, representation formula for $c_{\rm EH}$ and $c_{\rm HZ}$, a theorem by Evgeni Neduv, Brunn-Minkowski type inequality and Minkowski billiard trajectories proposed by Artstein-Avidan-Ostrover).Comment: Latex, 89 pages. Results in Section 1.6 are improved. Some typos are corrected. arXiv admin note: text overlap with arXiv:1903.0067

Coisotropic Hofer-Zehnder capacities of convex domains and related results

We prove representation formulas for the coisotropic Hofer-Zehnder capacities of bounded convex domains with special coisotropic submanifolds and the leaf relation (introduced by Lisi and Rieser recently), study their estimates and relations with the Hofer-Zehnder capacity, give some interesting corollaries, and also obtain corresponding versions of a Brunn-Minkowski type inequality by Artstein-Avidan and Ostrover and a theorem by Evgeni Neduv.Comment: Latex, 50 pages, extended last version, added more results and detai

Finite-Difference Simulations of Time Reversed Acoustics in a Layered Earth Model

Traditionally an earthquake is located by using the arrival times of P and S phases. This uses only a limited portion of the information on a seismogram. A large part of the information carried by the waveform is not used. In this study we investigate the applicability of the Time Reversed Acoustics (TRA) technique, and thus the whole waveform of the recorded signal, for earthquake locations and source characterization. The basic concept involved in TRA is the fundamental symmetry of time reversal invariance. Injecting the recorded signal, with time running backwards, reconstructs the whole wave field within the medium and can focus the wave field to the source. TRA has emerged as an important technique in acoustics with applications to medicine, underwater sound, and many other disciplines. The objective of this paper is to demonstrate the feasibility of applying TRA to seismological data by means of simulating the relevant features using a finite-difference approach. The following subjects are investigated: (1) Locating the earthquake hypocenter; (2) finding the source space-time function; and (3) characterizing the direction of fault rupture during an earthquake. The results show that the TRA technique can focus back to the source reasonably well in a layered earth model and can recover the source time function. The results also show that TRA has a good tolerance to noise. For efficient applications, calculation time can be reduced by generating a medium response library. The source location and source time function can then be determined by convolving the medium response library with the time-reversed signals recorded at the seismic stations.Massachusetts Institute of Technology. Earth Resources Laborator

Scheduling Based on Interruption Analysis and PSO for Strictly Periodic and Preemptive Partitions in Integrated Modular Avionics

Integrated modular avionics introduces the concept of partition and has been widely used in avionics industry. Partitions share the computing resources together. Partition scheduling plays a key role in guaranteeing correct execution of partitions. In this paper, a strictly periodic and preemptive partition scheduling strategy is investigated. First, we propose a partition scheduling model that allows a partition to be interrupted by other partitions, but minimizes the number of interruptions. The model not only retains the execution reliability of the simple partition sets that can be scheduled without interruptions, but also enhances the schedulability of the complex partition sets that can only be scheduled with some interruptions. Based on the model, we propose an optimization framework. First, an interruption analysis method to decide whether a partition set can be scheduled without interruptions is developed. Then, based on the analysis of the scheduling problem, we use the number of interruptions and the sum of execution time for all partitions in a major time frame as the optimization objective functions and use particle swarm optimization (PSO) to solve the optimization problem when the partition sets cannot be scheduled without interruptions. We improve the update strategy for the particles beyond the search space and round all particles before calculating the fitness value in PSO. Finally, the experiments with different partitions are conducted and the results validate the partition scheduling model and illustrate the effectiveness of the optimization framework. In addition, other optimization algorithms, such as genetic algorithm and neural networks, can also be used to solve the partition problem based on our model and solution framework

Measured radiation patterns of the scale model dipole tool

The sound field of finite dipole acoustic transducers in a steel tool was investigated and their horizontal by measuring their vertical radiation patterns in water at two different frequencies. Measurements were also made with the tool in scale models representative of sonic logging conditions in the field. A Lucite borehole model was used to represent a soft formation and an Austin Chalk borehole model was used to represent a hard formation. The presence of the tool as a finite baffle for the transducer, introduces differences between the vertical and horizontal radiation patterns. In contrast to the vertical pattern, the horizontal radiation pattern has a narrower main lobe with relatively larger side lobes. The angular location of the side lobes as seen in the water measurements, do not change much in the borehole.Massachusetts Institute of Technology. Earth Resources LaboratoryMassachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Orientation-Aware 3D SLAM in Alternating Magnetic Field from Powerlines

Identifying new sensing modalities for indoor localization is an interest of research. This paper studies powerline-induced alternating magnetic field (AMF) that fills the indoor space for the orientation-aware three-dimensional (3D) simultaneous localization and mapping (SLAM). While an existing study has adopted a uniaxial AMF sensor for SLAM in a plane surface, the design falls short of addressing the vector field nature of AMF and is therefore susceptible to sensor orientation variations. Moreover, although the higher spatial variability of AMF in comparison with indoor geomagnetism promotes location sensing resolution, extra SLAM algorithm designs are needed to achieve robustness to trajectory deviations from the constructed map. To address the above issues, we design a new triaxial AMF sensor and a new SLAM algorithm that constructs a 3D AMF intensity map regularized and augmented by a Gaussian process. The triaxial sensor’s orientation estimation is free of the error accumulation problem faced by inertial sensing. From extensive evaluation in eight indoor environments, our AMF-based 3D SLAM achieves sub-1m to 3m median localization errors in spaces of up to 500 m2 , sub-2° mean error in orientation sensing, and outperforms the SLAM systems based on Wi-Fi, geomagnetism, and uniaxial AMF by more than 30%

Coisotropic Ekeland-Hofer capacities

For subsets in the standard symplectic space $(\mathbb{R}^{2n},\omega_0)$ whose closures are intersecting with coisotropic subspace $\mathbb{R}^{n,k}$ we construct relative versions of their Ekeland-Hofer capacities with respect to $\mathbb{R}^{n,k}$, establish representation formulas for such capacities of bounded convex domains intersecting with $\mathbb{R}^{n,k}$, and also prove a product formula and a fact that the value of this capacity on a hypersurface $\mathcal{S}$ of restricted contact type containing the origin is equal to the action of a generalized leafwise chord on $\mathcal{S}$.Comment: We added an appendix in which the connectedness of the subgroup ${\rm Sp}(2n,k)$ was proved, corrected a few errors, and fixed some typos. 34 pages, 2 figure

Disitamab Vedotin (RC48) combined with bevacizumab for treatment of HR-negative/HER2-positive metastatic breast cancer with liver and brain involvement: A case report

BackgroundThe overexpression of human epidermal growth factor receptor 2 (HER2) is strongly correlated with an elevated risk of developing distant metastases, particularly brain metastases, in breast cancer (BC) cases. RC48 (also known as Disitamab vedotin), represents a promising antibody-drug conjugate (ADC), that comprises three well-defined components: hertuzumab against the prominent tumor target-HER2, monomethyl auristatin E (MMAE) and a cleavable linker. Preclinical studies have demonstrated its robust antitumor activity in BC patient-derived xenograft models with HER2-positive or HER2-low expression. Additionally, antiangiogenic drugs like bevacizumab have shown potential efficacy on advanced BC via inhibiting pathological neovascularizationits.Case presentationHere, we will share our experience in treating a 49-year-old woman initially diagnosed with stage IV breast cancer characterized by hormone receptor (HR)-negativity and HER2-positivity. This complex case entailed brain and liver metastases, and the patient exhibited resistance to various HER2-targeted treatment regimens. Finally, the patient received RC48 plus bevacizumab as the advanced forth-line treatment, which was well tolerated with no observed toxicities. Subsequent radiological assessments revealed remarkable regression in the brain metastatic lesions, classified as having partial response based on the RECIST 1.1 system. The period of progression-free survival (PFS) was 7 months.ConclusionThe present study underscores the efficacy of systemic treatment with RC48 in conjunction, showcasing substantial enhancement in both radiographic indicators and clinical symptomatology among patients with brain metastatic breast cancer (BMBC). More specifically, the sequential application of ADCs in combination with antiangiogenics presents a novel avenue for advancing the treatment landscape of metastatic BC

A Wideband and Polarization-Independent Metasurface Based on Phase Optimization for Monostatic and Bistatic Radar Cross Section Reduction

A broadband and polarization-independent metasurface is analyzed and designed for both monostatic and bistatic radar cross section (RCS) reduction in this paper. Metasurfaces are composed of two types of electromagnetic band-gap (EBG) lattice, which is a subarray with “0” or “” phase responses, arranged in periodic and aperiodic fashions. A new mechanism is proposed for manipulating electromagnetic (EM) scattering and realizing the best reduction of monostatic and bistatic RCS by redirecting EM energy to more directions through controlling the wavefront of EMwave reflected from the metasurface. Scattering characteristics of two kinds of metasurfaces, periodic arrangement and optimized phase layout, are studied in detail. Optimizing phase layout through particle swarm optimization (PSO) together with far field pattern prediction can produce a lot of scattering lobes, leading to a great reduction of bistatic RCS. For the designed metasurface based on optimal phase layout, a bandwidth of more than 80% is achieved at the normal incidence for the −9.5 dB RCS reduction for both monostatic and bistatic. Bistatic RCS reduction at frequency points with exactly 180∘ phase difference reaches 17.6 dB. Both TE and TM polarizations for oblique incidence are considered. The measured results are in good agreement with the corresponding simulations