L1 scheme for solving an inverse problem subject to a fractional diffusion equation

This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established with an arbitrary sectorial operator of spectral angle $< \pi/2$, that is the resolvent set of this operator contains $\{z\in\mathbb C\setminus\{0\}:\ |\operatorname{Arg} z|< \theta\}$ for some $\pi/2 < \theta < \pi$. The relationship between the time fractional order $\alpha \in (0, 1)$ and the constants in the error estimates is precisely characterized, revealing that the L1 scheme is robust as $\alpha$ approaches $1$. Then an inverse problem of a fractional diffusion equation is analyzed, and the convergence analysis of a temporal discretization of this inverse problem is given. Finally, numerical results are provided to confirm the theoretical results

Deep Imaging of the HCG 95 Field.I.Ultra-diffuse Galaxies

We present a detection of 89 candidates of ultra-diffuse galaxies (UDGs) in a 4.9 degree$^2$ field centered on the Hickson Compact Group 95 (HCG 95) using deep $g$- and $r$-band images taken with the Chinese Near Object Survey Telescope. This field contains one rich galaxy cluster (Abell 2588 at $z$=0.199) and two poor clusters (Pegasus I at $z$=0.013 and Pegasus II at $z$=0.040). The 89 candidates are likely associated with the two poor clusters, giving about 50 $-$ 60 true UDGs with a half-light radius $r_{\rm e} > 1.5$ kpc and a central surface brightness $\mu(g,0) > 24.0$ mag arcsec$^{-2}$. Deep $z$'-band images are available for 84 of the 89 galaxies from the Dark Energy Camera Legacy Survey (DECaLS), confirming that these galaxies have an extremely low central surface brightness. Moreover, our UDG candidates are spread over a wide range in $g-r$ color, and $\sim$26% are as blue as normal star-forming galaxies, which is suggestive of young UDGs that are still in formation. Interestingly, we find that one UDG linked with HCG 95 is a gas-rich galaxy with H I mass $1.1 \times 10^{9} M_{\odot}$ detected by the Very Large Array, and has a stellar mass of $M_\star \sim 1.8 \times 10^{8}$ $M_{\odot}$. This indicates that UDGs at least partially overlap with the population of nearly dark galaxies found in deep H I surveys. Our results show that the high abundance of blue UDGs in the HCG 95 field is favored by the environment of poor galaxy clusters residing in H I-rich large-scale structures.Comment: Published in Ap

The anti-sepsis activity of the components of Huanglian Jiedu Decoction with high lipid A-binding affinity

Huanglian Jiedu Decoction (HJD), one of the classic recipes for relieving toxicity and fever, is a common method for treating sepsis in China. However, the effective components of HJD have not yet been identified. This experiment was carried out to elucidate the effective components of HJD against sepsis. Thus, seven fractions from HJD were tested using a biosensor to test their affinity for lipid A. The components obtained that had high lipid A-binding fractions were further separated, and their affinities to lipid A were assessed with the aid of a biosensor. The levels of LPS in the blood were measured, and pathology experiments were conducted. The LPS levels and mRNA expression analysis of TNF-α and IL-6 of the cell supernatant and animal tissue were evaluated to investigate the molecular mechanisms. Palmatine showed the highest affinity to lipid A and was evaluated by in vitro and in vivo experiments. The results of the in vitro and in vivo experiments indicated that the levels of LPS, TNF-α and IL-6 of the palmatine group were significantly lower than those of the sepsis model group (p \u3c 0.01). The group treated with palmatine showed strong neutralizing LPS activity in vivo. The palmatine group exhibited stronger protective activity on vital organs compared to the LPS-induced animal model. This verifies that HJD is a viable treatment option for sepsis given that there are multiple components in HJD that neutralize LPS, decrease the release of IL-6 and TNF-α induced by LPS, and protect vital organs

A Hybrid Secure Scheme for Wireless Sensor Networks against Timing Attacks Using Continuous-Time Markov Chain and Queueing Model

Wireless sensor networks (WSNs) have recently gained popularity for a wide spectrum of applications. Monitoring tasks can be performed in various environments. This may be beneficial in many scenarios, but it certainly exhibits new challenges in terms of security due to increased data transmission over the wireless channel with potentially unknown threats. Among possible security issues are timing attacks, which are not prevented by traditional cryptographic security. Moreover, the limited energy and memory resources prohibit the use of complex security mechanisms in such systems. Therefore, balancing between security and the associated energy consumption becomes a crucial challenge. This paper proposes a secure scheme for WSNs while maintaining the requirement of the security-performance tradeoff. In order to proceed to a quantitative treatment of this problem, a hybrid continuous-time Markov chain (CTMC) and queueing model are put forward, and the tradeoff analysis of the security and performance attributes is carried out. By extending and transforming this model, the mean time to security attributes failure is evaluated. Through tradeoff analysis, we show that our scheme can enhance the security of WSNs, and the optimal rekeying rate of the performance and security tradeoff can be obtained. View Full-Tex

Assuring Safety of Vision-Based Swarm Formation Control

Vision-based formation control systems are attractive because they can use inexpensive sensors and can work in GPS-denied environments. The safety assurance for such systems is challenging: the vision component's accuracy depends on the environment in complicated ways, these errors propagate through the system and lead to incorrect control actions, and there exists no formal specification for end-to-end reasoning. We address this problem and propose a technique for safety assurance of vision-based formation control: First, we propose a scheme for constructing quantizers that are consistent with vision-based perception. Next, we show how the convergence analysis of a standard quantized consensus algorithm can be adapted for the constructed quantizers. We use the recently defined notion of perception contracts to create error bounds on the actual vision-based perception pipeline using sampled data from different ground truth states, environments, and weather conditions. Specifically, we use a quantizer in logarithmic polar coordinates, and we show that this quantizer is suitable for the constructed perception contracts for the vision-based position estimation, where the error worsens with respect to the absolute distance between agents. We build our formation control algorithm with this nonuniform quantizer, and we prove its convergence employing an existing result for quantized consensus.Comment: 8 pages, 7 figures, submitted to the 2024 American Control Conference (ACC 2024

Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations

Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) schemes to solve the 2D Keller-Segel systems directly with minimal computational cost, while preserving positivity, energy dissipation law and mass conservation. One scheme unconditionally preserves positivity, while the other does so conditionally. Both schemes achieve second-order accuracy in space, with the former being first-order accuracy in time and the latter second-order accuracy in time. Besides, the former scheme preserves the energy dissipation law asymptotically. We validate these results through numerical experiments, and also compare the efficiency of our schemes with the standard five-point scheme, demonstrating that our approaches effectively reduce computational costs.Comment: 29 page