On the non-uniqueness of transport equation: the quantitative relationship between temporal and spatial regularity

In this paper, we consider the non-uniqueness of transport equation on the torus $\mathbb{T}^d$, with density $\rho\in L^{s}_tL_x^{p}$ and divergence-free vector field $\boldsymbol{u}\in L^{s'}_tL_x^{p'}\cap L^{\tilde{s}}_tW_x^{1,\tilde{p}}$. We prove that the non-uniqueness holds for $\frac{1}{p}+\frac{\tilde{s}'}{s\tilde{p}}>1+\frac{1}{d-1}$, with $d\ge 2$ and $s,p,\tilde{p}\in[1,\infty)$, $1\le\tilde{s}<s'$. The result can be extended to the transport-diffusion equation with diffusion operator of order $k$ in the class $\rho\in L^{s}_tL_x^{p}\cap L_t^{\bar{s}}C_x^{\bar{m}}$, $\boldsymbol{u}\in L^{s'}_tL_x^{p'}\cap L^{\tilde{s}}_tW_x^{1,\tilde{p}}$, under some conditions on $\bar{s},\bar{m},k$. In particular, when $\tilde{s}=1$, the additional condition is $\bar{m}<\frac{s}{\bar{s}}-1$, $k<\frac{s}{s'}+1$. These results can be considered as quantitative versions of Cheskidov and Luo's [Ann. PDE, 2021]. The main tool is the convex integration developed by Modena-Sattig-Sz\'ekelyhidi [Ann. PDE, 2018; Calc. Var. Partial Differ. Equ., 2019; Annales de l'Institut Henri Poincar\'e C, Analyse non lin\`eaire, 2020] and Cheskidov-Luo [Ann. PDE, 2021; arXiv, 2022 (forthcoming in Anal. PDE, 2023)].Comment: arXiv admin note: text overlap with arXiv:2308.0150

Synaptic Partner Assignment Using Attentional Voxel Association Networks

Connectomics aims to recover a complete set of synaptic connections within a dataset imaged by volume electron microscopy. Many systems have been proposed for locating synapses, and recent research has included a way to identify the synaptic partners that communicate at a synaptic cleft. We re-frame the problem of identifying synaptic partners as directly generating the mask of the synaptic partners from a given cleft. We train a convolutional network to perform this task. The network takes the local image context and a binary mask representing a single cleft as input. It is trained to produce two binary output masks: one which labels the voxels of the presynaptic partner within the input image, and another similar labeling for the postsynaptic partner. The cleft mask acts as an attentional gating signal for the network. We find that an implementation of this approach performs well on a dataset of mouse somatosensory cortex, and evaluate it as part of a combined system to predict both clefts and connections

Convolutional nets for reconstructing neural circuits from brain images acquired by serial section electron microscopy

Neural circuits can be reconstructed from brain images acquired by serial section electron microscopy. Image analysis has been performed by manual labor for half a century, and efforts at automation date back almost as far. Convolutional nets were first applied to neuronal boundary detection a dozen years ago, and have now achieved impressive accuracy on clean images. Robust handling of image defects is a major outstanding challenge. Convolutional nets are also being employed for other tasks in neural circuit reconstruction: finding synapses and identifying synaptic partners, extending or pruning neuronal reconstructions, and aligning serial section images to create a 3D image stack. Computational systems are being engineered to handle petavoxel images of cubic millimeter brain volumes

Model for Estimation Urban Transportation Supply-Demand Ratio

The paper establishes an estimation model of urban transportation supply-demand ratio (TSDR) to quantitatively describe the conditions of an urban transport system and to support a theoretical basis for transport policy-making. This TSDR estimation model is supported by the system dynamic principle and the VENSIM (an application that simulates the real system). It was accomplished by long-term observation of eight cities’ transport conditions and by analyzing the estimated results of TSDR from fifteen sets of refined data. The estimated results indicate that an urban TSDR can be classified into four grades representing four transport conditions: “scarce supply,” “short supply,” “supply-demand balance,” and “excess supply.” These results imply that transport policies or measures can be quantified to facilitate the process of ordering and screening them

CT-guided microcoil localization for scapula-blocked pulmonary nodules using penetrating lung puncture before video-assisted thoracic surgery

PURPOSETo retrospectively analyze the effectiveness and safety of computed tomography (CT)-guided microcoil localization for scapula-blocked pulmonary nodules using penetrating lung puncture prior to video-assisted thoracic surgery (VATS).METHODSOne hundred thirty-eight patients with 138 pulmonary nodules were included in this single-center retrospective study. Among them, 110 patients who underwent CT-guided microcoil localization using the routine puncture technique formed the routine group; the other 28 patients who underwent the CT-guided microcoil localization using the penetrating lung puncture technique formed the penetrating lung group. The main outcomes were the success rate and complication rate of the two groups.RESULTSThe localization success rate was 95.5% (105/110) in the routine group and 89.3% (25/28) in the penetrating lung group (P = 0.205). There was no statistical difference in any of the complications (pneumothorax, intrapulmonary hemorrhage, or moderate and severe chest pain) in both groups (P = 0.178, P = 0.204, P = 0.709, respectively). Localization procedure time was significantly increased in the penetrating lung group compared with the routine group (31.0 ± 3.0 min vs. 21.2 ± 2.8 min, P < 0.001).CONCLUSIONCT-guided microcoil localization for scapula-blocked pulmonary nodules using penetrating lung puncture prior to VATS resection is effective and safe. However, the deployment of the microcoil using penetrating lung puncture required more time than the routine puncture method

CEMIP Promotes Osteosarcoma Progression and Metastasis Through Activating Notch Signaling Pathway

Cell migration inducing protein (CEMIP) has been linked to carcinogenesis in several types of cancers. However, the role and mechanism of CEMIP in osteosarcoma remain unclear. This study investigated the role of CEMIP in the progression and metastasis of osteosarcoma, CEMIP was found to be overexpressed in osteosarcoma tissues when compared to adjacent non-tumor tissues, and its expression was positively associated with a poor prognosis in osteosarcoma patients. Silencing CEMIP decreased osteosarcoma cells proliferation, migration, and invasion, but enhanced apoptosis in vitro, and suppressed tumor growth and metastasis in vivo. Mechanistically, CEMIP promoted osteosarcoma cells growth and metastasis through activating Notch signaling pathway, silencing CEMIP would reduce the protein expression and activation of Notch/Jagged1/Hes1 signaling pathway in vitro and in vivo, activation of Notch signaling pathway could partially reversed cell proliferation and migration in shCEMIP osteosarcoma cells. In conclusion, our study demonstrated that CEMIP plays a substantial role in the progression of osteosarcoma via Notch signaling pathway, providing a promising therapeutic target in osteosarcoma

Evolution Game Model of Travel Mode Choice in Metropolitan

The paper describes an evolution game model of travel mode choice to determine whether transportation policies would have the desired effect. The model is first expressed as a two-stage sequential game in the extensive form based on the similarity between evolution game theory and the travel mode choice process. Second, backward induction is used to solve for Nash equilibrium of the game based on the Folk Theorem. Third, the sensitivity analysis suggests that a payoff reduction of travel by any mode will result in a rising proportion of inhabitants travelling by that mode and falling proportions of inhabitants travelling by other modes. Finally, the model is applied to Beijing inhabitants’ travel mode choices during morning peak hours and draws the conclusion that the proportion of inhabitants travelling by rail would increase when traffic congestion is more severe. This confirms that fast construction of the urban rail transit would be an effective means of alleviating traffic congestion. The model may be a useful tool for policy makers for analyzing the complex influence of travel mode choice processes on transport policies and transport construction projects

Model for Estimation Urban Transportation Supply-Demand Ratio

The paper establishes an estimation model of urban transportation supply-demand ratio (TSDR) to quantitatively describe the conditions of an urban transport system and to support a theoretical basis for transport policy-making. This TSDR estimation model is supported by the system dynamic principle and the VENSIM (an application that simulates the real system). It was accomplished by long-term observation of eight cities&apos; transport conditions and by analyzing the estimated results of TSDR from fifteen sets of refined data. The estimated results indicate that an urban TSDR can be classified into four grades representing four transport conditions: &quot;scarce supply,&quot; &quot;short supply,&quot; &quot;supply-demand balance,&quot; and &quot;excess supply.&quot; These results imply that transport policies or measures can be quantified to facilitate the process of ordering and screening them