Formal degrees of genuine Iwahori-spherical representations

For square-integrable genuine Iwahori-spherical representations of central covers, we verify the Hiraga--Ichino--Ikeda formula for their formal degrees. We also compute the Whittaker dimensions of these representations, when their associated modules over the genuine Iwahori--Hecke algebra are one-dimensional

Workflow-based Fast Data-driven Predictive Control with Disturbance Observer in Cloud-edge Collaborative Architecture

Data-driven predictive control (DPC) has been studied and used in various scenarios, since it could generate the predicted control sequence only relying on the historical input and output data. Recently, based on cloud computing, data-driven predictive cloud control system (DPCCS) has been proposed with the advantage of sufficient computational resources. However, the existing computation mode of DPCCS is centralized. This computation mode could not utilize fully the computing power of cloud computing, of which the structure is distributed. Thus, the computation delay could not been reduced and still affects the control quality. In this paper, a novel cloud-edge collaborative containerised workflow-based DPC system with disturbance observer (DOB) is proposed, to improve the computation efficiency and guarantee the control accuracy. First, a construction method for the DPC workflow is designed, to match the distributed processing environment of cloud computing. But the non-computation overheads of the workflow tasks are relatively high. Therefore, a cloud-edge collaborative control scheme with DOB is designed. The low-weight data could be truncated to reduce the non-computation overheads. Meanwhile, we design an edge DOB to estimate and compensate the uncertainty in cloud workflow processing, and obtain the composite control variable. The UUB stability of the DOB is also proved. Third, to execute the workflow-based DPC controller and evaluate the proposed cloud-edge collaborative control scheme with DOB in the real cloud environment, we design and implement a practical workflow-based cloud control experimental system based on container technology. Finally, a series of evaluations show that, the computation times are decreased by 45.19% and 74.35% for two real-time control examples, respectively, and by at most 85.10% for a high-dimension control example.Comment: 58 pages and 23 figure

Hardness of Graph-Structured Algebraic and Symbolic Problems

In this paper, we study the hardness of solving graph-structured linear systems with coefficients over a finite field $\mathbb{Z}_p$ and over a polynomial ring $\mathbb{F}[x_1,\ldots,x_t]$. We reduce solving general linear systems in $\mathbb{Z}_p$ to solving unit-weight low-degree graph Laplacians over $\mathbb{Z}_p$ with a polylogarithmic overhead on the number of non-zeros. Given the hardness of solving general linear systems in $\mathbb{Z}_p$ [Casacuberta-Kyng 2022], this result shows that it is unlikely that we can generalize Laplacian solvers over $\mathbb{R}$, or finite-element based methods over $\mathbb{R}$ in general, to a finite-field setting. We also reduce solving general linear systems over $\mathbb{Z}_p$ to solving linear systems whose coefficient matrices are walk matrices (matrices with all ones on the diagonal) and normalized Laplacians (Laplacians that are also walk matrices) over $\mathbb{Z}_p$. We often need to apply linear system solvers to random linear systems, in which case the worst case analysis above might be less relevant. For example, we often need to substitute variables in a symbolic matrix with random values. Here, a symbolic matrix is simply a matrix whose entries are in a polynomial ring $\mathbb{F}[x_1, \ldots, x_t]$. We formally define the reducibility between symbolic matrix classes, which are classified in terms of the degrees of the entries and the number of occurrences of the variables. We show that the determinant identity testing problem for symbolic matrices with polynomial degree $1$ and variable multiplicity at most $3$ is at least as hard as the same problem for general matrices over $\mathbb{R}$.Comment: 57 pages, submitted version to STOC2

Structural parameters optimization of internal mixing air atomizing nozzle based on orthogonal experiment

In order to grasp the influence of structural parameters of internal mixing air atomizing nozzles on the atomization characteristics and dust reduction efficiency, so as to obtain economical and reasonable nozzle structure parameters, the self-designed and developed spray dust reduction experimental platform and the orthogonal design method was used to carry out experiment on nozzle atomization characteristics and dust reduction efficiency under the combination of structural parameters. The experimental results shown that, with the diameter of the liquid cap injection hole increased, the nozzle water flow rate increased, while the air flow rate decreased continuously. Nozzle air flow increased with the number of liquid cap injection hole, whereas nozzle water flow was less affected by the number of liquid cap injection hole. When the diameter of the water injection hole gradually increased, the Sauter Mean Diameter (SMD) increased continuously. SMD with the increase of the number of air injection holes shown a change law of first decrease and then increase, and the minimum value was reached when the number of air injection holes was 4, where the atomization effect was the best. When the air cap outlet diameter was 2.0 mm and 2.5 mm, the nozzle droplet size was smaller. With the increase of the diameter of the water injection holes and the number of air injection holes of the liquid cap, the dust reduction efficiency of total dust and respirable dust both first increased and then decreased, and the best effect of the dust reduction was obtained in the diameter of water injection holes of 1.5 mm and the number of air injection holes of 4, respectively. With the diameter of the air cap outlet increased, the dust reduction efficiency of both total dust and respirable dust increased, but the increase of the dust reduction efficiency was smaller when the diameter of the air cap outlet was greater than 2.0 mm. Comprehensively considering the nozzle atomization characteristics and dust reduction efficiency, for the nozzle air cap, the outlet diameter should be 2.0 mm, for the nozzle liquid cap, it was reasonable to use a water injection hole diameter of 1.5 mm and the number of air injection holes to be 4, which can obtain the highest dust reduction efficiency. It is more reasonable to use the nozzles with the combination of above structure parameters for industrial applications, which can obtain smaller droplet size and higher dust reduction efficiency with lower air and water consumption

Rethink Baseline of Integrated Gradients from the Perspective of Shapley Value

Numerous approaches have attempted to interpret deep neural networks (DNNs) by attributing the prediction of DNN to its input features. One of the well-studied attribution methods is Integrated Gradients (IG). Specifically, the choice of baselines for IG is a critical consideration for generating meaningful and unbiased explanations for model predictions in different scenarios. However, current practice of exploiting a single baseline fails to fulfill this ambition, thus demanding multiple baselines. Fortunately, the inherent connection between IG and Aumann-Shapley Value forms a unique perspective to rethink the design of baselines. Under certain hypothesis, we theoretically analyse that a set of baseline aligns with the coalitions in Shapley Value. Thus, we propose a novel baseline construction method called Shapley Integrated Gradients (SIG) that searches for a set of baselines by proportional sampling to partly simulate the computation path of Shapley Value. Simulations on GridWorld show that SIG approximates the proportion of Shapley Values. Furthermore, experiments conducted on various image tasks demonstrate that compared to IG using other baseline methods, SIG exhibits an improved estimation of feature's contribution, offers more consistent explanations across diverse applications, and is generic to distinct data types or instances with insignificant computational overhead.Comment: 12 page

GNG12 as A Novel Molecular Marker for the Diagnosis and Treatment of Glioma

PurposeGNG12 influences a variety of tumors; however, its relationship with glioma remains unclear. The aim of this study was to comprehensively investigate the relationship between GNG12 and the clinical characteristics and prognosis of glioma patients and reveal the mechanisms causing the malignant process of GNG12.Materials and MethodsWe obtained information on clinical samples from multiple databases. The expression level of GNG12 was validated using a RT-qPCR and IHC. KM curves were used to assess the correlation between the GNG12 expression and OS of glioma patients. An ROC curve was drawn to assess the predictive performance of GNG12. Univariate and multivariate Cox analyses were performed to analyze the factors affecting the prognosis of patients with glioma. GSEA and TIMER databases were used to estimate the relationship between GNG12 expression, possible molecular mechanisms, and immune cell infiltration. CMap analysis was used to screen candidate drugs for glioma. Subsequent in vitro experiments were used to validate the proliferation and migration of glioma cells and to explore the potential mechanisms by which GNG12 causes poor prognosis in gliomas.ResultsGNG12 was overexpressed in glioma patients and GNG12 expression level correlated closely with clinical features, including age and histological type, etc. Subsequently, the K-M survival analysis indicated that the expression level of GNG12 was relevant to the prognosis of glioma, and the ROC curve implied that GNG12 can predict glioma stability. Univariate and multivariate analyses showed that GNG12 represents a risk factor for glioma occurrence. GNG12 expression is closely associated with some immune cells. Additionally, several in vitro experiments demonstrated that down-regulation of GNG12 expression can inhibits the proliferation and migration capacity of glioma cells. Ultimately, the results for the GSEA and WB experiments revealed that GNG12 may promote the malignant progression of gliomas by regulating the cell adhesion molecule cell signaling pathway.ConclusionIn this study, we identified GNG12 as a novel oncogene elevated in gliomas. Reducing GNG12 expression inhibits the proliferation and migration of glioma cells. In summary, GNG12 can be used as a novel biomarker for the early diagnosis of human gliomas and as a potential therapeutic target

An Experimental Study on the Establishment of Pulmonary Hypertension Model in Rats induced by Monocrotaline

Pulmonary hypertension is called PH for short. It is caused by the pulmonary artery vascular disease leading to pulmonary vascular resistance, and the increase right lung compartment load, which resulting in weakening or even collapse of the right ventricular function. The establishment of rat PH model under the action of monocrotaline is a repeatable, simple and accessible operation technique, which has been widely used in the treatment of pulmonary hypertension. This paper discusses the principle and properties of the PH model on rats under the monocrotaline action

Biological Bone Micro Grinding Temperature Field under Nanoparticle Jet Mist Cooling

Clinical neurosurgeons used micro grinding to remove bone tissues, and drip irrigation-type normal saline (NS) is used with low cooling efficiency. Osteonecrosis and irreversible thermal neural injury caused by excessively high grinding temperature are bottleneck problems in neurosurgery and have severely restricted the application of micro grinding in surgical procedures. Therefore, a nanoparticle jet mist cooling (NJMC) bio-bone micro grinding process is put forward in this chapter. The nanofluid convective heat transfer mechanism in the micro grinding zone is investigated, and heat transfer enhancement mechanism of solid nanoparticles and heat distribution mechanism in the micro grinding zone are revealed. On this basis, a temperature field model of NJMC bio-bone micro grinding is established. An experimental platform of NJMC bio-bone micro grinding is constructed, and bone micro grinding force and temperatures at different measuring points on the bone surface are measured. The results indicated that the model error of temperature field is 6.7%, theoretical analysis basically accorded with experimental results, thus certifying the correctness of the dynamic temperature field in NJMC bio-bone micro grinding

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory

Real-time Monitoring for the Next Core-Collapse Supernova in JUNO

Core-collapse supernova (CCSN) is one of the most energetic astrophysical events in the Universe. The early and prompt detection of neutrinos before (pre-SN) and during the SN burst is a unique opportunity to realize the multi-messenger observation of the CCSN events. In this work, we describe the monitoring concept and present the sensitivity of the system to the pre-SN and SN neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO), which is a 20 kton liquid scintillator detector under construction in South China. The real-time monitoring system is designed with both the prompt monitors on the electronic board and online monitors at the data acquisition stage, in order to ensure both the alert speed and alert coverage of progenitor stars. By assuming a false alert rate of 1 per year, this monitoring system can be sensitive to the pre-SN neutrinos up to the distance of about 1.6 (0.9) kpc and SN neutrinos up to about 370 (360) kpc for a progenitor mass of 30$M_{\odot}$ for the case of normal (inverted) mass ordering. The pointing ability of the CCSN is evaluated by using the accumulated event anisotropy of the inverse beta decay interactions from pre-SN or SN neutrinos, which, along with the early alert, can play important roles for the followup multi-messenger observations of the next Galactic or nearby extragalactic CCSN.Comment: 24 pages, 9 figure