On the Hecke Module of GLₙ(k[[z]])\GLₙ(k((z)))/GLₙ(k((z²)))

[See Abstract in text of thesis for correct representation of mathematics] Every double coset in GLₘ(k[[z]])\GLₘ(k((z)))/GLₘ(k((z²))) is uniquely represented by a block diagonal matrix with diagonal blocks in { 1,z, (11 z \\0 zⁱ \\) (i&gt;1) } if char(k) ≠ 2 and k is a finite field. These cosets form a (spherical) Hecke module H(G,H,K) over the (spherical) Hecke algebra H(G,K) of double cosets in K\G/H, where K=GLₘ(k[[z]]) and H=GLₘ(k((z²))) and G=GLₘ(k((z))). Similarly to Hall polynomial hλ,ν^µ from the Hecke algebra H(G,K), coefficients hλ,ν^µ arise from the Hecke module. We will provide a closed formula for hλ,ν^µ, under some restrictions over λ, ν, µ.</p

Pornographic Image Recognition via Weighted Multiple Instance Learning

In the era of Internet, recognizing pornographic images is of great significance for protecting children's physical and mental health. However, this task is very challenging as the key pornographic contents (e.g., breast and private part) in an image often lie in local regions of small size. In this paper, we model each image as a bag of regions, and follow a multiple instance learning (MIL) approach to train a generic region-based recognition model. Specifically, we take into account the region's degree of pornography, and make three main contributions. First, we show that based on very few annotations of the key pornographic contents in a training image, we can generate a bag of properly sized regions, among which the potential positive regions usually contain useful contexts that can aid recognition. Second, we present a simple quantitative measure of a region's degree of pornography, which can be used to weigh the importance of different regions in a positive image. Third, we formulate the recognition task as a weighted MIL problem under the convolutional neural network framework, with a bag probability function introduced to combine the importance of different regions. Experiments on our newly collected large scale dataset demonstrate the effectiveness of the proposed method, achieving an accuracy with 97.52% true positive rate at 1% false positive rate, tested on 100K pornographic images and 100K normal images.Comment: 9 pages, 3 figure

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The nonlinear inverse problem of electromagnetic induction to recover electrical conductivity is examined. As this is an ill-posed problem based on inaccurate data, there is a strong need to find the reliable features of the models of electrical conductivity. By using optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data, we attempt to make conclusions about Earth structure under assumptions of one-dimensional and two-dimensional structure. The forward modeling equations are constraints in an optimization problem solving for the fields and the conductivity simultaneously. The computational framework easily allows additional inequality constraints to be imposed.Under the one-dimensional assumption, we develop the optimization approach for use on the magnetotelluric inverse problem. After verifying its accuracy, we use our method to obtain bounds on Earth's average conductivity that all conductivity profiles must obey. There is no regularization required to solve the problem. With the emplacement of additional inequality constraints, we further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models.We take the lessons from the 1-D inverse problem and apply them to the 2-D inverse problem. The difficulty of the 2-D inverse problem requires that we first examine our ability to solve the forward problem, where the conductivity structure is known and the fields are unknown. Our forward problem is designed such that we are able to directly transfer it into the optimization approach used for the inversion. With the successful 2-D forward problem as the constraints, a one-dimensional 2-D inverse problem is stepped into a fully 2-D inverse problem for testing purposes. The computational machinery is incrementally modified to meet the challenge of the realistic two-dimensional magnetotelluric inverse problem. We then use two shallow-Earth data sets from different conductivity regimes and invert them for bounded and regularized structure

Synthetical Analysis on Geological Factors Ccontrolling Coalbed Methane

AbstractThe gas-controlling property is the important content for the coalbed methane (CBM) theoretical research, and it has the important role for guiding the CBM exploration and development. The evolution features of the coal-bearing strata and structure and the current CBM preservation condition are the keys determining the CBM enrichment and reservoir formation. In the case that the earth curst is stable in the sedimentary period of the coal-bearing strata and after the coal-bearing strata are deposited, the coal seam deposited by the coal-accumulation has the large and stable thickness, the earth curst is stably subsided after the coal-accumulation period or the strength of the structural movement is low and the uplifted amplitude is little, then it is favorable for the CBM enrichment. In the area there the coal-bearing strata have the simple structure, the enclosing rock of coal seam is stable and compact, the seam buried depth is deep, and in the stagnant area with the simple hydrogeological condition, the CBM-controlling property is well. The research on the CBM-controlling property is restricted by the exploration degree, with respect to the area with the low exploration degree, the research on the CBM-controlling property could be combined with the exploration results of the area with the high exploration degree, on the basis of analysing the CBM distribution features and control factors of the area with the high exploration degree, adopting the analysis method such as the geological analogy and so on, it conducts the research work from the evolution features of the coal-bearing strata andstructure and the current CBM preservation condition

New Dynamic Stability Rig for Tri-sonic Wind-tunnel

AbstractThe present-day unconventional and high-lifting aerospace configuration design has greatly increased the demand for accurate prediction and expanded measure dynamic stability derivatives envelopes of conventional aerospace vehicles. With these issues in mind, china academy of aerospace aerodynamics (CAAA) designed and built a forced oscillation test rig in the sub-, tran- and supersonic wind tunnel that provides new capabilities for aerodynamic researchers to accurately measure the dynamic derivatives and investigate the asymmetric coupling effects of high-lifting aerospace configuration vehicles

Unsupervised video anomaly detection in UAVs: a new approach based on learning and inference

In this paper, an innovative approach to detecting anomalous occurrences in video data without supervision is introduced, leveraging contextual data derived from visual characteristics and effectively addressing the semantic discrepancy that exists between visual information and the interpretation of atypical incidents. Our work incorporates Unmanned Aerial Vehicles (UAVs) to capture video data from a different perspective and to provide a unique set of visual features. Specifically, we put forward a technique for discerning context through scene comprehension, which entails the construction of a spatio-temporal contextual graph to represent various aspects of visual information. These aspects encompass the manifestation of objects, their interrelations within the spatio-temporal domain, and the categorization of the scenes captured by UAVs. To encode context information, we utilize Transformer with message passing for updating the graph's nodes and edges. Furthermore, we have designed a graph-oriented deep Variational Autoencoder (VAE) approach for unsupervised categorization of scenes, enabling the extraction of the spatio-temporal context graph across diverse settings. In conclusion, by utilizing contextual data, we ascertain anomaly scores at the frame-level to identify atypical occurrences. We assessed the efficacy of the suggested approach by employing it on a trio of intricate data collections, specifically, the UCF-Crime, Avenue, and ShanghaiTech datasets, which provided substantial evidence of the method's successful performance

FedMLSecurity: A Benchmark for Attacks and Defenses in Federated Learning and LLMs

This paper introduces FedMLSecurity, a benchmark that simulates adversarial attacks and corresponding defense mechanisms in Federated Learning (FL). As an integral module of the open-sourced library FedML that facilitates FL algorithm development and performance comparison, FedMLSecurity enhances the security assessment capacity of FedML. FedMLSecurity comprises two principal components: FedMLAttacker, which simulates attacks injected into FL training, and FedMLDefender, which emulates defensive strategies designed to mitigate the impacts of the attacks. FedMLSecurity is open-sourced 1 and is customizable to a wide range of machine learning models (e.g., Logistic Regression, ResNet, GAN, etc.) and federated optimizers (e.g., FedAVG, FedOPT, FedNOVA, etc.). Experimental evaluations in this paper also demonstrate the ease of application of FedMLSecurity to Large Language Models (LLMs), further reinforcing its versatility and practical utility in various scenarios

MCM4 Is a Novel Biomarker Associated With Genomic Instability, BRCAness Phenotype, and Therapeutic Potentials in Soft-Tissue Sarcoma

Soft-tissue sarcoma (STS) is represented by a heterogeneous group of rare malignancies with various molecular oncogenesis. Therapies targeting DNA repair pathways in STS have achieved minimal progress, potentially due to the lack of molecular biomarker(s) beyond the histology subtype. In this report, we comprehensively analyzed the expression profiles of 100 liposarcomas (LPSs), the most common STS subtype, in comparison with 21 adipose tissues from multiple GEO datasets to identify the potential prognostic and therapeutic biomarker for LPS. Furthermore, we investigated TCGA database, our archived tumor samples, and patient-derived tumor cell cultures (PTCCs) as a validation. We identified a total of 69 common differentially expressed genes (DEGs) among public datasets, with mini-chromosome maintenance protein 4 (MCM4) identified as a novel biomarker correlated with patients’ clinical staging and survival outcome. MCM4-high expression LPS was characterized by MCM4 copy number increase, genomic instability, and BRCAness phenotype compared with the MCM4-low expression counterpart. In contrast, the mutational and the immune landscape were minimally different between the two groups. Interestingly, the association of MCM4-high expression with genomic instability and BRCAness were not only validated in LPS samples from our institution (n = 66) but also could be expanded to the pan-sarcoma cohort from TCGA database (n = 263). Surprisingly, based on four sarcoma cell lines and eight PTCCs (three LPS and five other sarcoma), we demonstrated that MCM4 overexpression tumors were therapeutically sensitive to PARP inhibitor (PARPi) and platinum chemotherapy, independent of the histology subtypes. Our study, for the first time, suggested that MCM4 might be a novel prognostic biomarker, associated with dysregulated DNA repair pathways and potential therapeutic vulnerability in STS

Smart Room Control System

With the evolution of technology and the continuous enhancement of people’s standard of living, interactions between human and electrical devices have become quick and easy. However, elders and individuals with disabilities may find it tough to communicate with machines without external aid. There has been development of different technologies with regards to smart home control systems, yet elders and disabled people still have many troubles in managing their space. Alternatively, hiring home care professionals to provide an environment, which is conductive to keeping the client safe and independent, could put a financial and emotional squeeze on physically impaired individuals and their families. In addition, physically impaired people may feel frustrated and stripped of their independence and privacy.&nbsp; MOTUSCONTROL is eager to fill this void and provide this necessary supervised care to disabled people in an affordable manner, regardless of their impairment. MOTUSCONTROL is creating the Smart Room Control System to give disabled people the ability to control their own space by using expressive and meaningful hand gestures, which get converted to signals that are sent to a computing system. The system is programmed to operate lighting, temperature control, security, appliances, and many other features specifically chosen to ensure that our final product be a valuable utility for the physically impaired individuals