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Additional file 2: Table S1. Clinical characteristics of the enrolled patients for serum UPLC-MS/MS-based widely targeted metabolomics.

Additional file 1. Supplementary materials and methods: The details of metagenomic bioinformatic analysis and 2bRAD-M bioinformatic analysis.

Additional file 3: Figure S1. Diversity differences in the gut microbiome. Figure S2. Comparison of gut microbiota between recovers without GI symptoms at 3 months of follow-up after COVID-19 and those with mild disease. Figure S3. Diversity differences in the oral microbiome. Figure S4. Comparison of oral microbiota between recovers without GI symptoms at 3 months of follow-up after COVID-19 and those with mild disease. Figure S5. Alteration of specific metabolites in patient serum.

Additional file 5: Table S3. Differential metabolites in serum between follow-up group and normal group.

Additional file 4: Table S2. Differential metabolites in serum between follow-up group and mild group.

Homophily principle, i.e. nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over node-based Neural Networks on Node Classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) and neglects inter-class ND, which provides incomplete understanding of homophily. In this paper, we first demonstrate the aforementioned insufficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND, through which we can find how intra- and inter-class ND influence ND together. We visualize the results and give detailed analysis. Through experiments, we verified that the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels, based on which we propose a new performance metric beyond homophily, which is non-linear and feature-based. Experiments indicate it significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of GNNs on both synthetic and benchmark real-world datasets.

Bradysia odoriphaga (Diptera: Sciaridae) is a serious pest of Chinese chives cultivated in China. Chemosensory proteins (CSPs) are important components of insect olfactory systems that capture and bind environmental semiochemicals which are then transported to olfactory receptors. Despite their importance, the mechanism of olfaction and related behavioral processes in B. odoriphaga have not been characterized. Here, we found that BodoCSP4 has an important olfactory function. RT-qPCR indicated that BodoCSP4 expression was highest in the heads (antennae removed) of adult males, followed by the antennae of adult males. Competitive binding assays with 33 ligands indicated that BodoCSP4 binds well with methyl allyl disulfide, diallyl disulfide, and n-heptadecane; the corresponding dissolution constants (Ki) were as high as 5.71, 5.71, and 6.85 μM, respectively. 3D-structural and molecular docking indicated that BodoCSP4 has five α-helices and surrounds the ligand with certain hydrophobic residues including Leu60, Leu63, Leu64, Ala67, Val28, Ile30, Ile33, Leu34, and Val86, suggesting these residues help BodoCSP4 bind to ligands. Silencing of BodoCSP4 significantly decreased the attraction of B. odoriphaga males to diallyl disulfide and n-heptadecane but not to methyl allyl disulfide in Y-tube olfaction assays. These results increase our understanding of how BodoCSP4 contributes to host and female localization by B. odoriphaga males.

Lettuce (Lactuca sativa L.) is a leafy vegetable whose edible organs usually are leaf or stems, and thus high-temperature induced bolting followed by flower initiation is an undesirable trait in lettuce production. However, the molecular mechanism that controls lettuce bolting and flowering upon thermal treatments is largely unknown. Here, we identified a Lettuce auxin response factor 3 (LsARF3), the expression of which was enhanced by heat and auxin treatments. Interestingly, LsARF3 is preferentially expressed in stem apex, suggesting it might be associated with lettuce bolting. Transgenic lettuce overexpressing LsARF3 displayed early bolting and flowering, whereas knockout of LsARF3 dramatically delayed bolting and flowering in lettuce under normal or high temperature conditions. Furthermore, Exogenous application of IAA failed to rescue the late-bolting and -flowering phenotype of lsarf3 mutants. Several floral integrator genes including LsCO, LsFT, and LsLFY were co-expressed with LsARF3 in the overexpression and knockout lettuce plants. Yeast one-hybrid (Y1H) experiments suggested that LsARF3 could physically interact with the LsCO promoter, which was further confirmed by a dual luciferase assay in tobacco leaves. The results indicated that LsARF3 might directly modulate the expression of LsCO in lettuce. Therefore, these results demonstrate that LsARF3 could promote lettuce bolting in response to the high temperature by directly or indirectly activating the expression of floral genes such as LsCO, which provides new insights into lettuce bolting in the context of ARFs signaling and heat response.

Stearic acid-rich A. parviflora oil production has remained conventional over the past years despite its socioeconomic importance. Ultrasonication (ULT), microwave irradiation (MIC), and ultrasound-microwave (hybrid technique, ULT-MIC)-assisted extraction parameters were optimized. Their effects on the physicochemical, antioxidative, and structural properties of A. parviflora oil were evaluated. ULT ensured higher oil yield and extraction efficiency of 64.15% and 92.16%, respectively, with a 33.33% reduction in extraction time over the conventional method. Oil extraction yield with MIC and ULT-MIC were solvent dielectric constant, e (polarity) dependent. ULT, MIC, and ULT-MIC enhanced the freshness and stability of A. parviflora oil by reducing its acid and peroxide values significantly. MIC produced oil with high total phenol content (226.60 mg Gallic acid equivalents (GAE)/kg). Ultrasonic action had the highest impact on the seed meal structure. A high yield of edible oil that possesses strong antioxidant activity could be obtained by adopting the ULT-MIC hybrid extraction technique with a polar solvent.

The increase of waste products on the market will lead to a shortage of resources and the deterioration of the environment. The premise of the realization of remanufacturing engineering is the redundancy of product design life. The method is to give new life to scrapped parts. However, there will be problems with customer demand orientation and fragmentation of parts. Based on this research background, this paper proposes a remanufacturing process-oriented product structure information model, which mathematically models the mapping mechanism of remanufacturing design parameters and features. At the same time, the design goal conflict coordination and transformation under the constraints of the product model are analyzed to simulate the stochastic process generation algorithm. Finally, this paper uses the remanufacturing process of an auto part as a case to verify the algorithm's effectiveness.

In recent years, smart windows have been gradually applied and developed in the fields of environmental protection, energy management, smart camouflage and display. With the continuous upgrading of market demand, smart windows with both visible and infrared band modulation functions are the future development trends. However, the optical modulation of smart windows is usually limited in the visible light band (380-780 nm). In this paper, we report a novel smart window by doping antimony doped tin oxide (ATO) nanoparticles (NPs) into polymer stabilized liquid crystal (PSLC) films. These films have the widest waveband modulation function among those reported so far, covering the visible and infrared regions (380-5500 nm). The transmittance of the as-prepared smart films can be changed reversibly from highly transparent (78.5%) state to a strong light scattering (10%) state in the visible region. In addition, due to the localized surface plasmon resonance of ATO NPs, up to 80.7% of the infrared invisible light can be effectively shielded. The significance of this research is to provide theoretical and technical support for the broadband optical modulation of novel smart windows.

Titanium alloy is widely used in aerospace and other fields due to its low density, high specific strength, corrosion resistance, and other advantages. With the development of selective laser melting additive manufacturing technology, it is possible to manufacture triply periodic minimal surface porous structures. The effects of structural parameters on the mechanical properties of a Ti-6Al-4V Diamond (D)-type triply periodic minimal surface structure are studied. According to the characteristics of porous structures, the Gibson Ashby fitting formulas of D structures are modified using the concept of equivalent cross-sectional areas. The influence of cell size and surface thickness on the compressive modulus and strength of a D structure is discussed. Prediction formulas of the mechanical properties based on cell size and surface thickness are established by combining the relative density with the structural parameters. On this basis, the density optimization method is applied to the lightweight design of a rocket-related assembly based on D structure filling. The design results verify the feasibility of a lightweight design based on triply periodic minimal surface structure filling.

This paper presents the development and experimental evaluation of a surgical robotic system for total hip arthroplasty (THA). Although existing robotic systems used in joint replacement surgery have achieved some progresses, the robot arm must be situated accurately at the target position during operation, which depends significantly on the experience of the surgeon. In addition, handheld acetabulum reamers typically exhibit uneven strength and grinding file. Moreover, the lack of techniques to real-time measure femoral neck length may lead to poor outcomes. To tackle these challenges, we propose a real-time traceable optical positioning strategy to reduce unnecessary manual adjustments to the robotic arm during surgery, an end-effector system to stabilise grinding, and an optical probe to provide real-time measurement of the femoral neck length and other parameters used to choose the proper prosthesis. The lengths of the lower limbs are measured as the prosthesis is installed. The experimental evaluation results show that, based on its accuracy, execution ability, and robustness, the proposed surgical robotic system is feasible for THA.

A 3D convolutional neural network which was trained using simulated data only has been assessed for the purpose of estimating surrogate sO2 from multiwavelength photoacoustic images of experimental phantoms with well-defined ground truths.

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by additionally making use of graph structure based on the relational inductive bias (edge bias), rather than treating the nodes as collections of independent and identically distributed (\iid) samples. Though GNNs are believed to outperform basic NNs in real-world tasks, it is found that in some cases, GNNs have little performance gain or even underperform graph-agnostic NNs. To identify these cases, based on graph signal processing and statistical hypothesis testing, we propose two measures which analyze the cases in which the edge bias in features and labels does not provide advantages. Based on the measures, a threshold value can be given to predict the potential performance advantages of graph-aware models over graph-agnostic models.

Additional file 1: Fig. S1. FISH images of Malat1 on GC-2 cells. Fig. S2. 5��� and 3��� RACE results. Fig. S3. Tsx expression in germ cells. Fig. S4. Analysis of impact of Tsx deficiency on meiosis. Fig. S5. Analysis of impact of Tsx deficiency on Sertoli cells. Fig. S6. Functional impact of Tsx knockdown on male fertility.

Additional file 2: Table S1. Sequences of oligonucleotides used in this study.

Category: Ankle; Hindfoot; Other Introduction/Purpose: There is limited documentation of the results of the treatment of advanced progressive collapsing deformity with talar tilt. No article to our knowledge with pre-and post-operative ankle x-rays has more than eight patients and average follow up more than three years. Methods: This article presents the results of twenty consecutive patients with medium to long term follow up. All patients had deltoid reconstruction with tendon graft from the talus to the tibia and foot reconstruction to achieve a heel centered under the lower leg, a stable midfoot and a mild to moderately plantarflexed first metatarsal. Patients were followed an average 10.8 years (SD = 4.6, Range 4.6-17) and had standing pre-and post-operative radiographs along with FAOS and PROMIS scores. Radiographs were assessed for talar tilt preoperatively, early postoperatively and at final follow up. Data was analyzed with paired t-tests, Mann Whitney U test, fisher's exact test and univariable linear regression. All p-values are two-sided and statistical significance was evaluated at the 0.05 alpha level. Results: Two patients failed the procedure; one had an ankle fusion and the second infection eventually required a BKA. The remaining 18 patients were satisfied with their procedure, maintained significant improvement in outcome scores and talar tilt and required no other procedure on their ankle. The mean talar tilt preoperatively was 10.9 degrees (SD = 3.9) and at final follow up 4.2 degrees (SD = 2.8) (PConclusion: Combined deltoid and foot reconstruction, as described, has acceptable results in majority of patients at medium to long term follow up.

The lymphatic system acts as an avenue through which cancer cells can spread from tumour. Lymph nodes (LNs) linking the lymphatic vessels play a critical role in filtering the cancer cells. Thus, the presence of metastases in LN is an important indicator for cancer staging [1]. As angiogenesis is a key feature of cancer, any variations in LN microcirculation can be a biomarker for metastasis. However, a non-invasive technique capable of visualising and quantifying vasculature and blood flow in LNs is lacking and highly desirable. Contrast-enhanced ultrasound (CEUS) utilising microbubbles shows great potential for visualising lymphatic vessels and identifying sentinel LNs. It allows for the diagnosis of metastatic LNs through the visualisation of perfusion pattern. However, current CEUS imaging techniques have several limitations that prevent the accurate identification, visualisation and diagnosisof LNs: (i) Tissue artefacts and bubble disruption can reduce the image contrast. (ii) Limited spatial and temporal resolution diminishes the amount of information that can be captured by CEUS. (iii) The slow flow in both the lymphatic system and the micro-vessels inside LNs makes Doppler-based approaches less effective. (iv) The identification of enhancement pattern is subjective and can vary between different observers. In this thesis, we aim to improve the capability of CEUS in non-invasive identification and evaluation of LNs through the use of high frame rate (HFR) imaging and super-resolution (SR) ultrasound (US) imaging. Firstly, we evaluate the feasibility of using HFR CEUS for the detection of lymphatic vessels where flow is slow. The study is carried out on a lymphatic vessel phantom. Specifically, the work investigates how CEUS lymphatic imaging is affected by several key factors such as ultrasound pressure, flow velocity probe motion and image contrast. Experiments were also conducted to observe microbubble behaviour under HFR CEUS. Our results show that (i) HFR imaging and singular value decomposition (SVD) filtering can significantly reduce tissue artefacts in the phantom at high clinical frequencies; (ii) the slow flow rate within the lymphatic system makes image contrast and signal persistence more susceptible to changes in ultrasound amplitude or mechanical index (MI), and a suitable MI value can be chosen to reach a compromise between image contrast and bubble disruption under slow flow condition; (iii) probe motion significantly decreases image contrast of the vessel, which can be improved by applying motion correction before SVD filtering; (iv) the optical observation of the impact of ultrasound pressure on HFR CEUS further confirms the importance of optimising ultrasound amplitude. Secondly, the feasibility of in vivo three-dimensional SR US imaging for the visualisation and quantification of LN microvascular and blood flow was studied in a rabbit model. In vivo studies were carried out to image popliteal LNs of two healthy male New Zealand white rabbits aged 6–8 weeks. Three-dimensional, high-frame-rate, contrast enhanced US was achieved by mechanically scanning a linear imaging probe. Individual microbubbles were identified, localised, and tracked to form three-dimensional SR images and super-resolved velocity maps. Acoustic sub-aperture processing was used to improve image contrast and to generate enhanced power Doppler and colour Doppler images. Vessel size and blood flow velocity distributions were evaluated and assessed by using paired Student’s t-test. SR images is able to reveal microvessels in the rabbit LN with branches clearly resolved up to 30 μm. This is less than half the acoustic wavelength and not resolvable by power or colour Doppler. The apparent size distribution of most vessels in the SR images was below 80 μm which agrees with micro-CT data. In contrast, most vessels detected with Doppler techniques were larger than 80 μm. The blood flow velocity distribution indicated that most of the blood flow in rabbit popliteal LN was at velocities lower than 5 mm/sec. We demonstrate that three-dimensional super-resolution US imaging using microbubbles allows non-invasive, non-ionising visualisation and quantification of LN microvascular structures and blood flow dynamics with resolution below the wave diffraction limit. This technology has great potential for further study of the physiological functions of the lymphatic system and the clinical detection of LN metastasis. Finally, we explore the potential of using SR US for distinguishing metastatic LNs from reactive LNs in human. In this study, SR US images and super resolved velocity maps of LNs are generated from patient data acquired with a clinical ultrasound system. We discuss the challenges of acquiring suitable datasets in the clinical settings and suggest solutions to overcome these challenges. For example, destruction pulses are utilised to achieve suitable microbubble concentration for super-resolution ultrasound imaging. In addition, motion correction is applied before the detection of microbubble to compensate for the significant movement in real clinical settings. After obtaining the super resolution ultrasound images, multiple morphological and functional measures are derived from the super resolution images and super resolved velocity maps. These measures were compared for the reactive and metastatic LNs and assessed using a two sample student’s t-test. Our initial results indicate that metastatic LNs have significantly higher variance in blood flow direction compared to that of reactive LNs. Different factors affecting the quantifications of super-resolution ultrasound imaging are also studied and potential solutions are provided to take these factors into account. This study demonstrates the possibility of using quantifications obtained from super resolution ultrasound images to discriminate between metastatic and reactive LNs. Open Access

Network structures in various backgrounds play important roles in social, technological, and biological systems. However, the observable network structures in real cases are often incomplete or unavailable due to measurement errors or private protection issues. Therefore, inferring the complete network structure is useful for understanding complex systems. The existing studies have not fully solved the problem of inferring network structure with partial or no information about connections or nodes. In this paper, we tackle the problem by utilizing time series data generated by network dynamics. We regard the network inference problem based on dynamical time series data as a problem of minimizing errors for predicting future states and proposed a novel data-driven deep learning model called Gumbel Graph Network (GGN) to solve the two kinds of network inference problems: Network Reconstruction and Network Completion. For the network reconstruction problem, the GGN framework includes two modules: the dynamics learner and the network generator. For the network completion problem, GGN adds a new module called the States Learner to infer missing parts of the network. We carried out experiments on discrete and continuous time series data. The experiments show that our method can reconstruct up to 100% network structure on the network reconstruction task. While the model can also infer the unknown parts of the structure with up to 90% accuracy when some nodes are missing. And the accuracy decays with the increase of the fractions of missing nodes. Our framework may have wide application areas where the network structure is hard to obtained and the time series data is rich.

Gypsum-based composite boards reinforced with mono- and multilayer perforated amorphous Fe78Si9B13 ribbons were fabricated by pouring gypsum slurry directly into molds with prelaid epoxy-re...

P-type transparent conductive materials (TCMs) are urgently needed in the development of photoelectric devices. In particular, the P-type TCMs that can be applied in the mid-infrared range are even rarer due to the conflict between the transparent range and the conductivity of materials. In this work, a P-type mid-infrared transparent conductive LaSe2 film is obtained by a two-step method combining the RF sputtering and a selenized annealing process. The crystal structure of the film has been confirmed by x-ray diffraction and Raman spectrum analysis. According to the Hall effect measurement results, the LaSe2 film has a higher conductivity (about 3.6 S/cm) than that of traditional P-type mid-infrared TCMs, which is attributed to its ten times higher carrier concentration (about 1019 cm−3) and a much smaller hole effective mass (about 0.34 me) compared to the conventional P-type mid-infrared TCMs. The transmittance (about 75%) is at the same level as that of the traditional P-type mid-infrared TCMs. In a sense, the LaSe2 is a promising candidate material for the development of mid-infrared photoelectric devices.

Sharp local structure, like the leading edge of hypersonic aircraft, confronts a severe aerodynamic heating environment at a Mach number greater than 5. To eliminate the danger of a material failure, a semi-active thermal protection system is proposed by integrating a metallic heat pipe into the structure of the leading edge. An analytical heat-balance model is established from traditional aerodynamic theories, and then thermal and mechanical characteristics of the structure are studied at Mach number 6–8 for three refractory alloys, Inconel 625, C-103, and T-111. The feasibility of this simple analytical method as an initial design tool for hypersonic aircraft is assessed through numerical simulations using a finite element method. The results indicate that both the isothermal and the maximum temperatures fall but the von Mises stress increases with a longer design length of the leading edge. These two temperatures and the stress rise remarkably at a higher Mach number. Under all investigated hypersonic conditions, with a 3mm leading edge radius and a 0.15m design length, the maximum stress exceeds the yield strength of Inconel 625 at Mach numbers greater than 6, which means a material failure. Moreover, both C-103 and T-111 meet all requirements at Mach number 6–8.

Piezoelectric bimorph based on k32 mode of ternary 0.24Pb(In1/2Nb1/2)O3–0.46Pb(Mg1/3Nb2/3)O3–0.30PbTiO3 (0.24PIN–-0.46PMN–-0.30PT) single crystal poled along [011]c has been fabricated and tested. The bimorph features very large electromechanical coupling factor (0.80) and very low working frequency (less than half of PZT based bimorph for the same dimensions) owing to the super large lateral extensional piezoelectric constant d32 and large elastic compliances of the crystal. The bimorph design can be used for miniaturized low-frequency electromechanical sensors and actuators.

In this paper we present the problems associated with acquisition of ground truth, which is a critical step in facilitating accurate and automated care in Assisted Living Facilities. The approach permits both bottom up and top down methods of reasoning about data. The tradeoffs between granularity of ground truth acquisition and its impact on the detection rate are presented. It is suggested that the acquisition of ground truth should become a seamless operation incorporated transparently into the workflow of operations in these facilities. It is expected that with automation of collection, the increasing corpus of ground truth will lead to steady improvements in the detection rate and therefore the quality of automated monitoring and care provisioning. The methodology and models are substantiated with real data from two assisted living facilities, one in Singapore and the other in France. Although the results are preliminary they are quite promising.

Zhu, Jiaqi. M.S., Purdue University, December 2013. The Impact of Nutrition Information Delivery Methods on Restaurant Consumers' Attitudes and Behavior. Major Professors: Barbara A. Almanza, Carl A. Behnke. Obesity is a major public health threat. It not only creates challenges for those who are obese and overweight, but also brings an economic burden to the whole society. One important contributing factor for obesity is food eaten away from home, which accounts for more than 40% of American's food budget. Although chain quick-service restaurants are required by law to post calorie information on menus and menu boards, the efficacy of menu labeling for guiding consumers to choose the healthy food items has had mixed results. The purpose of the study was to find the best way to deliver the calorie information to the consumers leading to a change in purchase behavior. Three calorie information delivery methods (simple passive delivery, enhanced passive delivery and combined passive and active delivery) were developed in conjunction with three pairs of healthy and traditional food items. Over a four-week experiment, different delivery methods were applied, and sales and consumer choices were compared to the baseline week. Questionnaires were collected during the three treatment weeks. Ordinal logistic regression, analysis of variance, frequency and means tests were used to analyze the data. Ordinal logistic regression revealed that consumer attitudes towards healthy eating were significant in predicting healthy food item selection. However, the three treatments did not prove to be significant in guiding consumers to choose the healthy food items. Nevertheless, the treatments as a whole led 15% (N=25) of the respondents to change their original purchase intention from the traditional version to the healthy version. Using odds ratio comparison of the sales data, it could be concluded that the combined passive and active delivery methods was the most influential in helping the consumers make a healthy choice, followed by the simple passive delivery and the enhanced passive delivery methods. Apparently, consumers were more influenced if calorie information was delivered in a combined pattern (including passive and active information). Policy makers should consider the effect of other information delivery methods in addition to menus and menu boards in guiding consumers to choose healthy food items.

Complete sets of elastic, piezoelectric, and dielectric constants of 0.72Pb(Mg(1∕3)Nb(2∕3))O(3)-0.28PbTiO(3) single crystal poled along [111](c) (single domain) as well as non-polar axes [001](c) and [011](c) (multidomain) have been measured under natural conditions. These data allowed us to evaluate accurately the extrinsic contributions to the superior piezoelectric properties. Very large extrinsic contributions to the unusual anisotropies in multidomain crystals are confirmed. We found that the instability of domain structures is the origin of the low mechanical quality factor Q for the multidomain relaxor-based ferroelectric single crystals. Our results can provide useful guidance in future design of domain engineered materials.

Nearest neighbor search is used to identify which class a query sample belongs to. The most widely used method is the shortest Euclidean distance measure and it is accepted as the simplest and most effective method for pattern analysis. In pattern analysis, we are only interested in finding out the relevant class rather than the relevant training sample, thus existing algorithms are inefficient in that they try to find an exact training sample instead of a class, so it takes a long time to decide, especially when the dimension of a dataset is very high. In this paper we will present an efficient algorithm for directly searching the nearest class instead of the nearest training sample. Experiments show that our algorithm is much more efficient than the standard tree search methodologies.

M.Alekhnovich et al. recently have proposed a model of algorithms, called BT model, which covers Greedy, Backtrack and Simple Dynamic Programming methods and can be further divided into fixed, adaptive and fully adaptive three kinds, and have proved exponential time lower bounds of exact and approximation algorithms under adaptive BT model for Knapsack problem which are $\Omega(2^{n/2}/\sqrt n)=\Omega(2^{0.5n}/\sqrt n)$ and $\Omega((1/\epsilon)^{1/3.17})\approx\Omega((1/\epsilon)^{0.315})$(for approximation ratio $1-\epsilon$) respectively (M. Alekhovich, A. Borodin, J. Buresh-Oppenheim, R. Impagliazzo, A. Magen, and T. Pitassi, Toward a Model for Backtracking and Dynamic Programming, \emph{Proceedings of Twentieth Annual IEEE Conference on Computational Complexity}, pp308-322, 2005). In this note, we slightly improved their lower bounds to $\Omega(2^{(2-\epsilon)n/3}/\sqrt{n})\approx \Omega(2^{0.66n}/\sqrt{n})$ and $\Omega((1/\epsilon)^{1/2.38})\approx\Omega((1/\epsilon)^{0.420})$, and proposed as an open question what is the best achievable lower bounds for knapsack under adaptive BT models., Comment: 9 pages, 3 figures

This paper discusses properties of quantum fingerprinting with shared entanglement. Under certain restriction of final measurement, a relation is given between unitary operations of two parties. Then, by reducing to spherical coding problem, this paper gives a lower bound of worst case error probability for quantum fingerprinting with shared entanglement, showing a relation between worst case error probability and the amount of entanglement(measured by Schmidt number).