The Scalar Curvature Problem on the Four Dimensional Half Sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature to a metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.Comment: 19 page

Large System Analysis of Box-Relaxation in Correlated Massive MIMO Systems Under Imperfect CSI (Extended Version)

In this paper, we study the mean square error (MSE) and the bit error rate (BER) performance of the box-relaxation decoder in massive multiple-input-multiple-output (MIMO) systems under the assumptions of imperfect channel state information (CSI) and receive-side channel correlation. Our analysis assumes that the number of transmit and receive antennas ($n$,and $m$) grow simultaneously large while their ratio remains fixed. For simplicity of the analysis, we consider binary phase shift keying (BPSK) modulated signals. The asymptotic approximations of the MSE and BER enable us to derive the optimal power allocation scheme under MSE/BER minimization. Numerical simulations suggest that the asymptotic approximations are accurate even for small $n$ and $m$. They also show the important role of the box constraint in mitigating the so called double descent phenomenon

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Existence Theorems For a(u,v)-monotone of nonstandard Hemivariational Inequality

In this paper, we consider the existence result of a nonstandard hemivariational inequalities with a(u,v) -monotone mapping in reflexive and non reflexive Banachs space. Finally, we provide sufficient conditions for which that inequality has a solution in the case of unbounded sets, via the fixed point and KKM theorems

Effect of Tiamulin or Rescue-kit(R) on diet utilisation, growth and carcass yield of growing rabbits

[EN] A total of 192 CalifornianxNew Zealand rabbits weaned at 33 d old were used in this experiment. Animals were allocated at weaning to three homogenous treatment groups based on litter size and live weight. Rabbits in control treatment (C) were offered a standard feed (SF) containing Robenidin and Flavomycin. Rabbits in TI treatment were fed SF diet and supplemented between days 33 and 62 with Tiamulin. The third group of rabbits (RK treatment) were fed SF diet and supplemented with Rescue-Kit(R) (containing B. licheniformis and B. subtilis (1600x10(9) CFU), betain, vitamins and oligo-elements) in the drinking water from 41 to 50 d of age. Digestibility of the experimental diets was recorded from 47 to 50 d of age, growth performance from weaning to 77 d old and carcass performance at 77 d of age. In the second week after weaning, between days 41 and 50, average daily gain (ADG) and feed intake for the regime including Tiamulin increased by 19 and 7.5% (P<=0.051) compared to those fed C and RK treatments. In this period, animals supplemented with Tiamulin obtained the best feed conversion ratio (FCR) and the highest DM digestibility (P=0.023). Rabbits from RK treatment showed the same DM digestibility than those from the C group, but an intermediate FCR between TI and C rabbits. The retrieval of Tiamulin from the diet after day 62 and until day 77 led to a decrease in ADG of the rabbits, which was lower than for animals receiving RK (P=0.007), while C animals had intermediate growth traits. It resulted that for the whole fattening period, treatments had no effect on ADG, feed intake and FCR (32.1 and 143 g/d and 4.13 g/g, respectively). Overall mortality rates and dressing out percentage were also similar among treatments (26.6 and 59.8%, respectively).Haj Ayed, M.; Ben Saïd, B. (2008). Effect of Tiamulin or Rescue-kit(R) on diet utilisation, growth and carcass yield of growing rabbits. World Rabbit Science. 16(3). doi:10.4995/wrs.2008.62716

Multi-Estimator Full Left Ventricle Quantification through Ensemble Learning

Cardiovascular disease accounts for 1 in every 4 deaths in United States. Accurate estimation of structural and functional cardiac parameters is crucial for both diagnosis and disease management. In this work, we develop an ensemble learning framework for more accurate and robust left ventricle (LV) quantification. The framework combines two 1st-level modules: direct estimation module and a segmentation module. The direct estimation module utilizes Convolutional Neural Network (CNN) to achieve end-to-end quantification. The CNN is trained by taking 2D cardiac images as input and cardiac parameters as output. The segmentation module utilizes a U-Net architecture for obtaining pixel-wise prediction of the epicardium and endocardium of LV from the background. The binary U-Net output is then analyzed by a separate CNN for estimating the cardiac parameters. We then employ linear regression between the 1st-level predictor and ground truth to learn a 2nd-level predictor that ensembles the results from 1st-level modules for the final estimation. Preliminary results by testing the proposed framework on the LVQuan18 dataset show superior performance of the ensemble learning model over the two base modules.Comment: Jiasha Liu, Xiang Li and Hui Ren contribute equally to this wor