A Reinvestigation of Moving Punctured Black Holes with a New Code

We report on our code, in which the moving puncture method is applied and an adaptive/fixed mesh refinement is implemented, and on its preliminary performance on black hole simulations. Based on the BSSN formulation, up-to-date gauge conditions and the modifications of the formulation are also implemented and tested. In this work we present our primary results about the simulation of a single static black hole, of a moving single black hole, and of the head-on collision of a binary black hole system. For the static punctured black hole simulations, different modifications of the BSSN formulation are applied. It is demonstrated that both the currently used sets of modifications lead to a stable evolution. For cases of a moving punctured black hole with or without spin, we search for viable gauge conditions and study the effect of spin on the black hole evolution. Our results confirm previous results obtained by other research groups. In addition, we find a new gauge condition, which has not yet been adopted by any other researchers, which can also give stable and accurate black hole evolution calculations. We examine the performance of the code for the head-on collision of a binary black hole system, and the agreement of the gravitational waveform it produces with that obtained in other works. In order to understand qualitatively the influence of matter on the binary black hole collisions, we also investigate the same head-on collision scenarios but perturbed by a scalar field. The numerical simulations performed with this code not only give stable and accurate results that are consistent with the works by other numerical relativity groups, but also lead to the discovery of a new viable gauge condition, as well as clarify some ambiguities in the modification of the BSSN formulation.Comment: 17 pages, 8 figures, accepted for publication in PR

Hamiltonian Analysis of Poincar\'e Gauge Theory: Higher Spin Modes

We examine several higher spin modes of the Poincar\'e gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to non-linear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin 1 and the pure spin 2 modes. The coupled spin-$0^-$ and spin-$2^-$ modes also fail our test due to the appearance of constraint bifurcation. The ``promising'' case in the linearized theory of PGT given by Kuhfuss and Nitsch (KRNJ86) likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity.Comment: 30 pages, submitted to Int. J. Mod. Phys.

Communication-Efficient Federated Learning over Capacity-Limited Wireless Networks

In this paper, a communication-efficient federated learning (FL) framework is proposed for improving the convergence rate of FL under a limited uplink capacity. The central idea of the proposed framework is to transmit the values and positions of the top-$S$ entries of a local model update for uplink transmission. A lossless encoding technique is considered for transmitting the positions of these entries, while a linear transformation followed by the Lloyd-Max scalar quantization is considered for transmitting their values. For an accurate reconstruction of the top-$S$ values, a linear minimum mean squared error method is developed based on the Bussgang decomposition. Moreover, an error feedback strategy is introduced to compensate for both compression and reconstruction errors. The convergence rate of the proposed framework is analyzed for a non-convex loss function with consideration of the compression and reconstruction errors. From the analytical result, the key parameters of the proposed framework are optimized for maximizing the convergence rate for the given capacity. Simulation results on the MNIST and CIFAR-10 datasets demonstrate that the proposed framework outperforms state-of-the-art FL frameworks in terms of classification accuracy under the limited uplink capacity

MIMO Detection under Hardware Impairments: Learning with Noisy Labels

This paper considers a data detection problem in multiple-input multiple-output (MIMO) communication systems with hardware impairments. To address challenges posed by nonlinear and unknown distortion in received signals, two learning-based detection methods, referred to as model-driven and data-driven, are presented. The model-driven method employs a generalized Gaussian distortion model to approximate the conditional distribution of the distorted received signal. By using the outputs of coarse data detection as noisy training data, the model-driven method avoids the need for additional training overhead beyond traditional pilot overhead for channel estimation. An expectation-maximization algorithm is devised to accurately learn the parameters of the distortion model from noisy training data. To resolve a model mismatch problem in the model-driven method, the data-driven method employs a deep neural network (DNN) for approximating a-posteriori probabilities for each received signal. This method uses the outputs of the model-driven method as noisy labels and therefore does not require extra training overhead. To avoid the overfitting problem caused by noisy labels, a robust DNN training algorithm is devised, which involves a warm-up period, sample selection, and loss correction. Simulation results demonstrate that the two proposed methods outperform existing solutions with the same overhead under various hardware impairment scenarios

Hamiltonian analysis of Poincar\'e gauge theory scalar modes

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-$0^-$ mode has normal dynamical propagation but the associated massless $0^-$ is pure gauge. The spin-$0^+$ mode investigated here is also viable in general. Both modes exhibit a simple type of ``constraint bifurcation'' for certain special field/parameter values.Comment: 28 pages, LaTex, submitted to International Journal of Modern Physics

Construction and development of corporate knowledge in modern conditions

The study deals with issues related to the construction and development of corporate knowledge in modern conditions caused by transformational processes in the socio-economic sphere of Ukraine conditioned by the war and other challenges that stimulate the need for new knowledge. The need for rapid response to these requests actualises in theoretical and applied terms the definition of the subject segment of new knowledge and its use. The purpose of the study is to highlight the features of construction and the necessity of developing corporate knowledge in modern conditions. To achieve this goal, the study uses the following methods: analysis, synthesis, system method, combinational grouping, modelling, and statistical method. As a result of the study, the need for new corporate knowledge is generalised and the following main groups are identified: knowledge on reorientation of the labour market through war; on security activities; related to mental health and emotional stability; related to the skills of psychological adaptation and flexibility in war conditions; knowledge on the strategy of change, and their characteristics are given. It is proved that new corporate knowledge acquired during the war changes the labour market and reorients the current business processes, social processes, communication and worldview processes in various types of economic activity, which requires a revision of the principles of corporate knowledge construction. As a result of the research, a model of the life cycle of corporate knowledge management was created, the use of which will increase the efficiency of knowledge exchange and the use of intellectual resources, and the process of constructing corporate knowledge based on the factor of intellectual culture was proposed. The conclusions obtained from the results of the study are of applied value and can be useful for representatives of business, the public sector, educational and scientific institutions in developing strategies for change and development and forecasting trends in order to improve and update the corporate knowledge bas