Radio Resource Allocation in Wireless OFDM Systems

Ph.DDOCTOR OF PHILOSOPH

Linear scaling calculation of maximally-localized Wannier functions with atomic basis set

We have developed a linear scaling algorithm for calculating maximally-localized Wannier functions (MLWFs) using atomic orbital basis. An O(N) ground state calculation is carried out to get the density matrix (DM). Through a projection of the DM onto atomic orbitals and a subsequent O(N) orthogonalization, we obtain initial orthogonal localized orbitals. These orbitals can be maximally localized in linear scaling by simple Jacobi sweeps. Our O(N) method is validated by applying it to water molecule and wurtzite ZnO. The linear scaling behavior of the new method is demonstrated by computing the MLWFs of boron nitride nanotubes.Comment: J. Chem. Phys. in press (2006

A unified fused Lasso approach for sparse and blocky feature selection in regression and classification

In many applications, sparse and blocky coefficients often occur in regression and classification problems. The fused Lasso was designed to recover these sparse structured features especially when the design matrix encounters the situation of ultrahigh dimension. Quantile loss is well known as a robust loss function in regression and classification. In this paper, we combine quantile loss and fused Lasso penalty together to produce quantile fused Lasso which can achieve sparse and blocky feature selection in both regression and classification. Interestingly, our proposed model has the unified optimization formula for regression and classification. For ultrahigh dimensional collected data, we derive multi-block linearized alternating direction method of multipliers (LADMM) to deal with it. Moreover, we prove convergence and derive convergence rates of the proposed LADMM algorithm through an elegant method. Note that the algorithm can be easily extended to solve many existing fused Lasso models. Finally, we present some numerical results for several synthetic and real world examples, which illustrate the robustness, scalability, and accuracy of the proposed method

Precise expressions for random projections: Low-rank approximation and randomized Newton

It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even though there is an extensive literature on the worst-case performance of sketching, existing guarantees are typically very different from what is observed in practice. We exploit recent developments in the spectral analysis of random matrices to develop novel techniques that provide provably accurate expressions for the expected value of random projection matrices obtained via sketching. These expressions can be used to characterize the performance of dimensionality reduction in a variety of common machine learning tasks, ranging from low-rank approximation to iterative stochastic optimization. Our results apply to several popular sketching methods, including Gaussian and Rademacher sketches, and they enable precise analysis of these methods in terms of spectral properties of the data. Empirical results show that the expressions we derive reflect the practical performance of these sketching methods, down to lower-order effects and even constant factors.Comment: Minor corrections and clarifications of the previous version, including additional discussion in Appendix A.

Fashion Matrix: Editing Photos by Just Talking

The utilization of Large Language Models (LLMs) for the construction of AI systems has garnered significant attention across diverse fields. The extension of LLMs to the domain of fashion holds substantial commercial potential but also inherent challenges due to the intricate semantic interactions in fashion-related generation. To address this issue, we developed a hierarchical AI system called Fashion Matrix dedicated to editing photos by just talking. This system facilitates diverse prompt-driven tasks, encompassing garment or accessory replacement, recoloring, addition, and removal. Specifically, Fashion Matrix employs LLM as its foundational support and engages in iterative interactions with users. It employs a range of Semantic Segmentation Models (e.g., Grounded-SAM, MattingAnything, etc.) to delineate the specific editing masks based on user instructions. Subsequently, Visual Foundation Models (e.g., Stable Diffusion, ControlNet, etc.) are leveraged to generate edited images from text prompts and masks, thereby facilitating the automation of fashion editing processes. Experiments demonstrate the outstanding ability of Fashion Matrix to explores the collaborative potential of functionally diverse pre-trained models in the domain of fashion editing.Comment: 13 pages, 5 figures, 2 table

Measurement of the effective weak mixing angle at the CEPC

We present a study of the measurement of the effective weak mixing angle parameter (\sin^2\theta_{\text{eff}}^{\text{\ell}}) at the Circular Electron Positron Collider (CEPC). As a fundamental physics parameter, \sin^2\theta_{\text{eff}}^{\text{\ell}} plays a key role not only in the global test of the standard model electroweak sector, but also in constraining the potential beyond standard model new physics at high energy frontier. CEPC proposes a two year running period around the $Z$ boson mass pole at high instantaneous luminosity. It is demonstrated that with one month data taken, the uncertainty of \sin^2\theta_{\text{eff}}^{\text{\ell}} at $Z$ pole can be reduced to 0.00001 both in the lepton and heavy quark final states, which is much smaller than the theoretical uncertainty of the calculation with two-loop radiative corrections. It will not only improve the precision with respect to the measurements from previous colliders including the LEP, SLC, Tevatron and LHC, but also provide direct comparison between different final states. In this paper, we also study the measurement of \sin^2\theta_{\text{eff}}^{\text{\ell}} at high mass region. With one month data taken, the precision of \sin^2\theta_{\text{eff}}^{\text{\ell}} measured at 130 GeV from $b$ quark final state is 0.00007, which will be an important experimental observation on the energy-running effect of \sin^2\theta_{\text{eff}}^{\text{\ell}}