Greedy MAXCUT Algorithms and their Information Content

MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning, computer vision and statistical physics. Greedy algorithms to approximately solve MAXCUT rely on greedy vertex labelling or on an edge contraction strategy. These algorithms have been studied by measuring their approximation ratios in the worst case setting but very little is known to characterize their robustness to noise contaminations of the input data in the average case. Adapting the framework of Approximation Set Coding, we present a method to exactly measure the cardinality of the algorithmic approximation sets of five greedy MAXCUT algorithms. Their information contents are explored for graph instances generated by two different noise models: the edge reversal model and Gaussian edge weights model. The results provide insights into the robustness of different greedy heuristics and techniques for MAXCUT, which can be used for algorithm design of general USM problems.Comment: This is a longer version of the paper published in 2015 IEEE Information Theory Workshop (ITW

Carry On

Carry On is my thesis project for a MFA in Film and Animation at Rochester Institute of Technology. The entire process took more than two years from start to finish. In November 2011, I wrote the first draft of the script. In April 2013, we finished filming. I did not wrap up editing and the final stages of production until December 2013. I ran into many difficulties and faced many challenges during this special experience, yet I also received more help than I had ever imagined in getting me through these hard times. Truthfully, there would be no way for me to finish a project of this magnitude all on my own. I have learned so much and solidified many professional relationships through this project. I believe this invaluable experience will serve as a cornerstone for my future career development. Carry On tells a story set in Japan-occupied China during World War II. In 1944, the tide turned against Japan and the war began winding down. Prior to their retreat, Japanese troops looted every Chinese village in their path. They took only food and women from these villages followed by massacring all others and burning everything to the ground. To save his daughter, a Chinese father in my film stuffs her into a large bag disguised as food. As he loads the bag onto the back of a truck along with other bags with food, a Japanese army officer spots his secret. But, surprisingly, moved by the Chinese father\u27s love and courage the officer plays along and lets the daughter go

SAIBench: A Structural Interpretation of AI for Science Through Benchmarks

Artificial Intelligence for Science (AI4S) is an emerging research field that utilizes machine learning advancements to tackle complex scientific computational issues, aiming to enhance computational efficiency and accuracy. However, the data-driven nature of AI4S lacks the correctness or accuracy assurances of conventional scientific computing, posing challenges when deploying AI4S models in real-world applications. To mitigate these, more comprehensive benchmarking procedures are needed to better understand AI4S models. This paper introduces a novel benchmarking approach, known as structural interpretation, which addresses two key requirements: identifying the trusted operating range in the problem space and tracing errors back to their computational components. This method partitions both the problem and metric spaces, facilitating a structural exploration of these spaces. The practical utility and effectiveness of structural interpretation are illustrated through its application to three distinct AI4S workloads: machine-learning force fields (MLFF), jet tagging, and precipitation nowcasting. The benchmarks effectively model the trusted operating range, trace errors, and reveal novel perspectives for refining the model, training process, and data sampling strategy. This work is part of the SAIBench project, an AI4S benchmarking suite

A Spatial Sigma-Delta Approach to Mitigation of Power Amplifier Distortions in Massive MIMO Downlink

In massive multiple-input multiple-output (MIMO) downlink systems, the physical implementation of the base stations (BSs) requires the use of cheap and power-efficient power amplifiers (PAs) to avoid high hardware cost and high power consumption. However, such PAs usually have limited linear amplification ranges. Nonlinear distortions arising from operation beyond the linear amplification ranges can significantly degrade system performance. Existing approaches to handle the nonlinear distortions, such as digital predistortion (DPD), typically require accurate knowledge, or acquisition, of the PA transfer function. In this paper, we present a new concept for mitigation of the PA distortions. Assuming a uniform linear array (ULA) at the BS, the idea is to apply a Sigma-Delta ($\Sigma \Delta$) modulator to spatially shape the PA distortions to the high-angle region. By having the system operating in the low-angle region, the received signals are less affected by the PA distortions. To demonstrate the potential of this spatial $\Sigma \Delta$ approach, we study the application of our approach to the multi-user MIMO-orthogonal frequency division modulation (OFDM) downlink scenario. A symbol-level precoding (SLP) scheme and a zero-forcing (ZF) precoding scheme, with the new design requirement by the spatial $\Sigma \Delta$ approach being taken into account, are developed. Numerical simulations are performed to show the effectiveness of the developed $\Sigma \Delta$ precoding schemes

Effectivity on Continuous Functions in Topological Spaces

AbstractIn this paper we investigate aspects of effectivity and computability on partial continuous functions in topological spaces. We use the framework of TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We generalize the representations introduced in [Weihrauch, K., “Computable Analysis,” Springer, Berlin, 2000] for the Euclidean case to computable T0-spaces and computably locally compact Hausdorff spaces respectively. We show their equivalence and in particular, prove an effective version of the Stone-Weierstrass approximation theorem