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Theory and Algorithms Commons

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2021

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Articles 91 - 120 of 143

Full-Text Articles in Theory and Algorithms

Implications Of The Quantum Dna Model For Information Sciences, F. Matthew Mihelic Apr 2021

Implications Of The Quantum Dna Model For Information Sciences, F. Matthew Mihelic

Faculty Publications

The DNA molecule can be modeled as a quantum logic processor, and this model has been supported by pilot research that experimentally demonstrated non-local communication between cells in separated cell cultures. This modeling and pilot research have important implications for information sciences, providing a potential architecture for quantum computing that operates at room temperature and is scalable to millions of qubits, and including the potential for an entanglement communication system based upon the quantum DNA architecture. Such a system could be used to provide non-local quantum key distribution that could not be blocked by any shielding or water depth, would …


Distfold: Distance-Guided Protein Folding, Matthew Bernardini Apr 2021

Distfold: Distance-Guided Protein Folding, Matthew Bernardini

Theses

Protein structure prediction and its associated key sub-problems such as distance map prediction are of significance importance in biology and bioinformatics. The inter-residue distance prediction problem, or distance prediction in short, is to predict the physical distance between amino acids in a three-dimensional (3D) space, given a protein's one-dimensional sequence information. While there exist many methods to predict distance maps, there are currently no methods that can take those predicted distance maps and build 3D models from them in an ab initio way, i.e., without using any other information. This works aims to fill this gap by: a) developing a …


Technological Tethereds: Potential Impact Of Untrustworthy Artificial Intelligence In Criminal Justice Risk Assessment Instruments, Sonia M. Gipson Rankin Apr 2021

Technological Tethereds: Potential Impact Of Untrustworthy Artificial Intelligence In Criminal Justice Risk Assessment Instruments, Sonia M. Gipson Rankin

Faculty Scholarship

Issues of racial inequality and violence are front and center in today’s society, as are issues surrounding artificial intelligence (AI). This Article, written by a law professor who is also a computer scientist, takes a deep dive into understanding how and why hacked and rogue AI creates unlawful and unfair outcomes, particularly for persons of color.

Black Americans are disproportionally featured in criminal justice, and their stories are obfuscated. The seemingly endless back-to-back murders of George Floyd, Breonna Taylor, and Ahmaud Arbery, and heartbreakingly countless others have finally shaken the United States from its slumbering journey towards intentional criminal justice …


A Comprehensive Mapping And Real-World Evaluation Of Multi-Object Tracking On Automated Vehicles, Alexander Bassett Apr 2021

A Comprehensive Mapping And Real-World Evaluation Of Multi-Object Tracking On Automated Vehicles, Alexander Bassett

Doctoral Dissertations and Master's Theses

Multi-Object Tracking (MOT) is a field critical to Automated Vehicle (AV) perception systems. However, it is large, complex, spans research fields, and lacks resources for integration with real sensors and implementation on AVs. Factors such those make it difficult for new researchers and practitioners to enter the field.

This thesis presents two main contributions: 1) a comprehensive mapping for the field of Multi-Object Trackers (MOTs) with a specific focus towards Automated Vehicles (AVs) and 2) a real-world evaluation of an MOT developed and tuned using COTS (Commercial Off-The-Shelf) software toolsets. The first contribution aims to give a comprehensive overview of …


Dijkstra’S Pathfinder, Taylor F. Malamut Apr 2021

Dijkstra’S Pathfinder, Taylor F. Malamut

Honors Theses

Dijkstra’s algorithm has been widely studied and applied since it was first published in 1959. This research shows that Dijkstra’s algorithm can be used to find the shortest path between two stations on the Washington D.C. Metro. After exploring different types of research and applying Dijkstra’s algorithm, it was found that the algorithm will always yield the shortest path, even if visually a shorter path was initially expected.


A Fully Dynamic Algorithm For K-Regret Minimizing Sets, Yanhao Wang, Yuchen Li, Raymond Chi-Wing Wong, Kian-Lee Tan Apr 2021

A Fully Dynamic Algorithm For K-Regret Minimizing Sets, Yanhao Wang, Yuchen Li, Raymond Chi-Wing Wong, Kian-Lee Tan

Research Collection School Of Computing and Information Systems

Selecting a small set of representatives from a large database is important in many applications such as multi-criteria decision making, web search, and recommendation. The k-regret minimizing set (k-RMS) problem was recently proposed for representative tuple discovery. Specifically, for a large database P of tuples with multiple numerical attributes, the k-RMS problem returns a size-r subset Q of P such that, for any possible ranking function, the score of the top-ranked tuple in Q is not much worse than the score of the kth-ranked tuple in P. Although the k-RMS problem has been extensively studied in the literature, existing methods …


Toward A Quantum Neural Network: Proposing The Qaoa Algorithm To Replace A Feed Forward Neural Network, Erick Serrano Apr 2021

Toward A Quantum Neural Network: Proposing The Qaoa Algorithm To Replace A Feed Forward Neural Network, Erick Serrano

Undergraduate Research Symposium Posters

With a surge in popularity of machine learning as a whole, many researchers have sought optimization methods to reduce the complexity of neural networks; however, only recent attempts have been made to optimize neural networks via quantum computing methods. In this paper, we describe the training process of a feed forward neural network (FFNN) and the time complexity of the training process. We highlight the inefficiencies of the FFNN training process, particularly when implemented with gradient descent, and introduce a call to action for optimization of a FFNN. Afterward, we discuss the strides made in quantum computing to improve the …


Urban Perception: Sensing Cities Via A Deep Interactive Multi-Task Learning Framework, Weili Guan, Zhaozheng Chen, Fuli Feng, Weifeng Liu, Liqiang Nie Apr 2021

Urban Perception: Sensing Cities Via A Deep Interactive Multi-Task Learning Framework, Weili Guan, Zhaozheng Chen, Fuli Feng, Weifeng Liu, Liqiang Nie

Research Collection School Of Computing and Information Systems

Social scientists have shown evidence that visual perceptions of urban attributes, such as safe, wealthy, and beautiful perspectives of the given cities, are highly correlated to the residents' behaviors and quality of life. Despite their significance, measuring visual perceptions of urban attributes is challenging due to the following facts: (1) Visual perceptions are subjectively contradistinctive rather than absolute. (2) Perception comparisons between image pairs are usually conducted region by region, and highly related to the specific urban attributes. And (3) the urban attributes have both the shared and specific information. To address these problems, in this article, we present a …


Network-Based Analysis Of Early Pandemic Mitigation Strategies: Solutions, And Future Directions, Pegah Hozhabrierdi, Raymond Zhu, Maduakolam Onyewu, Sucheta Soundarajan Mar 2021

Network-Based Analysis Of Early Pandemic Mitigation Strategies: Solutions, And Future Directions, Pegah Hozhabrierdi, Raymond Zhu, Maduakolam Onyewu, Sucheta Soundarajan

Northeast Journal of Complex Systems (NEJCS)

Despite the large amount of literature on mitigation strategies for pandemic spread, in practice, we are still limited by naive strategies, such as lockdowns, that are not effective in controlling the spread of the disease in long term. One major reason behind adopting basic strategies in real-world settings is that, in the early stages of a pandemic, we lack knowledge of the behavior of a disease, and so cannot tailor a more sophisticated response. In this study, we design different mitigation strategies for early stages of a pandemic and perform a comprehensive analysis among them. We then propose a novel …


Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs Mar 2021

Optimizing Networking Topologies With Shortest Path Algorithms, Jordan Sahs

UNO Student Research and Creative Activity Fair

Communication networks tend to contain redundant devices and mediums of transmission, thus the need to locate, document, and optimize networks is increasingly becoming necessary. However, many people do not know where to start the optimization progress. What is network topology? What is this “Shortest Path Problem”, and how can it be used to better my network? These questions are presented, taught, and answered within this paper. To supplement the reader’s understanding there are thirty-eight figures in the paper that are used to help convey and compartmentalize the learning process needed to grasp the materials presented in the ending sections.

In …


Evaluation Of Algorithms For Randomizing Key Item Locations In Game Worlds, Caleb Johnson Mar 2021

Evaluation Of Algorithms For Randomizing Key Item Locations In Game Worlds, Caleb Johnson

LSU Master's Theses

In the past few years, game randomizers have become increasingly popular. In general, a game randomizer takes some aspect of a game that is usually static and shuffles it somehow. In particular, in this paper we will discuss the type of randomizer that shuffles the locations of items in a game where certain key items are needed to traverse the game world and access some of these locations. Examples of these types of games include series such as The Legend of Zelda and Metroid.

In order to accomplish this shuffling in such a way that the player is able to …


Quantum Simulation Of Schrödinger's Equation, Mohamed Eltohfa Mar 2021

Quantum Simulation Of Schrödinger's Equation, Mohamed Eltohfa

Capstone and Graduation Projects

Quantum computing is one of the promising active areas in physics research. This is because of the potential of quantum algorithms to outperform their classical counterparts. Grover’s search algorithm has a quadratic speed-up compared to the classical linear search. The quantum simulation of Schrödinger’s equation has an exponential memory save-up compared to the classical simulation. In this thesis, the ideas and tools of quantum computing are reviewed. Grover’s algorithm is studied and simulated as an example. Using the Qiskit quantum computing library, a code to simulate Schrödinger’s equation for a particle in one dimension is developed, simulated locally, and run …


An Efficient Algorithm To Test Potential Bipartiteness Of Graphical Degree Sequences, Kai Wang Mar 2021

An Efficient Algorithm To Test Potential Bipartiteness Of Graphical Degree Sequences, Kai Wang

Theory & Applications of Graphs

As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in polynomial time, at the expense of possibly producing an erroneous output on some ``yes'' instances but with very low error rate.


Efficient Algorithms For Trajectory-Aware Mobile Crowdsourcing, Chung-Kyun Han Mar 2021

Efficient Algorithms For Trajectory-Aware Mobile Crowdsourcing, Chung-Kyun Han

Dissertations and Theses Collection (Open Access)

Mobile crowdsourcing, a subclass of crowdsourcing dealing with location-specific tasks, is prevalent in our daily life. From sensing urban environment such as noise, air pollution to package delivery, various location-specific tasks are posted on mobile crowdsourcing platforms to tap on the pool of crowdsourced workers. Many digital platforms compete with each other to expand and retain their pool of crowdsourced workers. Comparing with the traditional workforce, crowdsourced workers do not dedicate their time to do tasks fully and have strong spatiotemporal preferences. The ignorance of crowdsourced workers’ mobility patterns and the lack of personalization would lead to crowdsourced workers’ exodus, …


Wg2An: Synthetic Wound Image Generation Using Generative Adversarial Network, Salih Sarp, Murat Kuzlu, Emmanuel Wilson, Ozgur Guler Mar 2021

Wg2An: Synthetic Wound Image Generation Using Generative Adversarial Network, Salih Sarp, Murat Kuzlu, Emmanuel Wilson, Ozgur Guler

Engineering Technology Faculty Publications

In part due to its ability to mimic any data distribution, Generative Adversarial Network (GAN) algorithms have been successfully applied to many applications, such as data augmentation, text-to-image translation, image-to-image translation, and image inpainting. Learning from data without crafting loss functions for each application provides broader applicability of the GAN algorithm. Medical image synthesis is also another field that the GAN algorithm has great potential to assist clinician training. This paper proposes a synthetic wound image generation model based on GAN architecture to increase the quality of clinical training. The proposed model is trained on chronic wound datasets with various …


Improving Multi-Hop Knowledge Base Question Answering By Learning Intermediate Supervision Signals, Gaole He, Yunshi Lan, Jing Jiang, Wayne Xin Zhao, Ji Rong Wen Mar 2021

Improving Multi-Hop Knowledge Base Question Answering By Learning Intermediate Supervision Signals, Gaole He, Yunshi Lan, Jing Jiang, Wayne Xin Zhao, Ji Rong Wen

Research Collection School Of Computing and Information Systems

Multi-hop Knowledge Base Question Answering (KBQA) aims to find the answer entities that are multiple hops away in the Knowledge Base (KB) from the entities in the question. A major challenge is the lack of supervision signals at intermediate steps. Therefore, multi-hop KBQA algorithms can only receive the feedback from the final answer, which makes the learning unstable or ineffective. To address this challenge, we propose a novel teacher-student approach for the multi-hop KBQA task. In our approach, the student network aims to find the correct answer to the query, while the teacher network tries to learn intermediate supervision signals …


Laser Illuminated Imaging: Beam And Scene Deconvolution Algorithm, Benjamin W. Davis Mar 2021

Laser Illuminated Imaging: Beam And Scene Deconvolution Algorithm, Benjamin W. Davis

Theses and Dissertations

Laser illuminated imaging systems deal with several physical challenges that must be overcome to achieve high-resolution images of the target. Noise sources like background noise, photon counting noise, and laser speckle noise will all greatly affect the imaging systems ability to produce a high-resolution image. An even bigger challenge to laser illuminated imaging systems is atmospheric turbulence and the effect that it will have on the imaging system. The illuminating beam will experience tilt, causing the beam to wander off the center of the target during propagation. The light returning to the detector will similarly be affected by turbulence, and …


Amplitude Estimation For The Large Clutter Discrete Removal Algorithm, Hannah Gjermo Chomitz Mar 2021

Amplitude Estimation For The Large Clutter Discrete Removal Algorithm, Hannah Gjermo Chomitz

Theses and Dissertations

A large clutter discrete (LCD) is spectrally bright localized clutter that can cause a false alarm or missed target detection in space-time adaptive processing (STAP) radar data. For passive bistatic STAP, the four step LCD removal (LCDR) algorithm estimates the spatial/Doppler frequency and complex amplitude of the LCD and then removes it from the data. Once the LCD is removed from the data, homogeneous clutter suppression techniques can be used to process the data and search for targets. This research focuses on reducing the complexity of estimating the LCDs complex amplitude. This research proposes a method that directly solves for …


Optimizing Large-Scale Hyperparameters Via Automated Learning Algorithm, Bin Gu, Guodong Liu, Yanfu Zhang, Xiang Geng, Heng Huang Feb 2021

Optimizing Large-Scale Hyperparameters Via Automated Learning Algorithm, Bin Gu, Guodong Liu, Yanfu Zhang, Xiang Geng, Heng Huang

Machine Learning Faculty Publications

Modern machine learning algorithms usually involve tuning multiple (from one to thousands) hyperparameters which play a pivotal role in terms of model generalizability. Black-box optimization and gradient-based algorithms are two dominant approaches to hyperparameter optimization while they have totally distinct advantages. How to design a new hyperparameter optimization technique inheriting all benefits from both approaches is still an open problem. To address this challenging problem, in this paper, we propose a new hyperparameter optimization method with zeroth-order hyper-gradients (HOZOG). Specifically, we first exactly formulate hyperparameter optimization as an A-based constrained optimization problem, where A is a black-box optimization algorithm (such …


Unsupervised Data Mining Technique For Clustering Library In Indonesia, Robbi Rahim, Joseph Teguh Santoso, Sri Jumini, Gita Widi Bhawika, Daniel Susilo, Danny Wibowo Feb 2021

Unsupervised Data Mining Technique For Clustering Library In Indonesia, Robbi Rahim, Joseph Teguh Santoso, Sri Jumini, Gita Widi Bhawika, Daniel Susilo, Danny Wibowo

Library Philosophy and Practice (e-journal)

Organizing school libraries not only keeps library materials, but helps students and teachers in completing tasks in the teaching process so that national development goals are in order to improve community welfare by producing quality and competitive human resources. The purpose of this study is to analyze the Unsupervised Learning technique in conducting cluster mapping of the number of libraries at education levels in Indonesia. The data source was obtained from the Ministry of Education and Culture which was processed by the Central Statistics Agency (abbreviated as BPS) with url: bps.go.id/. The data consisted of 34 records where the attribute …


Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev Feb 2021

Modeling And Analysis Of Affiliation Networks With Subsumption, Alexey Nikolaev

Dissertations, Theses, and Capstone Projects

An affiliation (or two-mode) network is an abstraction commonly used for representing systems with group interactions. It consists of a set of nodes and a set of their groupings called affiliations. We introduce the notion of affiliation network with subsumption, in which no affiliation can be a subset of another. A network with this property can be modeled by an abstract simplicial complex whose facets are the affiliations of the network.

We introduce a new model for generating affiliation networks with and without subsumption (represented as simplicial complexes and hypergraphs, respectively). In this model, at each iteration, a constant number …


Norm-Based Generalisation Bounds For Deep Multi-Class Convolutional Neural Networks, Antoine Ledent, Waleed Mustafa, Yunwen Lei, Marius Kloft Feb 2021

Norm-Based Generalisation Bounds For Deep Multi-Class Convolutional Neural Networks, Antoine Ledent, Waleed Mustafa, Yunwen Lei, Marius Kloft

Research Collection School Of Computing and Information Systems

We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the Frobenius-norm of the weight matrices, where previous bounds exhibit at least a squareroot dependence on the number of classes. (2) We adapt the classic Rademacher analysis of DNNs to incorporate weight sharing—a task of fundamental theoretical importance which was previously attempted only under very restrictive assumptions. In our results, each convolutional filter contributes only once …


Fine-Grained Generalization Analysis Of Vector-Valued Learning, Liang Wu, Antoine Ledent, Yunwen Lei, Marius Kloft Feb 2021

Fine-Grained Generalization Analysis Of Vector-Valued Learning, Liang Wu, Antoine Ledent, Yunwen Lei, Marius Kloft

Research Collection School Of Computing and Information Systems

Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific algorithms under the empirical risk minimization principle, a unifying analysis of vector-valued learning under a regularization framework is still lacking. In this paper, we initiate the generalization analysis of regularized vector-valued learning algorithms by presenting bounds with a mild dependency on the output dimension and a fast rate on the sample size. Our discussions relax the existing assumptions on the restrictive constraint of hypothesis spaces, smoothness of loss …


Mimoa: A Membrane-Inspired Multi-Objective Algorithm For Green Vehicle Routing Problem With Stochastic Demands, Yunyun Niu, Yongpeng Zhang, Zhiguang Cao, Kaizhou Gao, Jianhua Xiao, Wen Song, Fangwei Zhang Feb 2021

Mimoa: A Membrane-Inspired Multi-Objective Algorithm For Green Vehicle Routing Problem With Stochastic Demands, Yunyun Niu, Yongpeng Zhang, Zhiguang Cao, Kaizhou Gao, Jianhua Xiao, Wen Song, Fangwei Zhang

Research Collection School Of Computing and Information Systems

Nowadays, an increasing number of vehicle routing problem with stochastic demands (VRPSD) models have been studied to meet realistic needs in the field of logistics. In this paper, a bi-objective vehicle routing problem with stochastic demands (BO-VRPSD) was investigated, which aims to minimize total cost and customer dissatisfaction. Different from traditional vehicle routing problem (VRP) models, both the uncertainty in customer demands and the nature of multiple objectives make the problem more challenging. To cope with BO-VRPSD, a membrane-inspired multi-objective algorithm (MIMOA) was proposed, which is characterized by a parallel distributed framework with two operation subsystems and one control subsystem, …


To Thine Own Self Be True? Incentive Problems In Personalized Law, Jordan M. Barry, John William Hatfield, Scott Duke Kominers Feb 2021

To Thine Own Self Be True? Incentive Problems In Personalized Law, Jordan M. Barry, John William Hatfield, Scott Duke Kominers

William & Mary Law Review

Recent years have seen an explosion of scholarship on “personalized law.” Commentators foresee a world in which regulators armed with big data and machine learning techniques determine the optimal legal rule for every regulated party, then instantaneously disseminate their decisions via smartphones and other “smart” devices. They envision a legal utopia in which every fact pattern is assigned society’s preferred legal treatment in real time.

But regulation is a dynamic process; regulated parties react to law. They change their behavior to pursue their preferred outcomes— which often diverge from society’s—and they will continue to do so under personalized law: They …


Visual Analysis Of Discrimination In Machine Learning, Qianwen Wang, Zhenghua Xu, Zhutian Chen, Yong Wang, Shixia Liu, Huamin Qu Feb 2021

Visual Analysis Of Discrimination In Machine Learning, Qianwen Wang, Zhenghua Xu, Zhutian Chen, Yong Wang, Shixia Liu, Huamin Qu

Research Collection School Of Computing and Information Systems

The growing use of automated decision-making in critical applications, such as crime prediction and college admission, has raised questions about fairness in machine learning. How can we decide whether different treatments are reasonable or discriminatory? In this paper, we investigate discrimination in machine learning from a visual analytics perspective and propose an interactive visualization tool, DiscriLens, to support a more comprehensive analysis. To reveal detailed information on algorithmic discrimination, DiscriLens identifies a collection of potentially discriminatory itemsets based on causal modeling and classification rules mining. By combining an extended Euler diagram with a matrix-based visualization, we develop a novel set …


Divide And Capture: An Improved Cryptanalysis Of The Encryption Standard Algorithm Rsa, Willy Susilo, Joseph Tonien, Guomin Yang Feb 2021

Divide And Capture: An Improved Cryptanalysis Of The Encryption Standard Algorithm Rsa, Willy Susilo, Joseph Tonien, Guomin Yang

Research Collection School Of Computing and Information Systems

RSA is a well known standard algorithm used by modern computers to encrypt and decrypt messages. In some applications, to save the decryption time, it is desirable to have a short secret key d compared to the modulus N. The first significant attack that breaks RSA with short secret key given by Wiener in 1990 is based on the continued fraction technique and it works with d < 1/4 root 18 N-.(25). A decade later, in 2000, Boneh and Durfee presented an improved attack based on lattice technique which works with d < N-.(292). Until this day, Boneh-Durfee attack remain as the best attack on RSA with short secret key. In this paper, we revisit the continued fraction technique and propose a new attack on RSA. Our main result shows that when d < root t (2 root 2 + 8/3) N-.(75)/root e, where e is the public exponent and t is a chosen parameter, our attack can break the RSA with the running time of O(tlog (N)). Our attack is especially well suited for the case where e is much smaller than N. When e approximate to N, the Boneh-Durfee attack outperforms ours. As a result, we could simultaneously run both attacks, our new attack and the classical Boneh-Durfee attack as a backup.


Using Torchattacks To Improve The Robustness Of Models With Adversarial Training, William S. Matos Díaz Jan 2021

Using Torchattacks To Improve The Robustness Of Models With Adversarial Training, William S. Matos Díaz

Cybersecurity: Deep Learning Driven Cybersecurity Research in a Multidisciplinary Environment

Adversarial training has proven to be one of the most successful ways to defend models against adversarial examples. This process consists of training a model with an adversarial example to improve the robustness of the model. In this experiment, Torchattacks, a Pytorch library made for importing adversarial examples more easily, was used to determine which attack was the strongest. Later on, the strongest attack was used to train the model and make it more robust against adversarial examples. The datasets used to perform the experiments were MNIST and CIFAR-10. Both datasets were put to the test using PGD, FGSM, and …


Hybrid Models As Transdisciplinary Research Enablers, Andreas Tolk, Alison Harper, Navonil Mustafee Jan 2021

Hybrid Models As Transdisciplinary Research Enablers, Andreas Tolk, Alison Harper, Navonil Mustafee

Computational Modeling & Simulation Engineering Faculty Publications

Modelling and simulation (M&S) techniques are frequently used in Operations Research (OR) to aid decision-making. With growing complexity of systems to be modelled, an increasing number of studies now apply multiple M&S techniques or hybrid simulation (HS) to represent the underlying system of interest. A parallel but related theme of research is extending the HS approach to include the development of hybrid models (HM). HM extends the M&S discipline by combining theories, methods and tools from across disciplines and applying multidisciplinary, interdisciplinary and transdisciplinary solutions to practice. In the broader OR literature, there are numerous examples of cross-disciplinary approaches in …


The Complexity Of Symmetry, Matthew Lemay Jan 2021

The Complexity Of Symmetry, Matthew Lemay

HMC Senior Theses

One of the main goals of theoretical computer science is to prove limits on how efficiently certain Boolean functions can be computed. The study of the algebraic complexity of polynomials provides an indirect approach to exploring these questions, which may prove fruitful since much is known about polynomials already from the field of algebra. This paper explores current research in establishing lower bounds on invariant rings and polynomial families. It explains the construction of an invariant ring for whom a succinct encoding would imply that NP is in P/poly. It then states a theorem about the circuit complexity partial …