Complexity Theory

Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes

Towards ultrahigh dimensional feature selection for big data

In this paper, we present a new adaptive feature scaling scheme for ultrahigh-dimensional feature selection on Big Data, and then reformulate it as a convex semi-infinite programming (SIP) problem. To address the SIP, we propose an eficient feature generating paradigm. Different from traditional gradient-based approaches that conduct optimization on all input features, the proposed paradigm iteratively activates a group of features, and solves a sequence of multiple kernel learning (MKL) subproblems. To further speed up the training, we propose to solve the MKL subproblems in their primal forms through a modified accelerated proximal gradient approach. Due to such optimization scheme, some eficient cache techniques are also developed. The feature generating paradigm is guaranteed to converge globally under mild conditions, and can achieve lower feature selection bias. Moreover, the proposed method can tackle two challenging tasks in feature selection: 1) group-based feature selection with complex structures, and 2) nonlinear feature selection with explicit feature mappings. Comprehensive experiments on a wide range of synthetic and real-world data sets of tens of million data points with O(1014) features demonstrate the competitive performance of the proposed method over state-of-the-art feature selection methods in terms of generalization performance and training eficiency. © 2014 Mingkui Tan, Ivor W. Tsang and Li Wang

A Survey on Quantum Reinforcement Learning

Quantum reinforcement learning is an emerging field at the intersection of quantum computing and machine learning. While we intend to provide a broad overview of the literature on quantum reinforcement learning (our interpretation of this term will be clarified below), we put particular emphasis on recent developments. With a focus on already available noisy intermediate-scale quantum devices, these include variational quantum circuits acting as function approximators in an otherwise classical reinforcement learning setting. In addition, we survey quantum reinforcement learning algorithms based on future fault-tolerant hardware, some of which come with a provable quantum advantage. We provide both a birds-eye-view of the field, as well as summaries and reviews for selected parts of the literature.Comment: 62 pages, 16 figure

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

State of the Art Report : Verified Computation

This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the verifier, and the second agent is the prover. The verifier wants the prover to perform a computation. The verifier sends a description of the computation to the prover. Once the prover has completed the task, the prover returns the output to the verifier. The output will contain proof. The verifier can use this proof to check if the prover computed the output correctly. The check is not required to verify the algorithm used in the computation. Instead, it is a check that the prover computed the output using the computation specified by the verifier. The effort required for the check should be much less than that required to perform the computation. This state-of-the-art report surveys 128 papers from the literature comprising more than 4,000 pages. Other papers and books were surveyed but were omitted. The papers surveyed were overwhelmingly mathematical. We have summarised the major concepts that form the foundations for verifiable computation. The report contains two main sections. The first, larger section covers the theoretical foundations for probabilistically checkable and zero-knowledge proofs. The second section contains a description of the current practice in verifiable computation. Two further reports will cover (i) military applications of verifiable computation and (ii) a collection of technical demonstrators. The first of these is intended to be read by those who want to know what applications are enabled by the current state of the art in verifiable computation. The second is for those who want to see practical tools and conduct experiments themselves

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Approximate degree in classical and quantum computing

In this book, the authors survey what is known about a particularly natural notion of approximation by polynomials, capturing pointwise approximation over the real numbers.FG-2022-18482 - Alfred P. Sloan Foundation; CNS-2046425 - National Science Foundation; CCF-1947889 - National Science FoundationAccepted manuscrip

New approaches to protein docking

In the first part of this work, we propose new methods for protein docking. First, we present two approaches to protein docking with flexible side chains. The first approach is a fast greedy heuristic, while the second is a branch -&-cut algorithm that yields optimal solutions. For a test set of protease-inhibitor complexes, both approaches correctly predict the true complex structure. Another problem in protein docking is the prediction of the binding free energy, which is the the final step of many protein docking algorithms. Therefore, we propose a new approach that avoids the expensive and difficult calculation of the binding free energy and, instead, employs a scoring function that is based on the similarity of the proton nuclear magnetic resonance spectra of the tentative complexes with the experimental spectrum. Using this method, we could even predict the structure of a very difficult protein-peptide complex that could not be solved using any energy-based scoring functions. The second part of this work presents BALL (Biochemical ALgorithms Library), a framework for Rapid Application Development in the field of Molecular Modeling. BALL provides an extensive set of data structures as well as classes for Molecular Mechanics, advanced solvation methods, comparison and analysis of protein structures, file import/export, NMR shift prediction, and visualization. BALL has been carefully designed to be robust, easy to use, and open to extensions. Especially its extensibility, which results from an object-oriented and generic programming approach, distinguishes it from other software packages.Der erste Teil dieser Arbeit beschäftigt sich mit neuen Ansätzen zum Proteindocking. Zunächst stellen wir zwei Ansätze zum Proteindocking mit flexiblen Seitenketten vor. Der erste Ansatz beruht auf einer schnellen, gierigen Heuristik, während der zweite Ansatz auf branch-&-cut-Techniken beruht und das Problem optimal lösen kann. Beide Ansätze sind in der Lage die korrekte Komplexstruktur für einen Satz von Testbeispielen (bestehend aus Protease-Inhibitor-Komplexen) vorherzusagen. Ein weiteres, grösstenteils ungelöstes, Problem ist der letzte Schritt vieler Protein-Docking-Algorithmen, die Vorhersage der freien Bindungsenthalpie. Daher schlagen wir eine neue Methode vor, die die schwierige und aufwändige Berechnung der freien Bindungsenthalpie vermeidet. Statt dessen wird eine Bewertungsfunktion eingesetzt, die auf der Ähnlichkeit der Protonen-Kernresonanzspektren der potentiellen Komplexstrukturen mit dem experimentellen Spektrum beruht. Mit dieser Methode konnten wir sogar die korrekte Struktur eines Protein-Peptid-Komplexes vorhersagen, an dessen Vorhersage energiebasierte Bewertungsfunktionen scheitern. Der zweite Teil der Arbeit stellt BALL (Biochemical ALgorithms Library) vor, ein Rahmenwerk zur schnellen Anwendungsentwicklung im Bereich MolecularModeling. BALL stellt eine Vielzahl von Datenstrukturen und Algorithmen für die FelderMolekülmechanik,Vergleich und Analyse von Proteinstrukturen, Datei-Import und -Export, NMR-Shiftvorhersage und Visualisierung zur Verfügung. Beim Entwurf von BALL wurde auf Robustheit, einfache Benutzbarkeit und Erweiterbarkeit Wert gelegt. Von existierenden Software-Paketen hebt es sich vor allem durch seine Erweiterbarkeit ab, die auf der konsequenten Anwendung von objektorientierter und generischer Programmierung beruht

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum