Computational Theory Research Articles

Computational Algebra, Coding Theory, and Cryptography: Theory and Applications

The primary aim of this Special Issue is to explore innovative encoding and decoding procedures that leverage various algebraic structures to enhance error-control coding techniques [...]

PPSZ for General k-SAT and CSP—Making Hertli’s Analysis Simpler and 3-SAT Faster

The currently fastest known algorithm for k-SAT is PPSZ, named afterits inventors (Paturi et al. in J ACM 52(3):337-364, 2005. http://dx.doi.org/10.1145/1066100.1066101). Analyzing its running timeis much easier for input formulas with a unique satisfying assignment.In this paper, we achieve three goals. First, we simplify the analysisof Hertli (in 2011 IEEE 52nd Annual Symposium on Foundations ofComputer Science-FOCS 2011, Los Alamitos, 2011) for input formulaswith multiple satisfying assignments. Second, we show a “liftingresult”: if you improve PPSZ for k-CNF formulas with a unique satisfyingassignment, you will immediately get a (weaker) improvement forgeneral k-CNF formulas. In combination this with results by Hansen etal. (in Charikar and Cohen (ed) Proceedings of the 51st Annual ACMSIGACT Symposium on Theory of Computing, 2019) and Scheder (in62nd IEEE Annual Symposium on Foundations of Computer Science,2021), who all prove improved time bounds for Unique-k-SAT, this givesimproved bounds for general k-SAT. We also generalize our results tothe domain of Constraint Satisfaction Problems, i.e., satisfiability withmore than two truth values.

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Efficient Implementation of Interior-Point Methods for Quantum Relative Entropy

Quantum relative entropy (QRE) programming is a recently popular and challenging class of convex optimization problems with significant applications in quantum computing and quantum information theory. We are interested in modern interior-point (IP) methods based on optimal self-concordant barriers for the QRE cone. A range of theoretical and numerical challenges associated with such barrier functions and the QRE cones have hindered the scalability of IP methods. To address these challenges, we propose a series of numerical and linear algebraic techniques and heuristics aimed at enhancing the efficiency of gradient and Hessian computations for the self-concordant barrier function, solving linear systems, and performing matrix-vector products. We also introduce and deliberate about some interesting concepts related to QRE such as symmetric quantum relative entropy. We design a two-phase method for performing facial reduction that can significantly improve the performance of QRE programming. Our new techniques have been implemented in the latest version (DDS 2.2) of the software package Domain-Driven Solver (DDS). In addition to handling QRE constraints, DDS accepts any combination of several other conic and nonconic convex constraints. Our comprehensive numerical experiments encompass several parts, including (1) a comparison of DDS 2.2 with Hypatia for the nearest correlation matrix problem, (2) using DDS 2.2 for combining QRE constraints with various other constraint types, and (3) calculating the key rate for quantum key distribution (QKD) channels and presenting results for several QKD protocols. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the National Science Foundation [Grant CMMI-2347120] and Discovery Grants from the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0570 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0570 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Electron-positron pair creation under Gaussian and super-Gaussian pulse trains

The electron-positron pair (EPP) creation under Gaussian and super-Gaussian pulse trains are studied by the computational quantum field theory (CQFT) in the single-photon regime. The details of the EPP creation are studied from the time evolution of the EPP number, energy spectra and spatial distribution of the electrons. The results indicate that the final created EPPs is the non-linear accumulation of the multi-pulses, which depends on the time interval, pulse shape and pulse number. The optimal time interval can be chosen based on the pulse resonance condition, which is derived by the perturbation method. Besides, steeper super-Gaussian pulses and adding more pulses facilitate the EPP creation as well. The results indicate that, under optimal multi-pulse parameters, the number of the EPPs obtained is much larger than the sum of the EPPs created under the same number of single pulses. This finding not only can enhance the EPP creation, but also can improve the multi-pulse utilization and guide future experimental research on the EPP creation.

Growth Kinetics of Graphene on Cu(111) Foils from Methane, Ethyne, Ethylene, and Ethane

AbstractChemical vapor deposition of carbon precursors on Cu‐based substrates at temperatures exceeding 1000 °C is currently a typical route for the scalable synthesis of large‐area high‐quality single‐layer graphene (SLG) films. Using molecules with higher activities than CH4 may afford lower growth temperatures that might yield fold‐ and wrinkle‐free graphene. The kinetics of growth of graphene using hydrocarbons other than CH4 are of interest to the scientific and industrial communities. We measured the growth rates of graphene islands on Cu(111) foils by using C2H2, C2H4, C2H6 and CH4, respectively (each mixed with H2). From such kinetics data we obtain the activation enthalpy (ΔH≠) of graphene growth as shown in parentheses (C2H2 (0.93±0.09 eV); C2H4 (2.05±0.19 eV); C2H6 (2.50±0.11 eV); CH4 (4.59±0.26 eV)); C2Hy (y=2, 4, 6) show similar growth behavior but CH4 is different. Computational fluid dynamics and density functional theory simulations suggest that C2Hy differs from CH4 due to different values of adsorption energy and the lifetime of relevant carbon precursors on the Cu(111) surface. Combining experimental and simulation results, we find that the rate determining step (RDS) is the dissociation of the first C−H bond of CH4 molecules in the gas phase, while the RDS using C2Hy is the first dehydrogenation of adsorbed C2Hy that happens with assistance of H atoms adsorbed on the Cu(111) surface. By using C2H2 as the carbon precursor, high‐quality single‐crystal adlayer‐free SLG films are achieved on Cu(111) foils at 900 °C.

Growth Kinetics of Graphene on Cu(111) Foils from Methane, Ethyne, Ethylene, and Ethane.

Chemical vapor deposition of carbon precursors on Cu-based substrates at temperatures exceeding 1000 °C is currently a typical route for the scalable synthesis of large-area high-quality single-layer graphene (SLG) films. Using molecules with higher activities than CH4 may afford lower growth temperatures that might yield fold- and wrinkle-free graphene. The kinetics of growth of graphene using hydrocarbons other than CH4 are of interest to the scientific and industrial communities. We measured the growth rates of graphene islands on Cu(111) foils by using C2H2, C2H4, C2H6 and CH4, respectively (each mixed with H2). From such kinetics data we obtain the activation enthalpy (ΔH≠) of graphene growth as shown in parentheses (C2H2 (0.93±0.09 eV); C2H4 (2.05±0.19 eV); C2H6 (2.50±0.11 eV); CH4 (4.59±0.26 eV)); C2Hy (y=2, 4, 6) show similar growth behavior but CH4 is different. Computational fluid dynamics and density functional theory simulations suggest that C2Hy differs from CH4 due to different values of adsorption energy and the lifetime of relevant carbon precursors on the Cu(111) surface. Combining experimental and simulation results, we find that the rate determining step (RDS) is the dissociation of the first C-H bond of CH4 molecules in the gas phase, while the RDS using C2Hy is the first dehydrogenation of adsorbed C2Hy that happens with assistance of H atoms adsorbed on the Cu(111) surface. By using C2H2 as the carbon precursor, high-quality single-crystal adlayer-free SLG films are achieved on Cu(111) foils at 900 °C.

A Unified Framework for Covariate Adjustment Under Stratified Randomisation

ABSTRACTRandomisation, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomised experiments, the treatment effect is a parameter of general interest. Researchers have explored the validity of using linear models to estimate the treatment effect and perform covariate adjustment and thus improve the estimation efficiency. However, the relationship between covariates and outcomes is not necessarily linear, and is often intricate. Advances in statistical theory and related computer technology allow us to use nonparametric and machine learning methods to better estimate the relationship between covariates and outcomes and thus obtain further efficiency gains. However, theoretical studies on how to draw valid inferences when using nonparametric and machine learning methods under stratified randomisation are yet to be conducted. In this paper, we discuss a unified framework for covariate adjustment and corresponding statistical inference under stratified randomisation and present a detailed proof of the validity of using local linear kernel‐weighted least squares regression for covariate adjustment in treatment effect estimators as a special case. In the case of high‐dimensional data, we additionally propose an algorithm for statistical inference using machine learning methods under stratified randomisation, which makes use of sample splitting to alleviate the requirements on the asymptotic properties of machine learning methods. Finally, we compare the performances of treatment effect estimators using different machine learning methods by considering various data generation scenarios, to guide practical research.

Ted Chiang imagines a computational theory of robots.

Two short science fiction stories, "Exhalation" and "Seventy-Two Letters", explore robots inside and out.

Exploring Mean Cordial Labeling Possible Combination Position of Vertices in Graphs: A Computational Approach

Objectives: We have developed the Python module of mean cordial labeling for the different types of graphs, like Path, Cycle, and Subdivision of Star graphs. We aim to identify the number of combination positions of vertices that satisfy the mean cordial labeling rules. We have found mathematical equations that describe the labeling behavior in these graphs. Methods: In this paper, a Python program was developed to find the mean cordial labeling of the Path, Cycle, and Subdivision of the Star graph. We have obtained the number of combination positions of vertex obeying the mean cordial labeling condition using this Python module. We have drawn the graph between the number of vertices and the number of combination positions of the vertex. Findings: We have found that the different graph types like Path, Cycle, and Subdivision of Star graph satisfy the mean cordial labeling condition. The result indicates that the number of combination positions of the Path and cycle graph fulfill the power equation Y=a*xb and the Subdivision of the Star graph meets the exponential growth equation Y=a*bx. Novelty: In this paper, a new method has been developed to find the number of combination position of varies graphs using the Python module. This computational approach will be useful to analyze the biological networking and protein-protein interaction study. Keywords: Mean Cordial, Path, Cycle, Subdivision of Star graph, Computational graph theory

A Synergistic Perspective on Multivariate Computation and Causality in Complex Systems.

What does it mean for a complex system to "compute" or perform "computations"? Intuitively, we can understand complex "computation" as occurring when a system's state is a function of multiple inputs (potentially including its own past state). Here, we discuss how computational processes in complex systems can be generally studied using the concept of statistical synergy, which is information about an output that can only be learned when the joint state of all inputs is known. Building on prior work, we show that this approach naturally leads to a link between multivariate information theory and topics in causal inference, specifically, the phenomenon of causal colliders. We begin by showing how Berkson's paradox implies a higher-order, synergistic interaction between multidimensional inputs and outputs. We then discuss how causal structure learning can refine and orient analyses of synergies in empirical data, and when empirical synergies meaningfully reflect computation versus when they may be spurious. We end by proposing that this conceptual link between synergy, causal colliders, and computation can serve as a foundation on which to build a mathematically rich general theory of computation in complex systems.

Ring-Opening Reactions of Imidazolidines and Hexahydropyrimidines with Grignard Reagents.

We herein report an unprecedented ring-opening of unstrained cyclic aminals such as imidazolidines and hexahydropyrimidines by the use of Grignard and cuprate reagents to give secondary sulfonamides bearing diversely substituted tertiary amines in the β- or γ-position. This synthetic procedure can be carried out in a one-pot fashion without collateral reactions that are commonly associated with sp3-organometallic multicomponent Mannich-type reactions, indicating the fundamental role of sulfonamide protection of the second nitrogen atom in the generation of the cyclic aminal and in the ring-opening process. Computational density functional theory (DFT) data point to the formation of a transient iminium ion intermediate, in which the Lewis acidity of the cationic component of the organometallic reagent triggers the ring-opening process by coordination. The presented method allows the nucleophilic decoration of diamines including those bearing an adjacent chiral center to the tertiary amine not easily achievable by means of alternative standard synthetic procedures.

Towards a Computational Theory of Perceptions under Neutrosophic Environment

Computing and reasoning with perceptions in AI are shifting from traditional methods to those that mimic human cognitive processes. Humans intuitively measure and evaluate without explicit computations, using sensory input and past experiences for quick judgments. The theory of perceptions can enhance AI's ability to replicate human-like assessment by providing a framework for handling the nuances of human reasoning. Traditionally, information granularity is either crisp (c-granular) or fuzzy (f-granular), focusing on measurement-based and perception-based information. This paper outlines a neutrosophic-based computational theory of perceptions (n-CTP), introducing neutrosophic granular (n-granular) information and neutrosophic constraint-centered semantics of natural languages (n-CSNL). Based on the neutrosophy theory, which deals with truth, falsity, and indeterminacy, managing uncertainties and vagueness in real-world data can be done more effectively than with traditional methods. The n-CTP has the potential to enhance AI's ability to process and reason with complex, uncertain, and ambiguous information.

The number of spanning trees in K n -chain and ring graphs

The problem of counting spanning trees of graphs or networks is a fundamental and crucial area of research in combinatorics, while has numerous important applications in statistical physics, network theory and theoretical computer science. Very recently, Kosar, Zaman, Ali and Ullah obtained a nice formula on the number of spanning trees of a K 5-chain network K5ℓ constructed by connecting ℓcopys of complete graphs K 5. They made extensive use of matrix theory and spectral graph theory, especially the normalized Laplacian of graphs. In this paper, by using a rather simple and more physical treatment (the mesh-star transformation in electrical network) without any linear algebra, we generalize their result to K n -chain graphs and K n -ring graphs. The results show that there is a simple relation between the number of spanning trees of the K n -chain graph Lnℓ and the K n -ring graph Cnℓ . We also calculate the corresponding tree entropy (or so called ‘the asymptotic growth constant’) and find that the tree entropy of the corresponding K n -chain graphs and K n -ring graphs are totally the same.

Embodied and Contextual Intelligence: Towards a Policy Framework for Higher Education

This article explores the diverse epistemic perspectives on intelligence, tracing its conceptual evolution across early Indian philosophy, Western philosophical thought and contemporary computational theories. Intelligence is examined as a dynamic, multifaceted phenomenon that transcends mere cognition, extending into embodied, ecological and meta-intelligent domains. The discussion juxtaposes traditional views—where intelligence is seen as a divine or innate quality, a product of sagacious prudence, or a computational system—with more contemporary understandings that emphasize the role of context, embodiment and ecological interaction. Through a critique of pancomputationalism and an exploration of the non-computable aspects of intelligence, the article argues for a more holistic view that recognizes intelligence as an adaptive, contextually grounded and evolutionarily emergent property.

On Scheduling Mechanisms Beyond the Worst Case

AbstractThe problem of scheduling unrelated machines has been studied since the inception of algorithmic mechanism design (Nisan and Ronen, Algorithmic mechanism design(extended abstract). In: Proceedings of the Thirty First Annual ACM Symposium on Theory of Computing (STOC), pp. 129–140, 1999. It is a resource allocation problem that entails assigning m tasks to n machines for execution. Machines are regarded as strategic agents who may lie about their execution costs so as to minimize their time cost. To address the situation when monetary payment is not an option to compensate the machines’ costs, Koutsoupias (Theory Comput Syst 54:375–387, 2014) devised two truthful mechanisms, K and P respectively, that achieves an approximation ratio of $$\frac{n+1}{2}$$ n + 1 2 and n, for social cost minimization. In addition, no truthful mechanism can achieve an approximation ratio better than $$\frac{n+1}{2}$$ n + 1 2 . Hence, mechanism K is optimal. While the approximation ratio provides a strong worst-case guarantee, it also limits us to a comprehensive understanding of mechanism performance on various inputs. This paper investigates these two scheduling mechanisms beyond the worst case. We first show that mechanism K achieves a smaller social cost than mechanism P on every input. That is, mechanism K is pointwise better than mechanism P. Next, for each task, when machines’ execution costs are independent and identically drawn from a task-specific distribution, we show that the average-case approximation ratio of mechanism K converges to a constant determined by the task-specific distribution. This bound is tight for mechanism K. For a better understanding of this distribution-dependent constant, on the one hand, we estimate its value by plugging in a few common distributions; on the other, we show that this converging bound improves a known bound (Zhang in Algorithmica 83(6):1638–1652, 2021)) which only captures the single-task setting. Last, we find that the average-case approximation ratio of mechanism P converges to the same constant.

Fixing the earth: whole-systems thinking in Silicon Valley’s environmental ideology

Today, American tech actors express optimistic ideas about how to fix the Earth and halt climate change. Such “green” initiatives have in common that they capture the world in systems and propose large systemic, and mostly technological, solutions. Because of their reliance on techno-fixes, representatives of Silicon Valley express an ideology of ecomodernism, which believes that human progress can be “decoupled” from environmental decline. In this article, I show how “whole-systems thinking” has become a key discursive element in today’s ecomodernist discourses. This discourse has developed from the 1960s onwards – inspired by cybernetic, ecological and computational theories – within the tech culture of California. This paper discusses three key periods in this development, highlighting key publications: the Whole Earth Catalog of the 1960s, the Limits to Growth report in 1972 and the cyberspace manifestoes of the mid 1990s. These periods are key to understand how techno-fixes became a popular answer to the climate crisis, eventually leading to a vision of the world as an ecosystem that can be easily controlled and manipulated, and of technological innovation as harmless and beneficial. I argue that “whole-systems” thinking offers a naive and misleading narrative about the development of the climate crisis, that offers a hopeful yet unrealistic perspective for a future threatened by climate change, built on a misconception of Earth as a datafied planet.

Continuous measurement in neurocritical care of cerebral blood flow (CBF) calculated from ICP and central venous pressure

The cerebral blood flow, CBF, is an important clinical parameter in neuro-intensive care. The possibility to continuously monitor CBF, computed from referential ICP, rICP (calculated from measured intracranial pressure, ICP, and central venous pressure, CVP) and venous outflow resistance, Rv, could importantly improve patient care. For the CBF(1) method the pulsative part of CBF (with rICP increase due to vascular volume increase) gives the venous outflow resistance, Rv. The CBF max method finds Rv from the close correlation between rICP and Rv. For both CBF(1) and CBF max, rICP divided with Rv gives CBF. The parameters rICP, Rv and CBF were calculated from measurements of ICP increase, and of intracerebral venous volume increase in nine subjects, by the CBF(1) method. The result, together with the finding of a close correlation between rICP and Rv, which made CBF dependent on rICP only, gave confirmation of the theory for computation of CBF, with two methods for continuous monitoring of CBF from rICP, one (CBF(1)) using the systolic ICP increase to find Rv, and one (CBF max) using the relationship between Rv and rICP at rICP exceeding about 10 mmHg in this study.

Computer Models Assist Innovative Design of Graphic Arts

In order to study the theory and application of computer aided design (CAD) related to the composition of art, the theory of symbolic matrix was introduced to realize the purpose of the study of the interaction between perceptual and rational problems. In this paper, the original image was extracted from the design object, and the transformation between the original image and the symbol matrix was realized by the correspondence with the elements in the matrix. Based on the research route, four kinds of mathematical models were established, namely random distribution, symmetric distribution, central diffusion, and reorganization. By applying the mathematical model constructed in this paper, the picture was transformed, the combination of various styles of graphics was added, and how to put the simple image picture into a meaningful integrated image picture was discussed. The computer-aided design method of the existing verification examples was summarized in this paper, and the design method was accurate and effective. Compared with traditional graphic art design methods, the computer-aided design method mentioned in the paper has the following advantages. Computer-aided design can quickly process and analyze images, convert and combine them through mathematical models and algorithms, greatly saving designers time and energy. By introducing symbol matrix theory and establishing various mathematical models, computer-aided design can provide diverse graphic combinations and style transformations, helping designers explore more innovative design solutions.

Multiscale Sieve for Smart Prime Generation and Application in Info-Security, IoT and Blockchain

The huge computational cost required to test whether a number is prime and the inefficiency of the known sieving algorithms for extremely large inputs have posed significant challenges in computational number theory. Traditional deterministic prime generation methods struggle to maintain performance when the input sizes increase exponentially. In this work, we show that, through multiscale distribution and deterministic prime number generation, it is possible to create a multiscale sieve with drastically better performance than the deterministic algorithms known to date, providing a more efficient solution for large-scale prime number generation, demonstrated by several benchmarks that highlight the potential of our approach. Consequently, we can gain some advantages in cryptography and in info-security, such as in IoT and blockchain environments.