Computational Theory Research Articles

Synthesis of a dual-response signal sensor and naked-eye recognition of hypochlorite in real water samples

An innovative dual-modal colorimetric and fluorometric probe MDXM is synthesized based on the dihydro-1H-xanthene motif via Knoevenagel reaction. The incorporation of a malononitrile group into the dihydro-1H-xanthene motif via a double bond results in an extensive macroconjugated π-system, which endows MDXM with a pronounced molar absorptivity and effectively quenches the intramolecular charge transfer (ICT) effect. Upon exposure to hypochlorite, the C = C bond in MDXM undergoes cleavage, resulting in the formation of an aldehyde group. This process restores the ICT effect and manifests as a clear fluorescent ''turn-on'' signal at 530 nm, with a remarkably linear response across the ClO− concentration range of 0–60 μM. The probe achieves a notably low detection limit of 7.14 nM, reflecting its exceptional sensitivity. In the presence of 15 common metal ions and oxidizing agents, MDXM can specifically identify hypochlorite with excellent anti-interference ability. The response mechanism of MDXM to hypochlorite was confirmed through Nuclear Magnetic Resonance (NMR) spectroscopy and computational Density Functional Theory (DFT) calculations. The practical applicability of MDXM is underscored by its successful implementation in analyzing hypochlorite in 5 varied real water samples. This showcases MDXM's promise for environmental and analytical chemistry, providing a robust tool for hypochlorite detection in diverse settings.

The Impact of GeoGebra in Analytic Algebra: A Bibliometric Review

GeoGebra is a software that is often used in mathematics learning. GeoGebra is an electronic program that contains a set of tools that equip students with mathematical skills. This research aims to look at research trends related to algebra learning that integrates GeoGebra. This research is literature review research, there are 95 publications collected from the Scopus database which are then analyzed using the bibliometric analysis method assisted by the Vos viewer application. Data taken from the Scopus database was refined in 4 stages, namely identification, filtering, eligibility, and inclusion, resulting in 95 publications. The research results show that Spain and Austria are the most influential countries and have high cooperation with other countries in this field. The focus of research related to GeoGebra on algebra material is, 1) geometry and students; 2) GeoGebra and algebra; 3) elementary geometry and computational theory; 4) dynamic geometry and computer algebra. The new themes in this research are symbolic computation, quantifier elimination and real quantifier elimination. This research not only enriches the scientific literature in the fields of GeoGebra and algebra but also provides practical guidance for educators and researchers to improve mathematics teaching and learning methods in the future.

Integrated Experiment-Theory Framework for Studying Mass Transport Effects in Electrochemical CO2 Reduction on Copper

Electrochemical carbon dioxide reduction (eCO2R) has emerged as a promising approach to produce high-value fuels and chemicals using renewable energy sources. In particular, Cu catalysts can convert CO2 to a wide range of hydrocarbon and oxygenate products, including CO, formate, ethanol and ethylene. However, the activity and selectivity of eCO2R is highly dependent on mass transport and the corresponding reaction microenvironment present under operating conditions. In this talk, we present an integrated framework that combines experiments with computational fluid dynamics (CFD) and density functional theory (DFT) based microkinetic modeling to predict the effect of varying mass transport on eCO2R in a custom-designed flow cell. The flow cell is designed with multiple electrolyte jets impinging onto the electrocatalyst surface for rapid and homogeneous reactant transport. We first demonstrate the effect of mass transport in a flow cell architecture by controlling the flow rate of CO2-saturated 0.1 M KHCO3 to a Cu electrocatalyst. Significant increases in the production rates of formate and CO are observed with increasing flow rate, as well as an enhancement in multi-carbon products at high overpotentials. Increasing flow rate promotes hydrogen evolution at low overpotentials but has little effect at large overpotentials, suggesting a transition from HCO3 - to water as the dominant proton donor with increasing overpotential. CFD simulations are employed to model the distribution of boundary layer thicknesses within the flow cell, which subsequently set the boundary conditions for the coupled 1D transport-microkinetic model. The calculated boundary layer thickness values are corroborated by experimentally measured transport-limited currents. Our model successfully predicts experimentally observed trends in selectivity with mass transport, such as an increase in the production of ethylene and ethanol at high flow rates due to enhanced CO2 transport. The slight suppression of hydrogen reduction at higher flow rates due to an increase in *CO coverage is also predicted and supported by experimental results. This work demonstrates the importance of incorporating transport processes in the CFD-DFT coupled modeling of device performance for electrochemical CO2 reduction.This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL release number: LLNL-ABS-857566.

Anderson Localization Transition in Disordered Hyperbolic Lattices.

We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the {8,3} and {8,8} lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics.

Multiaxial fatigue rule applied to disc specimens with variable thickness subjected to an equibiaxial stress state

AbstractAssessing multiaxial fatigue theories requires experimental verification of a failure criterion, posing a significant challenge. This study aims to investigate the validity of a multiaxial fatigue method based on the Lagoda‐Macha‐Sakane (LMS) theory. The LMS theory links the critical strain energy density to the fatigue crack initiation cycles through a non‐linear equation defined by a set of empirical parameters calibrated by a strain‐controlled uniaxial fatigue test. This work adopts the LMS formulation, numerically calibrating the fatigue curve based on strain energy density from uniaxial fatigue experimental data and considering only the LMS theory for the critical strain energy density computation. This method avoids compatibility condition uncertainties and previous identification of material parameters. The study uses bi‐axial bending tests on AISI 316 L steel plate specimens with 3D finite element analyses to support computational assessment. The predictive capability of the model and the effectiveness of the testing method are presented and discussed.

Leveraging individual differences in cue-reward learning to investigate the psychological and neural basis of shared psychiatric symptomatology: The sign-tracker/goal-tracker model.

In our modern environment, we are bombarded with stimuli or cues that exert significant influence over our actions. The extent to which such cues attain control over or disrupt goal-directed behavior is dependent on several factors, including one's inherent tendencies. Using a rodent model, we have shown that individuals vary in the value they place on stimuli associated with reward. Some individuals, termed "goal-trackers," primarily attribute predictive value to reward cues, whereas others, termed "sign-trackers," attribute predictive and incentive value. Thus, for sign-trackers, the reward cue is transformed into an incentive stimulus that is capable of eliciting maladaptive behaviors. The sign-tracker/goal-tracker animal model has allowed us to refine our understanding of behavioral and computational theories related to reward learning and to parse the underlying neural processes. Further, the neurobehavioral profile of sign-trackers is relevant to several psychiatric disorders, including substance use disorder, impulse control disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, and posttraumatic stress disorder. This model, therefore, can advance our understanding of the psychological and neurobiological mechanisms that contribute to individual differences in vulnerability to psychopathology. Notably, initial attempts at translation-capturing individual variability in the propensity to sign-track in humans-have been promising and in line with what we have learned from the animal model. In this review, we highlight the pivotal role played by the sign-tracker/goal-tracker animal model in enriching our understanding of the psychological and neural basis of motivated behavior and psychiatric symptomatology. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

New degradable PCL/thiazole composite for biological applications; characterization and spectroscopic studies

Polycaprolactone (PCL) is a biodegradable polymer widely used for medical implants and devices due to its biocompatibility, processability, and tunable degradation behavior. This study explores the incorporation of a thiazole-based antimicrobial compound into PCL at varying concentrations to develop new composite materials with both biodegradability and antibacterial function. Samples were solution cast and characterized using techniques like X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, UV–vis spectroscopy, antibacterial assays, and computational density functional theory (DFT) modeling. XRD showed up to 54 % crystallinity at the highest 0.03 g dye loading, indicating the thiazole impacted ordering and lamellar packing. FTIR and DFT calculations demonstrated multiple possible intermolecular bonding modes between the compounds. UV–vis spectra revealed the superimposed absorptions of the PCL matrix and emergent thiazole chromophore. Antibacterial tests exhibited marked growth inhibition of both gram-positive and gram-negative bacteria proportional to the thiazole concentration. The customizable PCL-thiazole blends offer biocompatible materials with functional antibacterial behavior for specialized applications in biomedicine.

Bending and linear dynamic response of nanoplates in thermal environment

The article combines the finite element method with the novel-type sinusoidal hyperbolic shear strain hypothesis to study the static bending response and dynamics of nanoplates subjected to simultaneous mechanical, thermal, and voltage loads. The plate equilibrium equation is developed from the concept of potential work, which takes into account the impact of the flexoelectricity effect. The formula for the electric field that is operating on the plate becomes more complicated when the new strain theory is used; nonetheless, its complexity adequately displays both the mechanical and electrical components, as well as the electromechanical components, that are acting on the nanoplate. The computational theory is also verified through comparison with previously published data. The article also investigates the influence of some material factors, temperature, and external voltage on displacement response and charge polarization of nanoplates in the case of subjecting to static and time-varying loads. The results demonstrate that the thermomechanical-electrical response of nanoplates is dependent on numerous factors, which serve as the foundation for the practical design and application of nanostructures.

From Wald to Schnorr: von Mises’ definition of randomness in the aftermath of Ville’s Theorem

The first formal definition of randomness, seen as a property of sequences of events or experimental outcomes, dates back to Richard von Mises’ work in the foundations of probability and statistics. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak. This is, to a large extent, due to the work of Jean Ville, which is often described as having dealt the death blow to von Mises’ approach, and which was integral to the development of algorithmic randomness—the now-standard theory of randomness for elements of a probability space. The main goal of this article is to trace the history and provide an in-depth appraisal of two lesser-known, yet historically and methodologically notable proposals for how to modify von Mises’ definition so as to avoid Ville’s objection. The first proposal is due to Abraham Wald, while the second one is due to Claus-Peter Schnorr. We show that, once made precise in a natural way using computability theory, Wald’s proposal constitutes a much more radical departure from von Mises’ framework than intended. Schnorr’s proposal, on the other hand, does provide a partial vindication of von Mises’ approach: it demonstrates that it is possible to obtain a satisfactory randomness notion—indeed, a canonical algorithmic randomness notion—by characterizing randomness in terms of the invariance of limiting relative frequencies. More generally, we argue that Schnorr’s proposal, together with a number of little-known related results, reveals that there is more continuity than typically acknowledged between von Mises’ approach and algorithmic randomness. Even though von Mises’ exclusive focus on limiting relative frequencies did not survive the passage to the theory of algorithmic randomness, another crucial aspect of his conception of randomness did endure; namely, the idea that randomness amounts to a certain type of stability or invariance under an appropriate class of transformations.

Early artificial intelligence education: Effects of cooperative play and direct instruction on kindergarteners' computational thinking, sequencing, self‐regulation and theory of mind skills

Early artificial intelligence education: Effects of cooperative play and direct instruction on kindergarteners' computational thinking, sequencing, self‐regulation and theory of mind skills

Computation Theory of Large-Scale Partially Coherent Imaging by the Modified Modal Expansion Method

The numerical calculation of partially coherent imaging involves a fourfold integral, which is numerically complex and impracticable to be calculated directly. The use of coherent-mode decomposition (CMD) can make this problem more manageable but finding the coherent-modes for complicated partial coherent fields (without already-known coherent-mode expansion) are rather computationally intensive. In this letter, a modified modal expansion method is proposed, which significantly reduces the requirement of computational resources. The propagation of partial coherence in imaging systems with extremely large sampling number could be handled by an ordinary computer. A comparison between the new method and the traditional method in terms of memory resource requirements and computational time consumption is also detailed in this article. We will also show that this method could deal with the anisoplanatic imaging cases while maintaining the same computational efficiency.

The surjection property and computable type

We provide a detailed study of two properties of spaces and pairs of spaces, the surjection property and the ϵ-surjection property, that were recently introduced to characterize the notion of computable type arising from computability theory. For a class of spaces including the finite simplicial complexes, we develop techniques to prove or disprove these properties using homotopy and homology theories, and give applications of these results. In particular, we answer an open question on the computable type property, showing that it is not preserved by taking products. We also observe that computable type is decidable for finite simplicial complexes.

Research on Load Decomposition and Optimization of Intelligent Elderly Care Service Based on Heuristic and Event Detection Algorithm

Against the backdrop of the digital age, the openness, equality and interaction of the Internet economy have injected new vitality into China’s traditional industries. The application of big data technology, especially in information integration and analysis, has become a key force in promoting the sustainable and healthy development of the national economy. This study focuses on the “Internet +” environment, discusses the impact of the aging problem of community workers on home care services, and proposes an optimization scheme based on a heuristic algorithm. The heuristic algorithm, inspired by the foraging behavior of ants in nature, optimizes the route selection problem by simulating an ant colony to choose the path with a high concentration of pheromones and shows outstanding application potential in the field of home care. The accuracy of the event detection algorithm is directly related to the performance of the load decomposition algorithm, and the change point detection algorithm can effectively identify the change point of the probability distribution in the time series data, which provides important input data for unsupervised clustering. Advanced computer theory, including the Hidden Markov model (HMM) and swarm intelligence optimization algorithm, is used in this research. By comparing different swarm intelligence algorithms, we find that the standard Gray Wolf optimization (SGWO) model is better than the basic Gray Wolf optimization (BGWO) algorithm and the improved Gray Wolf optimization (DGWO) algorithm in terms of stability and output results. The SGWO model significantly improves the efficiency of the load decomposition algorithm, which has been verified in the application of the smart elderly care service platform. The platform not only supports the operation of related technologies and information products but also realizes the seamless integration of information among various subjects of elderly care services. In addition, the factor hidden in the Markov model that can be selectively activated effectively monitors equipment status in the Internet of Things environment, provides real-time monitoring of user consumption behavior and fault information and further enhances the quality and efficiency of smart elderly care services.

Bounding Random Test Set Size with Computational Learning Theory

Bounding Random Test Set Size with Computational Learning Theory

Structural iterative rounding for generalized k-median problems

AbstractThis paper considers approximation algorithms for generalized k-median problems. These problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution, with a constant number of fractional variables. The algorithm builds on the iterative rounding framework introduced by Krishnaswamy, Li, and Sandeep for k-median with outliers as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018). The main technical innovation is allowing richer constraint sets in the iterative rounding and using the structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios $$6.994 + \epsilon $$ 6.994 + ϵ and $$6.387 + \epsilon $$ 6.387 + ϵ for k-median with outliers and knapsack median, respectively. These improve on the best-known approximation ratio $$7.081 + \epsilon $$ 7.081 + ϵ for both problems as reported (Krishnaswamy et al. in: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018).

Computably and punctually universal spaces

We prove that the standard computable presentation of the space C[0,1] of continuous real-valued functions on the unit interval is computably and punctually (primitively recursively) universal. From the perspective of modern computability theory, this settles a problem raised by Sierpiński in the 1940s.We prove that the original Urysohn's construction of the universal separable Polish space U is punctually universal. We also show that effectively compact, punctual Stone spaces are punctually homeomorphically embeddable into Cantor space 2ω; note that we do not require effective compactness be primitive recursive. We also prove that effective compactness cannot be dropped from the premises by constructing a counterexample.

Bases for optimising stabiliser decompositions of quantum states

Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser decompositions: ways of being expressed as a superposition of stabiliser states. Understanding the structure of stabiliser decompositions has significant applications in verifying and simulating near-term quantum computers. We introduce and study the vector space of linear dependencies of n-qubit stabiliser states. These spaces have canonical bases containing vectors whose size grows exponentially in n. We construct elegant bases of linear dependencies of constant size three. Critically, our sparse bases can be computed without first compiling a dictionary of all n-qubit stabiliser states. We utilise them to explicitly compute the stabiliser extent of states of more qubits than is feasible with existing techniques. Finally, we delineate future applications to improving theoretical bounds on the stabiliser rank of magic states.

No existence of a linear algorithm for the one-dimensional Fourier phase retrieval

Fourier phase retrieval, which aims to reconstruct a signal from its Fourier magnitude, is of fundamental importance in fields of engineering and science. In this paper, we provide a theoretical understanding of algorithms for the one-dimensional Fourier phase retrieval problem. Specifically, we demonstrate that if an algorithm exists which can reconstruct an arbitrary signal x∈CN in Poly(N)log⁡(1/ϵ) time to reach ϵ-precision from its magnitude of discrete Fourier transform and its initial value x(0), then P=NP. This partially elucidates the phenomenon that, despite the fact that almost all signals are uniquely determined by their Fourier magnitude and the absolute value of their initial value |x(0)|, no algorithm with theoretical guarantees has been proposed in the last few decades. Our proofs employ the result in computational complexity theory that the Product Partition problem is NP-complete in the strong sense.

Limitations of Classically Simulable Measurements for Quantum State Discrimination.

In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from nonstabilizer operations within the quantum computational theory. In this Letter, we investigate the limitations of classically simulable measurements in distinguishing quantum states. We demonstrate that any pure magic state and its orthogonal complement of odd prime dimensions cannot be unambiguously distinguished by stabilizer operations, regardless of how many copies of the states are supplied. We also reveal intrinsic similarities and distinctions between the quantum resource theories of magic states and entanglement in quantum state discrimination. The results emphasize the inherent limitations of classically simulable measurements and contribute to a deeper understanding of the quantum-classical boundary.

Creativity and Machine Learning: A Survey

There is a growing interest in the area of machine learning and creativity. This survey presents an overview of the history and the state of the art of computational creativity theories, key machine learning techniques (including generative deep learning), and corresponding automatic evaluation methods. After presenting a critical discussion of the key contributions in this area, we outline the current research challenges and emerging opportunities in this field.