Double Truncation Method for Simulation of Stochastic Chemical Reaction Networks

Mathematical SciencesWe develop Double Truncation Method(DTM) to understand the stochasticity of chemical reaction network on the mesoscopic scale. The Chemical Master Equation(CME) describes the probability distribution of the system accurately under the markov assumption. But solving CME is computationally heavy. It faces the curse of dimensionality because it considers reactions on every different states. To settle the issue, stochastic approach came out, typically Gillspie's stochastic simulation algorithm(SSA). SSA lifts the curse of dimensionality, but it needs too many realizations, which makes it less practical, in cases of the system consisting of large numbers of molecules or very different time scale reactions. A recently developed Probability Generating Function(PGF) method supplements those weaknesses. It is a deterministic description and sparks the reactions in stead of considering those for all the states. By doing that, though it expresses the system efficiently, but it implements the symbolic computation and converges still slowly. So here we suggest DTM to speed up. As suggested from the name, DTM has two truncations for time and for coefficients based on PGF method. We perform the first truncation for a short time and second truncation for small coefficients at each time step. First truncation or superimposition can be performed underlying the power series expansion on time. And next truncation can be conducted with the elimination of relatively small coefficient terms. Since the coefficient of PGF means the probability of a specific state, the sum of coefficient can be understood as an weight for the system. This observation enables us to ignore a great deal of small terms which do not affect the system significantly. The method is procedurally simple and powerful, especially for mesoscopic scale problems. It works well even for open systems, such as brusselator. We apply the method to simulation of binding reactions, enzyme kinetics, transition model and brusselator and compare the results with those of SSA or matrix exponential.ope

A population-based optimization method using Newton fractal

Department of Mathematical SciencesMetaheuristic is a general procedure to draw an agreement in a group based on the decision making of each individual beyond heuristic. For last decade, there have been many attempts to develop metaheuristic methods based on swarm intelligence to solve global optimization such as particle swarm optimizer, ant colony optimizer, firefly optimizer. These methods are mostly stochastic and independent on specific problems. Since metaheuristic methods based on swarm intelligence require no central coordination (or minimal, if any), they are especially well-applicable to those problems which have distributed or parallel structures. Each individual follows few simple rules, keeping the searching cost at a decent level. Despite its simplicity, the methods often yield a fast approximation in good precision, compared to conventional methods. Exploration and exploitation are two important features that we need to consider to find a global optimum in a high dimensional domain, especially when prior information is not given. Exploration is to investigate the unknown space without using the information from history to find undiscovered optimum. Exploitation is to trace the neighborhood of the current best to improve it using the information from history. Because these two concepts are at opposite ends of spectrum, the tradeoff significantly affects the performance at the limited cost of search. In this work, we develop a chaos-based metaheuristic method, ???Newton Particle Optimization(NPO)???, to solve global optimization problems. The method is based on the Newton method which is a well-established mathematical root-finding procedure. It actively utilizes the chaotic nature of the Newton method to place a proper balance between exploration and exploitation. While most current population-based methods adopt stochastic effects to maximize exploration, they often suffer from weak exploitation. In addition, stochastic methods generally show poor reproducing ability and premature convergence. It has been argued that an alternative approach using chaos may mitigate such disadvantages. The unpredictability of chaos is correspondent with the randomness of stochastic methods. Chaos-based methods are deterministic and therefore easy to reproduce the results with less memory. It has been shown that chaos avoids local optimum better than stochastic methods and buffers the premature convergence issue. Newton method is deterministic but shows chaotic movements near the roots. It is such complexity that enables the particles to search the space for global optimization. We initialize the particle???s position randomly at first and choose the ???leading particles??? to attract other particles near them. We can make a polynomial function whose roots are those leading particles, called ???a guiding function???. Then we update the positions of particles using the guiding function by Newton method. Since the roots are not updated by Newton method, the leading particles survive after update. For diverse movements of particles, we use modified newton method, which has a coefficient $m$ in the variation of movements for each particle. Efficiency in local search is closely related to the value of m which determines the convergence rate of the Newton method. We can control the balance between exploration and exploitation by choice of leading particles. It is interesting that selection of excellent particles as leading particles not always results in the best result. Including mediocre particles in the roots of guiding function maintains the diversity of particles in position. Though diversity seems to be inefficient at first, those particles contribute to the exploration for global search finally. We study the conditions for the convergence of NPO. NPO enjoys the well-established analysis of the Newton method. This contrasts with other ???nature-inspired??? algorithms which have often been criticized for lack of rigorous mathematical ground. We compare the results of NPO with those of two popular metaheuristic methods, particle swarm optimizer(PSO) and firefly optimizer(FO). Though it has been shown that there are no such algorithms superior to all problems by no free lunch theorem, that is why the researchers are concerned about adaptable global optimizer for specific problems. NPO shows good performance to CEC 2013 competition test problems comparing to PSO and FO.ope

Improving Zero-shot Reader by Reducing Distractions from Irrelevant Documents in Open-Domain Question Answering

Large language models (LLMs) enable zero-shot approaches in open-domain question answering (ODQA), yet with limited advancements as the reader is compared to the retriever. This study aims at the feasibility of a zero-shot reader that addresses the challenges of computational cost and the need for labeled data. We find that LLMs are distracted due to irrelevant documents in the retrieved set and the overconfidence of the generated answers when they are exploited as zero-shot readers. To tackle these problems, we mitigate the impact of such documents via Distraction-aware Answer Selection (DAS) with a negation-based instruction and score adjustment for proper answer selection. Experimental results show that our approach successfully handles distraction across diverse scenarios, enhancing the performance of zero-shot readers. Furthermore, unlike supervised readers struggling with unseen data, zero-shot readers demonstrate outstanding transferability without any training.Comment: Findings of EMNLP 2023 Camera Read

Knowledge-Augmented Language Model Verification

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be inaccurate, incomplete, and outdated. To address this problem, previous works propose to augment LMs with the knowledge retrieved from an external knowledge source. However, such approaches often show suboptimal text generation performance due to two reasons: 1) the model may fail to retrieve the knowledge relevant to the given query, or 2) the model may not faithfully reflect the retrieved knowledge in the generated text. To overcome these, we propose to verify the output and the knowledge of the knowledge-augmented LMs with a separate verifier, which is a small LM that is trained to detect those two types of errors through instruction-finetuning. Then, when the verifier recognizes an error, we can rectify it by either retrieving new knowledge or generating new text. Further, we use an ensemble of the outputs from different instructions with a single verifier to enhance the reliability of the verification processes. We validate the effectiveness of the proposed verification steps on multiple question answering benchmarks, whose results show that the proposed verifier effectively identifies retrieval and generation errors, allowing LMs to provide more factually correct outputs. Our code is available at https://github.com/JinheonBaek/KALMV.Comment: EMNLP 202

Perturbation and Truncation of Probability Generating Function Methods for Stiff Chemical Reactions

One can reformulate chemical master equations of the stochastic reaction network into a partial differential equation (PDE) of a probability generating function (PGF). In this paper, we present two improvements in such PGF-PDE approach, based on perturbation and double-truncation, respectively. The stiff system that involves fast and slow reactions together often requires high computational cost. By applying the perturbation method to PGF-PDEs, we expand the equation in terms of a small reaction rate which is often responsible for such stiffness of the system. Also by doubly truncating, we dump relatively small terms and reduce the computational load significantly at each time step. The terms corresponding to rare events are sieved out through truncations of Taylor expansion. It is shown through numerical examples of enzyme kinetics, transition model, and Brusselator model that the suggested method is accurate and efficient for approximation of the state probabilities. © 2015 Soyeong Jeong et al.close

A hybrid similarity measure based on binary and decimal data for data mining

We suggest a new similarity measure to improve the quality of data mining, especially for recommender system. A similarity measure is widely used for classification, clustering, anomaly detection and so on. Many recommender systems predict unrated score through clustering similar users. This method is so called collaborative filtering(CF), which is being widely used. In CF, how to define a similarity measure is a major concern. Conventional measures based on Pearson Correlation Coefficient(PCC) are hard to reflect the implicit and explicit information at the same time. We propose a hybrid similarity measure, named BD PCC, which is a type of PCC, named after the first letter of ???Binary??? and ???Decimal??? types respectively. As we suggest from its name, BD PCC is defined by concatenating two PCCs on two different types of data. Although other hybrid measures need some processes to concatenate, BD PCC is free from scale issue. Because it consists of both PCCs unlike other hybrid measures consisting of values in different ranges. Since PCC for binary data can be defined if the user bought at least one item, BD PCC relieves the sparsity of data. We tested the proposed similarity measure in recommender systems and the prediction accuracy has been improved for real data sets, MovieLens 100K[8], MovieLens 1M[8], MovieLens latest small[8], and FilmTrust 35K[9]. ?? 2019 Association for Computing Machinery

A Population-Based Optimization Method Using Newton Fractal

We propose a deterministic population-based method for a global optimization, a Newton particle optimizer (NPO). The algorithm uses the Newton method with a guiding function and drives particles toward the current best positions. The particles??? movements are influenced by the fractal nature of the Newton method and are greatly diversified in the approach to the temporal best optimums. As a result, NPO generates a wide variety of searching paths, achieving a balance between exploration and exploitation. NPO differs from other metaheuristic methods in that it combines an exact mathematical operation with heuristics and is therefore open to more rigorous analysis. The local and global search of the method can be separately handled as properties of an associated multidimensional mapping

Anti-Markovnikov Hydroamination of Alkenes with Aqueous Ammonia by Metal-Loaded Titanium Oxide Photocatalyst

光触媒による第一級アミンの新合成ルートを確立 --アンモニア水を窒素源とする直接合成法の開発--. 京都大学プレスリリース. 2020-07-10.A completely new route was established to synthesize valuable primary amines from alkenes by using aqueous ammonia, that is, a simple photocatalytic hydroamination of alkenes using aqueous ammonia with a metal-loaded TiO2 photocatalyst. Although the photochemical hydroamination prefers to form amines according to the Markovnikov rule, the new photocatalytic hydroamination gives anti-Markovnikov products predominantly. With an Au-loaded TiO2 photocatalyst, the amine yield reached up to 93% and the regioselectivity of anti-Markovnikov products was above 98%. The reaction mechanism was proposed for the new photocatalytic hydroamination

Strategies to Improve Electrical and Electronic Properties of PEDOT:PSS for Organic and Perovskite Optoelectronic Devices

Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) is the most successful commercialized conducting polymer. PEDOT:PSS is a mixture of two ionomers: positively-charged PEDOT and negatively-charged PSS. PEDOT is a conducting polymer, which has - conjugation in its main backbone, and PSS increases charge carrier density in PEDOT by removing electrons from PEDOT during the synthesis process. Many researchers have tried to increase the electrical conductivity, k, of PEDOT:PSS films and applied them to organic and metal halide perovskite optoelectronic devices as transparent electrodes. Recently, the electrical properties of PEDOT:PSS, including k and work function, have been optimized for those optoelectronic devices. Here, we review recent strategies for optimizing the electrical properties of PEDOT:PSS to use them as transparent electrodes.