Learning to Branch in Combinatorial Optimization With Graph Pointer Networks

Traditional expert-designed branching rules in branch-and-bound(B&B) are static, often failing to adapt to diverse and evolving problem instances. Crafting these rules is labor-intensive, and may not scale well with complex problems.Given the frequent need to solve varied combinatorial optimization problems, leveraging statistical learning to auto-tune B&B algorithms for specific problem classes becomes attractive. This paper proposes a graph pointer network model to learn the branch rules. Graph features, global features and historical features are designated to represent the solver state. The graph neural network processes graph features, while the pointer mechanism assimilates the global and historical features to finally determine the variable on which to branch. The model is trained to imitate the expert strong branching rule by a tailored top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. It also outperforms state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances.

Combinatorial Enzyme Approach to Convert Wheat Insoluble Arabinoxylan to Bioactive Oligosaccharides

Combinatorial enzyme technology was applied for the conversion of wheat insoluble arabinoxylan to oligosaccharide structural variants. The digestive products were fractionated by Bio-Gel P4 column and screened for bioactivity. One fraction pool was observed to exhibit antimicrobial property resulting in the suppression of cell growth of the test organism ATCC 8739 E. coli. It has a MIC value of 1.5% (w/v, 35°C, 20 hr) and could be useful as a new source of prebiotics or preservatives. The present results further confirm the science and useful application of combinatorial enzyme approach.

Drug-Treatment Generation Combinatorial Algorithm Based on Machine Learning and Statistical Methodologies

Finding out the desired drug combinations is a challenging task because of the number of different combinations that exist and the adversarial effects that may arise. In this work, we generate drug combinations over multiple stages using distance calculation metrics from supervised learning, clustering, and a statistical similarity calculation metric for deriving the optimal treatment sequences. The combination generation happens for each patient based on the characteristics (features) observed during each stage of treatment. Our approach considers not the drug-to-drug (one-to-one) effect, but rather the effect of group of drugs with another group of drugs. We evaluate the combinations using an FNN model and identify future improvement directions.

Simultaneous detection and differentiates of Brucella abortus and Brucella melitensis by combinatorial PCR

Objective:To evaluate simultaneous detection and differentiates of Brucella abortus(B.abortus) and Brucella melitensis(B.melitensis) through the combinatorial POR method.Methods:This study was designed using three primers that could simultaneously identify and differentiate two major species of pathogenic Brucella in humans and animals.Identification and differentiation of each species using the size of the PCR product were determined.To determine the specifieity of the method,bacteria close to the genus Brucella were used.Finally,to confirm PCR products.In addition to the products sequence,RFLP was performed on PCR products using restriction enzymes.Results:The method of optimized combinatorial PCR in this study could simultaneously detect and differentiate B.abortus and B.melitensis with high specificity and sensitivity in clinical samples.Differentiation of species is based on the resulting bands: therefore,the band 494 bp for B.abortus and 733 bp for B.melitensis were obtained.RFLP and sequencing results confirmed PCR results.Conclusions:The results of this study shows that without routine diagnostic methods such as culture and serology tests,using the molecular method of combinatorial PCR,important species of Brucella can be simultaneously identified and differentiated in clinical samples.

A COMBINATORIAL APPROACH TO THE OXIDATION RESISTANCE OF (Ti,Al)N AND Ti-Al-Si-N HARD COATINGS

The increasing complexity of modern functional materials leads to the demand of acost efficient tool for the development of new products. One possible approach to thisquestion is the adaptation of combinatorial methods to the specific requirements of ma-terials industry. These methods, originally developed for the pharmaceutical industry,have recently been applied to the screening of superconductive, magnetoresistant andphotoluminescent materials. The principle of these combinatorial approaches is thedeposition of large materials libraries in one process combined with fast methods forthe determination of the resulting properties. In this paper, the deposition and charac-terization of laterally graded materials libraries (composition spread) is presented. Thefilms have been deposited by reactive magnetron sputtering, using two or three metallictargets at a low angle to the substrate surface as well as a system of apertures. Toillustrate the advantages of combinatorial approaches for the development of advancedmaterials, the multicomponent metastable hardcoatings (Ti, Al)N and Ti-Al-Si-N arediscussed with special emphasis on the relations between structure and composition onthe one hand and the oxidation resistance of these coatings on the other. The resultsillustrate that the composition spread approach is a powerful and cost efficient tool forthe development and optimization of new multicomponent functional materials.

Combinatorial design-based quasi-cyclic LDPC codes with girth eight

This paper presents a novel regular Quasi-Cyclic (QC)Low Density Parity Check (LDPC)codes with columnweight three and girth at least eight.These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset.Considering the nonexistence of cycles four and six in the structure of the parity check matrix,a bound for their minimum weight is proposed.The simtdations conducted confirm that without applying a masking technique,the newly implemented codes have a performance similar to or better than other well-known codes.This is evident in the waterfall region, while their error floor at very low Bit Error Rate (BER)is expected.

Fenton metal nanomedicines for imaging-guided combinatorial chemodynamic therapy against cancer

Chemodynamic therapy(CDT)is considered as a promising modality for selective cancer therapy,which is realized via Fenton reaction-mediated decomposition of endogenous H_(2)O_(2) to produce toxic hydroxyl radical(•OH)for tumor ablation.While extensive efforts have been made to develop CDT-based therapeutics,their in vivo efficacy is usually unsatisfactory due to poor catalytic activity limited by tumor microenvironment,such as anti-oxidative systems,insufficient H_(2)O_(2),and mild acidity.To mitigate these issues,we have witnessed a surge in the development of CDT-based combinatorial nanomedicines with complementary or synergistic mechanisms for enhanced tumor therapy.By virtue of their bio-imaging capabilities,Fenton metal nanomedicines(FMNs)are equipped with intrinsic properties of imaging-guided tumor therapies.In this critical review,we summarize recent progress of this field,focusing on FMNs for imaging-guided combinatorial tumor therapy.First,various Fenton metals with inherent catalytic performances and imaging properties,including Fe,Cu and Mn,were introduced to illustrate their possible applications for tumor theranostics.Then,CDT-based combinatorial systems were reviewed by incorporating many other treatment means,including chemotherapy,photodynamic therapy(PDT),sonodynamic therapy(SDT),photothermal therapy(PTT),starvation therapy and immunotherapy.Next,various imaging approaches based on Fenton metals were presented in detail.Finally,challenges are discussed,and future prospects are speculated in the field to pave way for future developments.

Combinatorial Synthesis and High-Throughput Characterization of Microstructure and Phase Transformation in Ni-Ti-Cu-V Quaternary Thin-Film Library

Ni-Ti-based shape memory alloys(SMAs)have found widespread use in the last 70 years,but improving their functional stability remains a key quest for more robust and advanced applications.Named for their ability to retain their processed shape as a result of a reversible martensitic transformation,SMAs are highly sensitive to compositional variations.Alloying with ternary and quaternary elements to finetune the lattice parameters and the thermal hysteresis of an SMA,therefore,becomes a challenge in materials exploration.Combinatorial materials science allows streamlining of the synthesis process and data management from multiple characterization techniques.In this study,a composition spread of Ni-Ti-Cu-V thin-film library was synthesized by magnetron co-sputtering on a thermally oxidized Si wafer.Composition-dependent phase transformation temperature and microstructure were investigated and determined using high-throughput wavelength dispersive spectroscopy,synchrotron X-ray diffraction,and temperature-dependent resistance measurements.Of the 177 compositions in the materials library,32 were observed to have shape memory effect,of which five had zero or near-zero thermal hysteresis.These compositions provide flexibility in the operating temperature regimes that they can be used in.A phase map for the quaternary system and correlations of functional properties are discussed w让h respect to the local microstructure and composition of the thin-film library.

Combinatorial Optimization Based Analog Circuit Fault Diagnosis with Back Propagation Neural Network

Electronic components' reliability has become the key of the complex system mission execution. Analog circuit is an important part of electronic components. Its fault diagnosis is far more challenging than that of digital circuit. Simulations and applications have shown that the methods based on BP neural network are effective in analog circuit fault diagnosis. Aiming at the tolerance of analog circuit,a combinatorial optimization diagnosis scheme was proposed with back propagation( BP) neural network( BPNN).The main contributions of this scheme included two parts:( 1) the random tolerance samples were added into the nominal training samples to establish new training samples,which were used to train the BP neural network based diagnosis model;( 2) the initial weights of the BP neural network were optimized by genetic algorithm( GA) to avoid local minima,and the BP neural network was tuned with Levenberg-Marquardt algorithm( LMA) in the local solution space to look for the optimum solution or approximate optimal solutions. The experimental results show preliminarily that the scheme substantially improves the whole learning process approximation and generalization ability,and effectively promotes analog circuit fault diagnosis performance based on BPNN.

Combinatorial Enzyme Approach to Produce Oligosaccharides of Diverse Structures for Functional Screen

Combinatorial chemistry has been a focus of research activity in modern drug discovery and biotechnology. It is a concept by which a vast library of molecular diversity is synthesized and screened for target properties. This report is to illustrate the application of enzyme technology using the concept of combinatorial chemistry as a novel approach for the bioconversion of plant fibers. Citrus pectin was subjected to combinatorial enzyme digestion to create libraries of pectic oligosaccharides with diverse structural variants. Repeated cycles of fractionation and screening resulted in the isolation and identification of an active oligoGalA species with antimicrobial activity.

Half Rate Quasi Cyclic Low Density Parity Check Codes Based on Combinatorial Designs

This paper presents new half rate Quasi Cyclic Low Density Parity Check (QC- LDPC) codes formed on the basis of combinatorial designs. In these codes, circulant matrices of the parity check matrix are formed on the basis of subsets in which the difference between any two elements of a subset is unique with all differences obtained from the same or different subsets. This structure of circulant matrices guarantees non-existence of cycle-4 in the Tanner graph of QC-LDPC codes. First, an irregular code with girth 6 constituted by two rows of circulant matrices is proposed. Then, more criteria will be considered on the structure of subsets with the mentioned feature aiming to represent a new scheme of regular QC-LPDC codes with girth at least 8. From simulations, it is confirmed that codes have similar to or better performance than other well-known half rate codes, while require lower complexity in their design.

POWER VECTORS,COMBINATORIAL VECTOR NUMBERS AND ITS THEORY OF FUNCTIONS

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Optical wavelet-fractional squeezing combinatorial transform

By virtue of the method of integration within ordered product(IWOP)of operators we find the normally ordered form of the optical wavelet-fractional squeezing combinatorial transform(WFrST)operator.The way we successfully combine them to realize the integration transform kernel of WFr ST is making full use of the completeness relation of Dirac’s ket–bra representation.The WFr ST can play role in analyzing and recognizing quantum states,for instance,we apply this new transform to identify the vacuum state,the single-particle state,and their superposition state.

A Combinatorial Optimized Knapsack Linear Space for Information Retrieval

Key information extraction can reduce the dimensional effects while evaluating the correct preferences of users during semantic data analysis.Currently,the classifiers are used to maximize the performance of web-page recommendation in terms of precision and satisfaction.The recent method disambiguates contextual sentiment using conceptual prediction with robustness,however the conceptual prediction method is not able to yield the optimal solution.Context-dependent terms are primarily evaluated by constructing linear space of context features,presuming that if the terms come together in certain consumerrelated reviews,they are semantically reliant.Moreover,the more frequently they coexist,the greater the semantic dependency is.However,the influence of the terms that coexist with each other can be part of the frequency of the terms of their semantic dependence,as they are non-integrative and their individual meaning cannot be derived.In this work,we consider the strength of a term and the influence of a term as a combinatorial optimization,called Combinatorial Optimized Linear Space Knapsack for Information Retrieval(COLSK-IR).The COLSK-IR is considered as a knapsack problem with the total weight being the“term influence”or“influence of term”and the total value being the“term frequency”or“frequency of term”for semantic data analysis.The method,by which the term influence and the term frequency are considered to identify the optimal solutions,is called combinatorial optimizations.Thus,we choose the knapsack for performing an integer programming problem and perform multiple experiments using the linear space through combinatorial optimization to identify the possible optimum solutions.It is evident from our experimental results that the COLSK-IR provides better results than previous methods to detect strongly dependent snippets with minimum ambiguity that are related to inter-sentential context during semantic data analysis.

Combinatorial synthesis and high-throughput characterization of copper-oxide superconductors

Fast synthesis and screening of materials are vital to the advance of materials science and are an essential component of the Materials Genome Initiative. Here we use copper-oxide superconductors as an example to demonstrate the power of integrating combinatorial molecular beam epitaxy synthesis with high-throughput electric transport measurements. Leveraging this method, we have generated a phase diagram with more than 800 compositions in order to unravel the doping dependence of interface superconductivity. In another application of the same method, we have studied the superconductorto-insulator quantum phase transition with unprecedented accuracy in tuning the chemical doping level.

Application of the edge of chaos in combinatorial optimization

Many problems in science,engineering and real life are related to the combinatorial optimization.However,many combinatorial optimization problems belong to a class of the NP-hard problems,and their globally optimal solutions are usually difficult to solve.Therefore,great attention has been attracted to the algorithms of searching the globally optimal solution or near-optimal solution for the combinatorial optimization problems.As a typical combinatorial optimization problem,the traveling salesman problem(TSP)often serves as a touchstone for novel approaches.It has been found that natural systems,particularly brain nervous systems,work at the critical region between order and disorder,namely,on the edge of chaos.In this work,an algorithm for the combinatorial optimization problems is proposed based on the neural networks on the edge of chaos(ECNN).The algorithm is then applied to TSPs of 10 cities,21 cities,48 cities and 70 cities.The results show that ECNN algorithm has strong ability to drive the networks away from local minimums.Compared with the transiently chaotic neural network(TCNN),the stochastic chaotic neural network(SCNN)algorithms and other optimization algorithms,much higher rates of globally optimal solutions and near-optimal solutions are obtained with ECNN algorithm.To conclude,our algorithm provides an effective way for solving the combinatorial optimization problems.

Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities

In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.

Outlier Detection of Mixed Data Based on Neighborhood Combinatorial Entropy

Outlier detection is a key research area in data mining technologies,as outlier detection can identify data inconsistent within a data set.Outlier detection aims to find an abnormal data size from a large data size and has been applied in many fields including fraud detection,network intrusion detection,disaster prediction,medical diagnosis,public security,and image processing.While outlier detection has been widely applied in real systems,its effectiveness is challenged by higher dimensions and redundant data attributes,leading to detection errors and complicated calculations.The prevalence of mixed data is a current issue for outlier detection algorithms.An outlier detection method of mixed data based on neighborhood combinatorial entropy is studied to improve outlier detection performance by reducing data dimension using an attribute reduction algorithm.The significance of attributes is determined,and fewer influencing attributes are removed based on neighborhood combinatorial entropy.Outlier detection is conducted using the algorithm of local outlier factor.The proposed outlier detection method can be applied effectively in numerical and mixed multidimensional data using neighborhood combinatorial entropy.In the experimental part of this paper,we give a comparison on outlier detection before and after attribute reduction.In a comparative analysis,we give results of the enhanced outlier detection accuracy by removing the fewer influencing attributes in numerical and mixed multidimensional data.

Negotiation Based Combinatorial Double Auction Mechanism in Cloud Computing

Cloud computing is a demanding business platform for services related to the field of IT.The goal of cloud customers is to access resources at a sustainable price,while the goal of cloud suppliers is to maximize their services utilization.Previously,the customers would bid for every single resource type,which was a limitation of cloud resources allocation.To solve these issues,researchers have focused on a combinatorial auction in which the resources are offered by the providers in bundles so that the user bids for their required bundle.Still,in this allocation mechanism,some drawbacks need to be tackled,such as due to the lower average bid price the users are dropped from the auction process.To solve this problem,we proposed a“Negotiation based Combinatorial Double Auction Mechanism for Resource Allocation(N-CDARA)in cloud computing”.The proposed method negotiates with dropped users.Lower average bid price users are asked by our proposed mechanism to increase their bids,as by the quoted bids they will be dropped by the auctioneer.Most of the users that are close to winning accept the proposal and increase their bid prices.The proposed mechanism is implemented in a CloudSim simulation toolkit.Results are compared with the latest model and performance study shows that in our proposed scheme more users win and get their requested services and the utilization of offered services is increased up to 18.4%than the existing schemes.

Privacy-Aware Service Subscription in People-Centric Sensing:A Combinatorial Auction Approach

With the emergence of ambient sensing technologies which combine mobile crowdsensing and Internet of Things,large amount of people-centric data can be obtained and utilized to build people-centric services.Note that the service quality is highly related to the privacy level of the data.In this paper,we investigate the problem of privacy-aware service subscription in people-centric sensing.An efficient resource allocation framework using a combinatorial auction(CA)model is provided.Specifically,the resource allocation problem that maximizes the social welfare in view of varying requirements of multiple users is formulated,and it is solved by a proposed computationally tractable solution algorithm.Furthermore,the prices of allocated resources that winners need to pay are figured out by a designed scheme.Numerical results demonstrate the effectiveness of the proposed scheme.